Abstract:
The present application relates to a wireless communication system and related methods and apparatuses for transmitting a signal from a source apparatus to a destination apparatus, via at least one intermediate apparatus. In particular, the present invention relates to techniques which seek to improve the throughput of data in multi-hop communication systems.

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to a communication system and related methods for transmitting a signal from a source apparatus to a destination apparatus, via at least one intermediate apparatus. In particular, the present invention relates to techniques which seek to improve the throughput of data in multi-hop communication systems. 
     It is known that the occurrence of propagation loss, or “pathloss”, due to the scattering or absorption of a radio communication as it travels through space, causes the strength of a signal to diminish. Factors which influence the pathloss between a transmitter and a receiver include: transmitter antenna height, receiver antenna height, carrier frequency, clutter type (urban, sub-urban, rural), details of morphology such as height, density, separation, terrain type (hilly, flat). The pathloss L (dB) between a transmitter and a receiver can be modelled by:
 
 L=b+ 10 n  log  d   (A)
 
Where d (meters) is the transmitter-receiver separation, b(db) and n are the pathloss parameters and the absolute pathloss is given by l=10 (L/10) .
 
       FIG. 1A  illustrates a single-cell two-hop wireless communication system comprising a base station (known in the context of 3G communication systems as “node-B” (NB)) a relay node (RN) and a user equipment (UE). In the case where signals are being transmitted on the downlink (DL) from a base station to a destination user equipment (UE) via the relay node (RN), the base station comprises the source apparatus (S) and the user equipment comprises the destination apparatus (D). In the case where communication signals are being transmitted on the uplink (UL) from user equipment (UE), via the relay node, to the base station, the user equipment comprises the source apparatus and the base station comprises the destination apparatus. The relay node is an example of an intermediate apparatus (I) and comprises: a receiver, operable to receive a signal from the source apparatus; and a transmitter, operable to transmit this signal, or a derivative thereof, to the destination apparatus. 
     Table I below gives some examples of the calculated pathloss of a signal being transmitted over the different links: source to destination (SD), source to intermediate (SI) and intermediate to destination (ID), in a multi-hop transmission system where b and n are assumed to remain the same over each of the links. 
     
       
         
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE I 
               
             
             
               
                   
                   
               
               
                   
                 Separation 
                   
                   
               
               
                   
                 (metres) 
                 Pathloss in dB 
                 Absolute Pathloss 
               
             
          
           
               
                 b(dB) 
                 n 
                 SD 
                 SI 
                 ID 
                 SD 
                 SI 
                 ID 
                 SD 
                 SI 
                 ID 
               
               
                   
               
               
                 15.3 
                 3.76 
                 1000 
                 500 
                 500 
                 128.1 
                 116.8 
                 116.8 
                 6.46E12 
                 4.77E11 
                 4.77E11 
               
               
                 15.3 
                 3.76 
                 1000 
                 600 
                 600 
                 128.1 
                 119.76 
                 119.76 
                 6.46E12 
                 9.46E11 
                 9.46E11 
               
               
                 15.3 
                 3.76 
                 1000 
                 700 
                 700 
                 128.1 
                 122.28 
                 122.28 
                 6.46E12 
                 1.69E12 
                 1.69E12 
               
               
                   
               
             
          
         
       
     
     The examples calculated above demonstrate that the sum of the absolute path losses experienced over the indirect link SI+ID may be less than the pathloss experienced over the direct link SD. In other words it is possible for:
 
 L ( SI )+ L ( ID )&lt; L ( SD )  (B)
 
     Splitting a single transmission link into two shorter transmission segments therefore exploits the non-linear relationship between pathloss verses distance. From a simple theoretical analysis of the pathloss using equation (A), it can be appreciated that a reduction in the overall pathloss (and therefore an improvement, or gain, in signal strength and thus data throughput) should be achieved if a signal is sent from a source apparatus to a destination apparatus via an intermediate apparatus (eg relay node), rather than being sent directly from the source apparatus to the destination apparatus. If implemented, multi-hop communication systems could potentially allow for a reduction in the transmit power of transmitters which facilitate wireless transmissions, which would lead to a reduction in interference levels as well as decreasing exposure to electromagnetic emissions. 
     Clearly, due to the non-linear relationship between pathloss and distance, the position of an intermediate apparatus relative to the source and destination, will critically effect the potential gain that a multi-hop transmission may have as compared to a direct, or single-hop, transmission between the source and destination. This is illustrated in  FIG. 2A  which shows a graphical representation of the theoretical gain which may be achieved by multi-hop transmissions, and plots the total power loss (dB) against the relative normalised position of the intermediate apparatus between the source apparatus and the destination apparatus. 
     Considering firstly the case where the intermediate node is positioned on the line of the direct link between the source and destination (in which case the path extension factor (s)=1), it can be seen that the potential gain is reduced as the relay node is moved away from a mid-way position towards the source or destination apparatus. Likewise, as the position of the intermediate apparatus is moved away from the line of the direct link, thereby extending the total path length of the sum of the two transmission segments (and increasing the path extension factor to s=1.1, s=1.2 etc), it can be seen that the graphical region of theoretical gain is again reduced. 
     However, simulations carried out to test the applicability of multi-hop communication systems have revealed unexpectedly low gains in throughput of data. Indeed, the gains experienced are well below the potential gain suggested by a simple analysis based on the pathloss equation A. Consequently, and despite the potential advantages that multi-hop systems may demonstrate in terms of signal range extension, a possible reduction in the overall transmit power required to transmit a signal between a source and destination, and the connectivity of otherwise inaccessible nodes, wireless systems operators have been deterred from implementing multi-hop networks. 
     One of the reasons that such a discrepancy exists between the predicted gain and the simulated gain is that previous predictions have been based on the assumption that the pathloss parameters b and n are the same on all links. In actual fact, these values vary as a result of the antenna height of the source apparatus and destination apparatus as compared to the height of the relay node. Thus, a more realistic table of values is given below in table II. The values labelled 3 GPP are obtained from adapting the model employed by the 3 GPP to incorporate the fact that the antenna height of the intermediate apparatus is typically somewhere between the height of the antenna at the source and destination apparatus. The values labelled UoB are derived from modelling conducted by the University of Bristol based on a typical deployment in the city of Bristol. 
     
       
         
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE II 
               
             
             
               
                   
               
               
                   
                 Pathloss 
                 Link 
               
             
          
           
               
                   
                 Parameter 
                 S-D 
                 S-I 
                 I-D 
               
               
                   
               
             
          
           
               
                   
                 3GPP 
                 b (dB) 
                 15.3 
                 15.5 
                 28 
               
               
                   
                   
                 n 
                 3.76 
                 3.68 
                 4 
               
               
                   
                 UoB 
                 b(dB) 
                 13.07 
                 16.29 
                 10.04 
               
               
                   
                   
                 n 
                 4.88 
                 4.64 
                 5.47 
               
               
                   
               
             
          
         
       
     
     The graphical illustration of total pathloss verses normalised relay node position using the pathloss parameters tabulated in table II is shown in  FIG. 2B . It can be seen that the perfect “bell-shape” of  FIG. 2A  is not achieved when a more realistic set of pathloss parameters are used to calculate the variation in total pathloss as the position of a theoretical relay node is adjusted. Indeed, the region of gain is reduced and it is apparent that relatively small changes in the position of a relay node or a user equipment, leading to a change in the absolute pathloss over the communication link, will have a significant effect on the quality of a communication signal at the receiving apparatus. Thus, the positioning of an intermediate apparatus or relay node is critical if a gain is to be achieved by the occurrence of a multi-hop transmission, as compared to a direct transmission between the source and destination. 
     However, even when predictions are based on a more accurate reflection of the pathloss parameters likely to be encountered in the real world, simulations of multi-hop systems have revealed unexpectedly poor correspondence between the predicted and simulated gain. 
     SUMMARY OF THE INVENTION 
     Embodiments of the present invention seek to provide a communication system comprising a source apparatus, a destination apparatus and at least one intermediate apparatus, wherein the source apparatus and the or each intermediate apparatus each comprise a transmitter, operable to transmit a communication signal or a signal derived therefrom, in a communication direction towards said destination apparatus, and wherein the destination apparatus and the, or each, intermediate apparatus each comprise a receiver, operable to receive said communication signal, or a signal derived therefrom, wherein said communication system comprises a determining means, operable to determine a measure of, or a change in a measure of, the resource allocated to one or more of said transmitters that will tend to substantially attain or maintain a balance between: 
     i) a measure of the quality of the communication signal received at the destination apparatus; and 
     ii) measure of the quality of the communication signal received at the, or each, intermediate apparatus. 
     It will, of course, be appreciated that the communication signal actually received by the destination apparatus may be the communication signal transmitted by the source apparatus, or it may be a communication signal derived therefrom. 
     Thus, preferred embodiments of the present invention seek to maintain or achieve a “balance” in a measure of the quality of a communication signal being received at the or each intermediate apparatus and a measure of the quality of a communication signal being received at a destination apparatus. Preferably, the determining means is operable to determine a change in the transmit power of one or more of the apparatuses which are operable to transmit a communication signal present communication system embodying the present invention, in order to reduce or prevent substantial imbalance (i.e. achieve or maintain a substantial “balance”) between a measure of the quality of a communication signal received at the intermediate apparatus and a measure of the quality of a communication signal received at the destination apparatus. 
     The existence of an imbalance arising in a communication system embodying the present invention may be apparent from a direct comparison of a measure of a quality of a communication signal received at the destination apparatus and a measure of the quality of a communication signal received at the, or one of the, intermediate apparatuses. Alternatively, an imbalance may be apparent when a comparison is made via a mapping function. Hence the situation may exist where measures of equal value do not equate to a balanced system, and likewise where measures of differing value may equate to a balanced system. 
     It is envisaged that embodiments of the present invention may be used, prior to deployment of a multi-hop system, to optimise the system and/or to substantially balance a measure of the quality of a communication signal received at the, or each intermediate apparatus and a measure of the quality of a communication signal received at the destination apparatus. It is also envisaged that embodiments of the present invention may be implemented within an existing multi-hop system in order to seek to achieve and maintain “balance” in a measure of the quality of a communication signal across all links. Thus, the present invention may be employed within a multi-hop communication system to establish a substantial “balance” between an indicator of the RSS or the SINR at the destination apparatus and an indicator of the RSS or the SINR, at the, or each, intermediate apparatus. The transmit powers will advantageously be optimised initially with respect to a target received signal quality for one of the apparatuses operable to receive a communication signal in a multi-hop system. This will usually be the destination apparatus. Thus, an indicator of a measure of the variation of the quality of a communication signal received at the destination from a target received signal quality (=“variation from target” indicator), will advantageously be minimal when a system has been optimised according to embodiments of the present invention. Thereafter, if a change is detected in the variation from target indicator, which may be in a positive or negative sense, e.g. if the quality of the communication signal has deteriorated or improved, or if the target set for the apparatus has changed, the variation from target indicator will increase. In this case, embodiments of the present invention which enable a change in the variation from target indicator from a desired value to be detected, will advantageously seek to bring the variation from target indicator to the desired value. 
     Simulations of multi-hop communication systems embodying the present invention have been found to demonstrate a significant gain over systems in which a signal is transmitted directly to a destination apparatus. Indeed, the results of system level simulations carried out to test a preferred embodiment of the present invention indicate that a communication system which is “balanced” within the context of the present invention, can be expected to fulfil the advantages associated with multi-hop transmissions and to provide an improvement in the throughput of data. 
     It is believed that one explanation for the improved throughput demonstrated by preferred embodiments of the present invention is that they permit a reduction in the absolute transmit power required in a multi-hop system. This is considered in more detail below. 
     Starting from the principle already demonstrated above, that by splitting a single direct transmission link into two shorter transmission links, a reduction in the total pathloss experienced by a signal is achieved. Then, the total transmit power required to transmit a communication signal from a source apparatus to a destination apparatus via at least one intermediate apparatus, will be less than is required to transmit the communication signal directly between the source apparatus and the destination apparatus. Thus, less transmit power is needed in order to ensure that the destination apparatus (and possibly also the intermediate apparatus) receives a minimum or “target” signal quality. If no adjustment is made to the transmit power, then significant excess transmit power (i.e. transmit power exceeding that required to achieve a good, or target, signal quality at the destination apparatus and/or the intermediate apparatus) will result. Rather than serving to further increase the gain achieved by a multi-hop communication as compared to a direct communication between a source apparatus and a destination apparatus, this excess transmit power will merely increase interference levels leading to a deterioration in the quality of the communication link. This deterioration will tend to counteract the potential gain of a multi-hop system which accounts for the poor simulation results of previously considered multi-hop communication systems. 
     Furthermore, the overall throughput across a two-hop network (for example) is limited by the lower of: the number of data packets received at the intermediate apparatus and the number of data packets received at the destination apparatus. The number of data packets received at a receiver is dependent upon the quality of the communication link that terminates at that receiver. This may be reflected, for example, by a measure of the throughput, a measure of the received signal strength (RSS) or a measure of the signal-to-interference plus noise ratio (SINR). Thus, in effect, the receiver which receives the lowest quality communication signal within a multi-hop system forms a “bottle neck” for data packet transmission, thereby wasting capacity for data transfer on other links within the multi-hop system. An increase the transmit power at a transmitter which does not serve to improve the lowest quality communication signal, will result in additional excess transmit power. Consequently, a further degradation is experienced in the performance of the system. This is illustrated in  FIGS. 9A and 9B  which plot the variation of the gain in average packet throughput observed by users of a two-hop system compared to that observed for a single hop system, against the transmit power of the source apparatus (NB). Each graph includes four different plots, each representing a different transmit power of the intermediate apparatus. It can be seen that as the transmit power of the base station is increased beyond an optimal point, then a significant degradation in gain will be experienced despite the emission of more signal energy. 
     It can therefore be appreciated that the improvements made by preferred embodiments of the present invention can be attributed to the way in which the various aspects of the present invention seek to ensure that any imbalance between a measure of the quality of a communication signal received at the destination apparatus and a measure of the quality of a communication signal received at the, or each, intermediate apparatus is reduced or prevented. Thus, excess transmit power which cannot improve the throughput of data packets and which will only serve to raise interference levels, is minimised. 
     There are a number of different events which, if they arise, can potentially lead to an “imbalance” (i.e. a difference between a measure of the quality of a communication signal received at the destination apparatus and a measure of the quality of a communication signal received at the or each intermediate apparatus) in a multi-hop system:
         i) The pathloss arising over one of the links changes. This may be due to the position of one or both of the transmitter and receiver for that link changing, or due to a change in the environmental conditions or interference levels arising between the transmitter and the receiver;   ii) It is usual for an apparatus which is operable to receive a communication signal, to have a target RSS or target SINR. This is usually set by the network provider and may vary depending on the characteristics of the communication system or receiving apparatus, or depending on the type of data to be transmitted. The target RSS/SINR of a mobile phone or other user equipment may vary and any change in target can be accommodated for by adjusting the transmit power of the transmitting apparatus in such a way as to tend to minimise a measure of the variation of the quality of a communication signal received at the destination apparatus from a target received signal quality (i.e. “variation from target”). In the case of a multi-hop system, merely adjusting the transmit power of one apparatus in order to accommodate a change in target of one of the receiving apparatuses, will lead to an imbalance within the system.       

     Embodiments of the present invention seek to provide a way of responding to an imbalance, or a potential imbalance, which arises as a result of each of these possible events in order to improve the throughput of data being transmitted on the downlink (DL) from a base-station (source) to a destination user equipment via one or more intermediate apparatuses or the uplink (UL) from a destination apparatus to a base station. In a standard communications system the downlink is the link between the NB and the UE. In the multi-hop case the DL refers to the link in which communication is directed towards the UE (e.g. RN to UE, RN to RN in the direction of UE and NB to RN). In a standard communications system the uplink is the link between the UE and the NB. In the multi-hop case the UL refers to the link in which communication is directed towards the NB (e.g. UE to RN, RN to RN in the direction of NB and RN to NB). Furthermore, embodiments of the present invention seek to provide a way of optimising a multi-hop system whereby any target quality set by one or more of the receivers is substantially attained and the throughput of data across each link is substantially equal. 
     According to a first aspect of the present invention there is provided a communication system comprising a source apparatus, a destination apparatus and at least one intermediate apparatus, the source apparatus being operable to transmit a communication signal via the or each intermediate apparatus, to the destination apparatus, wherein the destination apparatus is operable to derive one or more indicators of the quality of a communication signal received at the destination apparatus, the communication system further comprising:
         i) a control means provided in the intermediate apparatus;   ii) indicator deviation detection means operable to detect a change in one said indicator derived by the destination apparatus from a desired value;   iii) determining means operable, following the detection of such a change, to determine a change in the transmit power of the intermediate apparatus that will tend to bring said indicator derived by the destination apparatus to said desired value, wherein the determining means further comprises request transmitting means operable to transmit a request for a change in the transmit power of the intermediate apparatus to the control means.       

     Embodiments of the first aspect of the present invention advantageously provide a way of responding to a deviation in the indicators derived by the destination apparatus from a desired value which may be due to i) a change in pathloss between the intermediate apparatus and the destination apparatus; or ii) a change in the target of the destination apparatus by determining a change that is required in the transmit power of the intermediate apparatus and/or the source apparatus. Advantageously, the change in transmit power that is required will be relative to the degree of the deviation detected by the indicator deviation detection means. 
     In accordance with an embodiment of the first aspect of the present invention, one of the indicators derived by said destination apparatus may comprises a measure of the strength of a communication signal received at the destination apparatus (eg RSS). Alternatively or additionally, one of the indicators derived by the destination apparatus may comprise a measure of the signal-to-interference plus noise ratio (SINR) of a communication signal received at the destination apparatus, or it may comprise a measure of the variation of the quality of a communication signal received at the destination apparatus from a target received signal quality set for the destination apparatus. An indicator of the variation from target may be a variation from target RSS, a variation from target SINR or a variation from a target which is based on a combination of RSS and SINR. 
     Preferably, the control means is operable, following receipt of a request for a change in the transmit power of the intermediate apparatus, to check that the intermediate apparatus is able to satisfy the request based on a maximum transmit power for the intermediate apparatus. If necessary, a revised request is derived. Preferably, the control means is operable to receive an input signal which allows the control means to determine if an increase in transmit power of the intermediate apparatus is prohibited. If the request received from the determining means is for an increase in transmit power, and following a determination by the control means that an increase in transmit power for the intermediate apparatus is prohibited, the control means is operable to ignore the request from said determining means such that no change will be made to the transmit power of said intermediate apparatus. 
     According to a second aspect of the present invention there is provided a communication system comprising a source apparatus, a destination apparatus and an intermediate apparatus, the source apparatus being operable to transmit a communication signal via the intermediate apparatus, to the destination apparatus, wherein each of the destination apparatus and the intermediate apparatus comprise: indicator derivation means operable to derive one or more indicators of the quality of a communication signal received at the destination apparatus or the intermediate apparatus respectively, the communication system further comprising:
         i) a control means provided in said intermediate apparatus;   ii) imbalance detection means operable to detect an imbalance between an indicator derived by the destination apparatus and an indicator derived by the intermediate apparatus; and   iii) determining means, operable following detection of such an imbalance by said imbalance detection means, to determine a required change in the transmit power of the source apparatus that will tend to reduce such an imbalance, wherein the control means is operable, following determination of said change, to issue a command to said source apparatus commanding a change in the transmit power of the source apparatus.       

     Embodiments of the second aspect of the present invention advantageously provide a way of adjusting the transmit power of the source apparatus in order to substantially restore or attain a balance between a measure of a quality of a communication signal received at the destination apparatus and a measure of the quality of a communication signal received at the intermediate apparatus. The imbalance may arise due to a change in pathloss between the source and the intermediate apparatus. Alternatively an imbalance may arise following operation by a communication system embodying the first aspect of the present invention to respond to a change in the target quality indicator of the destination apparatus, since in restoring the variation from target indicator to its original measure (by changing the transmit power of the intermediate apparatus), the quality indictors of the intermediate apparatus and the destination apparatus will no longer be balanced. 
     According to embodiments of the second aspect of the present invention, one said indicator derived by each of the intermediate apparatus and the destination apparatus comprises a measure of the strength of a communication signal received at the destination apparatus or the intermediate apparatus respectively (eg RSS). Alternatively or additionally, one said indicator derived by each of said intermediate apparatus and said destination apparatus comprises a measure of the signal-to-interference plus noise ratio (SINR) of a communication signal received at the destination apparatus or the intermediate apparatus respectively. 
     Preferably, the source apparatus is operable, following receipt of a command, and wherein said command is for an increase in transmit power, to determine if it can carry out the request based on a maximum transmit power of the source apparatus. If the source apparatus determines that it cannot carry out the said command, it is operable to determine a revised change in transmit power that will tend to reduce the said imbalance, and to carry out said revised change. 
     The control means is preferably operable, following issuance of a command to said source apparatus and wherein said command was for an increase in transmit power, to monitor the indicator derived by the intermediate apparatus in order to determine if said transmit power of said source apparatus has been changed in accordance with said command. If it is determined that a change in transmit power of the source apparatus has not been carried out in accordance with said command, said control means is operable to prohibit any subsequent increases in transmit power of said intermediate apparatus. This advantageously ensures that when the maximum transmit power of the source apparatus has been reached, the transmit power of the intermediate apparatus is not further increased as this will compound the imbalance caused due to the fact that the source apparatus is not able to further increase its transmit power. 
     There are a number of events which lead to the prohibition being lifted. If an increase in transmit power of said intermediate apparatus is prohibited, and if no subsequent imbalance is detected by said imbalance detection means, said control means apparatus is operable to allow a subsequent increase in transmit power of said intermediate apparatus. If an increase in transmit power of said intermediate apparatus is prohibited, and if a subsequent imbalance is detected by said imbalance detection means such that said intermediate apparatus is caused to issue a command to said source apparatus and wherein said request is for a decrease in transmit power, said control means is operable to allow a subsequent increase in transmit power of said intermediate apparatus. If an increase in transmit power of said intermediate apparatus is prohibited, and if a subsequent imbalance is detected by said imbalance detection means such that said intermediate apparatus is caused to issue a command to said source apparatus and wherein said command is for an increase in transmit power which can be carried out by said source apparatus, said control means is operable to allow a subsequent increase in transmit power of said intermediate apparatus. 
     The intermediate apparatus preferably comprises a receiver operable to receive the signal transmitted by the source apparatus; and a transmitter operable to transmit the received signal, or a signal derived therefrom, to the destination apparatus. Duplexing of signals to separate communication signals received by the intermediate apparatus from communication signals transmitted by the intermediate apparatus may be Frequency Division Duplex (FDD) or Time Division Duplex (TDD). One or more of the intermediate apparatuses may preferably comprise a so-called relay node (RN) or relay-station (RS). A relay node has the capability of receiving a signal for which it is not the intended final destination and then transmitting the signal on to another node such that it progress towards the intended destination. A relay node may be of the regenerative type, where the received signal is decoded to the bit level, making a hard decision. If the received packet is found to be in error then retransmission is requested, hence the RN incorporates ARQ or H-ARQ. ARQ or H-ARQ is a receiver technique for managing retransmission request and subsequent reception of retransmitted signals. Once the packet is successfully received, it is then scheduled for retransmission towards the destination, based on any radio resource management strategies incorporated into the RN. Alternatively a relay node may be of the non-regenerative type, whereby data is amplified at the relay node and the signal is forwarded to the next station. It is envisaged that the function of an intermediate apparatus or relay node may be provided by a mobile phone, or other user equipment. 
     Whilst embodiments of the present invention may only realistically operate where regenerative relays are employed as the intermediate apparatus, they benefit from a relatively simple determination of the transmit powers which does not require the performance of an explicit calculation. Transmit powers are advantageously determined by adjusting the transmit power of the relevant transmitter relative to the degree of indicator change detected by the indicator deviation detection means, in order to restore the indicator which has experienced a change to its value, and thereby balance the received SINR. 
     The first and second aspects of the present invention will each tend to reduce or prevent an imbalance which arises or may arise, as the case may be, under different circumstances. If the pathloss between the intermediate apparatus and the destination apparatus changes (which may be due to a change in the position of the destination apparatus or a change in environmental conditions) or if the target of the destination apparatus changes, this will be dealt with by the first aspect of the present invention which is triggered by detection of a change in the indicator derived by the destination apparatus. Preferably, a communication system embodying the first aspect of the present invention will comprise a deviation detection means which monitors the, or one of the, indicators of the destination apparatus at all times. Thus, any change or deviation, in the indicator derived by the destination apparatus from a desired value, can be detected quickly. 
     The first aspect alone may be sufficient to restore balance across a multi-hop system following a change in the pathloss between the intermediate apparatus and the destination apparatus. However, as discussed above, if the pathloss between the base station and the intermediate apparatus changes (which may be due to a change in the position of the intermediate apparatus in an ad-hoc network, or due to a change in the environmental conditions arising across that link), this must be dealt with by embodiments of the second aspect of the present invention. Moreover, in order to restore balance to a multi-hop communication system following a change in the target quality set by the destination apparatus, it is necessary for both the transmit power of the intermediate apparatus and the source apparatus to be adjusted. Thus, in order to deal with a change in the target quality indicator of the destination apparatus, a communication system which embodies both the first and second aspect of the present invention is preferably provided. Preferably, the imbalance detection of the second aspect of the present invention is performed periodically. Thus according to a preferred embodiment of the first aspect of the present invention said intermediate apparatus further comprises i) imbalance detection means operable to detect an imbalance between an indicator derived by the destination apparatus and an indicator derived by the intermediate apparatus; and ii) second determining means, operable following detection of such an imbalance by said imbalance detection means, to determine a required change in the transmit power of the source apparatus that will tend to reduce such an imbalance, wherein the control means is operable, following determination of said change, to issue a command to said source apparatus commanding a change in the transmit power of the source apparatus. 
     The situation may arise where a change in the target of the destination apparatus is accommodated by a substantially simultaneous change in the pathloss between the intermediate apparatus and the destination apparatus. Thus, in the case where the indicator deviation detection means of the first aspect of the present invention is provided in the destination apparatus such that the destination apparatus is operable to transmit a request to the control means for a change in the transmit power of the intermediate apparatus, no request for a change in transmit power of the intermediate apparatus will be generated by the destination apparatus if this situation does arise. This will lead to an imbalance in the system which will go un-corrected by the first aspect of the present invention, since the new target of the destination apparatus will have been met (inadvertently) but no corresponding change will have been made to the transmit power of the source apparatus. This, relatively rare, situation can be handled by a communication system which embodies both the first and second aspect of the present invention since a change in the measure of the pathloss experienced between the intermediate apparatus and the destination apparatus will also give rise to an imbalance between the signal quality indicators derived by the intermediate and destination apparatuses. The second determining means is then operable to determine the change in the transmit power of the base station that is required to in order to tend to reduce the imbalance between a measure of a quality of a communication signal received at the intermediate apparatus and a measure of the quality of a communication signal received at the destination apparatus. 
     According to a second embodiment of the first aspect of the present invention, there is provided a method of controlling the transmit power of one or more apparatus operable to transmit a communication signal in a multi-hop communication system, the communication system comprising a source apparatus, a destination apparatus and at least one intermediate apparatus, the source apparatus being operable to transmit a communication signal, via the or each intermediate apparatus, to the destination apparatus, the intermediate apparatus having a control means, wherein the method comprises the steps of:
         i) deriving, at the destination apparatus, one or more indicators of the quality of a communication signal received at the destination apparatus;   ii) detecting deviation in the, or one of the, indicators derived by the destination apparatus from a desired value;   iii) issuing a request to said control means for a required change in transmit power of the intermediate apparatus that will tend to bring said indicator derived by the destination apparatus to said desired value.       

     According to a second embodiment of the second aspect of the present invention there is provided a method of controlling the transmit power of one or more apparatus operable to transmit a communication signal in a multi-hop communication system, the communication system comprising a source apparatus, a destination apparatus and at least one intermediate apparatus, the method comprising the steps of:
         i) deriving, at the destination apparatus and the intermediate apparatus, a signal indicator of the quality of communication signal received at the destination apparatus, or at the intermediate apparatus, respectively;   ii) detecting an imbalance between an indicator derived by the destination apparatus and an said indicator derived by the intermediate apparatus;   iii) determining a required change in the transmit power of the source apparatus that will tend to reduce such an imbalance; and   ii) issuing a command to said source apparatus commanding a change in the transmit power of the source apparatus.       

     According to a third embodiment of the first aspect of the present invention there is provided an intermediate apparatus comprising receiving means, operable to receive a communication signal from a source apparatus, or from a previous intermediate apparatus, and transmitting means, operable to transmit said communication signal, or a signal derived therefrom, to a destination apparatus or a subsequent intermediate apparatus, the intermediate apparatus comprising:
         i) control means;   ii) indicator receiving means, operable to receive an indicator from a destination apparatus or, as the case may be, from a subsequent intermediate apparatus which receives said communication signal after said intermediate apparatus and before said destination apparatus, and to detect a deviation in said indicator from a desired value, the indicator being indicative of the quality of a communication signal received at said destination apparatus or said subsequent intermediate apparatus; or   iii) receiving means, operable to receive a request from a destination apparatus or, as the case may be from a subsequent intermediate apparatus, which receives said communication signal after said intermediate apparatus and before and said destination apparatus, for a change in transmit power of the intermediate apparatus; and   iv) determining means operable following detection of a change in said indicator from said destination apparatus, or following receipt of a request from said destination apparatus, to determine a required change in the transmit power of the intermediate apparatus that will tend to bring said indicator derived by the destination apparatus to said desired value, said determining means being operable to transmit a request for a change in the transmit power of the intermediate apparatus to the control means.       

     Preferably, the control means is operable, following receipt of a request from said destination apparatus or said subsequent intermediate apparatus, as the case may be, to check that the intermediate apparatus is able to satisfy the request. Preferably the control means is operable to receive an input signal which allows the control means to determine if an increase in transmit power of the intermediate apparatus is prohibited, and wherein, if the request received from said destination apparatus is for an increase in transmit power, and following a determination by the control means that an increase in transmit power for the intermediate apparatus is prohibited, the control means is operable to ignore said request such that no change will be made to the transmit power of said intermediate apparatus. 
     Preferably, the intermediate apparatus is operable to derive one or more indicators of quality of a communication signal received by the intermediate apparatus. Then, the intermediate apparatus may further comprise:
         i) an imbalance detection means operable to detect an imbalance between one said indicator derived by the destination apparatus or said subsequent intermediate apparatus, as the case may be, and one said indicator derived by the intermediate apparatus;   ii) determining means, operable following detection of such an imbalance by said imbalance detection means, to determine a change in the transmit power of the source apparatus that will tend to reduce such an imbalance; the control means comprising a source command means, operable following determination of said change, to issue a command to said source apparatus commanding a change in the transmit power of the source apparatus.       

     According to an embodiment of the second aspect of the present invention, there is provided an intermediate apparatus comprising receiving means, operable to receive a communication signal from a source apparatus, or from a previous intermediate apparatus, and transmitting means, operable to transmit said communication signal, or a signal derived therefrom, to a destination apparatus or a subsequent intermediate apparatus, the intermediate apparatus further comprising 
     comprising: 
     
         
         
           
             i) indicator derivation means operable to derive an indicator of the quality of a communication signal received by the intermediate apparatus; 
             ii) receiving means operable to receive, from the destination apparatus or, as the case may be, from a subsequent intermediate apparatus which receives said communication signal after said intermediate apparatus and before said destination apparatus, an indicator of the quality of a communication signal received by the destination apparatus or by said subsequent intermediate apparatus; 
             iii) imbalance detection means operable to detect an imbalance between an indicator derived by the intermediate apparatus and an indicator received from the destination apparatus or said subsequent apparatus, as the case may be; 
             iv) determining means, operable following detection of such an imbalance by said imbalance detection means, to determine a change in the transmit power of the source apparatus or, as the case may be, of a previous intermediate apparatus which receives said communication signal before said intermediate apparatus and after said source apparatus, that will tend to reduce such an imbalance; and 
             v) command means, operable following determination of said change, to issue a command to said source apparatus or said previous intermediate apparatus, as the case may be, commanding a change in the transmit power of the source apparatus or said previous intermediate apparatus. 
           
         
       
    
     A communication system may be provided according to an embodiment of the present invention which comprises a plurality of intermediate apparatuses, each embodying the third embodiment of the first aspect of the present invention. Thus the receiving means is operable to a) receive an indicator from a destination apparatus or, as the case may be, from a subsequent intermediate apparatus which receives said communication signal after said intermediate apparatus and before said destination apparatus, and to detect a deviation in said indicator from a desired value, the indicator being indicative of the quality of a communication signal received at said destination apparatus or said subsequent intermediate apparatus, or b) receive a request from a destination apparatus or, as the case may be from a subsequent intermediate apparatus, which is positioned between said intermediate apparatus and said destination apparatus; and wherein the determining means is operable following detection of such a deviation, or following receipt of a request from said destination apparatus, to determine a required change in the transmit power of the intermediate apparatus that will tend to bring said indicator derived by the destination apparatus to said desired value. 
     According to a third embodiment of the second aspect of the present invention, there is provided a communication system comprising source apparatus, a destination apparatus and a plurality of intermediate apparatuses, the source apparatus being operable to transmit a communication signal via each of the intermediate apparatuses, to the destination apparatus, each intermediate apparatus comprising an intermediate apparatus as claimed in any one of claims  38  to  42  or  44 , wherein:
         i) the receiving means is operable to a) receive an indicator from a destination apparatus or, as the case may be, from a subsequent intermediate apparatus which receives said communication signal after said intermediate apparatus and before said destination apparatus, and to detect a deviation in said indicator from a desired value, the indicator being indicative of the quality of a communication signal received at said destination apparatus or said subsequent intermediate apparatus, or b) receive a request from a destination apparatus or, as the case may be from a subsequent intermediate apparatus, which receives said communication signal after said intermediate apparatus and before and said destination apparatus;   ii) the determining means is operable, following detection of such a deviation, or following receipt of a request from said destination apparatus, as the case may be, to determine a required change in the transmit power of the intermediate apparatus that will tend to bring said indicator derived by the destination apparatus to said desired value.       

     A communication system may be provided according to an embodiment of the present invention which comprises a plurality of intermediate apparatuses, each embodying the third embodiment of the second aspect of the present invention. 
     A particular advantage of the embodiments of the present invention is that due to the location of the control means in the intermediate apparatus, embodiments of the present invention may be readily applicable to so-called “ad-hoc” networks, where a base station may not exist and connections between any two apparatuses may be formed via any other apparatus capable of relaying (receiving and transmitting) signals. Thus, the position of a relay node in an ad-hoc network may not be fixed. For example, the function of a relay node may be performed by a mobile user equipment. Furthermore, the present invention may be used in conjunction with either UL or DL data transmissions. 
     There are a number of ways in which the signalling required to carry out embodiments of the first aspect of the present invention may be implemented and some of these will be discussed later with reference to  FIGS. 5A , B and C which show parts of a communication system embodying the first aspect of the present invention. 
     The desired value may be the value of the indicator of the quality of a communication signal derived by the destination apparatus which is at, or close to, the target value set by the destination apparatus, and when the system is substantially balanced (i.e. a measure of a quality of a communication signal received at the destination apparatus is in balance with a measure of a quality of communication signal received at the, or each, intermediate apparatus). Thus, embodiments of the first aspect of the present invention may be advantageously used to maintain the quality of the communication signal received by the destination apparatus at, or near, the target value set by the destination apparatus. Thereafter, it may be necessary for embodiments of a second aspect of the present invention to optimise the systems ensuring a balance is achieved between the destination apparatus and the or each intermediate apparatus. 
     Thus, it should be appreciated that the indication deviation detection means may be used in a system which has already been balanced, or optimised. Thus, a deviation from the desired value, which may arise due to an event which results in a change in a measure of a quality of a communication signal at the destination apparatus will be detected, and the required change the resource allocated to the previous intermediate apparatus determined. 
     If the indicator deviation is due to a change in the pathloss such that the quality of the communication signal received by the destination deviates from target, embodiments of the first aspect will advantageously restore balance to the system by adjusting the transmit power of the preceding intermediate apparatus. However, if the indicator deviation is due to a change in the target quality set by the destination apparatus, whilst embodiments of the first aspect may be advantageously employed to adjust the transmit power at the intermediate apparatus in order that the new target can be attained, embodiments of the second aspect are needed in order to restore a balance by determining the corresponding change in transmit power for the other transmitters in the multi-hop system. 
     According to a further embodiment of the present invention there is provided a computer program which, when run on a computer, causes the computer to become an intermediate apparatus embodying the present invention. Communication methods carried out in a base station embodying the present invention, an intermediate apparatus embodying the present invention or in a destination apparatus embodying the present invention are also provided. 
     Embodiments of the present invention may be implemented within a wireless communication system employing any multiple access technique, including but not limited to: frequency division multiple access (FDMA), time division multiple access (TDMA) code division multiple access (CDMA) and orthogonal frequency division multiple access (OFDMA). In the case of a CDMA system, in which all transmissions occur in the same frequency band and each transmission is assigned a unique channelisation code, the Gp factor represents the spreading factor or length of the code used to spread the transmitted signal otherwise known as the processing gain. In the case of orthogonal spreading codes, up to Gp channels are available for simultaneous transmission. 
     It should be appreciated that the term “user equipment” encompasses any device which is operable for use in a wireless communication system. Furthermore, although the present invention has been described primarily with reference to terminology employed in presently known technology, it is intended that the embodiments of the present invention may be advantageously applied in any wireless communication systems which facilitates the transmission of a communication signal between a source and destination, via an intermediate apparatus. 
     In any of the above aspects, the various features may be implemented in hardware, or as software modules running on one or more processors, or as a combination of the two. The invention also provides operating programs (computer programs and computer program products) for carrying out any of the methods described herein, and computer readable media having stored thereon programs for implementing the techniques described herein. A program embodying the invention may be stored on a computer-readable medium, or it could, for example, be in the form of a signal such as a downloadable data signal provided from an Internet web site, or it could be in any other form. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a better understanding of the present invention and to show how the same may be carried into effect, reference will now be made, by way of example, to the accompanying drawings in which: 
         FIG. 1A  illustrates a single cell/relay model of a wireless communication system; 
         FIG. 1B  illustrates a two cell/relay model of a wireless communication system; 
         FIGS. 2A and 2B  each show a graphical representation of the theoretical gain that may be achieved by a multi-hop communication system based on pathloss equation (A); 
         FIGS. 3A and 3B  illustrate algorithms embodying the first and second aspects of the present invention; 
         FIG. 4  illustrates algorithms embodying the first and second aspects of the present invention; 
         FIG. 5  illustrates parts of a communication system embodying the first aspect of the present invention; 
         FIG. 6  illustrates the relationship between source transmit power and intermediate transmit power in the case of a multi-hop communication system having a non-regenerative relay node and using an FDD duplexing technique; 
         FIG. 7  illustrates the relationship between source transmit power and intermediate transmit power in the case of a multi-hop communication system having a non-regenerative relay node and using a TDD duplexing technique; 
         FIGS. 8A and 8B  illustrate the optimal NB transmit power as a function of RN transmit power; 
         FIG. 9  shows a graphical illustration of the variation in the average gain in throughput observed by users of a multi-hop system as compared to that observed for a single hop system; and 
         FIG. 10  illustrate the optimal NB transmit power as a function of RN transmit power where it is assumed that the communication link between the source and destination apparatus has a 3 dB gain compared with the shorter multi-hop links. 
     
    
    
     DETAILED DESCRIPTION 
     An example of an algorithm which implements an embodiment of the first aspect of the present invention will now be described with reference to  FIG. 3A  in the case of downlink transmission in which the source apparatus comprises a node-B (NB), the intermediate apparatus comprises a relay node (RN) which is of the regenerative type, and the destination apparatus comprises a user equipment (UE). The user equipment continually monitors the SINR and derives indicators of the SINR and the variation from target SINR. The destination apparatus is provided with an indicator deviation detection means for detecting a change in one or both of these indicators. The intermediate apparatus is provided with a control means according to an embodiment of the first aspect of the present invention. 
     The details of the algorithm are summarised as follows: 
     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                   
               
               
                 Downlink Algorithm 3: Part 1 
               
               
                 Trigger: RN receives request for change in RN transmit power from UE 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Algorithm Input 
                 Required by 
                 Origin 
               
               
                   
               
               
                 Request for change in RN Transmit Power 
                 RN 
                 Change derived 
               
               
                   
                   
                 in UE and 
               
               
                   
                   
                 processed by 
               
               
                   
                   
                 RN 
               
               
                 Block in increase in RN Transmit Power 
                 RN 
                 Block is 
               
               
                   
                   
                 set/cleared in 
               
               
                   
                   
                 part 2 
               
               
                   
                   
                 of the 
               
               
                   
                   
                 algorithm 
               
               
                   
               
             
          
           
               
                   
                   
                 Destination &amp; 
               
               
                   
                   
                 Signalling 
               
               
                 Algorithm Output 
                 Derivation 
                 Requirement 
               
               
                   
               
               
                 Change in RN transmit power 
                 Relative change 
                 Relative change 
               
               
                   
                   
                 derived at UE and 
               
               
                   
                   
                 made by RN 
               
               
                   
               
             
          
         
       
     
     The following sequence takes place following detection of a change in an indicator derived by the destination apparatus (UE) from a desired value which in this case is the target SINR. The destination apparatus (UE), following detection of a change, determines the change in the transmit power of the intermediate apparatus which will tend bring the indicator derived by the destination apparatus back to said desired value. Then: 
     1. The destination apparatus (UE) transmits a request for a change in the RN transmit power to the RN; 
     2. The RN checks whether the request can be satisfied. If the received request cannot be satisfied by the RN then it is modified to one that can be met. 
     3. If the requested change in transmit power of the RN is an increase, then a check is made to determine whether a block, or prohibition, has been placed on further increases. In this embodiment, the block is placed by the algorithm illustrated by  FIG. 3B  which embodies the second aspect of the present invention. If a block is in place then the request is ignored, otherwise the RN transmit power is changed accordingly. 
     The algorithm described above will manage the case of the propagation loss varying between the RN and UE and the case of the UE modifying its target RSS or SINR. In order to handle the case of the propagation loss varying between the NB and RN and the case that both the target in the UE and the propagation loss between the RN and UE varies, such that no request for change in RN transmit power is generated, an algorithm as shown in  FIG. 3B  which implements an embodiment of the second aspect of the present invention operates periodically as discussed below. 
     In this embodiment, the following algorithm is executed in addition to the algorithm discussed above with reference to  FIG. 3A . Thus, the intermediate apparatus comprises indicator derivation means for deriving an indicator of the RN. The intermediate apparatus further comprises imbalance detection means and a second determining means according to an embodiment of the second aspect of the present invention. Alternatively, it is also possible for the algorithm described with reference to  FIG. 3A , or the following algorithm shown in  FIG. 3B  to be implemented separately in a wireless multi-hop communication system. 
     The details of the algorithm are summarised as follows: 
                                                             Downlink Algorithm 3: Part 2       Trigger: Periodically executed in RN                                    Algorithm Input   Required by   Origin                   SINR at UE   RN   Signalled from UE           SINR at RN   RN   Known at RN                            Destination &amp;               Signalling       Algorithm Output   Derivation   Requirement               Change in NB transmit power   Relative change   Signalled to NB       Block on RN power increase   True/false test   Part 1 of the algorithm                    
1. The RN monitors the reported SINR from both the UE and the SINR at the RN. If an imbalance exists then the second determining means of the RN calculates the change in NB transmit power that is required to restore a balance in SINR.
 
2. The RN then signals a command to the NB for a change in the transmit power of the NB according to the change determined in step 1.
 
3. The NB receives the request and checks that the request can be met. If it can not then it is revised. The NB then changes its transmit power accordingly.
 
4. If the request from the RN was for an increase in NB transmit power then the RN monitors the received SINR to check that the required change was made. If it is detected that the required change was not made then a block, or prohibition, is placed on further increases in RN transmit power. If this block was not placed then as the NB cannot increase its transmit power, any increase in RN transmit power will cause an imbalance that cannot be rectified, as this would require a further increase in the NB transmit power, compounding any imbalance.
 
     Note that the block on further RN power increase is removed if: it is detected that the SINRs are balanced; a decrease in NB transmit power is requested; or a requested change in NB transmit power is detected to have been made. 
     Another embodiment of the first aspect of the present invention will now be described with reference to  FIG. 4A  in the case of uplink transmissions in which the source apparatus comprises a user equipment (UE), the intermediate apparatus comprises a relay node (RN) which is of the regenerative type, and the destination apparatus comprises a Node-B (NB). The NB continually monitors the SINR and derives indicators of the SINR and the variation from target SINR. The NB is provided with an indicator deviation detection means for detecting a change in one or both of these indicators. The intermediate apparatus is provided with a control means according to an embodiment of the first aspect of the present invention. 
     The details of the algorithm are summarised as follows: 
     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                   
               
               
                 Uplink Algorithm 4: Part 1 
               
               
                 Trigger: RN receives request for change in RN transmit power from NB 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Algorithm Input 
                 Required by 
                 Origin 
               
               
                   
               
               
                 Request for change in RN 
                 RN 
                 Change derived in NB and 
               
               
                 Transmit Power 
                   
                 processed by RN 
               
               
                 Block in increase in 
                 RN 
                 Block is set/cleared in part 2 
               
               
                 RN Transmit 
                   
                 of the algorithm 
               
               
                 Power 
               
               
                   
               
             
          
           
               
                   
                   
                 Destination &amp; 
               
               
                   
                   
                 Signalling 
               
               
                 Algorithm Output 
                 Derivation 
                 Requirement 
               
               
                   
               
               
                 Change in RN transmit power 
                 Relative change 
                 Relative change 
               
               
                   
                   
                 derived at NB and 
               
               
                   
                   
                 made by RN 
               
               
                   
               
             
          
         
       
     
     The following sequence takes place following detection of a change in an indicator derived by the destination apparatus (NB) from a desired value. The destination apparatus (NB), following detection of a change, determines the change in the transmit power of the intermediate apparatus which will tend bring the indicator derived by the destination apparatus back to said desired value. Then: 
     1. The destination apparatus (NB) transmits a request for a change in the RN transmit power to the RN; 
     2. The RN checks whether the request can be satisfied. If the received request cannot be satisfied by the RN then it is modified to one that can be met. 
     3. If the requested change in transmit power of the RN is an increase, then a check is made to determine whether a block, or prohibition, has been placed on further increases. In this embodiment, the block is placed by the algorithm illustrated by  FIG. 4B  which embodies the second aspect of the present invention. If a block is in place then the request is ignored, otherwise the RN transmit power is changed accordingly. 
     The algorithm described above will manage the case of the propagation loss varying between the RN and NB and the case of the NB modifying its target RSS or SINR. In order to handle the case of the propagation loss varying between the UE and RN and the case that both the target in the NB and the propagation loss between the RN and NB varies, such that no request for change in RN transmit power is generated, an algorithm as shown in  FIG. 4B  which implements an embodiment of the second aspect of the present invention operates periodically as discussed below. 
     In this embodiment, the following algorithm is executed in addition to the algorithm discussed above with reference to  FIG. 4A . Thus, the intermediate apparatus comprises indicator derivation means for deriving an indicator of the RN. The intermediate apparatus further comprises imbalance detection means and a second determining means according to an embodiment of the second aspect of the present invention. Alternatively, it is also possible for the algorithm described with reference to  FIG. 4A , or the following algorithm shown in  FIG. 4B  to be implemented separately in a wireless multi-hop communication system. 
     The details of the algorithm are summarised as follows: 
                                                             Uplink Algorithm 4: Part 2       Trigger: Periodically executed in RN                                    Algorithm Input   Required by   Origin                   SINR at NB   RN   Signalled from NB           SINR at RN   RN   Known at RN                            Destination &amp;               Signalling       Algorithm Output   Derivation   Requirement               Change in UE transmit power   Relative change   Signalled to UE       Block on RN power increase   True/false test   Part 1 of the algorithm                    
1. The RN monitors the reported SINR from both the NB and the SINR at the RN. If an imbalance exists then the second determining means of the RN calculates the change in UE transmit power that is required to restore a balance in SINR.
 
2. The RN then signals a command to the UE for a change in the transmit power of the UE according to the change determined in step 1.
 
3. The UE receives the request and checks that the request can be met. If it can not then it is revised. The UE then changes its transmit power accordingly.
 
4. If the request from the RN was for an increase in UE transmit power then the RN monitors the received SINR to check that the required change was made. If it is detected that the required change was not made then a block, or prohibition, is placed on further increases in RN transmit power.
 
     Note that the block on further RN power increase is removed if: it is detected that the SINRs are balanced; a decrease in UE transmit power is requested; or a commanded change in UE transmit power is detected to have been made. 
     There are a number of ways in which the signalling required to carry out embodiments of the first aspect of the present invention may be implemented and these are illustrated in  FIGS. 5A , B and C which show parts of a communication system embodying the first aspect of the present invention in which the same reference numerals are used to refer to parts which provide the same function. 
       FIG. 5A  shows a communication system in which the destination apparatus (D) is provided with an indicator derivation means ( 1 ), an indicator deviation detection means ( 2 ) and is operable, following detection of a change in the indicator derived by the destination apparatus, to transmit a request for a determination of a change in the transmit power of the intermediate apparatus to the intermediate apparatus. The intermediate apparatus (I) comprises a request receiving means ( 4 ) and a determining means ( 5 ) which is operable to determine a change in the transmit power of the intermediate apparatus that will tend to bring said indicator derived by the destination apparatus towards said desired value. Thus, said request for a change in the transmit power of the intermediate apparatus is transmitted locally from said determining means of the source apparatus to said control means ( 3 ) of the intermediate apparatus. 
       FIG. 5B  shows a communication system wherein, in addition to an indicator derivation means ( 1 ), the destination apparatus is provided with an indicator change ( 2 ) detection means and a determining means ( 5 ). Thus, said request is transmitted from the determining means of the destination apparatus to the control means ( 3 ) of the intermediate apparatus. 
       FIG. 5C  shows a communication system in which the intermediate apparatus (I) comprises an indicator receiving means ( 6 ), an indicator deviation detection means ( 2 ), a determining means ( 5 ) and a control means ( 3 ). Thus, said request for a change in the transmit power of the intermediate apparatus is transmitted locally from said determining means of the source apparatus to said control means ( 3 ) of the source apparatus. 
     It can be seen from  FIGS. 5A , B and C that an intermediate apparatus provided according to an embodiment of the first aspect of the present invention may comprise: i) a control means; ii) a determining means and a control means; or iii) an indicator deviation detection means, a determining means and a control means. Similarly a destination apparatus provided in accordance with an embodiment of the first aspect of the present invention may comprise, indicator derivation means; indicator derivation means and indicator deviation detection means; or indicator derivation means, indicator deviation detection means and determining means. 
     Theoretical Analysis 
     Although embodiments of the present invention seek to balance the quality indicators derived by the destination apparatus and intermediate apparatus without performing an explicit calculation of the transmit power required to achieve that balance, the following theoretical analysis, which derives possible solutions for explicitly calculating the optimal transmit power of the transmitting elements comprised in a multi-hop network for various deployment scenarios, is useful for understanding the present invention. The following theoretical analysis derives possible solutions for calculating the optimal transmit power of the transmitting elements comprised in a multi-hope network for various deployment scenarios. For each deployment scenario, theoretical solutions are obtained assuming a single-cell model and a two-cell model. In the case of a two cell model, it is assumed that the deployment in both cells is identical and that the transmit powers on the bas station (BS) and the intermediate apparatus (I) are the same. It is also assumed that where appropriate P tx     —     tot,RN =G p P tx,RN  and P tx     —     tot,NB =G p P tx,NB  and that for the case of TDD both RN&#39;s transmit at the same time. This in effect generates the worse case scenario for two cells. 
     Theoretical solutions may be evolved from a consideration of the signal-to-interference plus noise ratio (SINR) experienced by the receiving nodes in a multi-hope system (i.e. the or each intermediate apparatus (I) and the destination apparatus (D)). The SINR at a particular node is a measure of the quality of a communication signal received by that node and is a ratio of the received strength of the desired signal to the received signal strength of the undesired signals (noise and interference). 
     As previously discussed, the considerations required for noise and interference depend on the duplexing method used to separate signal received at an intermediate apparatus from those transmitted from an intermediate apparatus, the characteristics of the intermediate apparatus and also the level of inter-cell interference which is taken into account (i.e. interference from neighbouring cells). 
     The following equation represents the SINR of a communication signal sent from an intermediate apparatus to a destination apparatus for all scenarios, where different terms may be ignored depending upon the type of intermediate apparatus (e.g. non-regenerative or regenerative) and the duplexing method: 
     
       
         
           
             
               SINR 
               
                 RN 
                 - 
                 UE 
               
             
             = 
             
               
                 
                   G 
                   p 
                 
                 ⁢ 
                 
                   P 
                   
                     tx 
                     , 
                     RN 
                   
                 
               
               
                 
                   L 
                   
                     RN 
                     - 
                     UE 
                   
                 
                 ⁡ 
                 
                   ( 
                   
                     N 
                     + 
                     
                       
                         P 
                         
                           tx 
                           , 
                           RN 
                         
                       
                       
                         
                           L 
                           
                             RN 
                             - 
                             UE 
                           
                         
                         ⁢ 
                         
                           SINR 
                           
                             NB 
                             - 
                             RN 
                           
                         
                       
                     
                     + 
                     
                       
                         P 
                         
                           
                             tx 
                             ⁢ 
                             _ 
                             ⁢ 
                             tot 
                           
                           , 
                           NB 
                         
                       
                       
                         L 
                         
                           NB 
                           - 
                           UE 
                         
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
     For the case of FDD instead of TDD then the third term in the bracket is removed and for the case of regenerative instead of non-regenerative the second term in the bracket is removed. 
     In the case of a two-cell model as illustrated in  FIG. 1B , this becomes: 
     
       
         
           
             
               SINR 
               
                 RN 
                 - 
                 UE 
               
             
             = 
             
               
                 
                   G 
                   p 
                 
                 ⁢ 
                 
                   P 
                   
                     tx 
                     , 
                     RN1 
                   
                 
               
               
                 
                   L 
                   
                     RN1 
                     - 
                     UE 
                   
                 
                 ⁡ 
                 
                   ( 
                   
                     N 
                     + 
                     
                       
                         P 
                         
                           tx 
                           , 
                           RN1 
                         
                       
                       
                         
                           L 
                           
                             RN1 
                             - 
                             UE 
                           
                         
                         ⁢ 
                         
                           SINR 
                           
                             NB1 
                             - 
                             RN1 
                           
                         
                       
                     
                     + 
                     
                       
                         P 
                         
                           
                             tx 
                             ⁢ 
                             _ 
                             ⁢ 
                             tot 
                           
                           , 
                           NB1 
                         
                       
                       
                         L 
                         
                           NB1 
                           - 
                           UE 
                         
                       
                     
                     + 
                     
                       
                         P 
                         
                           
                             tx 
                             ⁢ 
                             _ 
                             ⁢ 
                             tot 
                           
                           , 
                           NB2 
                         
                       
                       
                         L 
                         
                           NB2 
                           - 
                           UE 
                         
                       
                     
                     + 
                     
                       
                         P 
                         
                           
                             tx 
                             ⁢ 
                             _ 
                             ⁢ 
                             tot 
                           
                           , 
                           Rn2 
                         
                       
                       
                         L 
                         
                           RN2 
                           - 
                           UE 
                         
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
     The first three terms in the bracket in (2) are the same as those in (1). The additional last two terms originate from the interference experienced from the neighbouring co-channel NB and RN respectively. Obviously if the neighbouring cell employs a different frequency or uses a different timeslot for relay transmission then the terms needed to model this interference will vary. It should be appreciated that these equations can be extended to a three-cell model or more for a higher level of accuracy. 
     Considering now the various possible deployment scenarios in turn, for the case of DL transmissions transmitted between a base-station or node-B (NB), via an intermediate relay node (RN) to a destination user equipment (UE). 
     1A. Regenerative Relay with FDD—Single-Cell Model as Illustrated in  FIG. 1A   
     In this case, the SINR at a destination UE which is connected to an intermediate RN is given by: 
     
       
         
           
             
               
                 
                   
                     SINR 
                     
                       RN 
                       - 
                       UE 
                     
                   
                   = 
                   
                     
                       
                         G 
                         p 
                       
                       ⁢ 
                       
                         P 
                         
                           tx 
                           , 
                           RN 
                         
                       
                     
                     
                       
                         L 
                         
                           RN 
                           - 
                           UE 
                         
                       
                       ⁢ 
                       N 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Where GP is the processing gain, P tx,RN  is the transmit power on the channel of interest at the RN, L RN-UE  is the propagation loss on the NB to RN link and N is the noise. Note this assumes that no intra-cell interference exists. 
     The SINR at an intermediate RN which is operable to receive signals from the NB is given by: 
     
       
         
           
             
               
                 
                   
                     SINR 
                     
                       NB 
                       - 
                       RN 
                     
                   
                   = 
                   
                     
                       
                         G 
                         p 
                       
                       ⁢ 
                       
                         P 
                         
                           tx 
                           , 
                           NB 
                         
                       
                     
                     
                       
                         L 
                         
                           NB 
                           - 
                           RN 
                         
                       
                       ⁢ 
                       N 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     Where P tx,NB  is the transmit power on the channel of interest at the NB and L NB-RN  is the propagation loss on the RN to UE link. Again, it is assumed that no intra-cell interference exists. 
     The overall throughput across the multi-hop link will be limited by the lower of the two SINR values as this will limit the rate at which data can be transmitted to that entity. Any increase in transmit power that causes an SINR imbalance will not improve the performance of the multi-hop system; it will simply result in wasted energy and an increase in interference to any co-channel users. 
     Thus, assuming that the receiver at the intermediate RN and the receiver at the destination UE perform the same, then it follows that the transmit power at the NB and RN should be set such that the SINR at the RN and UE is the same. Using this criterion for setting the ratio of the transmit powers, it follows that the ratio is given by: 
     
       
         
           
             
               
                 
                   
                     
                       P 
                       
                         tx 
                         , 
                         NB 
                       
                     
                     
                       P 
                       
                         tx 
                         , 
                         RN 
                       
                     
                   
                   = 
                   
                     
                       
                         L 
                         
                           NB 
                           - 
                           RN 
                         
                       
                       
                         L 
                         
                           RN 
                           - 
                           UE 
                         
                       
                     
                     = 
                     
                       
                         
                           b 
                           1 
                         
                         ⁢ 
                         
                           s 
                           1 
                           
                             n 
                             1 
                           
                         
                       
                       
                         
                           b 
                           2 
                         
                         ⁢ 
                         
                           s 
                           2 
                           
                             n 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     Where b 1  and n 1  are the pathloss parameters for the NB to RN link which is s 1  in length and b 2 , n n  and s 2  are associated with the RN to UE link. Thus using equation (3) it is possible to find either transmit power given the other. 
     1B. Regenerative Relay with FDD—Two Cell Model as Shown in  FIG. 1B   
     In this case, transmit power equations may be derived taking into account interference caused by transmissions arising in the other cell. 
     In this case the SINR at a destination UE that is operable to receive signals from an intermediate RN is now: 
     
       
         
           
             
               
                 
                   
                     SINR 
                     
                       RN 
                       - 
                       UE 
                     
                   
                   = 
                   
                     
                       
                         G 
                         p 
                       
                       ⁢ 
                       
                         P 
                         
                           tx 
                           , 
                           RN 
                         
                       
                     
                     
                       
                         L 
                         
                           RN 
                           - 
                           UE 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           N 
                           + 
                           
                             
                               
                                 G 
                                 p 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   RN 
                                 
                               
                             
                             
                               L 
                               
                                 RN 
                                 - 
                                 UE 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     The optimal NB transmit power can be found by setting (4) and (2) to be equal. Therefore: 
                             P     tx   ,   NB       =         L     NB   -   RN       ⁢     NP     tx   ,   RN             L     RN   -   UE       ⁡     (     N   +         G   p     ⁢     P     tx   ,   RN           L     RN   -   UE           )                     =         L     NB   -   RN       ⁢     P     tx   ,   RN           (       L     RN   -   UE       +         G   p     ⁢     P     tx   ,   RN         N       )                           (   5   )               
(5) can be rearranged to find the intermediate RN transmit power given the source NB transmit power:
 
                     P     tx   ,   RN       =       L     RN   -   UE         (         L     NB   -   RN         P     tx   ,   NB         -       G   p     N       )               (   6   )               
2A. Regenerative Relay with TDD: Single Cell Model— FIG. 1A 
 
     It is assumed that the two links (source to intermediate, intermediate to destination) operate on the same frequency with TDD being used to separate the receive and transmit operation of the RN (i.e. it is no longer full duplex). If it is assumed that the timeslot in which the RN transmits is not used by the NB then the equations described above for the case of a regenerative relay with an FDD duplexing scheme can be used. However, if the source NB uses the same timeslot as the intermediate RN to communicate with apparatuses or nodes other than the NB, interference will result to the transmission made by the RN. In this case the SINR at a destination UE that is operable to receive communication signals from an intermediate RN is given by: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             SINR 
                             
                               RN 
                               - 
                               UE 
                             
                           
                           = 
                           
                             
                               
                                 G 
                                 p 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   RN 
                                 
                               
                             
                             
                               
                                 L 
                                 
                                   RN 
                                   - 
                                   UE 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   N 
                                   + 
                                   I 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                           
                             
                               
                                 G 
                                 p 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   RN 
                                 
                               
                             
                             
                               
                                 L 
                                 
                                   RN 
                                   - 
                                   UE 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   N 
                                   + 
                                   
                                     
                                       P 
                                       
                                         
                                           tx 
                                           ⁢ 
                                           _ 
                                           ⁢ 
                                           tot 
                                         
                                         , 
                                         NB 
                                       
                                     
                                     
                                       L 
                                       
                                         NB 
                                         - 
                                         UE 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                     
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Where P tx     —     tot,NB  is the total transmission power from the NB and L NB-UE  is the propagation loss on the NB to UE link. In this case the transmit power at the RN that ensures equal SINR is given by: 
     
       
         
           
             
               
                 
                   
                     P 
                     
                       tx 
                       , 
                       RN 
                     
                   
                   = 
                   
                     
                       
                         P 
                         
                           tx 
                           , 
                           NB 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             L 
                             
                               RN 
                               - 
                               UE 
                             
                           
                           
                             L 
                             
                               NB 
                               - 
                               RN 
                             
                           
                         
                         ) 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         1 
                         + 
                         
                           
                             P 
                             
                               
                                 tx 
                                 ⁢ 
                                 _ 
                                 ⁢ 
                                 tot 
                               
                               , 
                               NB 
                             
                           
                           
                             NL 
                             
                               NB 
                               - 
                               UE 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     Comparing equation (3) and equation (8) it is apparent that a simple ratio no longer yields the ideal balance. Assuming that P tx     —     tot,NB =G p P tx,NB  it is possible to write equation (8) as: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           P 
                           
                             tx 
                             , 
                             RN 
                           
                         
                         = 
                         
                           
                             
                               P 
                               
                                 tx 
                                 , 
                                 NB 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   L 
                                   
                                     RN 
                                     - 
                                     UE 
                                   
                                 
                                 
                                   L 
                                   
                                     NB 
                                     - 
                                     RN 
                                   
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               1 
                               + 
                               
                                 
                                   
                                     G 
                                     p 
                                   
                                   ⁢ 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       NB 
                                     
                                   
                                 
                                 
                                   NL 
                                   
                                     NB 
                                     - 
                                     UE 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             ( 
                             
                               
                                 L 
                                 
                                   RN 
                                   - 
                                   UE 
                                 
                               
                               
                                 L 
                                 
                                   NB 
                                   - 
                                   RN 
                                 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                               + 
                               
                                 
                                   
                                     G 
                                     p 
                                   
                                   ⁢ 
                                   
                                     
                                       P 
                                       tx 
                                       2 
                                     
                                     
                                       , 
                                       NB 
                                     
                                   
                                 
                                 
                                   NL 
                                   
                                     NB 
                                     - 
                                     UE 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     From (9) it is possible to determine the ideal RN transmit power given the NB transmit power. It is worth noting that if the set-up of the system is arranged such that the second term in the second bracket is negligible (i.e. P tx     —     tot,NB /NL NB-UE &lt;&lt;1) then the criterion described above for the case of a regenerative relay with an FDD duplex scheme can be used. 
     It follows that the ideal NB transmit power given a certain RN transmit power can be found from the roots of (9). Expressing (9) in the following simplified form: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 L 
                                 
                                   RN 
                                   - 
                                   UE 
                                 
                               
                               
                                 L 
                                 
                                   NB 
                                   - 
                                   RN 
                                 
                               
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 NB 
                               
                             
                           
                           + 
                           
                             
                               
                                 L 
                                 
                                   RN 
                                   - 
                                   UE 
                                 
                               
                               
                                 L 
                                 
                                   NB 
                                   - 
                                   RN 
                                 
                               
                             
                             ⁢ 
                             
                               
                                 G 
                                 p 
                               
                               
                                 NL 
                                 
                                   NB 
                                   - 
                                   UE 
                                 
                               
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 NB 
                               
                               2 
                             
                           
                           - 
                           
                             P 
                             
                               tx 
                               , 
                               RN 
                             
                           
                         
                         = 
                         0 
                       
                     
                   
                   
                     
                       
                         
                           
                             ax 
                             2 
                           
                           + 
                           bx 
                           + 
                           c 
                         
                         = 
                         0 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     Where 
               x   =     P     tx   ,   NB         ,     a   =         G   p     ⁢     L     RN   -   UE             NL     NB   -   RN       ⁢     L     NB   -   UE             ,     b   =           L     RN   -   UE         L     NB   -   RN         ⁢           ⁢   and   ⁢           ⁢   c     =     -     P     tx   ,   RN                   
it follows that the roots of (10) are given by:
 
     
       
         
           
             
               
                 
                   x 
                   = 
                   
                     
                       
                         - 
                         b 
                       
                       ± 
                       
                         
                           
                             b 
                             2 
                           
                           - 
                           
                             4 
                             ⁢ 
                             ac 
                           
                         
                       
                     
                     
                       2 
                       ⁢ 
                       a 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     As the transmit power is a positive number, only one root is defined, it therefore follows that the optimal transmit power at the NB that ensures equal SINR at the RN and UE is given by: 
     
       
         
           
             
               
                 
                   x 
                   = 
                   
                     
                       P 
                       
                         tx 
                         , 
                         NB 
                       
                     
                     = 
                     
                       
                         
                           - 
                           b 
                         
                         + 
                         
                           
                             
                               b 
                               2 
                             
                             - 
                             
                               4 
                               ⁢ 
                               a 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   RN 
                                 
                               
                             
                           
                         
                       
                       
                         2 
                         ⁢ 
                         a 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     Finally, it is possible to use the definitions above to rewrite (9), which gives the optimal RN transmit power, in a similar simplified form:
 
 P   tx,RN   =bP   tx,NB   +aP   tx,NB   2   (13)
 
2A. Regenerative Relay with TDD: Two-Cell Model as Shown in  FIG. 1B 
 
     In addition to assuming that the deployment in both is identical and that the transmit powers on the NB and RN are the same, it is also assumed that where appropriate P tx     —     tot,RN =G p P tx,RN  and P tx     —     tot,NB =G p P tx,NB  and that for the case of TDD both RN&#39;s transmit at the same time. This in effect generates the worse case scenario for two cells. 
     In this case the SINR at the destination UE that is operable to receive signals from an intermediate RN is now: 
     
       
         
           
             
               
                 
                   
                     SINR 
                     
                       RN 
                       - 
                       UE 
                     
                   
                   = 
                   
                     
                       
                         G 
                         p 
                       
                       ⁢ 
                       
                         P 
                         
                           tx 
                           , 
                           RN 
                         
                       
                     
                     
                       
                         L 
                         
                           RN 
                           - 
                           UE 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           N 
                           + 
                           
                             
                               2 
                               ⁢ 
                               
                                 G 
                                 p 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                             
                               L 
                               
                                 NB 
                                 - 
                                 UE 
                               
                             
                           
                           + 
                           
                             
                               
                                 G 
                                 p 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   RN 
                                 
                               
                             
                             
                               L 
                               
                                 RN 
                                 - 
                                 UE 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     The optimal NB transmit power can be found by setting (14) and (2) to be equal: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               G 
                               p 
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 NB 
                               
                             
                           
                           
                             NL 
                             
                               NB 
                               - 
                               RN 
                             
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               G 
                               p 
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 RN 
                               
                             
                           
                           
                             
                               L 
                               
                                 RN 
                                 - 
                                 UE 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 N 
                                 + 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                       G 
                                       p 
                                     
                                     ⁢ 
                                     
                                       P 
                                       
                                         tx 
                                         , 
                                         NB 
                                       
                                     
                                   
                                   
                                     L 
                                     
                                       NB 
                                       - 
                                       UE 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     
                                       G 
                                       p 
                                     
                                     ⁢ 
                                     
                                       P 
                                       
                                         tx 
                                         , 
                                         RN 
                                       
                                     
                                   
                                   
                                     L 
                                     
                                       RN 
                                       - 
                                       UE 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           P 
                           
                             tx 
                             , 
                             RN 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               P 
                               
                                 tx 
                                 , 
                                 NB 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   L 
                                   
                                     RN 
                                     - 
                                     UE 
                                   
                                 
                                 
                                   L 
                                   
                                     NB 
                                     - 
                                     RN 
                                   
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               1 
                               + 
                               
                                 
                                   2 
                                   ⁢ 
                                   
                                     P 
                                     
                                       
                                         tx 
                                         ⁢ 
                                         _ 
                                         ⁢ 
                                         tot 
                                       
                                       , 
                                       NB 
                                     
                                   
                                 
                                 
                                   NL 
                                   
                                     NB 
                                     - 
                                     UE 
                                   
                                 
                               
                               + 
                               
                                 
                                   P 
                                   
                                     
                                       tx 
                                       ⁢ 
                                       _ 
                                       ⁢ 
                                       tot 
                                     
                                     , 
                                     RN 
                                   
                                 
                                 
                                   NL 
                                   
                                     RN 
                                     - 
                                     UE 
                                   
                                 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 L 
                                 
                                   RN 
                                   - 
                                   UE 
                                 
                               
                               
                                 L 
                                 
                                   NB 
                                   - 
                                   RN 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   
                                     G 
                                     p 
                                   
                                 
                                 
                                   NL 
                                   
                                     NB 
                                     - 
                                     RN 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 NB 
                               
                               2 
                             
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   L 
                                   
                                     RN 
                                     - 
                                     UE 
                                   
                                 
                                 
                                   L 
                                   
                                     NB 
                                     - 
                                     RN 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   
                                     
                                       G 
                                       p 
                                     
                                     ⁢ 
                                     
                                       P 
                                       
                                         tx 
                                         , 
                                         RN 
                                       
                                     
                                   
                                   
                                     NL 
                                     
                                       RN 
                                       - 
                                       UE 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           
                             P 
                             
                               tx 
                               , 
                               NB 
                             
                           
                           - 
                           
                             P 
                             
                               tx 
                               , 
                               RN 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     The optimal NB transmit power is found from the positive root of: 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         
                           ( 
                           
                             
                               L 
                               
                                 RN 
                                 - 
                                 UE 
                               
                             
                             
                               L 
                               
                                 NB 
                                 - 
                                 RN 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                           
                         ⁢ 
                         
                           ( 
                           
                             
                               2 
                               ⁢ 
                               
                                 G 
                                 p 
                               
                             
                             
                               NL 
                               
                                 NB 
                                 - 
                                 UE 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           P 
                           
                             tx 
                             , 
                             NB 
                           
                           2 
                         
                       
                       + 
                       
                         
                           ( 
                           
                             
                               L 
                               
                                 RN 
                                 - 
                                 UE 
                               
                             
                             
                               L 
                               
                                 NB 
                                 - 
                                 RN 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             1 
                             + 
                             
                               
                                 
                                   G 
                                   p 
                                 
                                 ⁢ 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     RN 
                                   
                                 
                               
                               
                                 NL 
                                 
                                   RN 
                                   - 
                                   UE 
                                 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           P 
                           
                             tx 
                             , 
                             NB 
                           
                         
                       
                       - 
                       
                         P 
                         
                           tx 
                           , 
                           RN 
                         
                       
                     
                     = 
                     0 
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     Which is given by: 
     
       
         
           
             
               
                 
                   x 
                   = 
                   
                     
                       P 
                       
                         tx 
                         , 
                         NB 
                       
                     
                     = 
                     
                       
                         
                           - 
                           b 
                         
                         + 
                         
                           
                             
                               b 
                               2 
                             
                             - 
                             
                               4 
                               ⁢ 
                               ac 
                             
                           
                         
                       
                       
                         2 
                         ⁢ 
                         a 
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     Where in this case 
               a   =       2   ⁢     G   p     ⁢     L     RN   -   UE               NL     NB   -   RN       ⁢     L     NB   -   UE         ⁢                 ,     b   =           L     RN   -   UE         L     NB   -   RN         ⁢     (     1   +         G   p     ⁢     P     tx   ,   RN           NL     RN   -   UE           )     ⁢           ⁢   and   ⁢           ⁢   c     =     -     P     tx   ,   RN             ,         
and both b and c are a function of the RN transmit power.
 
     Given the NB transmit power it is possible to rearrange (15) to find the RN transmit. It follows that the optimal RN transmit power is given by: 
                     P     tx   ,   RN       =           (         2   ⁢     G   p         NL     NB   -   UE         ⁢       L     RN   -   UE         L     NB   -   RN           )     ⁢     P     tx   ,   NB     2       +       (       L     RN   -   UE         L     NB   -   RN         )     ⁢     P     tx   ,   NB             1   -       (           ⁢                 ⁢     G   p         NL     NB   -   UE         ⁢       L     RN   -   UE         L     NB   -   RN           )     ⁢     P     tx   ,   NB                     (   18   )               
3A. Non-Regenerative Relay Node (RN) with FDD—Single Cell Model as Shown in  FIG. 1A 
 
     The difference between this case and that of a regenerative relay node being used in conjunction with a FDD duplexing scheme is that the SINR at the UE is a function of the SINR at the RN, where the SINR at the destination UE which is connected to the RN is given by: 
     
       
         
           
             
               
                 
                   
                     SINR 
                     
                       RN 
                       - 
                       UE 
                     
                   
                   = 
                   
                     
                       
                         G 
                         p 
                       
                       ⁢ 
                       
                         P 
                         
                           tx 
                           , 
                           RN 
                         
                       
                     
                     
                       
                         L 
                         
                           RN 
                           - 
                           UE 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           N 
                           + 
                           
                             
                               P 
                               
                                 tx 
                                 , 
                                 RN 
                               
                             
                             
                               
                                 L 
                                 
                                   RN 
                                   - 
                                   UE 
                                 
                               
                               ⁢ 
                               
                                 SINR 
                                 
                                   NB 
                                   - 
                                   RN 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     The result is that the ideal balance is no longer derived from setting the SINR at the UE equal to that at the RN. According to (19), the SINR at the RN needs to be set so that it does not prevent this target SINR at the UE from being obtained. However, the NB power must be controlled to limit the SINR at the RN rising beyond that practically required else excess interference and wasted transmit power will result. 
       FIG. 6  illustrates how the setting of NB and RN transmit power affects the SINR at the UE connected to the RN for a two different deployment scenarios. 
     Thus, it can be seen that the optimal solution is to select the transmit power of the NB and RN such that the system effectively operates on the diagonal fold in the surface shown in  FIG. 6 . It is possible to realise such a solution by taking the first derivative of (19) and finding the point at which increasing either the NB or RN transmit power results in minimal increase to SINR at UE. 
     In order to determine the first derivative of (19), it is rewritten as: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           SINR 
                           
                             RN 
                             - 
                             UE 
                           
                         
                         = 
                         
                           
                             
                               G 
                               p 
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 RN 
                               
                             
                           
                           
                             
                               L 
                               
                                 RN 
                                 - 
                                 UE 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 N 
                                 + 
                                 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       RN 
                                     
                                   
                                   
                                     
                                       L 
                                       
                                         RN 
                                         - 
                                         UE 
                                       
                                     
                                     ⁢ 
                                     
                                       
                                         
                                           G 
                                           p 
                                         
                                         ⁢ 
                                         
                                           P 
                                           
                                             tx 
                                             , 
                                             NB 
                                           
                                         
                                       
                                       
                                         NL 
                                         
                                           NB 
                                           - 
                                           RN 
                                         
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           1 
                           
                             
                               ( 
                               
                                 
                                   NL 
                                   
                                     RN 
                                     - 
                                     UE 
                                   
                                 
                                 
                                   
                                     G 
                                     p 
                                   
                                   ⁢ 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       RN 
                                     
                                   
                                 
                               
                               ) 
                             
                             + 
                             
                               ( 
                               
                                 
                                   NL 
                                   
                                     NB 
                                     - 
                                     RN 
                                   
                                 
                                 
                                   
                                     G 
                                     p 
                                     2 
                                   
                                   ⁢ 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       NB 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     Defining 
               y   =     SINR     RN   -   UE         ,       k   1     =           NL     RN   -   UE         G   p       ⁢           ⁢   and   ⁢           ⁢     k   2       =       NL     NB   -   RN         G   p   2                 
it is possible to simplify (20) to be:
 
     
       
         
           
             
               
                 
                   y 
                   = 
                   
                     
                       1 
                       
                         
                           
                             
                               k 
                               1 
                             
                             
                               P 
                               
                                 tx 
                                 , 
                                 RN 
                               
                             
                           
                           + 
                           
                             
                               k 
                               2 
                             
                             
                               P 
                               
                                 tx 
                                 , 
                                 RN 
                               
                             
                           
                         
                         ⁢ 
                         
                             
                         
                       
                     
                     = 
                     
                       
                         P 
                         
                           tx 
                           , 
                           NB 
                         
                       
                       
                         
                           
                             
                               k 
                               1 
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 NB 
                               
                             
                           
                           
                             P 
                             
                               tx 
                               , 
                               RN 
                             
                           
                         
                         + 
                         
                           k 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     In order to find the rate of change of SINR with P tx,NB  the quotient rule for differentiation is used: 
     
       
         
           
             
               
                 
                   
                     
                       ⅆ 
                       y 
                     
                     
                       ⅆ 
                       
                         ( 
                         
                           P 
                           
                             tx 
                             , 
                             NB 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         k 
                         2 
                       
                       
                         
                           ( 
                           
                             
                               
                                 
                                   k 
                                   1 
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     RN 
                                   
                                 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                             + 
                             
                               k 
                               2 
                             
                           
                           ) 
                         
                         2 
                       
                     
                     = 
                     
                       ∇ 
                       NB 
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     By solving (22) for P tx,NB  given the required gradient and P tx,RN  it is possible to find the optimal NB transmit power: 
     
       
         
           
             
               
                 
                   
                     P 
                     
                       tx 
                       , 
                       NB 
                     
                   
                   = 
                   
                     
                       
                         P 
                         
                           tc 
                           , 
                           RN 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               
                                 k 
                                 2 
                               
                               
                                 ∇ 
                                 NB 
                               
                             
                           
                           - 
                           
                             k 
                             2 
                           
                         
                         ) 
                       
                     
                     
                       k 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     In order to find the optimal RN transmit power given that of the NB, the differentiation of (21) is now performed with respect to P tx,RN . In this case the first order derivative is given by: 
     
       
         
           
             
               
                 
                   
                     
                       ⅆ 
                       y 
                     
                     
                       ⅆ 
                       
                         ( 
                         
                           P 
                           
                             tx 
                             , 
                             RN 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         k 
                         1 
                       
                       
                         
                           ( 
                           
                             
                               
                                 
                                   k 
                                   2 
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     NB 
                                   
                                 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   RN 
                                 
                               
                             
                             + 
                             
                               k 
                               1 
                             
                           
                           ) 
                         
                         2 
                       
                     
                     = 
                     
                       ∇ 
                       RN 
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
     And the optimal RN transmit power given that of the NB is: 
                     P     tx   ,   RN       =         P     tc   ,   NB       ⁡     (           k   1       ∇   RN         -     k   1       )         k   2               (   25   )               
3B. Non-Regenerative Relay Node (RN) with FDD—Two Cell Model as Shown in  FIG. 1B 
 
     In a two cell model the SINR for the worse case of a destination UE at the cell edge is given by: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           SINR 
                           
                             RN 
                             - 
                             UE 
                           
                         
                         = 
                         
                           
                             
                               G 
                               p 
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 RN 
                               
                             
                           
                           
                             
                               L 
                               
                                 RN 
                                 - 
                                 UE 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 N 
                                 + 
                                 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       RN 
                                     
                                   
                                   
                                     
                                       L 
                                       
                                         RN 
                                         - 
                                         UE 
                                       
                                     
                                     ⁢ 
                                     
                                       SINR 
                                       
                                         NB 
                                         - 
                                         RN 
                                       
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     
                                       G 
                                       p 
                                     
                                     ⁢ 
                                     
                                       P 
                                       
                                         tx 
                                         , 
                                         RN 
                                       
                                     
                                   
                                   
                                     L 
                                     
                                       RN 
                                       - 
                                       UE 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           1 
                           
                             
                               ( 
                               
                                 
                                   NL 
                                   
                                     RN 
                                     - 
                                     UE 
                                   
                                 
                                 
                                   
                                     G 
                                     p 
                                   
                                   ⁢ 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       RN 
                                     
                                   
                                 
                               
                               ) 
                             
                             + 
                             
                               ( 
                               
                                 
                                   NL 
                                   
                                     NB 
                                     - 
                                     RN 
                                   
                                 
                                 
                                   
                                     G 
                                     p 
                                     2 
                                   
                                   ⁢ 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       NB 
                                     
                                   
                                 
                               
                               ) 
                             
                             + 
                             1 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
     Assuming that the transmit power of the two RN&#39;s is equal, the deployment is identical across the two cells and that P tx     —     tot,RN =G p P tx,RN , then the simplified form of (26) is given by: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           SINR 
                           
                             RN 
                             - 
                             UE 
                           
                         
                         = 
                         
                           1 
                           
                             
                               
                                 k 
                                 1 
                               
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   RN 
                                 
                               
                             
                             + 
                             
                               
                                 k 
                                 2 
                               
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                             + 
                             1 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             P 
                             
                               tx 
                               , 
                               NB 
                             
                           
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       k 
                                       1 
                                     
                                     
                                       P 
                                       
                                         tx 
                                         , 
                                         RN 
                                       
                                     
                                   
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                             + 
                             
                               k 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
     The first derivative is now: 
     
       
         
           
             
               
                 
                   
                     
                       ⅆ 
                       y 
                     
                     
                       ⅆ 
                       
                         ( 
                         
                           P 
                           
                             tx 
                             , 
                             NB 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       k 
                       2 
                     
                     
                       
                         ( 
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     k 
                                     1 
                                   
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       RN 
                                     
                                   
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 NB 
                               
                             
                           
                           + 
                           
                             k 
                             2 
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
           
         
       
     
     Thus the optimal NB transmit power can be found by: 
     
       
         
           
             
               
                 
                   
                     P 
                     
                       tx 
                       , 
                       NB 
                     
                   
                   = 
                   
                     
                       
                         
                           P 
                           
                             tx 
                             , 
                             RN 
                           
                         
                         ⁢ 
                         
                           
                             
                               k 
                               2 
                             
                             ∇ 
                           
                         
                       
                       - 
                       
                         k 
                         2 
                       
                     
                     
                       
                         k 
                         1 
                       
                       + 
                       
                         P 
                         
                           tx 
                           , 
                           RN 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
           
         
       
     
     The optimal RN transmit power is found by taking the derivative of (27) with respect to P tx,RN : 
     
       
         
           
             
               
                 
                   
                     
                       ⅆ 
                       y 
                     
                     
                       ⅆ 
                       
                         ( 
                         
                           P 
                           
                             tx 
                             , 
                             RN 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       k 
                       1 
                     
                     
                       
                         ( 
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     k 
                                     2 
                                   
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       NB 
                                     
                                   
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 RN 
                               
                             
                           
                           + 
                           
                             k 
                             1 
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   30 
                   ) 
                 
               
             
           
         
       
     
     Thus the optimal RN transmit power can be found by: 
                     P     tx   ,   RN       =           P     tx   ,   NB       ⁢         k   1     ∇         -     k   1           k   2     +     P     tx   ,   NB                   (   31   )               
4A—Non-Regenerative Relay with TDD—Single Cell Model as Shown in  FIG. 1A 
 
     This case is similar to that described above for a non-regenerative except for the fact that now interference from the NB must be taken into account due to the fact that it transmits on the same frequency and at the same time as the RN. In this case the SINR at the UE which is receiving communication signals transmitted by the RN is given by: 
     
       
         
           
             
               
                 
                   
                     SINR 
                     
                       RN 
                       - 
                       UE 
                     
                   
                   = 
                   
                     
                       
                         G 
                         p 
                       
                       ⁢ 
                       
                         P 
                         
                           tx 
                           , 
                           RN 
                         
                       
                     
                     
                       
                         L 
                         
                           RN 
                           - 
                           UE 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           N 
                           + 
                           
                             
                               P 
                               
                                 tx 
                                 , 
                                 RN 
                               
                             
                             
                               
                                 L 
                                 
                                   RN 
                                   - 
                                   UE 
                                 
                               
                               ⁢ 
                               
                                 SINR 
                                 
                                   NB 
                                   - 
                                   RN 
                                 
                               
                             
                           
                           + 
                           
                             
                               P 
                               
                                 
                                   tx 
                                   ⁢ 
                                   _ 
                                   ⁢ 
                                   tot 
                                 
                                 , 
                                 NB 
                               
                             
                             
                               L 
                               
                                 NB 
                                 - 
                                 UE 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   32 
                   ) 
                 
               
             
           
         
       
     
     If the P tx,NB /P tx,RN  is too large the SINR at the UE is limited due to insufficient RN transmit power and it is likely the area in which the link performance of a connection to a RN outperforms that for a connection to the NB is reduced. Conversely, if it is too small then the SINR at the UE is limited by the low SINR at the RN. 
     In this case, the balance is even finer than of that described in the case of a non-regenerative relay node employed in conjunction with an FDD duplexing scheme, as illustrated by  FIG. 10 . The optimal operating point is given by finding the point at which the first derivative of (32) is equal to zero. In order to find this optimal point, (32) is first rearranged in the following form: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           SINR 
                           
                             RN 
                             - 
                             UE 
                           
                         
                         = 
                         
                           
                             
                               G 
                               p 
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 RN 
                               
                             
                           
                           
                             
                               L 
                               
                                 RN 
                                 - 
                                 UE 
                               
                             
                             ( 
                             
                               N 
                               + 
                               
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     RN 
                                   
                                 
                                 
                                   
                                     L 
                                     
                                       RN 
                                       - 
                                       UE 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         
                                           G 
                                           p 
                                         
                                         ⁢ 
                                         
                                           P 
                                           
                                             tx 
                                             , 
                                             NB 
                                           
                                         
                                       
                                       
                                         NL 
                                         
                                           NB 
                                           - 
                                           RN 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 
                                   P 
                                   
                                     
                                       tx 
                                       ⁢ 
                                       _ 
                                       ⁢ 
                                       tot 
                                     
                                     , 
                                     NB 
                                   
                                 
                                 
                                   L 
                                   
                                     NB 
                                     - 
                                     UE 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           1 
                           
                             
                               ( 
                               
                                 
                                   NL 
                                   
                                     RN 
                                     - 
                                     UE 
                                   
                                 
                                 
                                   
                                     G 
                                     p 
                                   
                                   ⁢ 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       RN 
                                     
                                   
                                 
                               
                               ) 
                             
                             + 
                             
                               ( 
                               
                                 
                                   NL 
                                   
                                     NB 
                                     - 
                                     RN 
                                   
                                 
                                 
                                   
                                     G 
                                     p 
                                     2 
                                   
                                   ⁢ 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       NB 
                                     
                                   
                                 
                               
                               ) 
                             
                             + 
                             
                               ( 
                               
                                 
                                   
                                     L 
                                     
                                       RN 
                                       - 
                                       UE 
                                     
                                   
                                   ⁢ 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       NB 
                                     
                                   
                                 
                                 
                                   
                                     L 
                                     
                                       NB 
                                       - 
                                       UE 
                                     
                                   
                                   ⁢ 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       RN 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   33 
                   ) 
                 
               
             
           
         
       
     
     Defining 
     
       
         
           
             
               y 
               = 
               
                 SINR 
                 
                   RN 
                   - 
                   UE 
                 
               
             
             , 
             
               
                 k 
                 1 
               
               = 
               
                 
                   
                     
                       NL 
                       
                         RN 
                         - 
                         UE 
                       
                     
                     
                       G 
                       p 
                     
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   and 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     k 
                     2 
                   
                 
                 = 
                 
                   
                     NL 
                     
                       NB 
                       - 
                       RN 
                     
                   
                   
                     G 
                     p 
                     2 
                   
                 
               
             
           
         
       
     
     Using the definitions from the description 3A above and 
               k   3     =     (       L     RN   -   UE         L     NB   -   UE         )           
it is possible to simplify (33) to:
 
     
       
         
           
             
               
                 
                   
                     
                       
                         y 
                         = 
                         
                           1 
                           
                             
                               ( 
                               
                                 
                                   k 
                                   1 
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     RN 
                                   
                                 
                               
                               ) 
                             
                             + 
                             
                               ( 
                               
                                 
                                   k 
                                   2 
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     NB 
                                   
                                 
                               
                               ) 
                             
                             + 
                             
                               ( 
                               
                                 
                                   
                                     k 
                                     3 
                                   
                                   ⁢ 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       NB 
                                     
                                   
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     RN 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             P 
                             
                               tx 
                               , 
                               NB 
                             
                           
                           
                             
                               
                                 ( 
                                 
                                   
                                     k 
                                     1 
                                   
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       RN 
                                     
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                             + 
                             
                               k 
                               2 
                             
                             + 
                             
                               
                                 ( 
                                 
                                   
                                     k 
                                     3 
                                   
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       RN 
                                     
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                                 2 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   34 
                   ) 
                 
               
             
           
         
       
     
     The next step is to find the single maxima of the parabolic function in (34) by solving: 
     
       
         
           
             
               
                 
                   
                     
                       ⅆ 
                       y 
                     
                     
                       ⅆ 
                       x 
                     
                   
                   = 
                   0 
                 
               
               
                 
                   ( 
                   35 
                   ) 
                 
               
             
           
         
       
     
     Using the quotient rule to find the first derivative of (34): 
     
       
         
           
             
               
                 
                   
                     
                       ⅆ 
                       y 
                     
                     
                       ⅆ 
                       
                         ( 
                         
                           P 
                           
                             tx 
                             , 
                             NB 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   k 
                                   1 
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     RN 
                                   
                                 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                             + 
                             
                               k 
                               2 
                             
                             + 
                             
                               
                                 
                                   k 
                                   3 
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     RN 
                                   
                                 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                                 2 
                               
                             
                             - 
                           
                         
                       
                       
                         
                           
                             
                               P 
                               
                                 tx 
                                 , 
                                 NB 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     k 
                                     1 
                                   
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       RN 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     
                                       2 
                                       ⁢ 
                                       
                                         k 
                                         3 
                                       
                                     
                                     
                                       P 
                                       
                                         tx 
                                         , 
                                         RN 
                                       
                                     
                                   
                                   ⁢ 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       NB 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         ( 
                         
                           
                             
                               
                                 k 
                                 1 
                               
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   RN 
                                 
                               
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 NB 
                               
                             
                           
                           + 
                           
                             k 
                             2 
                           
                           + 
                           
                             
                               
                                 k 
                                 3 
                               
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   RN 
                                 
                               
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 NB 
                               
                               2 
                             
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   36 
                   ) 
                 
               
             
           
         
       
     
     The maxima of y is found by setting (36) equal to zero and solving for P tx,NB . It follows that the maximum SINR at the UE is obtained by setting: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             k 
                             1 
                           
                           
                             P 
                             
                               tx 
                               , 
                               RN 
                             
                           
                         
                         ⁢ 
                         
                           P 
                           
                             tx 
                             , 
                             NB 
                           
                         
                       
                       + 
                       
                         k 
                         2 
                       
                       + 
                       
                         
                           
                             k 
                             3 
                           
                           
                             P 
                             
                               tx 
                               , 
                               RN 
                             
                           
                         
                         ⁢ 
                         
                           P 
                           
                             tx 
                             , 
                             NB 
                           
                           2 
                         
                       
                     
                     = 
                     
                       
                         P 
                         
                           tx 
                           , 
                           NB 
                         
                         2 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               k 
                               1 
                             
                             
                               P 
                               
                                 tx 
                                 , 
                                 RN 
                               
                             
                           
                           + 
                           
                             
                               
                                 2 
                                 ⁢ 
                                 
                                   k 
                                   3 
                                 
                               
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   RN 
                                 
                               
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 NB 
                               
                               2 
                             
                           
                         
                         ) 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       P 
                       
                         tx 
                         , 
                         NB 
                       
                     
                     = 
                     
                       
                         
                           
                             P 
                             
                               tx 
                               , 
                               RN 
                             
                           
                           ⁢ 
                           
                             k 
                             2 
                           
                         
                         
                           2 
                           ⁢ 
                           
                             k 
                             3 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   37 
                   ) 
                 
               
             
           
         
       
     
     Therefore, given the transmit power of the RN it is possible to use (37) to find the corresponding NB transmit power that ensures maximum SINR at the UE that is connected to the RN. 
     For the case of finding the optimal RN transmit power given the NB transmit power a similar approach to that described in above in the case of a non-regenerative relay node employed in conjunction with an FDD duplexing scheme, can be used as the SINR at the UE is not a parabolic function of RN transmit power. In order to find the optimal RN transmit power, (34) is rearranged to the following: 
     
       
         
           
             
               
                 
                   
                     
                       
                         y 
                         ⁢ 
                         
                             
                         
                         = 
                         
                             
                         
                         ⁢ 
                         
                           1 
                           
                             
                               ( 
                               
                                 
                                   k 
                                   1 
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     
                                         
                                     
                                     ⁢ 
                                     RN 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                                 
                             
                             + 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   k 
                                   2 
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     
                                         
                                     
                                     ⁢ 
                                     NB 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                                 
                             
                             + 
                             
                                 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     k 
                                     3 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       
                                           
                                       
                                       ⁢ 
                                       NB 
                                     
                                   
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     
                                         
                                     
                                     ⁢ 
                                     RN 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           = 
                           
                               
                           
                         
                         ⁢ 
                         
                           
                             P 
                             
                               tx 
                               , 
                               
                                   
                               
                               ⁢ 
                               RN 
                             
                           
                           
                             
                               ( 
                               
                                 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       
                                           
                                       
                                       ⁢ 
                                       RN 
                                     
                                   
                                   ⁢ 
                                   
                                     k 
                                     2 
                                   
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     
                                         
                                     
                                     ⁢ 
                                     NB 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                                 
                             
                             + 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 k 
                                 3 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                             + 
                             
                               k 
                               1 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   38 
                   ) 
                 
               
             
           
         
       
     
     The first derivative is now: 
     
       
         
           
             
               
                 
                   
                     
                       ⅆ 
                       y 
                     
                     
                       ⅆ 
                       
                         ( 
                         
                           P 
                           
                             tx 
                             , 
                             RN 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         
                           
                             k 
                             3 
                           
                           ⁢ 
                           
                             P 
                             
                               tx 
                               , 
                               NB 
                             
                           
                         
                         + 
                         
                           k 
                           1 
                         
                       
                       
                         
                           ( 
                           
                             
                               ( 
                               
                                 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       
                                           
                                       
                                       ⁢ 
                                       RN 
                                     
                                   
                                   ⁢ 
                                   
                                     k 
                                     2 
                                   
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     
                                         
                                     
                                     ⁢ 
                                     NB 
                                   
                                 
                               
                               ) 
                             
                             + 
                             
                               
                                 k 
                                 3 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                             + 
                             
                               k 
                               1 
                             
                           
                           ) 
                         
                         2 
                       
                     
                     = 
                     ∇ 
                   
                 
               
               
                 
                   ( 
                   39 
                   ) 
                 
               
             
           
         
       
     
     Solving (39) for P tx,RN  gives the optimal RN transmit power given the NB transmit power: 
     
       
         
           
             
               
                 
                   
                     P 
                     
                       tx 
                       , 
                       RN 
                     
                   
                   = 
                   
                     
                       
                         P 
                         
                           tx 
                           , 
                           NB 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               
                                 
                                   
                                     k 
                                     3 
                                   
                                   ⁢ 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       NB 
                                     
                                   
                                 
                                 + 
                                 
                                   k 
                                   1 
                                 
                               
                               ∇ 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 
                                   k 
                                   3 
                                 
                                 ⁢ 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     NB 
                                   
                                 
                               
                               + 
                               
                                 k 
                                 1 
                               
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     
                       k 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   40 
                   ) 
                 
               
             
           
         
       
     
     By observing the surface in  FIG. 5  and from the form of (34) and the result in (40) it is apparent that if the NB transmit power is small then the rate of change of SINR with RN transmit power will decrease with increasing RN transmit power. However, for the case of large NB transmit power, the SINR at the UE approximates to a linear function of RN transmit power. The result is that in this case the solution to the problem, as summarised in (40) will be infinite. 
     4B—Non-Regenerative Relay with TDD—Two Cell Model as Shown in  FIG. 1B   
     The worse case, from the perspective of a UE at the cell edge, is when the neighbouring cell employs a TDD scheme with the same timeslot used for RN transmission. If it is assumed that the cells are equal in size with the same deployment and transmit power settings and that P tx     —     tot,RN/NB =G p P tx,RN/NB  then: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           SINR 
                           
                             RN 
                             - 
                             UE 
                           
                         
                         = 
                         
                           
                             
                               G 
                               p 
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 RN 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     
                                       L 
                                       
                                         RN 
                                         - 
                                         UE 
                                       
                                     
                                     ( 
                                     
                                       N 
                                       + 
                                       
                                         
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             P 
                                             
                                               tx 
                                               , 
                                               
                                                   
                                               
                                               ⁢ 
                                               RN 
                                             
                                           
                                         
                                         
                                           
                                             L 
                                             
                                               RN 
                                               - 
                                               UE 
                                             
                                           
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             SINR 
                                             
                                               NB 
                                               - 
                                               
                                                 R 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 1 
                                               
                                             
                                           
                                         
                                       
                                       + 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           G 
                                           P 
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           P 
                                           
                                             tx 
                                             , 
                                             NB 
                                           
                                         
                                       
                                       
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           L 
                                           
                                             NB 
                                             - 
                                             UE 
                                           
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         
                                           G 
                                           p 
                                         
                                         ⁢ 
                                         
                                           P 
                                           
                                             tx 
                                             , 
                                             RN 
                                           
                                         
                                       
                                       
                                         L 
                                         
                                           RN 
                                           - 
                                           UE 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           1 
                           
                             
                               
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             NL 
                                             
                                               RN 
                                               - 
                                               UE 
                                             
                                           
                                         
                                         
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             
                                               G 
                                               p 
                                             
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               P 
                                               
                                                 tx 
                                                 , 
                                                 RN 
                                               
                                             
                                           
                                         
                                       
                                       ) 
                                     
                                     + 
                                     
                                       ( 
                                       
                                         
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             NL 
                                             
                                               NB 
                                               - 
                                               RN 
                                             
                                           
                                         
                                         
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             
                                               G 
                                               p 
                                               2 
                                             
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               P 
                                               
                                                 tx 
                                                 , 
                                                 NB 
                                               
                                             
                                           
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     
                                         
                                     
                                     + 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     ( 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           L 
                                           
                                             RN 
                                             - 
                                             UE 
                                           
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           P 
                                           
                                             tx 
                                             , 
                                             NB 
                                           
                                         
                                       
                                       
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           
                                             L 
                                             
                                               NB 
                                               - 
                                               UE 
                                             
                                           
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             P 
                                             
                                               tx 
                                               , 
                                               RN 
                                             
                                           
                                         
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   + 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   41 
                   ) 
                 
               
             
           
         
       
     
     In this case the simplified form of (4) is: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           SINR 
                           
                             RN 
                             - 
                             UE 
                           
                         
                         = 
                         
                           1 
                           
                             
                               
                                 k 
                                 1 
                               
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   RN 
                                 
                               
                             
                             + 
                             
                               
                                 k 
                                 2 
                               
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                             + 
                             
                               
                                 
                                   2 
                                   ⁢ 
                                   
                                     k 
                                     3 
                                   
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     RN 
                                   
                                 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                             + 
                             1 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             P 
                             
                               tx 
                               , 
                               NB 
                             
                           
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       k 
                                       1 
                                     
                                     
                                       P 
                                       
                                         tx 
                                         , 
                                         RN 
                                       
                                     
                                   
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                             + 
                             
                               k 
                               2 
                             
                             + 
                             
                               
                                 
                                   2 
                                   ⁢ 
                                   
                                     k 
                                     3 
                                   
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     RN 
                                   
                                 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                                 2 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   42 
                   ) 
                 
               
             
           
         
       
     
     And the first derivative is: 
     
       
         
           
             
               
                 
                   
                     
                       ⅆ 
                       y 
                     
                     
                       ⅆ 
                       
                         ( 
                         
                           P 
                           
                             tx 
                             , 
                             NB 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       k 
                                       1 
                                     
                                     
                                       P 
                                       
                                         tx 
                                         , 
                                         RN 
                                       
                                     
                                   
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                             + 
                             
                               k 
                               2 
                             
                             + 
                             
                               
                                 
                                   2 
                                   ⁢ 
                                   
                                     k 
                                     3 
                                   
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     RN 
                                   
                                 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                                 2 
                               
                             
                             - 
                           
                         
                       
                       
                         
                           
                             
                               P 
                               
                                 tx 
                                 , 
                                 NB 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     k 
                                     1 
                                   
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       RN 
                                     
                                   
                                 
                                 + 
                                 1 
                                 + 
                                 
                                   
                                     
                                       4 
                                       ⁢ 
                                       
                                         k 
                                         3 
                                       
                                     
                                     
                                       P 
                                       
                                         tx 
                                         , 
                                         RN 
                                       
                                     
                                   
                                   ⁢ 
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       NB 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         ( 
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     k 
                                     1 
                                   
                                   
                                     P 
                                     
                                       tx 
                                       , 
                                       RN 
                                     
                                   
                                 
                                 + 
                                 1 
                               
                               ) 
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 NB 
                               
                             
                           
                           + 
                           
                             k 
                             2 
                           
                           + 
                           
                             
                               
                                 2 
                                 ⁢ 
                                 
                                   k 
                                   3 
                                 
                               
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   RN 
                                 
                               
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 NB 
                               
                               2 
                             
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   43 
                   ) 
                 
               
             
           
         
       
     
     Finally, the maxima is given by setting (43) equal to zero and solving for P tx,NB : 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             ( 
                             
                               
                                 
                                   k 
                                   1 
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     RN 
                                   
                                 
                               
                               + 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           
                             P 
                             
                               tx 
                               , 
                               NB 
                             
                           
                         
                         + 
                         
                           k 
                           2 
                         
                         + 
                         
                           
                             
                               2 
                               ⁢ 
                               
                                 k 
                                 3 
                               
                             
                             
                               P 
                               
                                 tx 
                                 , 
                                 RN 
                               
                             
                           
                           ⁢ 
                           
                             P 
                             
                               tx 
                               , 
                               NB 
                             
                             2 
                           
                         
                       
                       = 
                       
                         
                           P 
                           
                             tx 
                             , 
                             NB 
                           
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 k 
                                 1 
                               
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   RN 
                                 
                               
                             
                             + 
                             1 
                             + 
                             
                               
                                 
                                   4 
                                   ⁢ 
                                   
                                     k 
                                     3 
                                   
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     RN 
                                   
                                 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         k 
                         2 
                       
                       + 
                       
                         
                           
                             2 
                             ⁢ 
                             
                               k 
                               3 
                             
                           
                           
                             P 
                             
                               tx 
                               , 
                               RN 
                             
                           
                         
                         ⁢ 
                         
                           P 
                           
                             tx 
                             , 
                             NB 
                           
                           2 
                         
                       
                     
                     = 
                     
                       
                         
                           4 
                           ⁢ 
                           
                             k 
                             3 
                           
                         
                         
                           P 
                           
                             tx 
                             , 
                             RN 
                           
                         
                       
                       ⁢ 
                       
                         P 
                         
                           tx 
                           , 
                           NB 
                         
                         2 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       P 
                       
                         tx 
                         , 
                         NB 
                       
                     
                     = 
                     
                       
                         
                           
                             P 
                             
                               tx 
                               , 
                               RN 
                             
                           
                           ⁢ 
                           
                             k 
                             2 
                           
                         
                         
                           2 
                           ⁢ 
                           
                             k 
                             3 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   44 
                   ) 
                 
               
             
           
         
       
     
     In order to find the optimal RN transmit power given the NB transmit power (42) is rearranged to: 
     
       
         
           
             
               
                 
                   
                     
                       
                         y 
                         = 
                           
                         ⁢ 
                         
                           1 
                           
                             
                               
                                 k 
                                 1 
                               
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   RN 
                                 
                               
                             
                             + 
                             
                               
                                 k 
                                 2 
                               
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                             + 
                             
                               
                                 
                                   2 
                                   ⁢ 
                                   
                                     k 
                                     3 
                                   
                                 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     RN 
                                   
                                 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                             + 
                             1 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             P 
                             
                               tx 
                               , 
                               RN 
                             
                           
                           
                             
                               k 
                               1 
                             
                             + 
                             
                               
                                 
                                   k 
                                   2 
                                 
                                 ⁢ 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     RN 
                                   
                                 
                               
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                             + 
                             
                               2 
                               ⁢ 
                               
                                 k 
                                 3 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                             + 
                             
                               P 
                               
                                 tx 
                                 , 
                                 RN 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   45 
                   ) 
                 
               
             
           
         
       
     
     The first derivative is now: 
     
       
         
           
             
               
                 
                   
                     
                       ⅆ 
                       y 
                     
                     
                       ⅆ 
                       
                         ( 
                         
                           P 
                           
                             tx 
                             , 
                             RN 
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         
                           k 
                           1 
                         
                         + 
                         
                           2 
                           ⁢ 
                           
                             k 
                             3 
                           
                           ⁢ 
                           
                             P 
                             
                               tx 
                               , 
                               NB 
                             
                           
                         
                       
                       
                         
                           ( 
                           
                             
                               k 
                               1 
                             
                             + 
                             
                               2 
                               ⁢ 
                               
                                 k 
                                 3 
                               
                               ⁢ 
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   NB 
                                 
                               
                             
                             + 
                             
                               
                                 P 
                                 
                                   tx 
                                   , 
                                   RN 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   
                                     
                                       k 
                                       2 
                                     
                                     
                                       P 
                                       
                                         tx 
                                         , 
                                         NB 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           ) 
                         
                         2 
                       
                     
                     = 
                     ∇ 
                   
                 
               
               
                 
                   ( 
                   46 
                   ) 
                 
               
             
           
         
       
     
     Solving (46) for P tx,RN  gives the optimal RN transmit power given the NB transmit power: 
     
       
         
           
             
               
                 
                   
                     P 
                     
                       tx 
                       , 
                       RN 
                     
                   
                   = 
                   
                     
                       
                         
                           P 
                           
                             tx 
                             , 
                             NB 
                           
                         
                         ⁢ 
                         
                           
                             
                               
                                 k 
                                 1 
                               
                               + 
                               
                                 2 
                                 ⁢ 
                                 
                                   k 
                                   3 
                                 
                                 ⁢ 
                                 
                                   P 
                                   
                                     tx 
                                     , 
                                     NB 
                                   
                                 
                               
                             
                             ∇ 
                           
                         
                       
                       - 
                       
                         ( 
                         
                           
                             k 
                             1 
                           
                           + 
                           
                             2 
                             ⁢ 
                             
                               k 
                               3 
                             
                             ⁢ 
                             
                               P 
                               
                                 tx 
                                 , 
                                 NB 
                               
                             
                           
                         
                         ) 
                       
                     
                     
                       ( 
                       
                         
                           P 
                           
                             tx 
                             , 
                             NB 
                           
                         
                         + 
                         
                           k 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   47 
                   ) 
                 
               
             
           
         
       
     
     Again, in the case of large NB transmit power, the SINR at the UE approximates to a linear function of RN transmit power. The result is that the solution to (47) will be infinite. 
     The optimal transmit power balance will now be determined based on the solutions developed above for the different relay and duplexing schemes and for two separate deployment scenarios. These deployment scenarios are summarised in Table IIIII and the propagation parameters of the pathloss equation in (48) are in Table IV.
 
 L=b+ 10 n  log  d   (48)
 
     Where L is the pathloss in dB, b is in dB and is given in Table II along with n, and d is the transmitter-receiver separation in metres. 
     
       
         
               
             
               
               
               
             
               
               
               
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE III 
               
             
             
               
                   
               
               
                 Deployment scenarios 
               
             
          
           
               
                   
                 Scenario 
                   
               
             
          
           
               
                   
                 Parameter 
                 1 
                 2 
               
               
                   
               
             
          
           
               
                   
                 Cell Radius 
                 1867 m 
                   
               
             
          
           
               
                   
                 Relay Position 
                 933 m 
                 1400 m 
               
               
                   
               
             
          
         
       
     
     The transmitter receiver separation is the same as the cell radius (i.e. the UE is located at the cell radius). The RN position quoted is relative to the centre of the cell which is where the NB is located. The RN positions are therefore the distance from the NB to the RN. The RN-UE is then the difference of the cell radius and the NB-RN separation. 
                                                                           TABLE IIV                   Propagation parameters.                Link                Parameter   NB-UE   NB-RN   RN-UE                        b (dB)   15.3   15.5   28           n   3.76   3.68   4                    
Regenerative Relay
 
     Substituting the values given in Table III and Table IV into equations (3) and (5) for FDD and (12) and (17) for TDD it is possible to find the optimal NB transmit power given the RN transmit power.  FIG. 8A  shows the optimal NB transmit power as a function of RN transmit power for both FDD and TDD for the two deployment scenarios. 
     Non-Regenerative Relay with FDD 
     Substituting the parameters into (23) and (24) it is possible to find the optimal NB transmit power for the two deployment scenarios, as shown in  FIG. 8B . 
     Non-Regenerative Relay with TDD 
     Substituting the parameters into (37) and (44) it is possible to find the optimal NB transmit power for the two deployment scenarios, as shown in  FIG. 8C . 
     System Level Simulation Results 
     System simulation of a multi-hop HSDPA network employing non-regenerative relays with TDD duplexing with relays transmitting in every third transmission time interval have been conducted in order to validate the predicted optimal transmit power setting based on results of  FIG. 8C , with the average packet call throughput gain being determined as the transmit powers of the RN and NB are varied around the optimal point. 
     Results of a system level simulation for the two deployment scenarios detailed above in Table III will now be presented. The simulation parameters are listed below in Table V and Table VI. 
     
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE V 
               
             
             
               
                   
               
               
                 Deployment parameters 
               
             
          
           
               
                   
                 Parameter 
                   
                 Value 
               
               
                   
               
             
          
           
               
                   
                 Base Station 
                 Inter-cell Separation 
                 2.8 km 
               
               
                   
                   
                 Sectors/cell 
                 3 
               
               
                   
                   
                 Antenna Height 
                 15 m 
               
               
                   
                   
                 Antenna Gain 
                 17 dBi 
               
               
                   
                 Relay Station 
                 RN antenna 
                 120° 
               
               
                   
                   
                 position 
                 ½ and ¾ cell radius 
               
               
                   
                   
                 Num/cell 
                 9 
               
               
                   
                   
                 Antenna Height 
                 5 m 
               
               
                   
                   
                 Antenna Gain 
                 17 dBi 
               
               
                   
                 User 
                 Number per sector 
                 50 
               
               
                   
                 Equipment 
                 Initial Distribution 
                 Random 
               
               
                   
                   
                 Velocity 
                 3 km/h 
               
               
                   
                   
                 Direction 
                 Semi-directed 
               
               
                   
                   
                 Update 
                 20 m 
               
               
                   
                 Traffic Models 
                   
                 WWW 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE II 
               
             
             
               
                   
               
               
                 Simulation parameters 
               
             
          
           
               
                   
                 Parameters 
                   
                 Value 
               
               
                   
               
             
          
           
               
                   
                 Base Station/ 
                 HS-DSCH power 
                 Variable 
               
               
                   
                 Relay Node 
                 CPICH power 
                 20% of total 
               
               
                   
                   
                 HARQ scheme 
                 Chase 
               
               
                   
                   
                 HS-DSCH/frame 
                 15 
               
               
                   
                   
                 Relay buffer size 
                 1.78 Mbits 
               
               
                   
                   
                 Ack/NAck Detection 
                 Error free 
               
               
                   
                   
                 NB Scheduler 
                 Round Robin 
               
               
                   
                   
                 Relay type 
                 Amplify &amp; Forward 
               
               
                   
                 User 
                 Thermal Noise Density 
                 10-174 dBm/Hz 
               
               
                   
                 Equipment 
                 Noise Figure 
                 5 dBm 
               
               
                   
                   
                 Detector 
                 MMSE 
               
               
                   
               
             
          
         
       
     
     For both deployment scenarios the gain in the average packet call throughput experienced by the users on that observed for the case of a single hop system with NB transmission power of 30 dBm is plotted as a function of NB transmit power for four different RN transmit powers.  FIG. 9A  shows the gain for deployment scenario  1  and  FIG. 9B  shows the gain for scenario  2 . Note that the channel gain for the NB to UE link was 3 dB higher than for the NB to RN and RN to UE link. This means that the interference experienced by a UE connected to a RN from another NB is double that used in the link analysis discussed above with reference to  FIGS. 8A ,  8 B and  8 C. The channel gain is due to the fact that a number of replicas of the transmitted signal are received, when the power on all these is added it is found that for the case of the NB to UE channel the total power is double that on the NB to RN or RN to UE channel. This accounts for the 3 dB gain, as 3 dB equates to double. As a result of the channel gain being higher for the NB to UE channel, this means that the received signal power will be 3 dB (or double) higher than that used in the analysis up to that point where no channel gain through multi-path was considered. 
     Comparison of Link Based Prediction and System Simulation 
       FIG. 10  shows the optimal NB transmit power as a function of RN transmit power for a non-regenerative relay for TDD for each deployment scenario where it is assumed the NB to UE link has a 3 dB gain compared with the other links. In this case, the predicted transmit power at the NB for the RN transmit power used in the simulation are listed in Table VII along with the throughput gain that would be experienced if these settings were used and the maximum achievable. 
     
       
         
               
             
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE IIIII 
               
             
             
               
                   
               
               
                 Predicted optimal NB transmit power and resulting simulated throughput 
               
               
                 gain that would have been achieved from this setting compared with the maximum gain 
               
               
                 observed. 
               
             
          
           
               
                   
                 NB Transmit Power (dBm) &amp; User Packet Throughput Gain 
               
             
          
           
               
                   
                   
                 Scenario 1 
                   
                   
                 Scenario 2 
                   
               
               
                 RN Transmit 
                   
                 Throughput 
                   
                   
                 Throughput 
               
               
                 Power (dBm) 
                 Predicted 
                 Gain 
                 Max Gain 
                 Predicted 
                 Gain 
                 Max Gain 
               
               
                   
               
             
          
           
               
                 16 
                 −0.5 
                 33% 
                 40% 
                 8.8 
                 60% 
                 67% 
               
               
                 19 
                 1 
                 38% 
                 43% 
                 10.3 
                 65% 
                 74% 
               
               
                 22 
                 2.5 
                 41% 
                 46% 
                 11.8 
                 68% 
                 74% 
               
               
                 25 
                 4 
                 49% 
                 51% 
                 13.3 
                 72% 
                 75% 
               
               
                   
               
             
          
         
       
     
     Table VII,  FIG. 8A  and  FIG. 9A  suggest that if power balancing is performed according to a preferred embodiment of the present invention using a technique based on the equations developed above then the selected power balance will in general be in the region of the optimal point. In particular, for the transmit powers used the gain was shown to always be within 10% of the achievable maximum, with the difference being due to shortcomings of using of a two-cell model to model a multi-cell system. 
     The necessity of transmit power balancing is apparent in the results presented in both  FIG. 9A  and  FIG. 9B  where it is shown that if the NB transmit is increased beyond the optimal point then a significant degradation in gain will be experienced despite the emission of more signal energy. It also shows that if the NB transmit power is selected carefully then the sensitivity of the gain to RN transmit power is reduced.