Patent Publication Number: US-9414321-B2

Title: Uplink power control for MU-MIMO

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a 35 U.S.C. §371 National Phase Entry Application from PCT/CN2011/002171, filed Dec. 23, 2011, and designating the United States. 
     TECHNICAL FIELD 
     The invention relates in general to Long Term Evolution (LTE) wireless communications, and more specifically to uplink power control in multi-user multiple-input multiple-output (MU-MIMO) transmissions. 
     BACKGROUND 
     In Release 8 of 3GPP, the user equipment (UE) supports multiple receive antennas but only a single transmit antenna. As such, single-user MIMO (SU-MIMO) can only be supported in the downlink, but MU-MIMO can be supported in the uplink. 
     MU-MIMO allows for uplink transmissions from multiple UEs to a radio base station, e.g., an eNode-B, using common time-frequency resources, i.e., schedule blocks. To separate the transmissions, MU-MIMO relies on the availability of multiple receive antennas at the radio base station and on significantly different spatial radio channels between the UEs and the radio base station. 
     An important benefit of uplink MU-MIMO is that a similar gain in system throughput as in SU-MIMO may be achieved, without need for multiple transmit antennas at the UE. This allows for a less complex implementation of UEs, i.e., handsets. However, the potential system gain of uplink MU-MIMO relies on more than one UE being available for transmission using a common time-frequency resource. The process of “pairing” UEs for MU-MIMO transmissions is non-trivial and requires favorable radio-channel conditions. 
     Ideally, paired, i.e., co-scheduled, UEs should have orthogonal channels in order to minimize mutual interference. If the transmissions from two UEs can be perfectly separated at the receiver, and both signals are transmitted with the same power as in single-user mode, there is a potential 100% gain in cell or user throughput due to the increased transmission power. However, co-scheduled UEs are seldom ideally orthogonal, giving rise to mutual interference. The more orthogonal the channels are the less intra-cell interference will be created by MU-MIMO. At the same time, the increase of total transmission power on the schedule blocks used for MU-MIMO transmissions will increase inter-cell interference, thereby reducing the potential gain. 
     SUMMARY 
     It is an object of the present invention to provide a more efficient alternative to the above techniques and prior art. 
     More specifically, it is an object of the present invention to provide an improved power control for MU-MIMO transmissions. In particular, it is an object of the present invention to provide an improved power control for uplink MU-MIMO transmissions in LTE communication networks. 
     These and other objects of the present invention are achieved by means of a method of uplink MU-MIMO wireless transmissions defined in independent claim  1 , and by means of a radio base station having the features defined independent claim  8 . Embodiments of the invention are characterized by the dependent claims. 
     For the purpose of describing the present invention, a radio base station may, e.g., be a Node B, an eNode-B, an access point, or any other type of device capable of supporting uplink MU-MIMO wireless transmissions. Further, a mobile terminal may, e.g., be a UE, a mobile phone, a modem, a portable computer, a handset, or any other type of device capable of supporting uplink MU-MIMO wireless transmissions. In this respect, uplink transmissions are transmissions from the mobile terminal to the radio base station. It will also be appreciated that, in order to support uplink MU-MIMO transmissions, downlink control signaling, i.e., from the radio base station to the mobile terminal, may be required. 
     According to a first aspect of the invention, a method of power control for uplink MU-MIMO wireless transmissions between a pair of mobile terminals and a radio base station is provided. The pair of mobile terminals comprises a first mobile terminal and a second mobile terminal. The method comprises determining a first single-user signal-to-interference-noise ratio (SU-SINR), determining a second SU-SINR, determining a channel orthogonality, and jointly determining a first power adjustment value and a second power adjustment value. The first SU-SINR pertains to a first radio channel between the first mobile terminal and the radio base station. The second SU-SINR pertains to a second radio channel between the second mobile terminal and the radio base station. The channel orthogonality is the degree of orthogonality between the first radio channel and the second radio channel. The first power adjustment value pertains to the first mobile terminal. The second power adjustment value pertains to the second mobile terminal. The first power adjustment value and the second power adjustment value are determined based on the first SU-SINR, the second SU-SINR, and the channel orthogonality. 
     According to a second aspect of the invention, a radio base station is provided. The radio base station is arranged for uplink MU-MIMO wireless transmissions between a pair of mobile terminals and the radio base station. The pair of mobile terminals comprises a first mobile terminal and a second mobile terminal. The radio base station comprises a channel condition estimation unit and a multi-user power control unit. The channel condition estimation unit is arranged for determining a first SU-SINR, determining a second SU-SINR, and determining a channel orthogonality. The first SU-SINR pertains to a first radio channel between the first mobile terminal and the radio base station. The second SU-SINR pertains to a second radio channel between the second mobile terminal and the radio base station. The channel orthogonality is the degree of orthogonality between the first radio channel and the second radio channel. The multi-user power control unit is arranged for jointly determining a first power adjustment value and a second power adjustment value. The first power adjustment value pertains to the first mobile terminal. The second power adjustment value pertains to the second mobile terminal. The first power adjustment value and the second power adjustment value are determined based on the first SU-SINR, the second SU-SINR, and the channel orthogonality. 
     The SINR of a radio channel is to be understood as a measure of the SINR of a transmission originating from a mobile terminal and being received by a radio base station, which transmission is carried by the radio channel between the mobile terminal and the radio base station. The SU-SINR pertains to the transmission of a single mobile terminal in single-user mode, i.e., not utilizing MU-MIMO. In the present disclosure, the expressions SINR of a UE and SINR of a radio channel are used synonymously. 
     The present invention makes use of an understanding that the system gain resulting from uplink MU-MIMO transmissions may be improved by optimizing the transmission power of the mobile terminals engaged in MU-MIMO transmissions, i.e., the mobile terminals which are co-scheduled for transmission using a common time-frequency resource. By optimizing the transmission power of the co-scheduled mobile terminals, the potential loss in system gain due to the increase of intra-cell and inter-cell interference may be minimized. An embodiment of the present invention is further advantageous in that the quality of service (QoS) experience of co-scheduled users may be improved. Finally, uplink MU-MIMO power control in accordance with an embodiment of the invention is advantageous in that power optimization may be performed directly, without relying on a time consuming iterative procedure. 
     The transmission power of co-scheduled mobile terminals may be optimized by way of different schemes and/or criteria pertaining to system throughput, user throughput, QoS, air interface efficiency, and the like, in accordance with embodiments of the present invention, as described hereinafter. To this end, an embodiment of the invention may be applied to different scenarios, such as improving cell throughput or user QoS experience, or reducing harmful inter-cell interference. 
     According to an embodiment of the invention, the first power adjustment value and the second power adjustment value are determined based on a first MU-MIMO-SINR (MU-SINR) target and a second MU-SINR target. The first MU-SINR target pertains to the first radio channel. The second MU-SINR target pertains to the second radio channel. The first MU-SINR is the SINR of the first radio channel in MU-MIMO transmission mode after power control, i.e., after the transmit power of the first mobile terminal is adjusted by the first power adjustment value, and the transmit power of the second mobile terminal is adjusted by the second power adjustment value. Correspondingly, the second MU-SINR is the SINR of the second radio channel in MU-MIMO transmission mode after power control. Determining the first power adjustment value and the second power adjustment value based on MU-SINR targets for the two radio channels is advantageous in that the transmission power of the two mobile terminals may be adjusted so as to attain specific MU-SINR target values. Such MU-SINR targets may be set according to certain requirements. For instance, MU-SINR targets may be set so as to reduce transmission power, thereby minimizing harmful inter-cell interference. Alternatively, MU-SINR targets may be set so as to maintain the SINRs as in single-user transmission mode. In this way, frequent changes in QoS, which may be perceived unsatisfactorily by a user of the mobile terminal, may be avoided, or at least reduced, when repeatedly switching between single-user transmission and MU-MIMO transmission. 
     According to an embodiment of the invention, the first power adjustment value and the second power adjustment value are determined based on a power budget constraint while maximizing a transmission sum rate for the pair of mobile terminals. This is advantageous in that the transmission power of the co-scheduled mobile terminals may be optimized so as to maximize, or at least increase, the total transmission rate from the co-scheduled mobile terminals. In this respect, the total transmission rate is the sum of the transmission rates between each mobile terminal and the radio base station, i.e., the sum of the transmission rate over the first radio channel and the transmission rate over the second radio channel. This is advantageous in that performance may be optimized from a system point of view. Besides maximizing the transmission sum rate, an increase in inter-cell interference is avoided by imposing a power budget constraint. 
     According to an embodiment of the invention, the first SU-SINR, the second SU-SINR, and the channel orthogonality, are determined based on instantaneous radio channel conditions. This is advantageous in that power control in accordance with an embodiment of the invention takes into account the actual radio channel conditions. In that way, the available transmit power may be distributed between the co-scheduled mobile terminals with regard to radio channel conditions between the mobile terminals and the radio base station, the radio channel conditions being reflected by the first and the second SU-SINR, and the channel orthogonality. The first and the second SU-SINR, and the channel orthogonality, may, e.g., be determined from sounding reference signals (SRS) or demodulation reference signals (DMRS). 
     According to an embodiment of the invention, the method further comprises determining a first MU-SINR for the first radio channel, determining a second MU-SINR for the second radio channel, and evaluating whether to schedule the pair of mobile terminals for MU-MIMO transmissions. The evaluation, whether to schedule the pair of mobile terminals for MU-MIMO transmissions, is based on the first MU-SINR and the second MU-SINR. This is advantageous in that the potential gain from co-scheduling a pair of mobile terminals for MU-MIMO transmissions, which potential gain is represented by the first MU-SINR and the second MU-SINR, may be taken into consideration by the scheduler. 
     Even though advantages of the present invention have in some cases been described with reference to embodiments of the method according to the first aspect of the present invention, corresponding reasoning applies to embodiments of the radio base station according to the second aspect of the invention. 
     Further objectives of, features of, and advantages with, the present invention will become apparent when studying the following detailed disclosure, the drawings and the appended claims. Those skilled in the art realize that different features of the present invention can be combined to create embodiments other than those described in the following. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above, as well as additional objects, features and advantages of the present invention, will be better understood through the following illustrative and non-limiting detailed description of embodiments of the present invention, with reference to the appended drawings, in which: 
         FIG. 1  illustrates the concept of MU-MIMO. 
         FIG. 2  is a known protocol stack of a radio base station for UL MU-MIMO transmissions. 
         FIG. 3  illustrates a method of power control for UL-MIMO transmissions, in accordance with an embodiment of the invention. 
         FIG. 4  is a protocol stack of a radio base station for UL MU-MIMO transmissions with power control, in accordance with an embodiment of the invention. 
     
    
    
     All the figures are schematic, not necessarily to scale, and generally only show parts which are necessary in order to elucidate the invention, wherein other parts may be omitted or merely suggested. 
     DETAILED DESCRIPTION 
     For the purpose of elucidating the present invention, the concept of MU-MIMO is described with reference to  FIG. 1 . 
     In  FIG. 1 , a communication system  100  capable of supporting MU-MIMO transmissions is illustrated. Communication system  100  may, e.g., be an LTE network comprising a radio base station  110 , such as an eNode-B, which is engaged in wireless communications with a first UE  111  and a second UE  112 . Wireless communications between eNode-B  110  and first UE  111  are effected over a first radio channel  113 . Correspondingly, wireless communications between eNode-B  110  and second UE  112  are effected over a second radio channel  114 . 
     Wireless communications between eNode-B  110  and first  111  and second UE  112  may be effected in the downlink, i.e., from eNode-B  110  to UEs  111  and  112 , and in the uplink, i.e., from UEs  111  and  112  to eNode-B  110 . In this respect, the term ‘radio channel’ is to be understood as comprising a plurality of physical channels, both in downlink and uplink, which may be used for transmitting user data, i.e., payload, as well as control signaling. In the LTE uplink, user data is transmitted on the physical uplink shared channel (PUSCH). Typically, in order to effect uplink transmissions in an LTE communication system, such as communication system  100 , downlink control signaling is required. 
     In LTE communications, transmissions are scheduled on time-frequency resources, so called schedule blocks, which are assigned by a scheduler based on different criteria, such as an amount and a type of data to be transmitted, QoS, priority, and radio channel conditions. Scheduling for both downlink and uplink transmissions is performed on the network side, i.e., in the eNode-B. Thus, in order to enable uplink transmissions from UEs  111  and  112  to eNode-B  110 , scheduling information is transmitted from eNode-B  110  to UEs  111  and  112  by means of downlink control signaling. 
     For the purpose of exemplifying the distinct transmission modes referred to in the present disclosure, single-user (SU) and MU-MIMO, the scheduling of first  111  and second UE  112  in time-frequency domain is illustrated in  FIG. 1 . 
     In SU transmission mode  121 , each schedule block  123 , corresponding to 180 kHz bandwidth during a 1 ms timeslot, is assigned to either first UE  111  (UE1) or second UE  112  (UE2), but not both UEs  111  and  112  simultaneously. For instance, in the first time slot, three schedule blocks are assigned to first UE  111  (UE1), and two schedule blocks are assigned to second UE  112  (UE2). In the next time slot, two schedule blocks are assigned to first UE  111  (UE1) and three schedule blocks are assigned to second UE  112  (UE2). In the third time slot, five schedule blocks are assigned to first UE  111  (UE1), and in the fourth time slot five schedule blocks are assigned to second UE  112  (UE2). 
     In MU-MIMO transmission mode  122 , on the other hand, first UE  111  and second UE  112  are scheduled on common schedule blocks  123 . For the scenario exemplified in  122 , for all time slots, all schedule blocks  123  are assigned to both first  111  UE (UE1) and second UE  112  (UE2) simultaneously, i.e., UEs  111  and  112  are co-scheduled for transmission using common time-frequency resources. 
     Note that, whereas only five schedule blocks  123  are illustrated for each time slot in  121  and  122 , the number of schedule blocks  123  which are available for transmission during any given time slot depends on the available bandwidth. 
     In order to separate the transmissions from first UE  111  and second UE  112  at eNode-B  110 , MU-MIMO relies on significantly different spatial radio channels  113  and  114 , and the availability of multiple receive antennas  115  at eNode-B  110 . 
     In the following, uplink scheduling, as performed by a known eNode-B, is described with reference to  FIG. 2 . Note that  FIG. 2  illustrates only those parts of an eNode-B which are necessary for describing functionality related to scheduling and power control, whereas other features are omitted for the sake of simplicity. 
     Typically, an eNode-B, such as eNode-B  110  described with reference to  FIG. 1 , comprises multiple antennas  115 , transmitters and receivers, circuitry or processing means for data processing, and interfaces for interconnecting the eNode-B  110  with other eNode-Bs or a core network. The circuitry or processing means for data processing is arranged for implementing an LTE protocol stack, such as protocol stack  200  illustrated in  FIG. 2 , which comprises a physical layer  201  and a medium access control (MAC) layer  202 . 
     In general, the physical layer of an LTE protocol stack, such as physical layer  201 , typically performs tasks associated with mapping between transport channels and physical channels, error detection, forward error correction encoding/decoding, hybrid automatic repeat request (HARQ) processing, rate matching, modulation/demodulation, coding, power control, antenna mapping, and precoding. Further, the MAC layer of an LTE protocol stack, such as MAC layer  202 , typically performs tasks related to mapping between logical channels and transport channels, multiplexing and demultiplexing, transport format selection, and scheduling. 
     More specifically, physical layer  201  comprises a channel condition estimation unit  211  which, based on instantaneous channel condition information  221  determined, e.g., from SRS or DMRS, estimates an SU-SINR for each UE and signals that information  223  to a scheduler  212  comprised in MAC layer  202 . Physical layer  201  further comprises a power control unit  214  for controlling the transmission power of the UEs which are engaged in communications with the eNode-B by signaling power control commands  226  to such UEs. 
     Scheduler  212  is arranged for assigning schedule blocks to UEs for the purpose of uplink transmissions, i.e., for transmitting data from a UE to eNode-B  110 . Scheduling is performed based on a number of parameters, such as channel condition information, i.e., SINR information  223  received from channel condition estimation unit  211 , in addition to other information, e.g., the amount of data to be transmitted, the type of data to be transmitted, QoS requirements, priorities, and the like. 
     Typically, a known scheduler comprised in an MU-MIMO capable eNode-B performs the following steps. The scheme presented here is referred to as proportional pair scheduling in time and frequency (PFTF). Alternatively, similar schemes may be employed, such as round-robin or max-rate. 
     First, a list of scheduling candidates is generated. The candidate list comprises all users, i.e., UEs, having data for transmission, and all possible pairs of such UEs. In SU transmission mode, the list comprises only users and no pairs of users. 
     Then, while resources are available for uplink transmissions, such resources are allocated as follows:
         For each candidate on the list, if the number of schedule blocks in the currently scheduled resource allocation has increased, the estimated throughput for all available resource allocations having one more schedule block than the currently scheduled resource allocation is calculated, and the best candidate is selected. The throughput is estimated based on the SINR of the resource allocation, where intra-cell interference is considered.   A PFTF weight is calculated as the number of bits gained by being scheduled the best resource allocation in comparison to the already scheduled resource allocation, divided by the average rate. For candidate pairs, the PFTF weight is the sum of the two UEs&#39; respective weights. The candidate having the highest PFTF weight is selected and is assigned the best resource allocation.   Candidate pairs comprising one of the scheduled users are removed from the candidate list.       

     During the procedure outlined above, the transmission power of the scheduled UEs is not optimized. 
     In the following, an embodiment of the invention is described with reference to  FIG. 3  and the PFTF scheme described hereinbefore. More specifically, a method  310  of power control for uplink MU-MIMO transmissions is presented. 
     First, in step  311 , a candidate list of single UEs and UE pairs is compiled. In the next step  312 , the SU-SINR for each UE is determined from channel conditions. Further, the channel orthogonality is determined for each candidate pair. Based on the SU-SINR values, the throughput is estimated for all candidates in the following step  313 , and the best candidates are selected, i.e., scheduled for transmission. Depending  314  on the transmission mode of the scheduled UEs, i.e., SU or MU-MIMO, the method either returns to step  311  or continues to step  315 . If  314  no UEs are scheduled for MU-MIMO transmissions, i.e., if only candidates comprising single UEs are scheduled, method  310  returns to step  311  and starts over again with evaluating candidates for the next time slot. If  314  at least one pair of UEs is scheduled for MU-MIMO transmissions, method  310  continues to step  315 . In step  315 , the first and the second power adjustment value are determined, based on the SU-SINRs and the channel orthogonality, and signaled to the UEs. Preferably, the power adjustment values are converted to power control in accordance with 3GPP specifications and signaled to the UEs. 
     Further with reference to  FIG. 3  and the PFTF scheme described hereinbefore, another embodiment of the invention, an alternative method  320  of power control for uplink MU-MIMO transmissions, is presented. 
     First, in step  321 , a candidate list of single UEs and UE pairs is compiled. In the next step  322 , the SU-SINR for each UE is determined from channel conditions. Further, the channel orthogonality is determined for each candidate pair. In the following step  323 , the first and the second power adjustment value are determined, based on the SU-SINRs and the channel orthogonality. Further, the MU-SINRs after power control are determined, as is described further below. Then, based on the SINR values, i.e., SU-SINR for single-UE candidates and MU-SINR for candidate pairs, the throughput is estimated for all candidates in the following step  324 , and the best candidates are selected, i.e., scheduled for transmission. Depending  325  on the transmission mode of the scheduled UEs, i.e., SU or MU-MIMO, the method either returns to step  321  or continues to step  326 . 
     If  325  no UEs are scheduled for MU-MIMO transmissions, i.e., if only candidates comprising single UEs are scheduled, method  320  returns to step  321  and starts over again with evaluating candidates for the next time slot. If  325  at least one pair of UEs is scheduled for MU-MIMO transmissions, method  320  continues to step  326 . In step  326 , the power adjustment values are signaled to the UEs. Preferably, the power adjustment values are converted to power control in accordance with 3GPP specifications and signaled to the UEs. 
     In order to elucidate the invention and its embodiments in more detail, a mathematical model of MU-MIMO transmissions between first UE  111  and eNode-B  111 , as well as second UE  112  and eNode-B  110 , is outlined in the following. While the equations derived here apply to a minimum mean square error (MMSE) based receiver, corresponding equations may easily be derived for other receiver concepts. Thus, the present invention is not limited to MMSE based receivers. 
     First, a per-UE expression for SINR is derived for MU-MIMO transmissions, i.e., the MU-SINR. Defining the channel vectors for first radio channel  113  and second radio channel  114  as h 1 (k) and h 2 (k), respectively, the channel vector for the combined MU-MIMO channel can be written as
 
 H ( k )=( h   1 ( k ), h   2 ( k ))  (1),
 
where k is the subcarrier index. In the remainder, it is assumed that the transmit signal-to-noise ratio is included in H(k).
 
     The MU-SINR of first  113  and second radio channel  114 ,  S 1   MU    and  S 2   MU   , may be derived from the following expression for the demodulated signals at first UE  111  and second UE  112 , μ 1 (k) and μ 2 (k), respectively, 
                       (             μ   1     ⁡     (   k   )                   μ   2     ⁡     (   k   )             )     =         [           H   H     ⁡     (   k   )       ⁢     H   ⁡     (   k   )         +     I   ⁡     (   k   )         ]       -   1       ⁢     (             h   1   H     ⁡     (   k   )                   h   2   H     ⁡     (   k   )             )     ⁢       h   1     ⁡     (   k   )           ,           (   2   )               
which, after some algebra, can be written as
 
     
       
         
           
             
               
                 
                   
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                                               ⁢ 
                                               
                                                 
                                                   h 
                                                   1 
                                                 
                                                 ⁡ 
                                                 
                                                   ( 
                                                   k 
                                                   ) 
                                                 
                                               
                                             
                                             + 
                                             1 
                                           
                                           ) 
                                         
                                         ⁢ 
                                         
                                           ( 
                                           
                                             
                                               
                                                 
                                                   h 
                                                   2 
                                                   H 
                                                 
                                                 ⁡ 
                                                 
                                                   ( 
                                                   k 
                                                   ) 
                                                 
                                               
                                               ⁢ 
                                               
                                                 
                                                   h 
                                                   2 
                                                 
                                                 ⁡ 
                                                 
                                                   ( 
                                                   k 
                                                   ) 
                                                 
                                               
                                             
                                             + 
                                             1 
                                           
                                           ) 
                                         
                                       
                                       - 
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         
                                           h 
                                           1 
                                           H 
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                       ⁢ 
                                       
                                         
                                           h 
                                           2 
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                       ⁢ 
                                       
                                         
                                           h 
                                           2 
                                           H 
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                       ⁢ 
                                       
                                         
                                           h 
                                           1 
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     The MU-SINR for first radio channel  113  can be expressed as 
                         S   1   MU     _     =         1   N     ⁢       ∑     k   =   0       N   -   1       ⁢       μ   1     ⁡     (   k   )               1   N     ⁢       ∑     k   =   0       N   -   1       ⁢     [     1   -       μ   1     ⁡     (   k   )         ]             ,           (   4   )               
where the sum extends over all N subcarriers. In Eq. (4), the inter-cell interference is treated as white noise, which is a reasonable approximation since MU-MIMO is typically used in the high-SINR region where intra-cell interference is dominant.
 
     Using Eq. (3), the MU-SINR for first radio channel  113 , Eq. (4), may be written as 
     
       
         
           
             
               
                 
                   
                     
                       S 
                       1 
                       MU 
                     
                     _ 
                   
                   = 
                   
                     
                       
                         
                           1 
                           N 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               0 
                             
                             
                               N 
                               - 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               
                                 
                                    
                                   
                                     
                                       h 
                                       1 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                    
                                 
                                 2 
                               
                               + 
                               
                                 
                                   
                                      
                                     
                                       
                                         h 
                                         1 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                      
                                   
                                   2 
                                 
                                 ⁢ 
                                 
                                   
                                      
                                     
                                       
                                         h 
                                         2 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                      
                                   
                                   2 
                                 
                               
                               - 
                               
                                 
                                   
                                     h 
                                     1 
                                     H 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     h 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     h 
                                     2 
                                     H 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     h 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   ( 
                                   
                                     
                                       
                                          
                                         
                                           
                                             h 
                                             1 
                                           
                                           ⁡ 
                                           
                                             ( 
                                             k 
                                             ) 
                                           
                                         
                                          
                                       
                                       2 
                                     
                                     + 
                                     1 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       
                                          
                                         
                                           
                                             h 
                                             2 
                                           
                                           ⁡ 
                                           
                                             ( 
                                             k 
                                             ) 
                                           
                                         
                                          
                                       
                                       2 
                                     
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     h 
                                     1 
                                     H 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     h 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     h 
                                     2 
                                     H 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     h 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           1 
                           N 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               0 
                             
                             
                               N 
                               - 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               
                                 
                                    
                                   
                                     
                                       h 
                                       2 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                    
                                 
                                 2 
                               
                               + 
                               1 
                             
                             
                               
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                              
                                             
                                               
                                                 h 
                                                 1 
                                               
                                               ⁡ 
                                               
                                                 ( 
                                                 k 
                                                 ) 
                                               
                                             
                                              
                                           
                                           2 
                                         
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     
                                       ( 
                                       
                                         
                                           
                                              
                                             
                                               
                                                 h 
                                                 2 
                                               
                                               ⁡ 
                                               
                                                 ( 
                                                 k 
                                                 ) 
                                               
                                             
                                              
                                           
                                           2 
                                         
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     - 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         h 
                                         1 
                                         H 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       
                                         h 
                                         2 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       
                                         h 
                                         2 
                                         H 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       
                                         h 
                                         1 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Now, the MU-SINR for first UE  111  after power control in accordance with an embodiment of the invention,  S 1   MU,pc   , can be calculated by replacing h 1 →√{square root over (α 1 )}h 1  and h 2 →√{square root over (α 2 )}h 2  in Eq. (5), i.e., 
     
       
         
           
             
               
                 
                   
                     
                       S 
                       1 
                       
                         MU 
                         , 
                         pc 
                       
                     
                     _ 
                   
                   = 
                   
                     
                       
                         
                           1 
                           N 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               0 
                             
                             
                               N 
                               - 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               
                                 
                                   
                                     
                                       
                                         α 
                                         1 
                                       
                                       ⁢ 
                                       
                                         
                                            
                                           
                                             
                                               h 
                                               1 
                                             
                                             ⁡ 
                                             
                                               ( 
                                               k 
                                               ) 
                                             
                                           
                                            
                                         
                                         2 
                                       
                                     
                                     + 
                                     
                                       
                                         α 
                                         1 
                                       
                                       ⁢ 
                                       
                                         α 
                                         2 
                                       
                                       ⁢ 
                                       
                                         
                                            
                                           
                                             
                                               h 
                                               1 
                                             
                                             ⁡ 
                                             
                                               ( 
                                               k 
                                               ) 
                                             
                                           
                                            
                                         
                                         2 
                                       
                                       ⁢ 
                                       
                                         
                                            
                                           
                                             
                                               h 
                                               2 
                                             
                                             ⁡ 
                                             
                                               ( 
                                               k 
                                               ) 
                                             
                                           
                                            
                                         
                                         2 
                                       
                                     
                                     - 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       α 
                                       1 
                                     
                                     ⁢ 
                                     
                                       α 
                                       2 
                                     
                                     ⁢ 
                                     
                                       
                                         h 
                                         1 
                                         H 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       
                                         h 
                                         2 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       
                                         h 
                                         2 
                                         H 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       
                                         h 
                                         1 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                             α 
                                             1 
                                           
                                           ⁢ 
                                           
                                             
                                                
                                               
                                                 
                                                   h 
                                                   1 
                                                 
                                                 ⁡ 
                                                 
                                                   ( 
                                                   k 
                                                   ) 
                                                 
                                               
                                                
                                             
                                             2 
                                           
                                         
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     
                                       ( 
                                       
                                         
                                           
                                             α 
                                             2 
                                           
                                           ⁢ 
                                           
                                             
                                                
                                               
                                                 
                                                   h 
                                                   2 
                                                 
                                                 ⁡ 
                                                 
                                                   ( 
                                                   k 
                                                   ) 
                                                 
                                               
                                                
                                             
                                             2 
                                           
                                         
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     - 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       α 
                                       1 
                                     
                                     ⁢ 
                                     
                                       α 
                                       2 
                                     
                                     ⁢ 
                                     
                                       
                                         h 
                                         1 
                                         H 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       
                                         h 
                                         2 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       
                                         h 
                                         2 
                                         H 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       
                                         h 
                                         1 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           1 
                           N 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               0 
                             
                             
                               N 
                               - 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               
                                 
                                   α 
                                   2 
                                 
                                 ⁢ 
                                 
                                   
                                      
                                     
                                       
                                         h 
                                         2 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                      
                                   
                                   2 
                                 
                               
                               + 
                               1 
                             
                             
                               
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                             α 
                                             1 
                                           
                                           ⁢ 
                                           
                                             
                                                
                                               
                                                 
                                                   h 
                                                   1 
                                                 
                                                 ⁡ 
                                                 
                                                   ( 
                                                   k 
                                                   ) 
                                                 
                                               
                                                
                                             
                                             2 
                                           
                                         
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     + 
                                     
                                       ( 
                                       
                                         
                                           
                                             α 
                                             2 
                                           
                                           ⁢ 
                                           
                                             
                                                
                                               
                                                 
                                                   h 
                                                   2 
                                                 
                                                 ⁡ 
                                                 
                                                   ( 
                                                   k 
                                                   ) 
                                                 
                                               
                                                
                                             
                                             2 
                                           
                                         
                                         + 
                                         1 
                                       
                                       ) 
                                     
                                     - 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       α 
                                       1 
                                     
                                     ⁢ 
                                     
                                       α 
                                       2 
                                     
                                     ⁢ 
                                     
                                       
                                         h 
                                         1 
                                         H 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       
                                         h 
                                         2 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       
                                         h 
                                         2 
                                         H 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       
                                         h 
                                         1 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Note that α 1  and α 2  are defined to be linear power adjustment values, i.e., the transmission power P 1  of first UE  111  is adjusted to be α 1 P 1  after power control, and correspondingly for second UE  112 . 
     In order to simplify Eq. (6), an approximation is made which is first derived for the simpler scenario of SU-SIMO transmissions, for which the per-UE SINR can be expressed as 
                         S   SU     _     =         1   N     ⁢       ∑     k   =   0       N   -   1       ⁢           ⁢              h   ⁡     (   k   )            2                h   ⁡     (   k   )            2     +   1               1   N     ⁢       ∑     k   =   0       N   -   1       ⁢           ⁢     1              h   ⁡     (   k   )            2     +   1               ,           (   7   )               
where h(k) is the channel vector and N is the number of subcarriers. Taking into account the power adjustment value α, i.e., replacing h→√{square root over (α)}h, yields
 
                         S   SU     _     =     α   ×         1   N     ⁢       ∑     k   =   0       N   -   1       ⁢           ⁢              h   ⁡     (   k   )            2         α   ⁢            h   ⁡     (   k   )            2       +   1               1   N     ⁢       ∑     k   =   0       N   -   1       ⁢           ⁢     1       α   ⁢            h   ⁡     (   k   )            2       +   1                 ,           (   8   )               
which may be approximated by
 
     
       
         
           
             
               
                 
                   
                     
                       S 
                       SU 
                     
                     _ 
                   
                   ≅ 
                   
                     α 
                     × 
                     
                       
                         
                           
                             1 
                             N 
                           
                           ⁢ 
                           
                             
                               ∑ 
                               
                                 k 
                                 = 
                                 0 
                               
                               
                                 N 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 
                                    
                                   
                                     h 
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                    
                                 
                                 2 
                               
                               
                                 
                                   
                                      
                                     
                                       h 
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                      
                                   
                                   2 
                                 
                                 + 
                                 1 
                               
                             
                           
                         
                         
                           
                             1 
                             N 
                           
                           ⁢ 
                           
                             
                               ∑ 
                               
                                 k 
                                 = 
                                 0 
                               
                               
                                 N 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               1 
                               
                                 
                                   
                                      
                                     
                                       h 
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                      
                                   
                                   2 
                                 
                                 + 
                                 1 
                               
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     In Eq. (9), it is assumed that approximating the denominators (α|h(k)| 2 +1) by (|h(k)| 2 +1) has only negligible impact on the ratio in Eq. (9), which is mainly dictated by the two numerators, |h(k)| 2  and 1. 
     Applying the same approximation as for the SU-SIMO case, Eq. (9), to Eq. (6), the MU-SINR for first UE  111  after power control, Eq. (6), can be calculated as 
                         S   1     MU   ,   pc       _     ≅         1   N     ⁢       ∑     k   =   0       N   -   1       ⁢           ⁢           α   1     ⁢       S   1     ⁡     (   k   )         +       α   1     ⁢     α   2     ⁢       S   1     ⁡     (   k   )       ⁢       S   2     ⁡     (   k   )         -       α   1     ⁢     α   2     ⁢     Δ   ⁡     (   k   )       ⁢       S   1     ⁡     (   k   )       ⁢       S   2     ⁡     (   k   )             R   ⁡     (   k   )                 1   N     ⁢       ∑     k   =   0       N   -   1       ⁢           ⁢           α   2     ⁢       S   2     ⁡     (   k   )         +   1       R   ⁡     (   k   )                 ,           (   10   )               
where the following definitions for per-subcarrier values have been used:
 
     
       
         
           
             
               
                 
                   
                     
                       
                         S 
                         1 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     ≡ 
                     
                       
                         h 
                         1 
                         H 
                       
                       ⁢ 
                       
                         h 
                         1 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   
                     11 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     a 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         S 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     ≡ 
                     
                       
                         h 
                         2 
                         H 
                       
                       ⁢ 
                       
                         h 
                         2 
                       
                     
                   
                   , 
                   and 
                 
               
               
                 
                   ( 
                   
                     11 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     b 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       Δ 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     ≡ 
                     
                       
                         
                           h 
                           1 
                           H 
                         
                         ⁢ 
                         
                           h 
                           2 
                         
                         ⁢ 
                         
                           h 
                           2 
                           H 
                         
                         ⁢ 
                         
                           h 
                           1 
                         
                       
                       
                         
                           h 
                           1 
                           H 
                         
                         ⁢ 
                         
                           h 
                           1 
                         
                         ⁢ 
                         
                           h 
                           2 
                           H 
                         
                         ⁢ 
                         
                           h 
                           2 
                         
                       
                     
                   
                   , 
                   and 
                 
               
               
                 
                   ( 
                   
                     11 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     c 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     R 
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   ≡ 
                   
                     
                       
                         ( 
                         
                           
                             
                               S 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           + 
                           1 
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               S 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           + 
                           1 
                         
                         ) 
                       
                     
                     - 
                     
                       
                         Δ 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           S 
                           1 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           
                             S 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     Eq. (10) may be rearranged to read 
     
       
         
           
             
               
                 
                   
                     
                       S 
                       1 
                       
                         MU 
                         , 
                         pc 
                       
                     
                     _ 
                   
                   ≅ 
                   
                     
                       
                         
                           
                             
                               α 
                               1 
                             
                             ⁢ 
                             
                               1 
                               N 
                             
                             ⁢ 
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   0 
                                 
                                 
                                   N 
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   
                                     S 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 
                                   R 
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               1 
                               N 
                             
                             ⁢ 
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   0 
                                 
                                 
                                   N 
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 1 
                                 
                                   R 
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         + 
                         
                             
                         
                         ⁢ 
                         
                           
                             
                               α 
                               1 
                             
                             ⁢ 
                             
                               α 
                               2 
                             
                             ⁢ 
                             
                               1 
                               N 
                             
                             ⁢ 
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   0 
                                 
                                 
                                   N 
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               S 
                                               1 
                                             
                                             ⁡ 
                                             
                                               ( 
                                               k 
                                               ) 
                                             
                                           
                                           ⁢ 
                                           
                                             
                                               S 
                                               2 
                                             
                                             ⁡ 
                                             
                                               ( 
                                               k 
                                               ) 
                                             
                                           
                                         
                                         - 
                                       
                                     
                                   
                                   
                                     
                                       
                                         
                                           Δ 
                                           ⁡ 
                                           
                                             ( 
                                             k 
                                             ) 
                                           
                                         
                                         ⁢ 
                                         
                                           
                                             S 
                                             1 
                                           
                                           ⁡ 
                                           
                                             ( 
                                             k 
                                             ) 
                                           
                                         
                                         ⁢ 
                                         
                                           
                                             S 
                                             2 
                                           
                                           ⁡ 
                                           
                                             ( 
                                             k 
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                 
                                 
                                   R 
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               1 
                               N 
                             
                             ⁢ 
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   0 
                                 
                                 
                                   N 
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 1 
                                 
                                   R 
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               α 
                               2 
                             
                             ⁢ 
                             
                               1 
                               N 
                             
                             ⁢ 
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   0 
                                 
                                 
                                   N 
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   
                                     S 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 
                                   R 
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               1 
                               N 
                             
                             ⁢ 
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   0 
                                 
                                 
                                   N 
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 1 
                                 
                                   R 
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             1 
                             N 
                           
                           ⁢ 
                           
                             
                               ∑ 
                               
                                 k 
                                 = 
                                 0 
                               
                               
                                 N 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               1 
                               
                                 R 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     Using the following definitions for expressing the per-UE values for the first SU-SINR  S 1   , the second SU-SINR  S 2   , and channel orthogonality  Δ , in terms of their per-subcarrier equivalents S 1 (k), S 2 (k), and Δ(k), Eqs. (11a-c) and (12), respectively, 
                         S   _     1     ≡       1   N     ⁢       ∑     k   =   0       N   -   1       ⁢           ⁢         S   1     ⁡     (   k   )         R   ⁡     (   k   )               ,           (     14   ⁢           ⁢   a     )                     S   _     2     ≡       1   N     ⁢       ∑     k   =   0       N   -   1       ⁢           ⁢         S   2     ⁡     (   k   )         R   ⁡     (   k   )               ,   and           (     14   ⁢           ⁢   b     )                   Δ   _     ≡     1   -           ∑     k   =   0       N   -   1       ⁢           ⁢             S   1     ⁡     (   k   )       ⁢       S   2     ⁡     (   k   )         -       Δ   ⁡     (   k   )       ⁢       S   1     ⁡     (   k   )       ⁢       S   2     ⁡     (   k   )             R   ⁡     (   k   )               1   N     ⁢       ∑     k   =   0       N   -   1       ⁢           ⁢     1     R   ⁡     (   k   )                     S   1     ⁢     S   2       _           ,           (     14   ⁢           ⁢   c     )               
Eq. (13) can be written as
 
     
       
         
           
             
               
                 
                   
                     
                       S 
                       1 
                       
                         MU 
                         , 
                         pc 
                       
                     
                     _ 
                   
                   ≅ 
                   
                     
                       
                         α 
                         1 
                       
                       ⁢ 
                       
                         
                           S 
                           _ 
                         
                         1 
                       
                     
                     - 
                     
                       
                         
                           
                             Δ 
                             _ 
                           
                           ⁢ 
                           
                             α 
                             1 
                           
                           ⁢ 
                           
                             α 
                             2 
                           
                           ⁢ 
                           
                             
                               
                                 S 
                                 1 
                               
                               ⁢ 
                               
                                 S 
                                 2 
                               
                             
                             _ 
                           
                         
                         
                           
                             
                               α 
                               2 
                             
                             ⁢ 
                             
                               
                                 S 
                                 _ 
                               
                               2 
                             
                           
                           + 
                           1 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     In general,  S 1   ,  S 2   , and  Δ , are functions of S 1 (k), S 2  (k), and Δ(k), respectively, averaged over all subcarriers k allocated to a specific UE. The exact form of transforming per-subcarrier values to per-UE values may depend on implementation. Therefore, the transformation presented here is only an example, and the present invention is not limited to this particular way of transforming per-subcarrier values to per-UE values. 
     Eq. (15) is the expression used for calculating the MU-SINR for first UE  111  after power control. A corresponding expression may be derived for the MU-SINR for second UE  112  after power control, 
     
       
         
           
             
               
                 
                   
                     
                       S 
                       2 
                       
                         MU 
                         , 
                         pc 
                       
                     
                     _ 
                   
                   ≅ 
                   
                     
                       
                         α 
                         2 
                       
                       ⁢ 
                       
                         
                           S 
                           _ 
                         
                         2 
                       
                     
                     - 
                     
                       
                         
                           
                             Δ 
                             _ 
                           
                           ⁢ 
                           
                             α 
                             1 
                           
                           ⁢ 
                           
                             α 
                             2 
                           
                           ⁢ 
                           
                             
                               
                                 S 
                                 1 
                               
                               ⁢ 
                               
                                 S 
                                 2 
                               
                             
                             _ 
                           
                         
                         
                           
                             
                               α 
                               1 
                             
                             ⁢ 
                             
                               
                                 S 
                                 _ 
                               
                               1 
                             
                           
                           + 
                           1 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     Using Eqs. (15) and (16), first and second power adjustment values α 1  and α 2  may be determined in accordance with embodiments of the invention, as is elucidated below. Further, Eqs. (15) and (16) may be used for calculating the UEs&#39; MU-SINRs after power control, and  S 1   MU,pc    and  S 2   MU,pc   . Optionally, these values may be taken into consideration during the scheduling process, as was described with reference to  FIG. 3 . 
     In accordance with an embodiment of the invention, the first and the second power adjustment value are jointly determined based on MU-SINR targets for the co-scheduled UEs. More specifically, a first MU-SINR target for first UE  111  may be expressed as φ 1   S 1   . Correspondingly, a second MU-SINR target for second UE  112  may be expressed as φ 2   S 2   . Using φ 1  and φ 2 , the first and the second MU-SINR target may be expressed in terms of the UEs&#39; respective SU-SINR, i.e., the SINRs before switching to MU-MIMO transmission mode. The targets may be set according to different criteria. For instance, the first and the second MU-SINR target may be set so as to maintain the UEs&#39; respective SINR as in SU transmission mode, i.e., φ 1 =1 and φ 2 =1. In that way, QoS fluctuations may be avoided. Alternatively, the first and the second MU-SINR target may be reduced, as compared to the SU-SINR values, so as to reduce harmful inter-cell interference, i.e., φ 1 &lt;1 and φ 2 &lt;1. 
     The problem of deriving equations for α 1  and α 2  amounts to setting target values for the UEs&#39; MU-SINR after power adjustment, i.e.,  S 1   MU,pc    and  S 2   MU,pc    (Eqs. (15) and (16)): 
                         φ   1     ⁢       S   _     1       =         α   1     ⁢       S   _     1       -           Δ   _     ⁢     α   1     ⁢     α   2     ⁢         S   1     ⁢     S   2       _             α   1     ⁢       S   _     2       +   1       ⁢           ⁢   and         ⁢           ⁢     
     ⁢           φ   2     ⁢       S   _     2       =         α   2     ⁢       S   _     2       -         Δ   _     ⁢     α   1     ⁢     α   2     ⁢         S   1     ⁢     S   2       _             α   2     ⁢       S   _     1       +   1           ,             (   17   )               
which may be rearranged to read
 
     
       
         
           
             
               
                 
                   
                     
                       φ 
                       1 
                     
                     
                       α 
                       1 
                     
                   
                   = 
                   
                     
                       1 
                       - 
                       
                         
                           
                             
                               Δ 
                               _ 
                             
                             ⁢ 
                             
                               α 
                               1 
                             
                             ⁢ 
                             
                               α 
                               2 
                             
                             ⁢ 
                             
                               
                                 S 
                                 2 
                               
                               _ 
                             
                           
                           
                             
                               
                                 α 
                                 1 
                               
                               ⁢ 
                               
                                 
                                   S 
                                   _ 
                                 
                                 2 
                               
                             
                             + 
                             1 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         and 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             φ 
                             2 
                           
                           
                             α 
                             2 
                           
                         
                       
                     
                     = 
                     
                       1 
                       - 
                       
                         
                           
                             
                               Δ 
                               _ 
                             
                             ⁢ 
                             
                               α 
                               1 
                             
                             ⁢ 
                             
                               α 
                               2 
                             
                             ⁢ 
                             
                               
                                 S 
                                 2 
                               
                               _ 
                             
                           
                           
                             
                               
                                 α 
                                 2 
                               
                               ⁢ 
                               
                                 
                                   S 
                                   _ 
                                 
                                 1 
                               
                             
                             + 
                             1 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     Replacing 1/α 1 →β 1  and 1/α 2 →β 2 , and combining the resulting equations, yields 
     
       
         
           
             
               
                 
                   
                     β 
                     2 
                   
                   = 
                   
                     
                       1 
                       
                         φ 
                         2 
                       
                     
                     - 
                     
                       
                         
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               S 
                               1 
                             
                           
                           _ 
                         
                         
                           
                             
                               φ 
                               2 
                             
                             ⁢ 
                             
                               
                                 S 
                                 _ 
                               
                               1 
                             
                           
                           + 
                           
                             
                               φ 
                               2 
                             
                             
                               φ 
                               1 
                             
                           
                           - 
                           
                             
                               
                                 φ 
                                 2 
                               
                               ⁢ 
                               
                                 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     S 
                                     2 
                                   
                                 
                                 _ 
                               
                             
                             
                               
                                 
                                   φ 
                                   1 
                                 
                                 ⁢ 
                                 
                                   
                                     S 
                                     2 
                                   
                                   _ 
                                 
                               
                               + 
                               
                                 
                                   φ 
                                   1 
                                 
                                 ⁢ 
                                 
                                   β 
                                   2 
                                 
                               
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     Eq. (19) is a quadratic equation in one variable which may be solved to obtain equations for the first power adjustment value,
 
α 1   =−b   1 +√{square root over ( b   1   2 −4α 1   c   1 )}/2α 1   (20a), with
 
α 1 =−φ 1 φ 2 (   S   2   +1/φ 2 )  (20b),
 
 b   1 =φ 1 φ 2 (   S   2   +1/φ 2 )(1/φ 1 −   S   1   )+ Δ (φ 1     S   1   −φ 2     S   2   )  (20c), and
 
 c   1 =φ 2     S   1   (   S   2   +1/φ 2 )(1− Δ )  (20d)
 
and the second power adjustment value,
 
α 2   =−b   2 +√{square root over ( b   2   2 −4α 2   c   2 )}/2α 2   (21a), with
 
α 2 =−φ 1 φ 2 (   S   1   +1/φ 1 )  (21b),
 
 b   2 =φ 1 φ 2 (   S   1   +1/φ 1 )(1/φ 2 −   S   2   )+ Δ (φ 2     S   2   −φ 1     S   1   )  (21c), and
 
 c   2 =φ 1     S   2   (   S   1   +1/φ 1 )(1− Δ )  (21d).
 
     Using Eqs. (20a-d) and (21a-d), the first and the second power adjustment value may easily be calculated if the MU-SINR targets, expressed by φ 1  and φ 2 , are known. The only input which is needed are the per-UE SU-SINR values for the first and the second radio channel,  S 1    and  S 2   , as well as the per-UE channel orthogonality  Δ , as defined by Eqs. (14a-c). These values may be determined based on instantaneous radio channel conditions, as was described hereinbefore. 
     In the following, another embodiment of the invention, for jointly determining the first and the second power adjustment value, is presented. More specifically, the first and the second power adjustment value are determined so as to maximize a transmission sum rate for the pair of UEs, i.e., the sum of the transmission rate over the first radio channel and that over the second radio channel, while maintaining a power budget constraint K. This is a way of optimizing the performance of MU-MIMO transmissions from a system point of view. The power budget constraint is used to avoid increasing inter-cell interference. 
     To this end, jointly determining α 1  and α 2  amounts to solving
 
max α     1     α     2     ≦K [1+   S   1   MU,pc   ][1+   S   2   MU,pc   ]  (22),
 
where the sum throughput is modeled as a product of two factors, one for each UE, wherein each factor has the form (1+SINR), corresponding to the Shannon capacity expression. K is a constant used to constrain the UEs&#39; transmit power in order to limit inter-cell interference, and is defined as
 
 K≡α   1 α 2   (23).
 
     In practice, the power constraint results in a vanishing sum of power control adjustments sent to the UEs. In other words, if the first UE increases its transmit power by a certain amount, the second UE decreases its transmit power by the same amount. 
     Using Eqs. (15) and (16), Eq. (22) may be written as 
     
       
         
           
             
               
                 
                   
                     max 
                     
                       
                         
                           α 
                           1 
                         
                         ⁢ 
                         
                           α 
                           2 
                         
                       
                       ≤ 
                       K 
                     
                   
                   ⁢ 
                   
                     
                       
                         [ 
                         
                           1 
                           + 
                           
                             
                               α 
                               1 
                             
                             ⁢ 
                             
                               
                                 
                                   S 
                                   _ 
                                 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     
                                       
                                         Δ 
                                         _ 
                                       
                                       ⁢ 
                                       
                                         α 
                                         2 
                                       
                                       ⁢ 
                                       
                                         
                                           S 
                                           _ 
                                         
                                         2 
                                       
                                     
                                     
                                       
                                         
                                           α 
                                           2 
                                         
                                         ⁢ 
                                         
                                           
                                             S 
                                             _ 
                                           
                                           2 
                                         
                                       
                                       + 
                                       1 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         ] 
                       
                       ⁡ 
                       
                         [ 
                         
                           1 
                           + 
                           
                             
                               α 
                               2 
                             
                             ⁢ 
                             
                               
                                 
                                   S 
                                   _ 
                                 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     
                                       
                                         Δ 
                                         _ 
                                       
                                       ⁢ 
                                       
                                         α 
                                         1 
                                       
                                       ⁢ 
                                       
                                         
                                           S 
                                           _ 
                                         
                                         1 
                                       
                                     
                                     
                                       
                                         
                                           α 
                                           1 
                                         
                                         ⁢ 
                                         
                                           
                                             S 
                                             _ 
                                           
                                           1 
                                         
                                       
                                       + 
                                       1 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         ] 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
     Eq. (24) may be solved by replacing (1− Δ )→ξ, yielding 
                       max       α   1     ,     α   2         ⁢             (     1   +   ξ     )     ⁢     α   2     ⁢       S   2     _       +   2           α   2     ⁢       S   2     _       +   1       ·           (     1   +   ξ     )     ⁢     α   1     ⁢       S   1     _       +   2           α   1     ⁢       S   1     _       +   1           ,           (   25   )               
which is equal to
 
     
       
         
           
             
               
                 
                   
                     max 
                     
                       
                         α 
                         1 
                       
                       , 
                       
                         α 
                         2 
                       
                     
                   
                   ⁢ 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               ξ 
                             
                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 K 
                                 ⁢ 
                                 
                                   
                                     S 
                                     _ 
                                   
                                   1 
                                 
                                 ⁢ 
                                 
                                   
                                     S 
                                     _ 
                                   
                                   2 
                                 
                               
                               + 
                               
                                 2 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   α 
                                   1 
                                 
                                 ⁢ 
                                 
                                   
                                     S 
                                     _ 
                                   
                                   1 
                                 
                               
                               + 
                               
                                 2 
                                 ⁢ 
                                 
                                   α 
                                   2 
                                 
                                 ⁢ 
                                 
                                   
                                     S 
                                     _ 
                                   
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                         + 
                         4 
                       
                       
                         
                           K 
                           ⁢ 
                           
                             
                               S 
                               _ 
                             
                             1 
                           
                           ⁢ 
                           
                             
                               S 
                               _ 
                             
                             2 
                           
                         
                         + 
                         
                           
                             α 
                             1 
                           
                           ⁢ 
                           
                             
                               S 
                               _ 
                             
                             1 
                           
                         
                         + 
                         
                           
                             α 
                             2 
                           
                           ⁢ 
                           
                             
                               S 
                               _ 
                             
                             2 
                           
                         
                         + 
                         1 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
     The latter is equivalent to
 
min α     1     ,α     2   α 1   S 1   +α 2   S 2     (27).
 
     Thus, the sum throughput is maximized, while maintaining the power constraint, under the condition that
 
α 1   S 1   =α 2   S 2     (28),
 
which yields, using Eq. (23),
 
α 1 =√{square root over ( K     S   2   /   S   1   )} and α 2 =√{square root over ( K     S   1   /   S   2   )}  (29).
 
     Using Eqs. (29), the first and the second power adjustment value may easily be calculated using the power budget constraint K as well as the per-UE SU-SINRs for the first and the second UE,  S 1    and  S 2   , as an input. The power budget constraint K may be chosen so as to maintain the same inter-cell interference as in SU transmission mode (K=1), to reduce interference (K&lt;1), or to increase the sum throughput (K&gt;1). 
     In the following, an eNode-B in accordance with an embodiment of the invention is described with reference to  FIG. 4 . Note that  FIG. 4  illustrates only those parts of an eNode-B which are necessary for describing the present invention, whereas other parts are omitted for the sake of simplicity. 
     Typically, an eNode-B, comprises multiple antennas, transmitters and receivers, circuitry or processing means for data processing, and interfaces for interconnecting the eNode-B with other eNode-Bs or a core network. The circuitry or processing means for data processing is arranged for implementing an LTE protocol stack, such as protocol stack  400  illustrated in  FIG. 4 . 
       FIG. 4  illustrates a protocol stack  400  of an eNode-B capable of supporting uplink MU-MIMO transmissions from a pair of co-scheduled UEs, as was described with reference to  FIG. 1 . Protocol stack  400  has certain features in common with known protocol stack  200 , described with reference to  FIG. 2 . More specifically, protocol stack  400  comprises a physical layer  401  and a MAC layer  402 . Physical layer  401  comprises a channel condition estimation unit  411  which, based on instantaneous channel condition information  421  determined from SRS or DMRS, estimates and signals SU-SINR information  423  to scheduler  412  comprised in MAC layer  402 . Physical layer  401  further comprises a power control unit  414  for controlling the UEs&#39; transmission power by signaling control information  426  to UEs in communication with the eNode-B. 
     Protocol stack  400  differs from protocol stack  200  in that channel condition estimation unit  411  is further arranged for estimating the channel orthogonality from instantaneous channel condition information  421  and signaling  424  the estimated channel orthogonality to scheduler  412 . 
     Protocol stack  400  further comprises a multi-user power control (MUPC) unit  413 , which in  FIG. 4  is illustrated as being arranged with scheduler  412 . MUPC unit  413  is arranged for, if a least one pair of UEs is scheduled for uplink MU-MIMO transmissions, estimating an MU-SINR for each co-scheduled UE, i.e., and for adjusting the transmission power of the co-scheduled UEs, as was described hereinbefore. In particular, MUPC unit  413  is arranged for jointly determining the first and the second power adjustment value based on the first and the second SU-SINR and the channel orthogonality. For instance, MUPC unit  413  may be arranged for calculating the first and the second power adjustment value, using Eqs. (20a-d) and (21a-d), if MU-SINR targets for the co-scheduled UEs are known. The MU-SINR targets may be set according to different criteria, as was discussed hereinbefore. Alternatively, MUPC unit  413  may be arranged for calculating the first and the second power adjustment value using Eqs. (29), if the power budget constraint K is known. The power budget constraint may be chosen so as to maintain the same inter-cell interference as in SU transmission mode (K=1), to reduce interference (K&lt;1), or to increase the sum throughput (K&gt;1). 
     MUPC unit  413  is further arranged for signaling power control information  425  to power control unit  414 , which, in turn, controls the transmission power of the co-scheduled UEs by signaling power control commands  426 . In particular, the first and second power adjustment values, which are linear values, are converted to power control commands in accordance with 3GPP specifications and signaled to the UEs which are scheduled for MU-MIMO transmissions. Since the power control commands in LTE are defined to be 2-bit commands, which may represent any one of four discrete values expressing a power adjustment of {−1, 0, 1, 3} dB, α 1  and α 2  should be quantized accordingly. 
     Scheduler  412  is arranged for assigning schedule blocks, as was described with reference to  FIG. 1 , to UEs which are engaged in communication with eNode-B  110 . Scheduling is performed, if in SU transmission mode, based on SU-SINR information  423  received from SINR estimation unit  411 , in addition to other information, such as an amount of data to be transmitted, a type of data to be transmitted, QoS requirements, and the like. When in MU-MIMO mode, scheduling is performed based on MU-SINR information received from MUPC unit  413 , in addition to other information, such as an amount of data to be transmitted, a type of data to be transmitted, QoS requirements, and the like. The decision, whether to schedule a pair of UEs for MU-MIMO transmissions or not, is taken by scheduler  412 . 
     The person skilled in the art realizes that the present invention by no means is limited to the embodiments described above. On the contrary, many modifications and variations are possible within the scope of the appended claims. For example, the MUPC unit may be arranged in the physical layer of an LTE protocol stack. 
     In conclusion, a method of power control for MU-MIMO transmissions between a pair of mobile terminals and a radio base station is provided. The method comprises determining SINRs for the radio channels between the mobile terminals and the radio base station, determining a channel orthogonality between the radio channels, and jointly determining, based on the SINRs and the channel orthogonality, power adjustment values for the mobile terminals. The present invention makes use of an understanding that the system gain resulting from MU-MIMO transmissions may be improved by optimizing the transmission power of the co-scheduled mobile terminals. For instance, the power adjustment values may be determined so as to attain certain SINR targets. Alternatively, the power adjustment values may be determined so as to maximize the throughput while maintaining a power budget constraint. Further, a radio base station for MU-MIMO transmissions is provided.