Patent Publication Number: US-2022240200-A1

Title: Controlling Total Average Transmission Power of a Radio Base Station

Description:
TECHNICAL FIELD 
     Embodiments presented herein relate to a method, a control device, a computer program, and a computer program product for controlling total average transmission power of a radio base station. 
     BACKGROUND 
     When any radio equipment is to be deployed, regulatory radio frequency (RF) electromagnetic field (EMF) exposure requirements should be accounted for. These RF EMF exposure regulations may typically be based on the guidelines from the International Commission on Non-Ionizing Radiation Protection (ICNIRP) but may take different forms in some countries and regions. The aim of RF EMF exposure regulations is to ensure that human exposure to RF energy is kept within prescribed limits, which typically have been set with wide safety margins. 
     Some newly developed base stations and other radio equipment are equipped with so-called advanced antenna systems (AAS). These antenna systems increase the capacity and/or coverage compared to traditionally used antenna system by addition of one or more antenna arrays. In turn, this enables the simultaneous transmission of parallel data streams between a base station on the network side and a terminal device at the user-side by means of so-called multiple-input-multiple-output (MIMO) transmission. 
     For base stations and other radio equipment having AAS with a large number of antenna elements in order to achieve a high directivity, there may be a large maximum beamforming gain. A consequence of a large beamforming gain is typically that the radiated power is concentrated in directional beams, meaning that the Equivalent Isotropic Radiated Power (EIRP) rating of the base station, i.e. the power radiated from an antenna with unity antenna gain in all directions, is increased as compared to the situation without AAS. 
     The RF EMF exposure limitations are typically expressed in terms of the power density (in units of W/m 2 ) which in the far field is proportional to the EIRP. Consequently, the EIRP can be used to determine the power density in the far field. The ICNIRP and other RF EMF exposure limitations are usually expressed in terms of average power density over a specified averaging time interval T. This means that the momentary power density can be higher during a shorter time than T, however the time-averaged power density over any time period of duration T must be below the specified limit. To maintain a certain RF EMF compliance boundary or exclusion zone, that is smaller than what is obtained using the maximum EIRP of the AAS, the time-averaged total transmit power then needs to be controlled to be less than an average power threshold that is computed based on the RF exposure limitations and the selected exclusion zone. In cases where more than one power source share the same AAS or where several AASs are co-sited and aligned, the threshold may have to be computed in terms of the combined transmitted power or EIRP of the site. 
     Hence, there may be a need for efficient control of the average power or EIRP for base stations and other radio equipment. 
     SUMMARY 
     An object of embodiments herein is to provide efficient control of radio power sources of base stations and other radio equipment, so that certain RF EMF exclusion zones are maintained by the controlled time-averaged powers of the base stations and radio equipment. 
     This objective is generally solved by mechanisms performed by a control device for controlling total average transmission power of a radio base station. 
     According to a first aspect there is presented a method for controlling total average transmission power of a radio base station. The method is performed by a control device. The method comprises performing, for a current discrete time value t, control of total average transmission power  P tot   (t) of the radio base station according to a back-off power control loop. The total average transmission power  P tot   (t) is computed over an averaging time window T of the present value of momentary transmission power and the N−1 values of momentary transmission power preceding the present value of momentary transmission power. The method comprises evaluating, for a future discrete time value less than, or equal to, t+T, the total average transmission power, assuming that values of momentary transmission power for all discrete time values from t up to t+T, starting at the next discrete time value t+1, is limited to a minimum value of said momentary transmission power. The method comprises limiting the momentary transmission power to the minimum value for at least the next future discrete time value when the evaluated total average transmission power, for any of the future discrete time values, exceeds a power threshold value based on a regulatory limit. 
     According to a second aspect there is presented a control device for controlling total average transmission power of a radio base station. The control device comprises processing circuitry. The processing circuitry is configured to cause the control device to perform, for a current discrete time value t, control of total average transmission power  P tot   (t) of the radio base station according to a back-off power control loop.  The total average transmission power  P tot   (t) is computed over an averaging time window T of the present value of momentary transmission power and the N−1 values of momentary transmission power preceding the present value of momentary transmission power. The processing circuitry is configured to cause the control device to evaluate, for a future discrete time value less than, or equal to, t+T, the total average transmission power, assuming that values of momentary transmission power for all discrete time values from t up to t+T, starting at the next discrete time value t+1, is limited to a minimum value of said momentary transmission power. The processing circuitry is configured to cause the control device to limit the momentary transmission power to the minimum value for at least the next future discrete time value when the evaluated total average transmission power, for any of the future discrete time values, exceeds a power threshold value based on a regulatory limit. 
     According to a third aspect there is presented a control device for controlling total average transmission power of a radio base station. The control device comprises a control module configured to perform, fofa s t discrete time value t, control of total average transmission power  P tot   (t) of the radio base station according to a back-off power control loop. The total average transmission power  P tot   (t) is computed over an averaging time window T of the present value of momentyART transmission power and the N−1 values of momentary transmission power preceding the present value of momentary transmission power. The control device comprises an evaluate module configured to evaluate, for a future discrete time value less than, or equal to, t+T, the total average transmission power, assuming that values of momentary transmission power for all discrete time values from t up to t+T, starting at the next discrete time value t+1, is limited to a minimum value of said momentary transmission power. The control device comprises a limit module configured limit the momentary transmission power to the minimum value for at least the next future discrete time value when the evaluated total average transmission power, for any of the future discrete time values, exceeds a power threshold value based on a regulatory limit. 
     According to a fourth aspect there is presented a computer program for controlling total average transmission power of a radio base station, the computer program comprising computer program code which, when run on a control device, causes the control device to perform a method according to the first aspect. 
     According to a fifth aspect there is presented a computer program product comprising a computer program according to the fourth aspect and a computer readable storage medium on which the computer program is stored. The computer readable storage medium could be a non-transitory computer readable storage medium. 
     Advantageously this method, these control devices, this computer program and this computer program product enable efficient control of the total average transmission power of the radio base station. 
     Advantageously this method, these control devices, this computer program and this computer program product enable the total average transmission power to always be within the regulatory limit. 
     Advantageously this method, these control devices, this computer program and this computer program product require only a comparatively low computational complexity for controlling the total average transmission power of the radio base station. 
     Other objectives, features and advantages of the enclosed embodiments will be apparent from the following detailed disclosure, from the attached claims as well as from the drawings. 
     Generally, all terms used in the claims are to be interpreted according to their ordinary meaning in the technical field, unless explicitly defined otherwise herein. All references to “a/an/the element, apparatus, component, means, module, step, etc.” are to be interpreted openly as referring to at least one instance of the element, apparatus, component, means, module, step, etc., unless explicitly stated otherwise. The steps of any method disclosed herein do not have to be performed in the exact order disclosed, unless explicitly stated. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The inventive concept is now described, by way of example, with reference to the accompanying drawings, in which: 
         FIG. 1  is a schematic diagram illustrating a communications network according to embodiments; 
         FIG. 2  is a block diagram of a control device according to an embodiment; 
         FIGS. 3, 7, and 8 , show simulation results according to embodiments 
         FIGS. 4, and 6  are flowcharts of methods according to embodiments; 
         FIG. 5  schematically illustrates averaging windows according to embodiments; 
         FIG. 9  is a schematic diagram showing functional units of a control device according to an embodiment; 
         FIG. 10  is a schematic diagram showing functional modules of a control device according to an embodiment; and 
         FIG. 11  shows one example of a computer program product comprising computer readable storage medium according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     The inventive concept will now be described more fully hereinafter with reference to the accompanying drawings, in which certain embodiments of the inventive concept are shown. This inventive concept may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided by way of example so that this disclosure will be thorough and complete, and will fully convey the scope of the inventive concept to those skilled in the art. Like numbers refer to like elements throughout the description. Any step or feature illustrated by dashed lines should be regarded as optional. 
       FIG. 1  is a schematic diagram illustrating a communications network  100  where embodiments presented herein can be applied. The communications network  100  could be a third generation (3G) telecommunications network, a fourth generation (4G) telecommunications network, or a fifth (5G) telecommunications network and support any 3GPP telecommunications standard, where applicable. 
     The communications network  100  comprises a control device  200  configured to control a radio base station  140  that, via a transmission and reception point (TRP)  170  comprising an antenna array, provides network access to at least one terminal device  160  in a radio access network  110 , thus enabling the terminal device  160  to communicate over a wireless link  150 . The radio access network  110  is operatively connected to a core network  120 . The core network  120  is in turn operatively connected to a service network  130 , such as the Internet. The terminal device  160  is thereby enabled to, via the radio base station  140 , access services of, and exchange data with, the service network  130 . 
     Examples of radio base stations  140  are radio access network nodes, base transceiver stations, Node Bs, evolved Node Bs, gNBs, access points, and access nodes, and backhaul nodes. Examples of terminal devices  160  are wireless devices, mobile stations, mobile phones, handsets, wireless local loop phones, user equipment (UE), smartphones, laptop computers, tablet computers, network equipped sensors, network equipped vehicles, and so-called Internet of Things devices. 
     The control device  200  might comprise, be collocated with, integrated with, or be in operational communications with, the radio base station  140 . 
       FIG. 2  is a block diagram of the control device  200  where feedback control has been enabled by a feedback control loop, in this disclosure denoted a back-off power control loop. In  FIG. 2 ,  P tot     ref  denotes the setpoint for the averaged power (typically slightly less than the computed threshold value for the averaged power, which shall not be exceeded), 1/s denotes the actuator dynamics with lower and upper limits inactive,  γ (t) denotes the scheduler limitation after lower and upper limitation (inactive in  FIG. 2 ), and P max,site  denotes the maximal momentary total power of the radio transmitter of the radio base station  140 . Further, w(s) denotes a disturbance representing predicted power errors, 1/(sT+1) represents an autoregressive simplified model of the averaging,  P tot   (s) denotes the averaged total power, and e(s) denotes a measurement disturbance. All quantities are in  FIG. 2  expressed in the Laplace transform domain, which is allowed since the feedback control mechanism design is performed with constraints inactive. Neither w(s) nor e(s) are a part of the herein disclosed inventive concept, but are only shown to provide a model for controller design. 
     In some aspects the controller block is given by: 
         u ( s )= CT (1+ T   D   s )(   P   tot     ref   −     P   tot   ( s )). 
     Here, u(s) is the control signal. A controller implementing this controller block is of proportional-derivative (PD) type. C denotes the proportional gain, and T D  the differentiation time. 
     The poles of the closed loop system of  FIG. 2  are given by the following second order equation: 
         s   2 +(1/ T+P   max,site   CT   D ) s+P   max,site   C= 0. 
     These poles govern the closed loop dynamics of the feedback control mechanism, the actuator mechanism, and the averaged power. In order to determine the proportional gain and the differentiation time, a closed loop polynomial with desired poles in −α 1  and −α 2  is specified as: 
         s   2 +(α 1 +α 2 ) s+α   1 α 2 =0.
 
     An identification of coefficients and solution of the resulting system of equations reveal that the proportional gain and differentiation time shall be selected as: 
     
       
         
           
             
               
                 C 
                 = 
                 
                   
                     
                       α 
                       1 
                     
                     ⁢ 
                     
                       α 
                       2 
                     
                   
                   
                     P 
                     * 
                   
                 
               
               , 
                 
               and 
             
             ⁢ 
             
 
             
               
                 T 
                 D 
               
               = 
               
                 
                   
                     
                       α 
                       1 
                     
                     + 
                     
                       α 
                       2 
                     
                     - 
                     
                       1 
                       T 
                     
                   
                   
                     
                       α 
                       1 
                     
                     ⁢ 
                     
                       α 
                       2 
                     
                   
                 
                 . 
               
             
           
         
       
     
     A reason for this choice is that a system with two negative real poles can be expected to be well damped, which is a result of a significant differentiation action. 
     To implement the feedback control mechanism,  P tot     ref ,  P tot   (t) and  {dot over (P)} tot   (t) are needed. The first two quantities can be obtained by configuration and averaging of values of measured momentary powers, while the second quantity needs to be estimated. This can e.g. be achieved by autoregressive filtering of  P tot   (t) with the filter: 
     
       
         
           
             
               
                 
                   〈 
                   
                     
                       P 
                       . 
                     
                     tot 
                   
                   〉 
                 
                 ⁢ 
                 
                   ( 
                   s 
                   ) 
                 
               
               = 
               
                 
                   
                     α 
                     ⁢ 
                     s 
                   
                   
                     s 
                     + 
                     α 
                   
                 
                 ⁢ 
                 
                   〈 
                   
                     P 
                     tot 
                   
                   〉 
                 
                 ⁢ 
                 
                   ( 
                   s 
                   ) 
                 
               
             
             , 
           
         
       
     
     where α is a filter parameter. 
     In order to further emphasize the back-off control performance it could be advisable to only allow differential control action that reduces the scheduler threshold γ(t), meaning that only negative contributions from the second term of the feedback mechanism should be allowed. This means that in the time domain, the following restriction to the derivative  {dot over (P)} tot   (t) might be applied: 
         u ( t )= CTe ( t )− CTT   D max(0, ė ( t )).
 
     In some scenarios there might be a need to guarantee algorithmically that the regulated time-averaged power is always below the power threshold computed based on the designed RF EMF compliance boundary (exclusion zone) of the site. The functionality described above does not necessarily have this property. This is because linear control, such as PD control, is not designed to provide such guarantees. They only fallback to use a fraction γ low  of the maximum momentary transmission power in case the regulated average power gets very close to the threshold that is not to be exceeded. As shown in  FIG. 3 , there may still be overshoots.  FIG. 3  shows an example of controlling total average transmission power of the radio base station  140  according to the back-off power control loop of  FIG. 2 . One reason for this effect is that when the averaging window for some reason is first filled with very low values of momentary transmission power, followed by values of very high momentary transmission power for say 1.5 minutes, the total average transmission power reaches a level close to the threshold. During the remaining averaging time up to T there are nonzero values of momentary transmission power entering the averaging window, due e.g. to transmission of control signalling, that leads to an increased total average transmission power, since the very low values of momentary transmission power in the averaging window initially are shifted out. Hence an overshoot cannot be prevented. This is admittedly a rare situation—however since it can occur, at least theoretically, it can be expected to be a regulator and operator non-negotiable requirement to implement algorithms that prevents this behavior with a 100% guarantee. 
     The embodiments disclosed herein therefore relate to mechanisms for controlling total average transmission power of a radio base station  140 . In order to obtain such mechanisms there is provided a control device  200 , a method performed by the control device  200 , a computer program product comprising code, for example in the form of a computer program, that when run on a control device  200 , causes the control device  200  to perform the method. 
       FIG. 4  is a flowchart illustrating embodiments of methods for controlling total average transmission power of a radio base station  140 . The methods are performed by the control device  200 . The methods are advantageously provided as computer programs  1120 . 
     S 102 : The control device  200  performs, for a current discrete time value t, control of total average transmission power  P tot   (t) of the radio base station  140  according to a back-off power control loop. The total average transmission power  P tot   (t) is computed over an averaging time window T of the present value of momentary transmission power and the N−1 values of momentary transmission power preceding the present value of momentary transmission power. 
     S 104 : The control device  200  evaluates, for a future discrete time value less than, or equal to, t+T, the total average transmission power. The total average transmission power is evaluated assuming that values of momentary transmission power for all discrete time values from t up to t+T, starting at the next discrete time value t+1, is limited to a minimum value of said momentary transmission power. 
     S 106 : The control device  200  limits the momentary transmission power to the minimum value for at least the next future discrete time value when the total evaluated average transmission power, for any of the future discrete time values, exceeds a power threshold value. The power threshold value is based on a regulatory limit. 
     S 102  might then be entered for the discrete time value following the current discrete time value, i.e., for t+1. 
     Embodiments relating to further details of controlling total average transmission power of a radio base station  140  as performed by the control device  200  will now be disclosed. 
     There could be different types of back-off power control loops. One example of a back-off power control loop has been described above with reference to  FIG. 2 . Thus, in some examples, in the back-off power control loop, a setpoint value  P tot     ref  of the total average transmission power is compared with a value of the total average transmission power  P tot   (t). 
     There could be different points in time when the evaluating and the limiting as in S 104  and S 106  are performed. In some aspects, the check is performed for every k:th value of future discrete times. In particular, according to an embodiment, the evaluating is performed per every k:th value, where 1&lt;k&lt;, of the future discrete time. 
     There could be different definitions of the minimum value of the momentary transmission power. In some embodiments, the minimum value is defined as aP max,site , where a∈[0,1], and where P max,site  is the maximum transmission power of the radio base station  140 . 
     There could be different definitions of the power threshold value. In some embodiments, the power threshold value is defined as εP max,site −e, where ε is a limit based on the average EIRP threshold determined to obtain a certain RF EMF exclusion zone, and where e is a margin value. 
     In some examples the N values of momentary transmission power P tot (t) for t=t 0 , t 0 −T S , . . . , t 0 −(N−1)T S  are within the averaging time window T for a value of momentary transmission power with time index t 0 , and with sampling time T S . The control of the total average transmission power might then be limited when any  P tot   (t 0 +iT S )&gt;εP max,site −e, for i=1, . . . , N. 
     There could be different ways to evaluate the total average transmission power in S 104 . In some embodiments, the total average transmission power per each of the N future discrete time values is recursively evaluated. For example, for every value 1&lt;i&lt;N−1 of the N future discrete time values, the average transmission power of index i+1 is evaluated before the average transmission power of index i. Further, in some embodiments, the N values of average transmission power  P tot   (t 0 +iT S ), for a position of the averaging time window corresponding to future discrete time values i=1, . . . , N, are recursively determined from i=N down to i=1. 
     There could be different ways to start the recursive determination (i.e., when i=N) per each of the N future discrete time values. According to an example, for i=N: 
           P   tot ( t   0   +NT   S ) = aP   max,site . 
     There could be different ways to continue the recursive determination (i.e., when i&lt;N). According to an example, for N&gt;i≥0: 
     
       
         
           
             
               
                 〈 
                 
                   P 
                   tot 
                 
                 〉 
               
               ⁢ 
               
                 ( 
                 
                   
                     t 
                     0 
                   
                   + 
                   
                     i 
                     ⁢ 
                     
                       T 
                       S 
                     
                   
                 
                 ) 
               
             
             = 
             
               
                 
                   
                     
                       i 
                       ⁢ 
                       a 
                       ⁢ 
                       
                         P 
                         
                           max 
                           , 
                           site 
                         
                       
                     
                     + 
                     
                       
                         P 
                         tot 
                       
                       ( 
                       
                         t 
                         0 
                       
                       ) 
                     
                     + 
                     … 
                     + 
                     
                       
                         P 
                         tot 
                       
                       ( 
                       
                         
                           t 
                           0 
                         
                         + 
                         
                           
                             ( 
                             
                               i 
                               - 
                               
                                 ( 
                                 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             T 
                             S 
                           
                         
                       
                       ) 
                     
                   
                   ) 
                 
                 N 
               
               . 
             
           
         
       
     
     There could be different ways to control the average output power of the radio base station  140  for the future discrete time value. In some embodiments, the average output power of the radio base station  140  is controlled by a resource factor value γ(t). In some examples the control of the total average transmission power is obtained by limiting the momentary transmission power to the minimum value by setting the resource factor value γ(t) to its lower limit value γ hardlimit , where γ hardlimit ∈[0,1]. There could be different types of resource factor values. In some examples, the resource factor value γ(t) corresponds to which fraction of total number of physical resource blocks (PRBs) to schedule for the current discrete time value. 
     In view of the above, it is assumed that the values of momentary transmission power currently in the sliding window now will affect the total average transmission power a duration T (such as T minutes, where T=6 in some examples) ahead in time. Any action taken to avoid overshoot of the current value of momentary transmission power, needs to be evaluated for the coming duration T ahead in time to guarantee that there cannot be an overshoot due to the values of momentary transmission power currently in the sliding window. 
     Given a current time t 0 , a power profile P tot (t), t=t 0 , . . . , t 0 −(N−1)T S  representing values of momentary transmission power currently in the sliding window, and a minimum controlled momentary transmission power of aP max,site , where a∈[0,1], then an estimate of the maximum possible total average transmission power during the coming T time period (N samples), i.e. for t=t 0 +T S , . . . , t 0 +NT S , provided that regulation at future times is performed to limit the momentary transmission power to be less than or equal aP max,site  could be used to efficiently avoid an overshoot of the total average transmission power during the coming T time period. 
     Then, if any  P tot   (t 0 +iT S )&gt;εP max,site −e, for i=1, . . . , N, set γ(t)=γ hardlimit . As above, ε is the relative EIRP threshold, determined from the selected RF EMF exclusion zone and γ hardlimit ∈[0,1] is the hardlimit fraction of PRBs that can be scheduled, and e is a pre-configured margin. 
     With reference to  FIG. 5 , one efficient way to compute the total average transmission power for future times is to start by locating the lookahead window to predict a maximum of T ahead in time. In such a situation, there is no contribution from the backward window. Then the windows are moved one sample, leading to a recursive computation of the sought average power  P tot   (t 0 +iT S ), for i=1, . . . , N. 
     It follows first that: 
     
       
         
           
             
               〈 
               
                 
                   P 
                   tot 
                 
                 ( 
                 
                   
                     t 
                     0 
                   
                   + 
                   
                     N 
                     ⁢ 
                     
                       T 
                       S 
                     
                   
                 
                 ) 
               
               〉 
             
             = 
             
               
                 
                   N 
                   ⁢ 
                   a 
                   ⁢ 
                   
                     P 
                     
                       max 
                       , 
                       site 
                     
                   
                 
                 N 
               
               = 
               
                 a 
                 ⁢ 
                 
                   
                     P 
                     
                       max 
                       , 
                       site 
                     
                   
                   . 
                 
               
             
           
         
       
     
     Then, for the window positions indexed by N&gt;i≥0, it follows that: 
     
       
         
           
             
               
                 〈 
                 
                   P 
                   tot 
                 
                 〉 
               
               ⁢ 
               
                 ( 
                 
                   
                     t 
                     0 
                   
                   + 
                   
                     i 
                     ⁢ 
                     
                       T 
                       S 
                     
                   
                 
                 ) 
               
             
             = 
             
               
                 
                   
                     
                       i 
                       ⁢ 
                       a 
                       ⁢ 
                       
                         P 
                         
                           max 
                           , 
                           site 
                         
                       
                     
                     + 
                     
                       
                         P 
                         tot 
                       
                       ( 
                       
                         t 
                         0 
                       
                       ) 
                     
                     + 
                     … 
                     + 
                     
                       
                         P 
                         tot 
                       
                       ( 
                       
                         
                           t 
                           0 
                         
                         + 
                         
                           
                             ( 
                             
                               i 
                               - 
                               
                                 ( 
                                 
                                   N 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             T 
                             S 
                           
                         
                       
                       ) 
                     
                   
                   ) 
                 
                 N 
               
               . 
             
           
         
       
     
     It is noted that the contribution from the backward window contains the N−i last values of momentary transmission power, for N&gt;i≥0. This means that the sum of the contributions from the backward window can be recursively computed. For example, define the backward accumulated power as: 
     
       
         
           
             
               P 
               
                 
                   b 
                   ⁢ 
                   α 
                   ⁢ 
                   c 
                   ⁢ 
                   k 
                   ⁢ 
                   w 
                   ⁢ 
                   α 
                   ⁢ 
                   r 
                   ⁢ 
                   d 
                 
                 , 
                 i 
               
             
             = 
             
               
                 
                   P 
                   
                     b 
                     ⁢ 
                     α 
                     ⁢ 
                     c 
                     ⁢ 
                     k 
                     ⁢ 
                     w 
                     ⁢ 
                     α 
                     ⁢ 
                     r 
                     ⁢ 
                     d 
                   
                 
                 ( 
                 
                   
                     
                       t 
                       0 
                     
                     + 
                     
                       
                         ( 
                         
                           i 
                           - 
                           
                             ( 
                             
                               N 
                               - 
                               1 
                             
                             ) 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         T 
                         S 
                       
                     
                   
                   , 
                     
                   
                     = 
                     
                       
                         
                           P 
                           tot 
                         
                         ( 
                         
                           t 
                           0 
                         
                         ) 
                       
                       + 
                       … 
                       + 
                       
                         
                           P 
                           tot 
                         
                         ( 
                         
                           
                             t 
                             0 
                           
                           + 
                           
                             
                               ( 
                               
                                 i 
                                 - 
                                 
                                   ( 
                                   
                                     N 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               T 
                               S 
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 ) 
               
               . 
             
           
         
       
     
     This quantity can be recursively computed as follows: 
     
       
         
           
               
             
               
                   
               
             
            
               
                 Start 
               
               
                 P backward,N  = 0 
               
               
                 i = N 
               
               
                 While i&gt;2 
               
               
                  i − − 
               
               
                  P backward,i  = P backward,i+1  + P tot (t 0  + (i − (N − 1))T S )) 
               
               
                 End 
               
               
                   
               
            
           
         
       
     
     Here the notation “i--” denotes a decrease of i with one unit. The complete recursive algorithm for evaluation of future average power, together with the computation of the Boolean used to predictively trigger use of the hard limitation when performing the back-off power control loop, for all discrete time values up to T discrete time values ahead in time can therefore be formulated as follows, as also illustrated in the flowchart  600  of  FIG. 6 : 
     
       
         
           
               
               
             
               
                   
               
             
            
               
                   
                 Start 
               
               
                   
                 P backward,N  = 0 
               
               
                   
               
               
                   
                 
                   
                     
                       
                         
                           
                             〈 
                             
                               P 
                               tot 
                             
                             〉 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 t 
                                 0 
                               
                               + 
                               
                                 NT 
                                 S 
                               
                             
                             ) 
                           
                         
                         = 
                         
                           
                             
                               NaP 
                               
                                 max 
                                 , 
                                 site 
                               
                             
                             N 
                           
                           = 
                           
                             aP 
                             
                               max 
                               , 
                               site 
                             
                           
                         
                       
                     
                   
                 
               
               
                   
               
               
                   
                 MPCtrigger = false 
               
               
                   
                 i = N 
               
               
                   
                 while i&gt;2 &amp; ~MPCtrigger 
               
               
                   
                  i − − 
               
               
                   
                  P backward,i  = P backward,i+1  + P tot (t 0  + (i − (N − 1))T S )) 
               
               
                   
               
               
                   
                  
           〈     P   tot     〉     ⁢     (       t   0     +     iT   S       )       =         iaP     max   ,   site       +     P     backward   ,   i         N         
 
               
               
                   
               
               
                   
                 If   P tot     (t 0  + iT S ) &gt; εP max,site  − e 
               
               
                   
                  MPCtrigger = true 
               
               
                   
                 End 
               
               
                   
                 End 
               
               
                   
               
            
           
         
       
     
     Here the notation “˜MPCtrigger” denotes that the value of MPCtrigger is false. 
     The notation of  FIG. 6  relates to the above algorithm as follows (differences are listed); 
     MPCindex corresponds to i, 
     Naveraging=naveraging corresponds to N 
     MPCBackwardPower corresponds to P backward,i    
     Ptotw corresponds to P tot , i.e. the momentary power. 
     gammalower corresponds to γ γhardlimit  or a 
     Pmaxs and Pmax correspond to P max,site    
     Temp is a temporary variable, only used in  FIG. 6 . 
     MPCAveragePowerSample corresponds to  P tot   (t 0 +iT S ) 
     Threshold corresponds to ε 
     MPCmargin*Pmax corresponds to e. 
     There could be different ways to implement usage of the hard limitation when performing the back-off power control loop (once the hard limitation has been triggered; i.e., when MPCtrigger has been set to true). One conservative approach is given by: 
     
       
         
           
               
             
               
                   
               
             
            
               
                 Start 
               
               
                 If &lt;P tot &gt;(t) &gt; ϵP max,site  margin or MPCtrigger == true 
               
               
                 hardlimit = true 
               
               
                 End 
               
               
                 If &lt;P tot &gt;(t) &lt; δ 1 ϵP max,site  and MPCtrigger == false 
               
               
                 hardlimit = false 
               
               
                 End 
               
               
                 End 
               
               
                   
               
            
           
         
       
     
     Here margin is a value slightly lower than 1; for example typically margin=0.95. In this way the use of the hard limitation will be triggered more often than when only level-based triggering is used. Another way to implement usage of the hard limitation is to discard the level-based triggering altogether. That is: 
     
       
         
           
               
             
               
                   
               
             
            
               
                 Start 
               
               
                 If MPCtrigger == true 
               
               
                 hardlimit = true 
               
               
                 End 
               
               
                 If MPCtrigger == false 
               
               
                 hardlimit = false 
               
               
                 End 
               
               
                 End 
               
               
                   
               
            
           
         
       
     
     As the skilled person understands, yet further alternatives are possible. 
     Simulation results will now be shown with reference to  FIG. 7  and  FIG. 8 .  FIG. 7  shows the result of a simulation of the total average transmission power without application of the herein disclosed embodiments.  FIG. 8  shows the result of a simulation of the total average transmission power with application of the herein disclosed embodiments. From these figures follow that application of the herein disclosed embodiments consistently prevents the overshoots of the power threshold and also yields a higher PRB usage rate, which influences throughput and capacity. 
     Another approach to control the total average transmission power of the radio base station  140  to always keep the total average transmission power below the determined power threshold is to directly apply model predictive control (MPC). Such a direct approach could then constrain the total average transmission power to be below the power threshold computed from the selected RF EMF exclusion zone. An exact solution would require introduction of all samples in the averaging window as state components in a state vector, typically having a dimension of several hundreds (say, 600 when T=6 minutes). A medium complexity solution requires that the exponential model of the averaging process is used, which would then result in guarantees that are not 100%. A brief description of such an approach is given below. 
     An MPC control problem is defined by the state model, a cost function and constraints. The state model is here assumed to consist of states for exponential averaging and the dynamic actuator, i.e. 
     
       
         
           
             
               
                 
                   d 
                   dt 
                 
                 ⁢ 
                 
                   〈 
                   
                     P 
                     tot 
                   
                   〉 
                 
                 ⁢ 
                 
                   ( 
                   t 
                   ) 
                 
               
               = 
               
                 
                   
                     - 
                     
                       1 
                       T 
                     
                   
                   ⁢ 
                   
                     〈 
                     
                       P 
                       tot 
                     
                     〉 
                   
                   ⁢ 
                   
                     ( 
                     t 
                     ) 
                   
                 
                 + 
                 
                   
                     1 
                     T 
                   
                   ⁢ 
                   
                     P 
                     
                       max 
                       , 
                       site 
                     
                   
                   ⁢ 
                   
                     γ 
                     ⁡ 
                     ( 
                     t 
                     ) 
                   
                 
               
             
             , 
               
             
               
                 
                   d 
                   dt 
                 
                 ⁢ 
                 
                   γ 
                   ⁡ 
                   ( 
                   t 
                   ) 
                 
               
               = 
               
                 
                   u 
                   ⁡ 
                   ( 
                   t 
                   ) 
                 
                 . 
               
             
           
         
       
     
     This assumes that limitation of PRBs is active. The constraints are: γ low ≤γ(t)≤1 and  P tot   (t)≤∈P max,site −e. 
     The cost function J could e.g. be selected to be quadratic. For example, one example of a cost function J is given by: 
     
       
         
           
             J 
             = 
             
               
                 ∫ 
                 
                   t 
                   0 
                 
                 
                   
                     t 
                     0 
                   
                   + 
                   
                     T 
                     
                       look 
                       ⁢ 
                          
                       ahead 
                     
                   
                 
               
               
                 
                   
                     ( 
                     
                       
                         
                           
                             〈 
                             
                               P 
                               tot 
                             
                             〉 
                           
                           
                             r 
                             ⁢ 
                             e 
                             ⁢ 
                             f 
                           
                         
                         ⁢ 
                         
                           ( 
                           τ 
                           ) 
                         
                       
                       - 
                       
                         
                           〈 
                           
                             P 
                             tot 
                           
                           〉 
                         
                         ⁢ 
                         
                           ( 
                           τ 
                           ) 
                         
                       
                     
                     ) 
                   
                   2 
                 
                 ⁢ 
                 d 
                 ⁢ 
                 
                   τ 
                   . 
                 
               
             
           
         
       
     
     The skilled person would understand how to solve this problem, e.g. by consultation of one of many textbooks on MPC control. 
       FIG. 9  schematically illustrates, in terms of a number of functional units, the components of a control device  200  according to an embodiment. Processing circuitry  210  is provided using any combination of one or more of a suitable central processing unit (CPU), multiprocessor, microcontroller, digital signal processor (DSP), etc., capable of executing software instructions stored in a computer program product  1110  (as in  FIG. 11 ), e.g. in the form of a storage medium  230 . The processing circuitry  210  may further be provided as at least one application specific integrated circuit (ASIC), or field programmable gate array (FPGA). 
     Particularly, the processing circuitry  210  is configured to cause the control device  200  to perform a set of operations, or steps, as disclosed above. For example, the storage medium  230  may store the set of operations, and the processing circuitry  210  may be configured to retrieve the set of operations from the storage medium  230  to cause the control device  200  to perform the set of operations. The set of operations may be provided as a set of executable instructions. 
     Thus the processing circuitry  210  is thereby arranged to execute methods as herein disclosed. The storage medium  230  may also comprise persistent storage, which, for example, can be any single one or combination of magnetic memory, optical memory, solid state memory or even remotely mounted memory. The control device  200  may further comprise a communications interface  220  at least configured for communications with other entities, nodes, functions, and devices, such as the radio base station  140 . As such the communications interface  220  may comprise one or more transmitters and receivers, comprising analogue and digital components. The processing circuitry  210  controls the general operation of the control device  200  e.g. by sending data and control signals to the communications interface  220  and the storage medium  230 , by receiving data and reports from the communications interface  220 , and by retrieving data and instructions from the storage medium  230 . Other components, as well as the related functionality, of the control device  200  are omitted in order not to obscure the concepts presented herein. 
       FIG. 10  schematically illustrates, in terms of a number of functional modules, the components of a control device  200  according to an embodiment. The control device  200  of  FIG. 10  comprises a number of functional modules; a control module  210   a  configured to perform step S 102 , an evaluate module  210   b  configured to perform step S 104 , and a limit module  210   c  configured to perform step S 106 . The control device  200  of  FIG. 10  may further comprise a number of optional functional modules, such as symbolized by functional module  210   d . In general terms, each functional module  210   a - 210   d  may in one embodiment be implemented only in hardware and in another embodiment with the help of software, i.e., the latter embodiment having computer program instructions stored on the storage medium  230  which when run on the processing circuitry makes the control device  200  perform the corresponding steps mentioned above in conjunction with  FIG. 10 . It should also be mentioned that even though the modules correspond to parts of a computer program, they do not need to be separate modules therein, but the way in which they are implemented in software is dependent on the programming language used. Preferably, one or more or all functional modules  210   a - 210   d  may be implemented by the processing circuitry  210 , possibly in cooperation with the communications interface  220  and/or the storage medium  230 . The processing circuitry  210  may thus be configured to from the storage medium  230  fetch instructions as provided by a functional module  210   a - 210   d  and to execute these instructions, thereby performing any steps as disclosed herein. 
     The control device  200  may be provided as a standalone device or as a part of at least one further device. For example, the control device  200  may be provided in a node of the radio access network  110  or in a node of the core network  120 . Alternatively, functionality of the control device  200  may be distributed between at least two devices, or nodes. These at least two nodes, or devices, may either be part of the same network part (such as the radio access network  110  or the core network  120 ) or may be spread between at least two such network parts. In general terms, instructions that are required to be performed in real time may be performed in a device, or node, operatively closer to the cell than instructions that are not required to be performed in real time. 
     Thus, a first portion of the instructions performed by the control device  200  may be executed in a first device, and a second portion of the of the instructions performed by the control device  200  may be executed in a second device; the herein disclosed embodiments are not limited to any particular number of devices on which the instructions performed by the control device  200  may be executed. Hence, the methods according to the herein disclosed embodiments are suitable to be performed by a control device  200  residing in a cloud computational environment. Therefore, although a single processing circuitry  210  is illustrated in  FIG. 9  the processing circuitry  210  may be distributed among a plurality of devices, or nodes. The same applies to the functional modules  210   a - 210   d  of  FIG. 10  and the computer program  1120  of  FIG. 11 . 
       FIG. 11  shows one example of a computer program product  1110  comprising computer readable storage medium  1130 . On this computer readable storage medium  1130 , a computer program  1120  can be stored, which computer program  1120  can cause the processing circuitry  210  and thereto operatively coupled entities and devices, such as the communications interface  220  and the storage medium  230 , to execute methods according to embodiments described herein. The computer program  1120  and/or computer program product  1110  may thus provide means for performing any steps as herein disclosed. 
     In the example of  FIG. 11 , the computer program product  1110  is illustrated as an optical disc, such as a CD (compact disc) or a DVD (digital versatile disc) or a Blu-Ray disc. The computer program product  1110  could also be embodied as a memory, such as a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM), or an electrically erasable programmable read-only memory (EEPROM) and more particularly as a non-volatile storage medium of a device in an external memory such as a USB (Universal Serial Bus) memory or a Flash memory, such as a compact Flash memory. Thus, while the computer program  1120  is here schematically shown as a track on the depicted optical disk, the computer program  1120  can be stored in any way which is suitable for the computer program product  1110 . 
     The inventive concept has mainly been described above with reference to a few embodiments. However, as is readily appreciated by a person skilled in the art, other embodiments than the ones disclosed above are equally possible within the scope of the inventive concept, as defined by the appended claims.