Patent Publication Number: US-11399351-B2

Title: Power allocation method for non-orthogonal multiple access system and base station using the same

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the priority benefit of Taiwan application no. 109136605, filed on Oct. 22, 2020. The entirety of the above-mentioned patent application is hereby incorporated by reference herein and made a part of this specification. 
     TECHNICAL FIELD 
     The disclosure relates to a non-orthogonal multiple access system, and more particularly, to a power allocation method for a non-orthogonal multiple access system and a base station using the method. 
     BACKGROUND 
     Most of existing wireless communication systems use orthogonal multiple access (OMA) techniques, such as time-division multiple access, frequency-division multiple access, and code-division multiple access to avoid or reduce interference among signals from different users, so as to achieve good transmission performance. With the increasing popularity of network services and applications, the system capacity requirements for wireless communications will become higher and higher in the future, and thus it is necessary to continuously improve the multiple access technology. Recently, non-orthogonal multiple access (NOMA) has been considered a promising technique due to the fact that it can improve a utilization efficiency of system resources to achieve higher system capacity than OMA techniques. 
     In a NOMA system, user multiplexing can be performed in the power domain. Specifically, for downlink NOMA transmission, message signals intended to multiple pieces of user equipment (UE) can be superposed at the base station with appropriate power allocation among the users, such that the same channel resources (e.g., the same time and frequency) can be shared by the users for signal transmission. Although this power-domain NOMA transmission technique will cause inter-user interference, a successive interference cancellation (SIC) technique can be used at each UE being a receiver to recover the corresponding message signals. 
     Regarding design of a power-domain NOMA system, there are still a number of issues worthy of investigation. For example, power allocation among users will significantly affect the system performance and needs to be further improved. Most existing power allocation methods for NOMA transmission were developed under an assumption of perfect channel estimation, but channel estimation results for practical environments are usually imperfect. Therefore, it is important to develop a high-efficiency and high-performance power allocation method for NOMA systems with imperfect channel estimation. 
     SUMMARY 
     The disclosure provides a power allocation method for a non-orthogonal multiple access (NOMA) system and a base station using the same. The method allows the base station to determine a power allocation factor according to channel estimation errors returned by pieces of user equipment (UE), and can provide good system performance under practical environments with imperfect channel estimation. 
     The power allocation method provided by the disclosure is suitable for a NOMA system and adapted to a base station. The method includes the following steps: receiving a first channel estimation error parameter from first UE, and receiving a second channel estimation error parameter from second UE; configuring a first minimum rate requirement of the first UE and a second minimum rate requirement of the second UE; determining a power allocation factor according to the first channel estimation error parameter, the second channel estimation error parameter, the first minimum rate requirement, and the second minimum rate requirement; and determining first transmission power for the first UE and second transmission power for the second UE according to the power allocation factor. 
     The base station of the disclosure is adapted to serve first UE and second UE in a downlink NOMA system, and includes a transceiver, a storage circuit, and a processor. The transceiver is configured to transmit messages to the first UE and the second UE. The storage unit stores a plurality of modules. The processor is coupled to the storage circuit and the transceiver, and configured to access the modules and execute steps of: receiving a first channel estimation error parameter from the first UE, and receiving a second channel estimation error parameter from the second UE; configuring a first minimum rate requirement of the first UE and a second minimum rate requirement of the second UE; determining a power allocation factor according to the first channel estimation error parameter, the second channel estimation error parameter, the first minimum rate requirement, and the second minimum rate requirement; and determining first transmission power for the first UE and second transmission power for the second UE according to the power allocation factor. 
     Based on the above, in the embodiments of the disclosure, after performing channel estimation for a downlink NOMA system, the first UE and the second UE respectively return the first channel estimation error parameter and the second channel estimation error parameter to the base station. Then, the base station can determine the power allocation factor according to the first channel estimation error parameter and the second channel estimation error parameter, and allocate an amount of total transmission power to the first UE and the second UE according to the power allocation factor. In this way, the disclosure can effectively improve the performance of the NOMA system with imperfect channel estimation, and ensure the minimum rate requirements of the first UE and the second UE. 
     To make the aforementioned more comprehensible, several embodiments accompanied with drawings are described in detail as follows. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram illustrating a NOMA system according to an embodiment of the disclosure. 
         FIG. 2  is a block diagram illustrating a base station according to an embodiment of the disclosure. 
         FIG. 3  is a first flowchart illustrating a power allocation method according to an embodiment of the disclosure. 
         FIG. 4  is a second flowchart illustrating a power allocation method according to an embodiment of the disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Refer to  FIG. 1 . It is a schematic diagram illustrating a NOMA system according to an embodiment of the disclosure. In this embodiment, a NOMA system  100  includes a base station  110 , first user equipment (UE)  121 , and second UE  122 . The first UE  121  and the second UE  122  are located within a coverage  130  of the base station  110  and served by the base station  110 . Here, the first UE  121  (i.e., a strong user) has a larger channel gain, and the second UE  122  (i.e., a weak user) has a smaller channel gain. 
     The first UE  121  and the second UE  122  may be implemented as, for example, but not limited to, a mobile station, an advanced mobile station (AMS), a server, a user terminal, a desktop computer, a laptop computer, a network computer, a workstation, a personal digital assistant (PDA), a tablet personal computer (tablet PC), a scanner, a phone device, a pager, a camera, a television, a handheld video game device, a music device, a wireless sensor, and the like. 
     The base station  110  may be (but not limited to), for example, a gNB, an eNB, a home eNB, an advanced base station (ABS), a base transceiver system (BTS), an access point, a home BS, a relay, an intermediate node, an intermediate equipment, a satellite-based communication base station, or a combination thereof. 
     Refer to  FIG. 2 . It is a block diagram illustrating a base station according to an embodiment of the disclosure. In this embodiment, the base station  110  can at least include (but not limited to) a transceiver  210 , a storage circuit  220 , and a processor  230 . The transceiver  210  may include a transmitter circuit, an analog-to-digital converter, a digital-to-analog converter, a low-noise amplifier, a mixer, a filter, an impedance matcher, a transmission line, a power amplifier, one or more antenna circuits, and a local storage medium element, such that the base station  110  can provide wireless transmitting/receiving functions to the first UE  121  and the second UE  122 . The storage circuit  220  is, for example, a memory, a hard disk or other elements capable of storing data, and may be configured to record a plurality of program codes or modules. 
     The processor  230  is coupled to the transceiver  210  and the storage circuit  220 , and may be a processor for general purposes, a processor for special purposes, a conventional processor, a digital signal processor, a plurality of microprocessors, one or more microprocessors, controllers and microcontrollers which are combined with a core of the digital signal processor, an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), any other integrated circuits, a state machine, a processor based on advanced RISC machine (ARM), or the like. 
     In this embodiment, the processor  230  can access and execute the program codes stored in the storage circuit  220  to perform a power allocation method proposed by the disclosure. The corresponding details are described below. In order to clearly explain the principle of the disclosure, the following description is provided with an example in which the first UE  121  and the second UE  122  communicate with the base station  110  through a single-input single-output (SISO) channel. 
     Refer back to  FIG. 1 . In the NOMA system  100 , in order to correctly demodulate signals transmitted by the base station  110  at receiver ends (i.e., the first UE  121  and the second UE  122 ), the base station  110  can perform power allocation, where the signal of a weak user is allocated with more transmission power and the signal of a strong user is allocated with less transmission power. More specifically, the base station  110  can respectively allocate first transmission power P 1  and second transmission power P 2  to complex signals s 1  and s 2  to be transmitted to the first UE  121  and the second UE  122  before superposing the signals, and transmit a superposed complex signal x to the first UE  121  and the second UE  122 . In this embodiment, the superposed complex signal x to be transmitted can be expressed as equation (1):
 
 x =√{square root over ( P   1 )} s   1 +√{square root over ( P   2 )} s   2 .  (1)
 
In the case where a channel gain of the first UE  121  is assumed to be greater than a channel gain of the second UE  122 , the first transmission power P 1  needs to be less than the second transmission power P 2 , and a sum of the first transmission power P 1  and the second transmission power P 2  is equal to total transmission power P T  of the NOMA system  100 .
 
     In this embodiment, a true complex channel fading coefficient between the base station  110  and the first UE  121  is denoted by h 1 , and a true complex channel fading coefficient between the base station  110  and the second UE  122  is denoted by h 2 . Correspondingly, a channel (power) gain between the base station  110  and the first UE  121  can be denoted by |h 1 | 2 , and a channel (power) gain between the base station  110  and the second UE  122  can be denoted by |h 2 | 2 . Thus, the complex signals y 1  and y 2  received by the first UE  121  and the second UE  122  can be respectively expressed as equations (2) and (3):
 
 y   1   =h   1   x+v   1 =√{square root over ( P   1 )} h   1   s   1 +√{square root over ( P   2 )} h   1   s   2   +v   1   (2)
 
 y   2   =h   2   x+v   2 =√{square root over ( P   1 )} h   2   s   1 +√{square root over ( P   2 )} h   2   s   2   +v   2   (3)
 
where v 1  and v 2  are zero-mean complex additive white Gaussian noises (AWGN), and their corresponding variances or powers are respectively assumed to be N 0,1  and N 0,2 , i.e., v 1  and v 2  can be respectively denoted by CN(0, N 0,1 ) and CN(0, N 0,2 ). It is also assumed here that N 0,1 =N 0,2 =N 0 . Since |h 1 | 2 &gt;|h 2 | 2 , the received signal power of power of y 1  is greater than that of y 2 .
 
     In this embodiment, with consideration of the occurrence of imperfect channel estimation, equations (2) and (3) can be respectively expressed as equations (4) and (5):
 
 y   1 √{square root over ( P   1 )}( ĥ   1   +Δh   1 ) s   1 +√{square root over ( P   2 )}( ĥ   1   +Δh   1 ) s   2   +v   1   (4)
 
 y   2 √{square root over ( P   1 )}( ĥ   2   +Δh   2 ) s   1 +√{square root over ( P   2 )}( ĥ   2   +Δh   2 ) s   2   +v   2   (5)
 
where a channel fading coefficient estimate obtained from performing channel estimation by the first UE  121  is denoted by ĥ 1 , and a corresponding channel estimation error is denoted by Δh 1  with zero mean and variance σ Δh     1     2 ; a channel fading coefficient estimate obtained from performing channel estimation by the second UE  122  is denoted by ĥ 2 , and a corresponding channel estimation error is denoted by Δh 2  with zero mean and variance σ Δh     2     2 . Both Δh 1  and Δh 2  are assumed to be complex Gaussian distributed and can be respectively denoted by CN(0,σ Δh     1     2 ) and CN(0,σ Δh     2     2 ). Here, σ Δh     1     2  and σ Δh     2     2  can be interpreted as mean-squared errors (MSEs) of the corresponding channel estimations, and reflect channel estimation qualities for the first UE  121  and the second UE  122 , respectively.
 
     According to the NOMA principle, the strong user having a larger channel gain should be allocated with smaller transmission power. In this case, the first UE  121  can remove the interference based on the signal s 2  through an SIC process (e.g., a block  141  of  FIG. 1 ) and then directly decode its own signal s 1  (e.g., a block  142  of  FIG. 1 ) On the other hand, for the weak user having a smaller channel gain, since the interference caused by the signal of the strong user can be regarded as noise, the second UE  122  can directly decode its own signal (e.g., a block  143  of  FIG. 1 ). 
     In the case where the signals s 1  and s 2  are successfully decoded with imperfect channel estimation conditions, channel capacity lower bounds of the first UE  121  and the second UE  122  can be respectively expressed as equations (6) and (7): 
     
       
         
           
             
               
                 
                   
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     It should be noted that, when the first UE  121  uses a channel fading coefficient estimate ĥ 1  to perform a SIC procedure, because √{square root over (P 2 )}Δh 1 s 2  in equation (4) cannot be completely removed, the channel capacity lower bound C lower,1  of the first UE  121  can be expressed as equation (6); on the other hand, because √{square root over (P 2 )}h 2 s 2  generated based on the channel estimation error may be considered as an additional interference, the channel capacity lower bound C lower,2  of the second UE  122  can be expressed as equation (7). 
     According to equations (6) and (7), it can been seen that the channel capacity lower bounds C lower,1  and C lower,2  of the first UE  121  and the second UE  122  are related to the first transmission power P 1  and the second transmission power P 2 , respectively. In other words, the power allocation for the signals s 1  and s 2  can directly affect the channel capacity lower bounds C lower,1  and C lower,2  of the first UE  121  and the second UE  122 . It should be noted that, since the existence of channel estimation errors makes it difficult to obtain accurate channel capacity expressions, the subsequent derivation will be based on the channel capacity lower bounds defined in this embodiment. 
     In this embodiment, with consideration of quality of service (QoS) of the first UE  121  and the second UE  122 , minimum rate requirements are additionally defined. Specifically, the base station  110  configures a first minimum rate requirement R 1   T  for the first UE  121 , and configure a second minimum rate requirement R 2   T  for the second UE  122 . Therefore, a system outage may occur in the following three situations. (1) A data transmission rate at which the first UE  121  can successfully decode the signal s 2  is less than the second minimum rate requirement R 2   T . This situation will make the interference based on the signal s 2  unable to be smoothly removed through the SIC procedure, thereby reducing the probability and the data transmission rate at which the first UE  121  can successfully decode its own signal s 1 . (2) The data transmission rate at which the first UE  121  can successfully decode its own signal s 1  is less than the first minimum rate requirement R 1   T . (3) A data transmission rate at which the second UE  122  can successfully decode its own signal s 2  is less than the second minimum rate requirement R 2   T . 
     In the case where channel estimation errors occur, an accurate system outage probability cannot be obtained. Therefore, in this embodiment of the disclosure, the channel capacity lower bound corresponding to each UE in the NOMA system is regarded as a data transmission rate lower bound at which the corresponding UE can successfully decode its own signal or the signal of the other, and an upper bound of the system outage probability is determined based on a plurality of constraints related to the first minimum rate requirement R 1   T  (unit: bps/Hz) and the second minimum rate requirement R 2   T  (unit: bps/Hz). More specifically, by making R i,j  denote a data transmission rate lower bound at which i-th UE can successfully decode a signal of j-th UE, the constraints used for determining the system outage probability upper bound can be expressed as follows: 
                     R     1   ,   2       =         log   2     ⁡     (     1   +         P   2     ⁢              h   ^     1          2             P   T     ⁢     σ     Δ   ⁢           ⁢     h   1       2       +       P   1     ⁢              h   ^     1          2       +     N   0           )       ≥     R   2   T               (   8   )                 R     1   ,   1       =         log   2     ⁡     (     1   +         P   1     ⁢              h   ^     1          2             P   T     ⁢     σ     Δ   ⁢           ⁢     h   1       2       +     N   0           )       ≥     R   1   T               (   9   )                 R     2   ,   2       =         log   2     ⁡     (     1   +         P   2     ⁢              h   ^     2          2             P   T     ⁢     σ     Δ   ⁢           ⁢     h   2       2       +       P   1     ⁢              h   ^     2          2       +     N   0           )       ≥       R   2   T     .               (   10   )               
Here, expression (8) represents that a data transmission rate lower bound R 1,2  at which the first UE  121  can successfully decode the signal s 2  is greater than or equal to the second minimum rate requirement R 2   T ; expression (9) represents that a data transmission rate lower bound R 1,1  at which the first UE  121  can successfully decode its own signal s 1  is greater than or equal to the first minimum rate requirement R 1   T ; expression (10) represents that a data transmission rate lower bound R 2,2  at which the second UE  122  can successfully decode its own signal s 2  is greater than or equal to the second minimum rate requirement R 1   T .
 
     Based on the above, a system outage probability upper bound P upper  can be expressed as equation (11):
 
 P   upper =1− Pr{R   1,2   ≥R   2   T   ,R   1,1   ≥R   1   T   ,R   2,2   ≥R   2   T }.  (11)
 
Therefore, when the total transmission power is P T , an optimization problem for minimizing the system outage probability upper bound P upper  can be expressed as:
 
                     min     {       P   1     ⁢     P   2       }       ⁢     P   upper             (     12   ⁢   a     )                   subject   ⁢           ⁢   to   ⁢           ⁢     P   1       +     P   2       =     P   T             (     12   ⁢   b     )                   P   1     &gt;   0     ,       P   2     &gt;   0     ,       P   2     &gt;       P   1     .               (     12   ⁢   c     )               
In this optimization problem, expression (12a) means that the first transmission power P 1  and the second transmission power P 2  need to be found for minimizing the system outage probability upper bound P upper ; expression (12b) represents a constraint that the sum of the first transmission power P 1  and the second transmission power P 2  needs to match the total transmission power P T ; and expression (12c) represents the NOMA principle that the second transmission power P 2  (for the weak user) needs to be greater than the first transmission power P 1  (for the strong user).
 
     Here, for the first UE  121  and the second UE  122 , a power allocation factor can be defined and denoted by α. Accordingly, the first transmission power allocated for the first UE  121  can be expressed as P 1 =αP T , and the second transmission power allocated for the second UE  122  can be expressed as P 2 =P T −P 1 . In this case, the optimization problem above can be rewritten as: 
     
       
         
           
             
               
                 
                   
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     To solve the optimization problem of expressions (13a) to (13c), it is assumed that the channel fading coefficient estimate ĥ 1  is a complex Gaussian random variable with zero mean and variance σ ĥ     1     2 , i.e., ĥ 1  can be denoted by CN(0,σ ĥ     1     2 ); similarly, it is assumed that the channel fading coefficient estimate ĥ 2  is a complex Gaussian random variables with zero mean and variance σ ĥ     2     2 , i.e., ĥ 2  can be denoted by CN(0,σ ĥ     2     2 ) In this case, Pr{R 1,2 ≥R 2   T ,R 1,1 ≥R 1   T ,R 2,2 ≥R 2   T } in equation (11) can be expressed as equation (14): 
                     Pr   ⁢     {         R     1   ,   2       ≥     R   2   T       ,       R     1   ,   1       ≥     R   1   T       ,       R     2   ,   2       ≥     R   2   T         }       =     Pr   ⁢     {                 (     1   -   α   -     αϕ   2       )     ⁢     P   T     ⁢              h   ^     1          2       ≥       (       N   0     +       P   T     ⁢     σ     Δ   ⁢           ⁢     h   1       2         )     ⁢     ϕ   2         ,                     αP   T     ⁢              h   ^     1          2       ≥       (       N   0     +       P   T     ⁢     σ     Δ   ⁢           ⁢     h   1       2         )     ⁢     ϕ   1         ,                   (     1   -   α   -     αϕ   2       )     ⁢     P   T     ⁢              h   ^     2          2       ≥       (       N   0     +       P   T     ⁢     σ     Δ   ⁢           ⁢     h   2       2         )     ⁢     ϕ   2               }               (   14   )               
where ϕ 1 =2 R     1     T −1 and ϕ 2 =2 R     2     T −1.
 
     In equation (14), in the case where α≤0 or (1−α−αϕ 2 )≤0, Pr{R 1,2 ≥R 2   T ,R 1,1 ≥R 1   T ,R 2,2 ≥R 2   T }=0, which violates the operating principle of NOMA. When 0&lt;α&lt;1/(1+ϕ 2 ), because |ĥ 1 | 2  and |ĥ 2 | 2  are independent of each other, equation (14) can be expressed as Q 1 Q 2 , where Q 2  can be expressed as equation (15); Q 1  can be expressed as equation (16) under condition (17), and Q 1  can be expressed as equation (18) under condition (19). 
     
       
         
           
             
               
                 
                   
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     After Q 1  and Q 2  are obtained, equation (11) can be expressed as P upper =1−Q 1 Q 2 , which means that the optimization problem for minimizing P upper  is equivalent to maximizing Q 1 Q 2 . Thus, with f(α)=Q 1 Q 2 , and the optimization problem for minimizing P upper  is equivalent to an optimization problem for maximizing f(α) as follows: 
     
       
         
           
             
               
                 
                   
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                       α 
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                   ⁢ 
                   
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                     ⁢ 
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     In equation (16), when ϕ 1 /(ϕ 1 +ϕ 2 +ϕ 1 ϕ 2 )&lt;α&lt;1/(1+ϕ 2 ), Q 1  is a strictly decreasing function. In equation (18), when ϕ&lt;α&lt;ϕ 1 /(ϕ 1 +ϕ 2 +ϕ 1 ϕ 2 ), Q 1  is a strictly increasing function. In equation (15), when 0&lt;α&lt;1/(1+ϕ 2 ), Q 2  is a strictly decreasing function. Thus, a maximum value of f(α) is at 0&lt;α&lt;ϕ 1 /(ϕ 1 +ϕ 2 +ϕ 1 ϕ 2 ). 
     Based on the above description, f(α) can be expressed as equation (21): 
                     f   ⁡     (   α   )       =       e     -         (       N   0     +       P   T     ⁢     σ     Δ   ⁢           ⁢     h   1       2         )     ⁢     ϕ   1         α   ⁢           ⁢     P   T     ⁢     σ       h   ^     1     2             ⁢       e     -         (       N   0     +       P   T     ⁢     σ     Δ   ⁢           ⁢     h   2       2         )     ⁢     ϕ   2           (     1   -   α   -     αϕ   2       )     ⁢     P   T     ⁢     σ       h   ^     2     2             .               (   21   )               
By differentiating f(α), an optimal power allocation factor α IP   opt  for obtaining the maximum value of f(α) is expressed as equation (22):
 
                     α   IP   opt     =       1               σ       h   ^     1     2     ⁡     (       ϕ   2     +     ϕ   2   2       )       ⁢     (         σ     Δ   ⁢           ⁢     h   2       2     ⁢     P   T       +     N   0       )           σ       h   ^     2     2     ⁢       ϕ   1     ⁡     (         σ     Δ   ⁢           ⁢     h   1       2     ⁢     P   T       +     N   0       )             +   1   +     ϕ   2         .             (   22   )               
Here, to ensure that 0&lt;α IP   opt &lt;½, ϕ 1  and ϕ 2  need to satisfy (ϕ 1 /(1+ϕ 1 ))≤ϕ 2 . This optimal power allocation factor α IP   opt  can minimize the system outage probability upper bound P upper , and ensure that each of the first UE  121  and the second UE  122  has a minimum transmission rate; The base station  110  can perform the power allocation according to equation (22), so as to perform NOMA transmission with the first UE  121  and the second UE  122 .
 
     In addition, for the first UE  121  and the second UE  122 , normalized MSEs of the channel estimations can be defined and respectively expressed as {tilde over (σ)} Δh     1     2 =σ Δh     1     2 /σ h     1     2  and {tilde over (σ)} Δh     2     2 =σ Δh     2     2 /σ h     2     2 . In practical applications, it is assumed that channel estimation qualities of the first UE  121  and the second UE  122  are close (i.e {tilde over (σ)} Δh     1     2  approximates {tilde over (σ)} Δh     2     2 ). In this case, σ ĥ     1     2 /σ ĥ     2     2  in equation (22) can be replaced by σ Δh     1     2 /σ Δh     2     2 . Accordingly, in the case where the base station  110  does not know the variances σ ĥ     1     2  and σ ĥ     2     2  of the channel fading coefficient estimates, the base station  110  can perform the power allocation according to an approximate solution of the optimal power allocation factor α IP   opt  in equation (23) with (ϕ 1 /(1+ϕ 1 ))≤ϕ 2  so as to perform the NOMA transmission with the first UE  121  and the second UE  122 . 
     
       
         
           
             
               
                 
                   
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                     opt 
                   
                   ≈ 
                   
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                                   ⁢ 
                                   
                                       
                                   
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                                       ⁢ 
                                       
                                           
                                       
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                                 ⁢ 
                                 
                                     
                                 
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                       + 
                       
                         ϕ 
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                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     Thus, in an embodiment, after the channel estimation is performed by each of the first UE  121  and the second UE  122 , each the first UE  121  and the second UE  122  can generate channel estimation information. By returning the channel estimation information to the base station  110 , the base station  110  can directly determine the power allocation factor based on equation (22) or (23), and accordingly determine the first transmission power for the first UE  121  and the second transmission power for the second UE  122 . From the above description, it can be seen that the power allocation factor determined based on equation (22) or (23) can minimize (or approximately minimize) the system outage probability upper bound P upper , and ensure that each of the first UE  121  and the second UE  122  has a minimum transmission rate. 
     In the foregoing embodiment, it is assumed that the channel between the base station  110  and each of the first UE  121  and the second UE  122  is a single-input single-output (SISO) scenario. However, in other embodiments, the method proposed by the disclosure can also be extended to a multiple-input multiple-output (MIMO) scenario. Specifically, in an embodiment, the base station  110  can communicate with the first UE  121  and the second UE  122  through a MIMO channel. Here, it is assumed that the base station  110  has M T  transmitting antennas; each of the first UE  121  and the second UE  122  has M R  receiving antennas; and a smaller value between M T  and M R  is denoted by M min . 
     In this embodiment, true channel matrices between the base station  110  and the first UE  121  and the second UE  122  are respectively denoted by complex matrices H 1  and H 2  of M R ×M T , and Frobenius norms ∥H 1 | F   2  and ∥H 2 ∥ F   2  respectively represent corresponding MIMO channel gains. Under the assumption of ∥H 1 | F   2 &gt;∥H 2 ∥ F   2 , the base station  110  can respectively allocate the first transmission power P 1  and the second transmission power P 2  to M T ×1 complex vector signals s 1  and s 2  to be transmitted to the first UE  121  and the second UE  122  before superposing the signals, and transmit the superposed M T ×1 complex vector signal x to the first UE  121  and the second UE  122 . Here, the first transmission power P 1  is less than the second transmission power P 2 , and the sum of the first transmission power P 1  and the second transmission power P 2  is equal to the total transmission power P T  of the NOMA system  100 . In the case of uniformly allocating the first transmission power P 1  and the second transmission power P 2  for the M T  transmitting antennas, the superposed complex signal x to be transmitted can be expressed as equation (24):
 
 x =√{square root over ( P   1   M   T )} s   1 +√{square root over ( P   2   /M   T )} s   2 .  (24)
 
     Here, for the first UE  121  and the second UE  122 , a power allocation factor can be defined (denoted by α). Accordingly, the first transmission power allocated for the first UE  121  can be expressed as P 1 =αP T , and the second transmission power allocated for the second UE  122  can be expressed as P 2 =P T −P 1 . 
     Correspondingly, in the imperfect channel estimation environment, M T ×1 complex vector signals y 1  and y 2  received by the first UE  121  and the second UE  122  can be respectively expressed as equations (25) and (26):
 
 y   1 =√{square root over ( P   1   /M   T )}( Ĥ   1   +ΔH   1 ) s   1 +√{square root over ( P   2   /M   T )}( Ĥ   1   +H   1 ) s   2   +v   1   (25)
 
 y   2 =√{square root over ( P   1   /M   T )}( Ĥ   2   +ΔH   2 ) s   1 +√{square root over ( P   2   /M   T )}( Ĥ   2   +H   2 ) s   2   +v   2   (26)
 
where v 1  and v 2  are complex Gaussian noise vectors, and each element of the noise vectors is independent and identically distributed as CN(0, N 0 ). A channel fading coefficient matrix estimate obtained from performing channel estimation by the first UE  121  is denoted by a matrix Ĥ 1 , and a corresponding channel estimation error matrix is denoted by ΔH 1 . A channel fading coefficient matrix estimate obtained from performing channel estimation by the second UE  122  is denoted by a matrix Ĥ 2 , and a corresponding channel estimation error matrix is denoted by ΔH 2 . All of Ĥ 1 , H 2 , ΔH 1 , and ΔH 2  are M R ×M T  complex matrices.
 
     In this embodiment, each element of Ĥ 1  is assumed to be independent and identically complex Gaussian distributed as CN(0,σ Ĥ     1     2 ); each element of Ĥ 2  is assumed to be independent and identically complex Gaussian distributed as CN(0,σ Ĥ     2     2 ); each element of ΔH 1  is assumed to be independent and identically complex Gaussian distributed as CN(0,σ ΔH     1     2 ); each element of ΔH 2  is assumed to be independent and identically complex Gaussian distributed as CN(0,σ ΔH     2     2 ). It should be noted that σ Ĥ     1     2  and σ Ĥ     2     2  are respectively variances of each element of Ĥ 1  each element of Ĥ 2  obtained from performing channel estimations by the first UE  121  and the second UE  122 . σ ΔH     1     2  and σ ΔH     2     2  are respectively MSEs of the corresponding channel estimations for each element of H 1  and each element of H 2 , and reflect channel estimation qualities for the first UE  121  and the second UE  122 , respectively. 
     In the case where the signals s 1  and s 2  are successfully decoded with imperfect channel estimation conditions, channel capacity lower bounds of the first UE  121  and the second UE  122  can be respectively expressed as equations (27) to (28): 
                       C   ~       lower   ,   1       =       log   2     ⁢           ⁢     det   (           ⁢       I     M   R       +         (         (       P   T     /     M   T       )     ⁢     E   ⁡     [     Δ   ⁢           ⁢     H   1     ⁢   Δ   ⁢           ⁢       H   1     H       ]         +       N   0     ⁢     I     M   R           )       -   1       ⁢     (       P   1     /     M   T       )     ⁢     (         H   ^     1     ⁢         H   ^     1     H       )         )               (   27   )                       ⁢         C   ~       lower   ,   2       =       log   2     ⁢           ⁢     det   ⁡     (                   I     M   R       +     (         (       P   T     /     M   T       )     ⁢     E   ⁡     [     Δ   ⁢           ⁢     H   2     ⁢   Δ   ⁢           ⁢       H   2     H       ]         +                           (       P   1     /     M   T       )     ⁢     (         H   ^     2     ⁢         H   ^     2     H       )       +       N   0     ⁢     I     M   R           )       -   1                         (       P   2     /     M   T       )     ⁢     (         H   ^     2     ⁢         H   ^     2     H       )             )                   (   28   )               
where I M     R    is a M R ×M R  identity matrix and (•) H  represents a conjugate transpose operation.
 
     Specifically, through singular value decomposition (SVD), M R ×M T  MIMO channels can be regarded as a set of M min  parallel SISO subchannels. In addition, in a MIMO environment, the channel matrix estimates between the base station  110  and the first UE  121  and the second UE  122  are respectively Ĥ 1  and Ĥ 2 , and the square of each singular value of a channel matrix Ĥ n  (n=1, 2) is a channel gain of each of the subchannels. In this case, an effective channel gain of the channel matrix Ĥ n  is a sum of all squared singular values, which can be obtained by computing the Frobenius norm ∥Ĥ n ∥ F   2  of the channel matrix Ĥ n . Then, an average effective channel gain of each of the parallel SISO subchannels in Ĥ n  can be expressed by ∥Ĥ n ∥ F   2 /M min , and equations (27) and (28) can be respectively simplified as equations (29) and (30): 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         C 
                         ~ 
                       
                       
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                         , 
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                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
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                         ⁡ 
                         
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                   ( 
                   30 
                   ) 
                 
               
             
           
         
       
     
     Based on the assumptions and derivation principles similar to those in the aforementioned SISO scenario, in the MIMO environment, the optimal power allocation factor can be obtained by minimizing the system outage probability upper bound. When the base station  110  communicates with the first UE  121  and the second UE  122  through a MIMO channel, the corresponding optimal power allocation factor {tilde over (α)} IP   opt  can be expressed as equation (31): 
                       α   ~     IP   opt     ≈     1             (       σ       H   ^     1     2     /     (       M   min     ⁢     M   T       )       )     ⁢     (         ϕ   ~     2     +       ϕ   ~     2   2       )     ⁢     (         M   R     ⁢     σ     Δ   ⁢           ⁢     H   2       2     ⁢     P   T       +     N   0       )           (       σ       H   ^     2     2     /     (       M   min     ⁢     M   T       )       )     ⁢         ϕ   ~     1     ⁡     (         M   R     ⁢     σ     Δ   ⁢           ⁢     H   1       2     ⁢     P   T       +     N   0       )             +   1   +       ϕ   ~     2                 (   31   )               
where {tilde over (ϕ)} 1 =2 R     1       T     /M     min   −1, {tilde over (ϕ)} 2 =2 R     2       T     /M     min   −1, and ({tilde over (ϕ)} 1 /(1+{tilde over (ϕ)} 1 ))≤{tilde over (ϕ)} 2 .
 
     With an assumption that the channel estimation qualities of the first UE  121  and the second UE  122  are close, the optimal power allocation factor α IP   opt  of equation (31) can be approximated as equation (32): 
                       α   ~     IP   opt     ≈     1             (       σ     Δ   ⁢           ⁢     H   1       2     /     (       M   min     ⁢     M   T       )       )     ⁢     (         ϕ   ~     2     +       ϕ   ~     2   2       )     ⁢     (         M   R     ⁢     σ     Δ   ⁢           ⁢     H   2       2     ⁢     P   T       +     N   0       )           (       σ     Δ   ⁢           ⁢     H   2       2     /     (       M   min     ⁢     M   T       )       )     ⁢         ϕ   ~     1     ⁡     (         M   R     ⁢     σ     Δ   ⁢           ⁢     H   1       2     ⁢     P   T       +     N   0       )             +   1   +       ϕ   ~     2                 (   32   )               
where {tilde over (ϕ)} 1 =2 R     1       T     /M     min   −1, {tilde over (ϕ)} 2 =2 R     2       T     /M     min   −1, and ({tilde over (ϕ)} 1 /(1+{tilde over (ϕ)} 1 ))≤{tilde over (ϕ)} 2 .
 
     Based on the above, in an embodiment, when the first UE  121  and the second UE  122  communicate with the base station  110  through the MIMO channel, the base station  110  can directly determine the power allocation factor based on equation (31) or (32), and accordingly determine the first transmission power for the first UE  121  and the second transmission power for the second UE  122 . 
     In view of this, an embodiment of the disclosure proposes a power allocation method in the NOMA system  100 , which allows the base station  110  to efficiently determine the power allocation factor for the first UE  121  and the second UE  122  and improve the performance of the NOMA system  100  in the imperfect channel estimation environment. Further details are illustrated below. 
     Refer to  FIG. 3 . It is a first flowchart illustrating a power allocation method according to an embodiment of the disclosure. The method is adapted to the NOMA system  100  of  FIG. 1 , and each step of  FIG. 3  will be described below with reference to each element shown in  FIG. 1 . 
     In brief, in an embodiment, in a downlink transmission of the NOMA system  100 , the base station  110  can perform a power allocation according to imperfect channel estimation information to achieve better performance. Accordingly, in the embodiment shown in  FIG. 3 , in step S 301  and step S 302 , the base station  110  transmits reference signals (RS) to the first UE  121  and the second UE  122 . Next, in step S 303 , the first UE  121  can perform channel estimation according to the reference signal and obtain some imperfect channel estimation information. In step S 303 , the second UE  122  can perform channel estimation according to the reference signal and obtain some imperfect channel estimation information. For instance, the first UE  121  and the second UE  122  can perform the channel estimations by using a least-squares (LS) algorithm, a minimum mean-squared error (MMSE) algorithm, or other methods. 
     In step S 305 , the first UE  121  can return the imperfect channel estimation information to the base station  110 . Similarly, in step S 306 , the second UE  122  can return the imperfect channel estimation information to the base station  110 . In an embodiment, the first UE  121  and the second UE  122  can return the imperfect channel estimation information through a physical uplink control channel (PUCCH) or a physical uplink shared channel (PUSCH). The imperfect channel estimation information may be regarded as channel status information (CSI) including a channel estimation error parameter. In an embodiment, the first UE  121  and the second UE  122  can return their MSEs of the channel estimations. 
     In step S 307 , in the case where a first minimum rate requirement of the first UE  121  and a second minimum rate requirement of the second UE  122  are configured, the base station  110  can determine a power allocation factor according to the imperfect channel estimation information returned by the first UE  121  and the second UE  122 , so as to determine first transmission power for the first UE  121  and second transmission power for the second UE  122 . In an embodiment, the base station  110  determines the power allocation factor according to the MSEs of the channel estimations in the imperfect channel estimation information, generates a superposed signal according to the first transmission power for the first UE  121  and the second transmission power for the second UE  122  in step S 308 , and then send the superposed signal to the first UE  121  and the second UE  122  in step S 309 , so as to perform NOMA transmission. 
     Refer to  FIG. 4 . It is a second flowchart illustrating a power allocation method according to an embodiment of the disclosure. The method of this embodiment is adapted to the NOMA system  100  of  FIG. 1 , and each step of  FIG. 4  will be described in detail with reference to each element shown in  FIG. 1  and  FIG. 2 . 
     In step S 401 , the processor  230  receives a first channel estimation error parameter from first UE  121  and receives a second channel estimation error parameter from second UE  122  through the transceiver  210 . In an embodiment, the first channel estimation error parameter and the second channel estimation error parameter represent respectively the MSEs of the channel estimations corresponding to the first UE  121  and the second UE  122 , which can be respectively expressed as σ Δh     1     2  and σ Δh     2     2 , or σ ΔH     1     2  and σ ΔH     2     2  as described above; In other words, after performing the channel estimations, the first UE  121  and the second UE  122  respectively return their MSEs of the channel estimations to the base station  110 . 
     Further, in an embodiment, after performing the channel estimations, the first UE  121  and the second UE  122  can also return other channel estimation results to the base station  110 . Accordingly, the processor  230  can receive a first channel estimation parameter from the first UE and receives a second channel estimation parameter from the second UE through the transceiver  210 . In an embodiment, the first channel estimation parameter and the second channel estimation parameter are respectively variances of channel fading coefficient estimates corresponding to the first UE  121  and the second UE  122 ; that is, the first channel estimation parameter and the second channel estimation parameter can be respectively expressed as σ ĥ     1     2  and σ ĥ     2     2 , or σ Ĥ     1     2  and σ Ĥ     2     2 , as described above. 
     In step S 402 , the processor  230  configures a first minimum rate requirement (unit: bps/Hz) of the first UE  121  and a second minimum rate requirement (unit: bps/Hz) of the second UE  122 . In other words, the base station  110  configures the first minimum rate requirement of the first UE  121  and the second minimum rate requirement of the second UE  122  on the basis of ensuring the QoS of the first UE  121  and the second UE  122 . Here, the first minimum rate requirement and the second minimum rate requirement can be respectively expressed as R 1   T  and R 2   T  as described above, and their values may be the same or different, and may also be pre-configured or dynamically configured. The disclosure is not limited thereto. 
     In step S 403 , the processor  230  determines a power allocation factor according to the first channel estimation error parameter, the second channel estimation error parameter, the first minimum rate requirement, and the second minimum rate requirement. In an embodiment, the power allocation factor is determined based on minimizing a system outage probability upper bound, and the system outage probability upper bound is determined based on satisfying a plurality of constraints set according to the first minimum rate requirement and the second minimum rate requirement. Here, whether the constraints are satisfied or not is determined based on a channel capacity lower bound of the first UE  121  and a channel capacity lower bound of the second UE  122 . Based on the above principles and requirements, in an embodiment, in the case of communicating through the SISO channel, the processor  230  can directly obtain the power allocation factor α IP   opt  according to formula (23), where ϕ 1 =2 R     1       T   −1 and ϕ 2 =2 R     2       T   −1. In the case of communicating through the MIMO channel, the processor  230  can directly calculate the power allocation factor {tilde over (α)} IP   opt  according to equation (32). Here, the base station has M T  transmitting antennas; each of the first UE  121  and the second UE  122  has M R  receiving antennas; M min  is a smaller value between M R  and M T ; {tilde over (ϕ)} 1 =2 R     1       T     /M     min   −1; and {tilde over (ϕ)} 2 =2 R     2       T     /M     min   −1. Further, in an embodiment, the power allocation factor may also be determined according to the first channel estimation parameter returned by the first UE  121  and the second channel estimation parameter returned by the second UE  122 . In the SISO communication environment, the processor  230  can directly calculate the power allocation factor α IP   opt  according to equation (22), where ϕ 1 =2 R     1       T   −1 and ϕ 2 =2 R     2       T   −1. In the MIMO communication environment, the processor  230  can directly calculate the power allocation factor {tilde over (α)} IP   opt  according to equation (31). Here, the base station has M T  transmitting antennas; each of the first UE  121  and the second UE  122  has M R  receiving antennas; M min  is a smaller value between M T  and M R ; {tilde over (ϕ)} 1 =2 R     1       T     /M     min   −1; and {tilde over (ϕ)} 2 =2 R     1       T     /M     min   −1. In summary, regardless of whether it is the SISO or MIMO communication, the processor  230  can efficiently determine the power allocation factor with low computational complexity, and improve the performance of the NOMA system in the imperfect channel estimation environment. 
     In step S 404 , the processor  230  determines first transmission power for the first UE  121  and second transmission power for the second UE  122  according to the power allocation factor. In other words, the processor  230  can obtain the first transmission power by multiplying the power allocation factor α IP   opt  or {tilde over (α)} IP   opt  with total transmission power, and obtain the second transmission power by subtracting the first transmission power from the total transmission power. Here, it is assumed that a channel gain of the first UE  121  is greater than a channel gain of the second UE  122 , and thus the power allocation factor needs to be greater than 0 and less than ½. 
     To sum up, in the embodiments of the disclosure, a power allocation method is proposed for NOMA systems under practical environments with imperfect channel estimation. Compared with the traditional power allocation solutions that were developed based on an assumption of perfect channel estimation, the proposed power allocation method in the disclosure is developed according to the channel estimation error information retuned by the corresponding pieces of UE, and can provide better performance for NOMA systems with imperfect channel estimation. Also, the proposed power allocation method in the disclosure allows each UE to have a basic minimum rate while minimizing an upper bound of the system outage probability. Moreover, by using the closed-form formulas presented in the embodiments of the disclosure, the power allocation factor for NOMA systems can easily be determined with low computational complexity. 
     Although the disclosure has been described with reference to the above embodiments, it will be apparent to one of ordinary skill in the art that modifications to the described embodiments may be made without departing from the spirit of the disclosure. Accordingly, the scope of the disclosure will be defined by the attached claims and not by the above detailed descriptions.