Method of power allocation and base station using the same

The disclosure proposes a method of power allocation and a base station using the method. The method is applicable to a base station for transmitting information signals to at least two user equipments in a non-orthogonal multiple access (NOMA) system. The method includes: setting a first transmit power of a first user equipment to be smaller than a second transmit power of a second user equipment, where a channel gain of the first user equipment is larger than that of the second user equipment; calculating a first system capacity of the first user equipment according to the first transmit power, and calculating a second system capacity of the second user equipment according to the second transmit power; summing the first system capacity and the second system capacity to obtain a sum capacity; and calculating the first transmit power and the second transmit power based on maximizing the sum capacity.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the priority benefit of Taiwan application serial no. 105124901, filed on Aug. 5, 2016. The entirety of the above-mentioned patent application is hereby incorporated by reference herein and made a part of this specification.

BACKGROUND

Technical Field

The present disclosure relates to a method of power allocation, and more particularly, to a method of power allocation in a downlink non-orthogonal multiple access (NOMA) system and a base station using the method.

Description of Related Art

With advancements in technologies, the NOMA has been emerged as a promising technique in the development for next-generation wireless communication systems due to the significant gains in capacity.

In the NOMA system, the user multiplexing is performed in the power domain. Specifically, information signals of different users may be superposed by an appropriate power allocation at the transmitter (e.g., by using a superposition coding technique), and the multi-user signal may later be separated using the successive interference cancellation (SIC) technique at the receiver. Therefore, different users are able to transmit (or receive) information over the same channel resource (e.g., time and frequency) in the NOMA system.

However, there is lack of ideal evaluation criterion for developing a power allocation algorithm that is suitable for the NOMA system.

Nonetheless, in a multiple-input multiple-output non-orthogonal multiple access (MIMO-NOMA) system with two users, two power allocation algorithms have been proposed to maximize a sum capacity by taking into consideration of a minimum rate requirement of a weak user. One of the algorithms with the optimal performance is a bisection search method (i.e., an iterative algorithm) with high computational complexity, whereas another one of the algorithms is a suboptimal method based on a derived lower bound of the capacity of the weak user to reduce the complexity while still suffering certain loss in performance.

Therefore, the development of the power allocation algorithm with high efficiency and high performance for the NOMA system is still one of the subject matters concerned by person skilled in the art.

SUMMARY

The present disclosure provides a method of power allocation and a base station using the method. The method is applicable to a base station for transmitting information signals to at least two user equipments in an NOMA system. The at least two user equipments include a first user equipment and a second user equipment. The method includes: setting a first transmit power of a first user equipment to be smaller than a second transmit power of a second user equipment, where a channel gain of the first user equipment is larger than a channel gain of the second user equipment; calculating a first system capacity of the first user equipment according to the first transmit power, and calculating a second system capacity of the second user equipment according to the second transmit power; summing the first system capacity and the second system capacity to obtain a sum capacity; and calculating the first transmit power and the second transmit power based on maximizing the sum capacity, where Karush-Kuhn-Tucker (KKT) conditions are adopted to obtain the first transmit power and the second transmit power based on maximizing the sum capacity.

In an embodiment of the disclosure, the step in which the KKT conditions are adopted to obtain the first transmit power and the second transmit power based on maximizing the sum capacity includes: setting the first system capacity to be a first minimum rate requirement, where the first minimum rate requirement is a minimum value to be reached by the first system capacity; calculating a first power allocation factor based on maximizing the sum capacity by adopting the KKT conditions; and calculating the first transmit power and the second transmit power according to the first power allocation factor.

In an embodiment of the disclosure, the KKT conditions include a first parameter and a second parameter, where the step of calculating the first power allocation factor based on maximizing the sum capacity by adopting the KKT conditions further includes: setting the first parameter to be greater than zero, and setting the second parameter to be zero; and calculating the first power allocation factor based on maximizing the sum capacity according to the KKT conditions.

In an embodiment of the disclosure, the method further includes: calculating the first system capacity and the second system capacity according to the first transmit power and the second transmit power; and summing the first system capacity and the second system capacity to obtain a sum capacity.

In an embodiment of the disclosure, the step in which the KKT conditions are adopted to obtain the first transmit power and the second transmit power based on maximizing the sum capacity includes: setting the second system capacity to be a second minimum rate requirement, where the second minimum rate requirement is a minimum value to be reached by the second system capacity; calculating a second power allocation factor based on maximizing the sum capacity by adopting the KKT conditions; and calculating the first transmit power and the second transmit power according to the second power allocation factor.

In an embodiment of the disclosure, the KKT conditions include a first parameter and a second parameter, where the step of calculating the second power allocation factor based on maximizing the sum capacity by adopting the KKT conditions further includes: setting the first parameter to be zero, and setting the second parameter to be greater than zero; and calculating the second power allocation factor based on maximizing the sum capacity according to the KKT conditions.

In an embodiment of the disclosure, the method further includes: calculating the first system capacity and the second system capacity according to the first transmit power and the second transmit power; and summing the first system capacity and the second system capacity to obtain a sum capacity.

The disclosure provides a base station, which is applicable to an NOMA system. The base station includes a transceiver circuit, a storage circuit and a processing circuit. The transceiver circuit is configured to transmit information signals to at least two user equipments. The at least two user equipments include a first user equipment and a second user equipment. The storage unit stores a plurality of program codes. The processing circuit is coupled to the transceiver circuit and the storage circuit, and configured to access the program codes to execute following operations of: setting a first transmit power of a first user equipment to be smaller than a second transmit power of a second user equipment, where a channel gain of the first user equipment is larger than a channel gain of the second user equipment; calculating a first system capacity of the first user equipment according to the first transmit power, and calculating a second system capacity of the second user equipment according to the second transmit power; summing the first system capacity and the second system capacity to obtain a sum capacity; and calculating the first transmit power and the second transmit power based on maximizing the sum capacity, where KKT conditions are adopted to obtain the first transmit power and the second transmit power based on maximizing the sum capacity.

In an embodiment of the disclosure, the processing circuit further accesses the program codes to execute operations of: setting the first system capacity to be a first minimum rate requirement, where the first minimum rate requirement is a minimum value to be reached by the first system capacity; calculating a first power allocation factor based on maximizing the sum capacity by adopting the KKT conditions; and calculating the first transmit power and the second transmit power according to the first power allocation factor.

In an embodiment of the disclosure, the KKT conditions include a first parameter and a second parameter. The processing circuit further accesses the program codes to execute operations of: setting the first parameter to be greater than zero, and setting the second parameter to be zero; and calculating the first power allocation factor based on maximizing the sum capacity according to the KKT conditions.

In an embodiment of the disclosure, the processing circuit further accesses the program codes to execute operations of: calculating the first system capacity and the second system capacity according to the first transmit power and the second transmit power; and summing the first system capacity and the second system capacity to obtain a sum capacity.

In an embodiment of the disclosure, the processing circuit further accesses the program codes to execute operations of: setting the second system capacity to be a second minimum rate requirement, where the second minimum rate requirement is a minimum value to be reached by the second system capacity; calculating a second power allocation factor based on maximizing the sum capacity by adopting the KKT conditions; and calculating the first transmit power and the second transmit power according to the second power allocation factor.

In an embodiment of the disclosure, the KKT conditions include a first parameter and a second parameter. The processing circuit further accesses the program codes to execute operations of: setting the first parameter to be zero, and setting the second parameter to be greater than zero; and calculating the second power allocation factor based on maximizing the sum capacity according to the KKT conditions.

In an embodiment of the disclosure, the processing circuit further accesses the program codes to execute operations of: calculating the first system capacity and the second system capacity according to the first transmit power and the second transmit power; and summing the first system capacity and the second system capacity to obtain a sum capacity.

Based on the above, according to the method of power allocation and the base station using the method in the disclosure, the base station can divide the power allocation for the user equipments into two conditions in response to the requirements of the different user equipments. Both the two conditions can ensure that the system capacity related to one user equipment reaches the minimum rate requirement while maximizing the system capacity of the other user equipment.

DESCRIPTION OF THE EMBODIMENTS

In the NOMA system, a base station can share the same communication resource (e.g., the time domain or the frequency domain) to each of users on the power domain, so as to effectively improve a spectrum efficiency. Specifically, the base station superposes signals to be transmitted to multiple users by using the superposition coding and transmits a resulting signal. The users may separate the user signal at the receiver by using the SIC technique. Description regarding the SIC technique used in the NOMA system is provided below with reference toFIG. 1.

FIG. 1illustrates a schematic diagram of the SIC technique used by the users at the receiver. Referring toFIG. 1, it is assumed that a downlink system100has a base station110and two user equipments121and122, and the user equipments121and122are located within a coverage130of the base station110. Among them, it is assumed that the user equipment121has a larger channel gain and the user equipment122has a smaller channel gain.

In the SIC technique, in order to correctly demodulate the signal transmitted by the base station110at the receiver (i.e., the user equipments121and122), the base station110may perform a power allocation for signals to be transmitted to the user equipments121and122. Among them, the signal of a weak user is allocated with more transmit power, and the signal of a strong user is allocated with less transmit power.

In the present embodiment, the user equipment121having the larger channel gain is defined as the strong user and the user equipment122having the smaller channel gain is defined as the weak user. Accordingly, the base station110allocates more transmit power for the signal of the user equipment122and allocates less transmit power for the signal of the user equipment121. As such, the signal {circumflex over (x)} transmitted by the base station110to the user equipments121and122may be written as, for example, Equation (1) below:
{circumflex over (x)}=√{square root over (P1)}s1+√{square root over (P2)}s2Equation (1)
where s1denotes the signal to be transmitted to the user equipment121by the base station110, s2denotes the signal to be transmitted to the user equipment122by the base station110, and P1and P2denote the transmit powers allocated by the base station110for the signals s1and s2, respectively, where the transmit power P1is less than P2.

Signals y1and y2received at the user equipments121and122may be written as Equations (2) and (3) below, respectively,
y1=h1{circumflex over (x)}+n1=√{square root over (P1)}h1s1+√{square root over (P2)}h1s2+n1Equation (2)
y2=h2{circumflex over (x)}+n2=√{square root over (P1)}h2s1+√{square root over (P2)}h2s2+n2Equation (3)
where h1denotes a transmission channel between the base station110and the user equipment121, h2denotes a transmission channel between the base station110and the user equipment122, and n1and n2denote noises received by the user equipments121and122, respectively. Note that n1and n2are, for example, the additive white Gaussian noise (AWGN) with zero-mean and variance N0, but the disclosure is not limited to the above.

In the SIC technique, if the user equipment121is able to perfectly remove interference of the signal s2from the user equipment122by the SIC after receiving the signal y1(e.g., a block141inFIG. 1), the user equipment121can then demodulate the signal s1(e.g., a block142inFIG. 1) to be transmitted to the user equipment121by the base station110without having inference of the signal from the other user. On the other hand, after the signal y2is received by the user equipment122, because the base station110allocates less transmit power P1for the signal s1, the user equipment122can directly demodulate the signal s2(e.g., a block143inFIG. 1) to be transmitted to the user equipment122by the base station110with the signal s1considered as the noise.

After the signals s1and s2are successfully demodulated, system capacities of the user equipments121and122may be written as Equations (4) and (5) below, respectively,
C1=log2(1+P1|h1|2/N0),   Equation (4)
C2=log2(1+P2|h2|2/(P1|h2|2+N0)).   Equation (5)

It should be noted that, according to Equations (4) and (5), it shows that the system capacities C1and C2of the user equipments121and122are related to the transmit powers P1and P2. In other words, the power allocation for the signals s1and s2can directly affect the system capacities of the user equipments121and122. Therefore, with respect to the system capacities of the user equipments121and122, it is very important to appropriately perform the power allocation for the signals s1and s2to be transmitted to the user equipments121and122.

In the embodiments of the disclosure, in order to further improve a sum capacity of the NOMA system, the transmit powers P1and P2are allocated for the signals s1and s2based on maximizing the sum capacity under constraints of user powers and rate requirements.

In this case, an optimization problem based on maximizing the sum capacity CT(where CT=C1+C2) may be written as:

max{P1,P2}⁢C1+C2Equation⁢⁢(6⁢a)Constraint⁢:⁢⁢P1+P2=PTEquation⁢⁢(6⁢b)P1>0,P2>0,P2>P1Equation⁢⁢(6⁢c)C1≥C~1,C2≥C~2Equation⁢⁢(6⁢d)
where PTdenotes a total transmit power, {tilde over (C)}1denotes a minimum rate requirement of the system capacity C1, and {tilde over (C)}2denote a minimum rate requirement of the system capacity C2. Equation (6c) represents the more transmit power P2allocated to the user equipment122having the smaller channel gain and the less transmit power P1allocated to the user equipment121having the larger channel gain according to the NOMA principle, and thus P2>P1. Equation (6d) represents the fact that the system capacity of each of the user equipments must achieve the corresponding rate requirement in order to ensure quality of service (QoS) requirements in the NOMA system.

In order to verify the optimization problem based on maximizing the sum capacity CTmay indeed be solved, the embodiments of the disclosure intend to prove that the sum capacity CTis a strictly increasing function. In the present embodiment, with respect to the total transmit power PT, a power allocation factor α (0<α<1) is defined between the transmit powers P1and P2, where P1=αPTand P2=(1−α)PT. After substituting the transmit powers P1and P2into Equations (4) and (5), the sum capacity CTmay be written as:
CT=C1+C2=log2(1+f(α))  Equation(7)
where ƒ(α)=[αPT(|h1|2N0−|h2|2N0+PT|h1|2|h2|2)+PT|h2|2N0]/(αPT|h2|2N0+N02).

According to Equation (7), the optimization problem based on maximizing the sum capacity CTis equivalent to maximizing ƒ(α) in Equation (7). Accordingly, the optimization problem based on maximizing the sum capacity CTmay be rewritten as:

maxα⁢f⁡(α)Equation⁢⁢(8⁢a)Constraint⁢:⁢⁢μ1-1⁢ϕ1≤α≤(1-μ2-1⁢ϕ2)/(1+ϕ2)Equation⁢⁢(8⁢b)
where ϕ1=2{tilde over (C)}1−1, ϕ2=2{tilde over (C)}2−1, μ1=PT|h1|2/N0, μ2=PT|h2|2/N0. It should be noted that, according to the NOMA principle, an upper bound and a lower bound of Equation (8b) must be less than ½. Therefore, the following two conditions are derived to set ϕ1and ϕ2:
ϕ1<(PT|h1|2)/2N0Equation (9)
ϕ2>(PT|h2|2)/(PT|h2|2+2N0).  Equation(10)

Next, the function ƒ(α) is differentiated into the following:
Dαƒ(α)=(PTN02(|h1|2−|h2|2)(PT|h2|2+N0))/(αPT|h2|2N0+N02)2Equation(11)
According to Equation (11), because of |h1|2>|h2|2, a slope of the function f(α) may be derived to be a positive value. In other words, the function ƒ(α) is the strictly increasing function. When α is equal to the upper bound (1−μ2−1ϕ2)/(1+ϕ2), a maximum value of the function ƒ(α) may be obtained. This optimal solution of α implies that the amount of power allocated for the weak user's signal transmission just can meet the minimum rate requirement {tilde over (C)}2, while the remaining power is used for the strong user's signal transmission to maximize the sum capacity. In practical applications, it may also be desirable to maximize the data rate of the weak user while guaranteeing the minimum rate requirement {tilde over (C)}1of the strong user. However, the optimal solution for this case could not be derived in a similar way as described above.

In view of the above, the present disclosure proposes a method of power allocation, which is capable of appropriately performing the power allocation for the user equipments121and122based on maximizing the sum capacity under the constraints of the user power and the rate requirement.

In the present embodiment, the method of power allocation is applicable to the downlink system100depicted inFIG. 1. It should be noted that, althoughFIG. 1merely illustrates the two user equipments121and122as an example, the disclosure may be applied to more user equipments. In addition, each of the base station110and the user equipments121and122may be configured with M antennas to form the downlink system100of the MIMO-NOMA. M may be any positive integer greater than 1, but the disclosure is not limited thereto. Nonetheless, in the following embodiments, for clarity of the description, issues regarding the power allocation for are discussed based on the base station110and the user equipments121and122being the single-antenna system in the embodiments of the disclosure.

In the present embodiment, the user equipments121and122may be implemented by (but not limited to), for example, 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 or the like, which are not particularly limited by the disclosure.

The base station110may include (but not limited to), for example, 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 and/or a satellite-based communication base station, but the implementation of the disclosure is not limited to the above.

In the present embodiment, the base station110may at least be represented by function elements depicted inFIG. 2.FIG. 2is a block diagram illustrating a base station according to an embodiment of the disclosure. The base station110may at least include (but not limited to) a transceiver circuit210, a storage circuit220and a processing circuit230. The transceiver circuit210may include a transmitter circuit, an A/D (analog-to-digital) converter, a D/A 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 (but the disclosure is not limited thereto), such that the base station110can provide wireless transmitting/receiving functions to the user equipments121and122. The storage circuit220is, for example, a memory, a hard disk or other elements capable of storing data, and may be configured to store a plurality of program codes.

The processing circuit230is coupled to the transceiver circuit210and the storage circuit220, 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) and the like.

In the present embodiment, the processing circuit230can access and execute the program codes stored in the storage circuit220in order to perform each step in the method of power allocation proposed in the present disclosure.FIG. 3is a flowchart illustrating a method of power allocation according to an embodiment of the disclosure. Referring toFIGS. 1 to 3, the method ofFIG. 3may be executed by the base station110ofFIG. 2, and applicable to the downlink system100depicted inFIG. 1. Each step in the method of power allocation ofFIG. 3is described below with reference to each element of the base station110inFIG. 2.

In step S310, the processing circuit230sets a transmit power P1of the user equipment121to be smaller than a transmit power P2of the user equipment122, where a channel gain of the user equipment121is larger than a channel gain of the user equipment122.

In the present embodiment, it is assumed that h1denotes a transmission channel between the base station110and the user equipment121, and h2denotes a transmission channel between the base station110and the user equipment122. Also, it is further assumed that the user equipment121has a larger channel gain whereas the user equipment122has a smaller channel gain (i.e., |h1|2>|h2|2). In order to correctly demodulate the signals transmitted by the base station110at the receiver (i.e., the user equipments121and122) using the SIC technique, the user equipment122having the smaller channel gain is allocated with the more transmit power P2and the user equipment121with the larger channel gain is allocated with the less transmit power P1. In this case, the transmit power P1of the user equipment121is smaller than the transmit power P2of the user equipment (i.e., P1<P2).

In step S320, a system capacity C1of the user equipment121is calculated according to the transmit power P1, and a system capacity C2of the user equipment122is calculated according to the transmit power P2. In the present embodiment, expression of the system capacities C1and C2may refer to Equations (4) and (5) as mentioned above.

In step S330, the system capacities C1and C2are summed to obtain a sum capacity CT(i.e., CT=C1+C2).

In step S340, the processing circuit230calculates the transmit powers P1and P2based on maximizing the sum capacity, where Karush-Kuhn-Tucker (KKT) conditions are adopted to obtain the transmit powers P1and P2based on maximizing the sum capacity.

In the present embodiment, to achieve the QoS requirements of the two user equipments121and122in the NOMA system, the transmit powers P1and P2are allocated under the constraints of the user power and the rate requirement as set in advance in the optimization problem based on maximizing the sum capacity CT(where CT=C1+C2). The expression regarding the optimization problem based on maximizing the sum capacity CT(where CT=C1+C2) may refer to Equations (8a) and (8b).

Further, in the present embodiment, the transmit powers P1and P2based on maximizing the sum capacity are obtained by adopting the KKT conditions. The KKT conditions may be written as:
i)Dαg(α)+λ1Dα(ϕ1/μ1−α)+λ2Dα(α−(1/(1+ϕ2))(1−ϕ2/μ2))=0
ii)(ϕ1/μ1−α)λ1=0
iii)(α−(1/(1+ϕ2))(1−ϕ2/μ2))λ2=0
iv)ϕ1/μ1−α≤0
v)α−(1/(1+ϕ2))(1−ϕ2/μ2)≤0
vi)0<α<1/2
vii)λ1,λ2≥0  Equation(12)
where g(α)=−ƒ(α)≤0, and λ1and λ2are Lagrange multipliers of constraints C1≥{tilde over (C)}1and C2≥{tilde over (C)}2, respectively. The condition i) in Equation (12) may be written as:
(PTN02(|h2|2−|h1|2)(N0+PT|h2|2))/(αPT|h2|2N0+N02)2−λ1+λ2=0.   Equation (13)

With respect to λ2>0 and λ1>0, the conditions ii) and iii) in Equation (12) must be met to obtain the power allocation factor α. If λ2=0 is set for the case of λ1>0, the power allocation factor α may be obtained from the condition ii) in Equation (12), as shown below:
α1opt=(ϕ1N0)/(PT|h1|2)=ϕ1/μ1.  Equation(14)
On the other hand, if λ1=0 is set for the case of λ2>0, the power allocation factor α may be obtained from the condition iii) in Equation (12), as shown below:
α2opt=[1/(1+ϕ2)][1−(ϕ2N0)/(PT|h2|2)]=[1/(1+ϕ2)][1−ϕ2/μ2].  Equation(15)

It should be noted that the optimization problem [i.e., Equations (8a) and (8b)] for maximizing the sum capacity CTwithout the minimum rate requirements but with P2>P1has the optimal solution α very close to ½, implying almost equal power allocation for the strong user's and the weak user's signal transmission. This would make the user multiplexing in the power domain not useful. Hence, with the minimum rate requirements, α≥ϕ1/μ1or [α≤(1−ϕ2/μ2)/(1+ϕ2)] must be satisfied to achieve C1≥{tilde over (C)}1(or C2≥{tilde over (C)}2). The optimal α1opt(or α2opt) can ensure that the capacity of the strong user (or the weak user) always meets the rate requirement {tilde over (C)}1(or {tilde over (C)}2) (i.e., the equality holds). By guaranteeing the minimum rate of one user equipment, such optimal solutions can maximize the rate of the other user equipment.

In other words, when taking into consideration of the powers and the minimum rate requirements of the two user equipments, the optimal power allocation factor α may be different based on the powers and the minimum rate requirements of the user equipments. For instance, for allowing the system capacity C1to achieve the minimum rate requirement {tilde over (C)}1(i.e., C1≥{tilde over (C)}1), the power allocation factor α must be greater than or equal to ϕ1/μ1. In contrast, for allowing the system capacity C2to achieve the minimum rate requirement {tilde over (C)}2(i.e., C2≥{tilde over (C)}2), the power allocation factor α must be less than or equal to [1/(1+ϕ2)][1−ϕ2/μ2]. Accordingly, α1optcan ensure that the system capacity C1of the user equipment121meets the minimum rate requirement {tilde over (C)}1while maximizing the sum capacity C2of the user equipment122, whereas α2optcan ensure that the system capacity C2of the user equipment122meets the minimum rate requirement {tilde over (C)}2while maximizing the subscriber equipment C1of the user equipment121.

Hence, two methods may be further developed from step340to obtain the transmit powers P1and P2. In order to describe said two methods, the disclosure further divides step S340into steps S410to S430inFIG. 4and steps S510to S530inFIG. 5.

FIG. 4is a flowchart illustrating the method of power allocation executed by taking a system capacity of the user equipment121as a prime consideration according to an embodiment of the disclosure.

In step S410, the processing circuit230sets the system capacity C1to be the minimum rate requirement {tilde over (C)}1, where the minimum rate requirement {tilde over (C)}1is a minimum value to be reached by the system capacity C1.

In step S420, the processing circuit230calculates a first power allocation factor α1optbased on maximizing the sum capacity CTby adopting the KKT conditions. In the present embodiment, λ1>0 and λ2=0 are set according to the KKT conditions in Equation (12), so as to calculate the first power allocation factor α1optbased on maximizing the sum capacity CT. In an embodiment of the disclosure, the first power allocation factor α1optmay be directly calculated according to Equation (14).

In step S430, the processing circuit230calculates the transmit powers P1and P2according to the first power allocation factor α1opt. In the present embodiment, because the transmit power P1=α1optPTand the transmit power P2=(1−α1opt)PT, the transmit powers P1and P2may be calculated separately after the first power allocation factor α1optis obtained.

Next, the processing circuit230may then obtain the system capacity C1[based on Equation (4)] and the system capacity C2[based on Equation (5)] according to the transmit powers P1and P2, and sum the system capacity C1and the system capacity C2to obtain the sum capacity CT.

In another embodiment,FIG. 5is a flowchart illustrating the method of power allocation executed by taking a system capacity of the user equipment122as a prime consideration according to an embodiment of the disclosure.

In step S510, the processing circuit230sets the system capacity C2to be the minimum rate requirement {tilde over (C)}2, where the minimum rate requirement {tilde over (C)}2is a minimum value to be reached by the system capacity C2.

In step S520, the processing circuit230calculates a second power allocation factor α2optbased on maximizing the sum capacity CTby adopting the KKT conditions. In the present embodiment, λ1=0 and λ2>0 are set according to the KKT conditions in Equation (12), so as to calculate the second power allocation factor α2optbased on maximizing the sum capacity CT. In an embodiment of the disclosure, the second power allocation factor α2optmay be directly calculated according to Equation (15).

In step S530, the processing circuit230calculates the transmit powers P1and P2according to the second power allocation factor α2opt. In the present embodiment, because the transmit power P1=α2optPTand the transmit power P2=(1−α2opt)PT, the transmit powers P1and P2may be calculated separately after the second power allocation factor α2optis obtained.

Next, the processing circuit230may then obtain the system capacity C1[based on Equation (4)] and the system capacity C2[based on Equation (5)] according to the transmit powers P1and P2and sum the system capacity C1and the system capacity C2to obtain the sum capacity CT.

In brief, the KKT conditions are adopted to obtain the transmit power based on maximizing the sum capacity in the method of power allocation according to embodiments of the disclosure, such that the rate requirement of one user equipment may be preset under different situations to obtain the optimal allocation of the transmit power while maximizing the system capacity of another user equipment.

It should be noted that an extension of the method of power allocation to a MIMO scenario may be described as follows. Denoting a MIMO channel matrix between the base station and an nthuser by Hn, the singular value decomposition process may be adopted to obtain all the singular values, where the square of each singular value represents an independent subchannel gain. Regarding the MIMO channel as a “big single-input single-output channel” formed by a bundle of all independent subchannels, the effective channel gain may be obtained by computing the sum of all the squared singular values of Hn, which is equal to the squared Frobenius norm ∥Hn∥F2. By replacing |h1|2and |h2|2with ∥H1∥F2and ∥H2∥F2in Equations (14) and (15), the method of power allocation can be directly applied to a MIMO scenario, where the power allocated to each user is equally distributed among antennas for signal transmission.

FIG. 6andFIG. 7are schematic diagrams illustrating simulation results of the system capacity or the sum capacity of the user equipments versus the signal-to-noise ratio (SNR). The simulation results are used to describe the effectiveness of the method of power allocation proposed in the embodiments of the disclosure. InFIG. 6andFIG. 7, a horizontal axis represents SNR using dB as a unit, and a vertical axis represents the capacity measured using bit per second/Hertz (or bps/Hz) as a unit.

It should be noted that, the simulation results inFIG. 6andFIG. 7are obtained by averaging 105channel realizations. It is adopted the common path-loss model with path-loss exponent ν=3 for a fading channel, where the variance of the channel fading coefficient hn, n∈{1,2}, from the base station to user equipment (with distance dn) is normalized to be unity for unit reference distance, i.e., σhn2=dn−ν. The AWGN for each user equipment has unit variance (i.e., N0=1), and the SNR is defined as PT/N0. For the purpose of performance comparison, σh12/N0is set to be 20 dB and σh22/N0is set to be 10 dB, where the user equipment121(or the strong user) is closer to the base station110than the user equipment122(or the weak user). According to the NOMA principle, the larger the channel gain difference |h1|2−|h2|2between the user equipment121and122, the better the system performance. In other words, it would be better to pair/schedule a user closer to the base station and another user farther from the base station together for NOMA transmission.

In bothFIG. 6andFIG. 7, a system capacity of an orthogonal multiple access (OMA) system is adopted to compare with that of the present disclosure, where the system capacity of an nthuser equipment may be written as Cn,OMA=(1/2)log2(1+(Pn,OMA|hn|2)/(1/2)N0). Further, a transmit power Pn,OMAin the OMA system achieves maximizing the system capacity and the constraints of the user power and the rate requirement by adopting a Full-Search method. Solid lines are used to represent the method of power allocation for the NOMA system proposed in the embodiments of the disclosure, and dotted lines are used to represent the method of power allocation for the OMA system with the use of the Full-Search method. In each of the two methods of power allocation, it is assumed that the minimum rate requirement {tilde over (C)}2is 1 bps/Hz and the minimum rate requirement {tilde over (C)}1is 2 bps/Hz and the two methods are applied in the single-antenna system. C1,NOMAand C2,NOMAare used to denote the system capacities of the strong user and the weak user in the NOMA system in the embodiments of the disclosure, respectively. Similarly, C1,OMAand C2,OMAare used to denote the system capacities of the strong user and the weak user in the OMA system in the embodiments of the disclosure, respectively.

Referring toFIG. 6, the simulation result shows that each C2,NOMAmeets the minimum rate requirement {tilde over (C)}2, which is 1 bps/Hz. Despite C2,NOMAis less than C2,OMA, the sum capacity of the NOMA system is greater than the sum capacity of the OMA system (i.e., C1,NOMA+C2,NOMA>C1,OMA+C2,OMA)since C1,NOMAis greater than C1,OMA. Similarly, referring toFIG. 7, the simulation result shows that each C1,NOMAmeets the minimum rate requirement {tilde over (C)}1, which is 2 bps/Hz and C2,NOMAis far greater than C2,OMA(i.e., the system capacity of the weak user in the NOMA system is significantly increased), and thus the sum capacity of the NOMA system is greater than the sum capacity of the OMA system (i.e., C1,NOMA+C2,NOMA>C1,OMA+C2,OMA).

On the other hand,FIG. 8a schematic diagram illustrating a simulation result of the sum capacity versus the SNR using different methods of power allocation in the MIMO NOMA system. InFIG. 8, the method of power allocation proposed in the embodiments of the present disclosure is compared with the iterative algorithm and the low-complexity suboptimal power allocation mentioned in the prior art. Referring toFIG. 8, a symbol “∘” is used to denote the method of power allocation proposed in the embodiments of the present disclosure (i.e., Proposed NOMA-PA); a symbol “x” is used to denote the method of power allocation that adopts the iterative algorithm (i.e., Iterative NOMA-PA); and a symbol “Δ” is used to denote the suboptimal power allocation (i.e., Suboptimal NOMA-PA). In addition, M is used to denote a number of antennas. The simulation result shows that the method proposed in the embodiments of the disclosure can achieve a higher performance than the suboptimal power allocation and can achieve the system capacity similar to that of the iterative algorithm.

In addition, with respect to the comparison between complexities, the numbers of floating point operations (flops) are respectively evaluated in the present disclosure and the related methods. It is assumed that the numbers of antennas equipped at the base station and at each user equipment are NTand NR, respectively and the length of transmit symbols would denote M=min(NT,NR). In the present disclosure, the numbers of flops for calculating Equation (11) and (12) are 5 and 9, respectively. Hence, a MIMO scenario need 2NRNT+4 and 2NRNT+8 flops. When denoting N as the iteration number, the iterative algorithm needs N( 35/3M3−4M2+M) flops to find the optimal solution. Also, the suboptimal approach requires 8/3M3−M2+8 flops to find the optimal solution. Accordingly, it shows that the present disclosure has much lower computational complexity than the related works.

In summary, according to the method of power allocation and the base station using the method in embodiments of the disclosure, the base station can divide the power allocation for the user equipments into two conditions in response to the minimum rate requirements of the different user equipments. That is to say, the minimum rate requirement of one user equipment may be preset to obtain the optimal allocation for the transmit power while maximizing the system capacity of another user equipment. Other than that, in addition to the result of the method proposed in the embodiments of the present disclosure showing the lower computational complexity as compared to the iterative algorithm, the simulation result also indicates that their performances are very close.