CN115278848A - NOMA-based joint precoding and power distribution method - Google Patents

NOMA-based joint precoding and power distribution method Download PDF

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CN115278848A
CN115278848A CN202111220665.XA CN202111220665A CN115278848A CN 115278848 A CN115278848 A CN 115278848A CN 202111220665 A CN202111220665 A CN 202111220665A CN 115278848 A CN115278848 A CN 115278848A
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高志祥
刘爱军
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Army Engineering University of PLA
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/18—TPC being performed according to specific parameters
    • H04W52/24—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/04—Wireless resource allocation
    • H04W72/044—Wireless resource allocation based on the type of the allocated resource
    • H04W72/0473—Wireless resource allocation based on the type of the allocated resource the resource being transmission power
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention discloses a combined pre-coding and power distribution method based on NOMA, which is used for determining the reachable rate of each user in a selected wave beam based on the NOMA of a non-complete SIC; with the goal of maximizing the reachable rate of each user, considering beam power limitation and ensuring the minimum service quality of the user, establishing a combined precoding and power distribution problem based on NOMA; converting the problem into two sub-problems, wherein the first sub-problem is fixed power, and optimizing a precoding vector; the second sub-problem is to fix the precoding vector and optimize the power; and carrying out iterative solution on the global optimal solution based on the subproblem solution result, wherein the obtained global optimal solution is used as the precoding vector and the power of each user. When the method designs the precoding vector, the power distributed by the user and the channel state information of the user are simultaneously considered, and better rate performance can be obtained.

Description

NOMA-based joint precoding and power distribution method
Technical Field
The invention belongs to the field of information communication, and particularly relates to a joint precoding and power allocation method based on NOMA.
Background
The heaven-earth converged network can realize global deep coverage and heaven-earth integrated communication, and is an important direction for development of 5G and 6G in the future. Currently, satellite communication is mainly focused on geostationary satellite orbits and medium and high orbit satellite scenarios, using multi-color frequency multiplexing, orthogonal Multiple Access (OMA), and fixed power allocation. Compared with a geostationary orbit (GEO) satellite, the low-earth orbit (LEO) network has smaller transmission delay, can provide wider coverage for 5G and future 6G, has real-time access and realizes efficient communication.
The satellite network is limited in power and frequency due to the inherent characteristics of the satellite, and the problem of low frequency spectrum utilization rate exists when multi-color multiplexing is adopted; when the number of the users on the ground is far larger than that of the antennas, the adoption of the orthogonal multiple access mode requires multiple access scheduling to enable all the users to be served, so that the cost is high, and the frequency spectrum efficiency is low.
The multibeam antenna is widely used in a satellite communication system because it can cover a large ground area with high gain and can adjust the beam shape as needed. By using the multi-beam antenna technology, the satellite terminal can adopt the precoding technology to eliminate the influence of the interference between beams. In the past, the precoding method only considers the channel characteristics and does not consider the actual distributed power of the user, and the system cannot realize the optimal spectrum efficiency. In order to obtain larger system capacity or spectrum efficiency, the traditional power allocation algorithm sacrifices the user benefit of poor channel quality, so that the traditional power allocation algorithm can be served with little energy and lacks fairness. In the prior art, the influence of power on precoding is not considered, the spectrum efficiency of the system is reduced, and the same user can only be served in the same beam, so that the service efficiency is low.
Disclosure of Invention
The invention aims to provide a joint precoding and power allocation method based on NOMA (non-orthogonal multiple access) aiming at the technical problem that the influence of power on precoding is not considered in the prior art.
The invention adopts the following technical scheme.
A joint precoding and power allocation method based on NOMA is provided, which comprises the following steps:
determining the signal-to-interference-and-noise ratio of each user in the selected wave beam in a non-orthogonal multiple access mode, and determining the reachable rate of each user in the selected wave beam according to the signal-to-interference-and-noise ratio of each user;
the method comprises the steps of taking the reachable rate of each user in a selected beam as a target, considering beam power limitation and ensuring the minimum service quality of the user, and establishing a combined precoding and power distribution problem based on NOMA;
converting the joint precoding and power distribution problem based on NOMA into two sub-problems, wherein the first sub-problem is fixed power, and a precoding vector is optimized; the second sub-problem is to fix the precoding vector and optimize the power; and iteratively solving a global optimal solution based on the solving result of the subproblem, wherein the obtained global optimal solution is used as the precoding vector and the power of each user.
Further, the sir calculation formula for each user is as follows:
Figure BDA0003312508000000021
wherein the SINRmnFor user n in beam m,
Figure BDA0003312508000000022
for the signal strength of user n in beam m, WmnPrecoding vectors, p, for users n in a beam mmnFor user N in beam m, power, NmIs the number of users in the beam m, WmiPrecoding vector, p, for user i in beam mmiFor the power, σ, of user i in beam m2Is gaussian white noise power.
Still further, the achievable rate for each user in a beam is represented as:
Rmn＝log2(1+SINRmn) (2)
wherein R ismnThe achievable rate for user n in beam m.
Further, the NOMA-based joint precoding and power allocation problem is expressed as follows:
Figure BDA0003312508000000031
wherein
Figure BDA0003312508000000032
WmnPrecoding vectors, p, for users n in a beam mmnFor user N in beam m, power, NmIs the number of users in the beam m, RmnReachable rate, p, for user n in beam mmIs the total power of beam m, pmnFor the power of user n in beam m, r0The minimum quality of service for the user.
Still further, the first sub-problem is represented as:
Figure BDA0003312508000000041
still further, the solving method of the first sub-problem is as follows:
converting the maximized SINR into a maximized SINR, as follows:
Figure BDA0003312508000000042
the above problem is the generalized Rayleigh entropy problem, and the optimal solution of the precoding vector is
Figure BDA0003312508000000043
Wherein the content of the first and second substances,
Figure BDA0003312508000000044
and I is a standard matrix.
Still further, the second sub-problem is represented as:
Figure BDA0003312508000000045
wherein
Figure BDA0003312508000000046
Reachable rate R for user n in beam mmnAn approximation of (d).
Still further, the method for solving the second sub-problem includes:
order to
Figure BDA0003312508000000047
Figure BDA0003312508000000048
And transforming the sub-problem P2 into a convex optimization problem for the natural logarithm of the power of the user n in the wave beam m, solving a lower bound of the optimal power when the precoding vector is fixed by using a Lagrange dual method and a secondary gradient method, and obtaining the power of the user n in the wave beam m when the precoding vector is fixed by using an iteration method.
Still further, the method for iteratively obtaining the power of the user n in the beam m while fixing the precoding vector comprises:
step 1: set the maximum number of iterations lmaxIteration number l =0, initial value of randomly allocated power
Figure BDA0003312508000000051
Step 2: set the dual vector to be non-negative, update alphamn，
Figure BDA0003312508000000052
Figure BDA0003312508000000053
The SINR value of the user n in the wave beam m in the ith iteration is obtained;
and step 3: by using
Figure BDA0003312508000000054
And the following formula obtains the power p of the user n in the beam m at this timemn，
Figure BDA0003312508000000055
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003312508000000056
corresponding non-negative dual vectors of constraint C1 and C2 of formula (7), t is the iteration number of obtaining optimal dual variable by using a secondary gradient method, sigma2Is the power of white gaussian noise and is,
Figure BDA0003312508000000057
is the power, H, of user j in beam m at the l-th iterationin、HijIs an intermediate parameter that is a function of,
Figure BDA0003312508000000058
Figure BDA0003312508000000059
and 4, step 4: updating the dual vectors by using (14) and (15), if the dual vectors are converged, turning to the step 5, otherwise, returning to the step 3;
Figure BDA0003312508000000061
Figure BDA0003312508000000062
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003312508000000063
and τtThe t-th iteration step length (x) when obtaining the optimal dual variable for the sub-gradient method+Is the maximum of x and 0;
and 5: l = l +1, and/or,
Figure BDA0003312508000000064
step 6: if l > lmaxOr the power converges, then the power p is outputmnOtherwise, returning to the step 2.
The method for iteratively solving the global optimal solution based on the subproblem solving result comprises the following steps:
step 1: randomly allocating power to each user according to user gain
Figure BDA0003312508000000065
Sum rate
Figure BDA0003312508000000066
The current iteration number is q, and q =1;
step 2: according to the power of the q-1 iteration
Figure BDA0003312508000000067
And the formula (6) obtains the precoding vector of each user at the q iteration
Figure BDA0003312508000000068
And step 3: according to the precoding vector at the q iteration
Figure BDA0003312508000000069
And solving the second sub-problem to obtain the power of each user in the q iteration
Figure BDA00033125080000000610
And 4, step 4: substituting the power and the precoding vector obtained in the q-th iteration into a formula (2), calculating the reachable rate of each user in the beam m, and calculating the sum rate of the users in the q-th iteration
Figure BDA00033125080000000611
And the sum rate of q-1 iteration of each user is calculated according to the reachable rate of each user
Figure BDA00033125080000000612
If it is
Figure BDA00033125080000000613
And if zeta is a convergence parameter, outputting the precoding vector and power of each user, otherwise, q = q +1, and returning to the step 2.
Figure BDA0003312508000000071
Rmn＝log2(1+SINRmn) (2)
The invention has the following beneficial technical effects:
the method considers the incompleteness of serial interference elimination, dynamically allocates the power of each user according to the channel state information of each user, and compared with the traditional fixed allocation of power, the dynamic allocation of power can enable the system to obtain higher sum rate;
the traditional method for designing precoding only considers the channel state information and does not consider the power distributed by each user, when the method designs precoding, the power distributed by the user and the channel state information of the user are simultaneously considered, and a precoding vector closed expression (formula (6)) of each user based on the user state information and the power is deduced, compared with the traditional precoding, the precoding method can obtain better rate performance;
in the LEO satellite network, users are accessed in an OMA mode, the method adopts the NOMA mode to access the users, and precoding and power distribution are jointly optimized based on the NOMA, so that the whole system can provide services for the users in one beam compared with the OMA mode and the combined precoding and power distribution based on MIMO, higher sum rate is obtained, service efficiency is improved, and certain fairness is ensured.
Drawings
FIG. 1 is a flow chart of a method for solving a second sub-problem in an embodiment of the present invention;
FIG. 2 is a flowchart of a NOMA-based joint precoding and power allocation method according to an embodiment of the present invention;
FIG. 3 illustrates the convergence of the proposed method according to an embodiment of the present invention;
fig. 4 is a graph illustrating the performance of the proposed method as a function of signal to noise ratio according to an embodiment of the present invention.
Detailed Description
The invention is further described in the following with reference to the drawings and the specific embodiments.
Example 1: a joint precoding and power allocation method based on NOMA, as shown in fig. 2, comprising:
according to the basic principle of NOMA, it is assumed that the signal strength of a user receiving each beam at the LEO satellite end satisfies the following relationship:
Figure BDA0003312508000000081
wherein the content of the first and second substances,
Figure BDA0003312508000000082
representing the channel gain of user n in beam m, considering the user receiving end SIC: (Successive Interference Cancellation,Successive interference cancellation), the signal-to-interference-and-noise ratio of user n in beam m is
Figure BDA0003312508000000083
Wherein wmn，pmnPrecoding vector and power, N, respectively, for user N in beam mmFor the number of users in the beam m, μ is the incomplete successive interference cancellation (interference SIC) factor, σ2Is gaussian white noise. The achievable rate based on user n in beam m can be expressed as:
Rmn＝log2(1+SINRmn) (2)。
the method realizes the maximization of beam users and rate by combining time precoding and power allocation, considers beam power limitation and ensures the minimum service quality of users. Order to
Figure BDA0003312508000000084
Thus, the optimization objective function can be expressed as:
Figure BDA0003312508000000091
wherein, C1 is QoS constraint, C2 and C3 are power constraint, and C4 is precoding vector normalization constraint. N is a radical ofmFor the number of users in the beam m, pmTotal power of beam m, pmnFor the power of user n in beam m, r0The minimum quality of service for the user. Since the objective function is non-convex and the power is coupled with the precoding vector, it is difficult to directly solve the problem, which we decompose into two sub-problems, the first sub-problem: fixing power and optimizing a precoding vector; the second sub-problem: and fixing the precoding vector and optimizing the power. And finally, solving the optimal sum rate by iteration.
The first sub-problem is solved, and when the power is fixed, the original problem is converted into the maximization of the signal to interference and noise ratio of each user, namely
Figure BDA0003312508000000092
At this time, we cannot find the closed-form solution of the precoding vector, so the maximized signal-to-interference-and-noise ratio is converted into the maximized signal-to-leakage-and-noise ratio, that is, the maximum signal-to-interference-and-noise ratio
Figure BDA0003312508000000093
The above problem is the generalized Rayleigh entropy problem, and the optimal solution of the precoding vector is
Figure BDA0003312508000000101
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003312508000000102
Figure BDA0003312508000000103
is GmnI is a standard matrix.
And solving the second subproblem, wherein when the precoding vectors are fixed, the power distribution of each user is an optimization problem, and the subproblems are difficult to solve directly due to the fact that an objective function is not convex. Using formulas
Figure BDA0003312508000000104
Then the rate R can be reachedmn＝log2(1+SINRmn) Can be approximately expressed as
Figure BDA0003312508000000105
Wherein the content of the first and second substances,
Figure BDA0003312508000000106
Figure BDA0003312508000000107
is the SINR value of user n in beam m at the ith iteration. The original problem is approximated to
Figure BDA0003312508000000108
Wherein
Figure BDA0003312508000000109
Reachable rate R for user n in beam mmnIs approximately represented by pmnFor the power of user N in beam m, N =1,2, \8230;, Nm，NmFor the number of users in the beam m, pmFor the total power of beam m, order
Figure BDA00033125080000001010
Figure BDA00033125080000001011
N natural logarithm of power for m users of beamThe problem P2 translates into a convex optimization problem. Then lagrangian dual and secondary gradient methods can be used to solve. Order to
Figure BDA00033125080000001012
The lagrange function can be expressed as:
Figure BDA0003312508000000111
wherein the content of the first and second substances,
Figure BDA0003312508000000112
the non-negative dual vector of C1 is constrained for equation (7), and η is the non-negative dual vector of C2 is constrained for equation (7). Because the original problem is a convex optimization problem, the optimal solution of the dual problem is the optimal solution of the original problem, and the dual variable is updated by using a secondary gradient method.
For is to
Figure BDA0003312508000000113
Derivation, the first derivative of the Lagrange dual function is 0 and KKT condition is applied, so that
Figure BDA0003312508000000114
Figure BDA0003312508000000115
λmn(αmnln(SINRmn)+βmn-r0)＝0 (11)
Wherein Hin、HijIs an intermediate parameter, which can be expressed as
Figure BDA0003312508000000116
Figure BDA0003312508000000117
The power of user n in beam m can be expressed as
Figure BDA0003312508000000121
Figure BDA0003312508000000122
Respectively corresponding non-negative dual vectors of constraint C1 and C2 of formula (7), and t is the iteration number of obtaining optimal dual variable by the sub-gradient method, sigma2Is the power of white gaussian noise and is,
Figure BDA0003312508000000123
is the power of user j in beam m at the ith iteration. Using sub-gradient methods, parameters
Figure BDA0003312508000000124
And ηlCan be obtained by the following two formulas:
Figure BDA0003312508000000125
Figure BDA0003312508000000126
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003312508000000127
and τtThe t iteration step length (x) when obtaining the optimal dual variable for the secondary gradient method+Is the maximum of x and 0. And when the dual vector is converged, obtaining the optimal power of the problem P2 under the fixed precoding vector. The obtained optimal power is the lower bound of the problem P when the precoding vector is fixed, and in order to obtain the optimal power of the problem P when the precoding vector is fixed, an iterative method is adopted, which is summarized as an algorithm 1, and the steps are as follows:
1. set the maximum number of iterations lmaxIteration number l =0, initial value of randomly allocated power
Figure BDA0003312508000000128
2. Setting the dual vector to be non-negative and updating alphamn,
Figure BDA0003312508000000129
The SINR value of the user n in the beam m in the ith iteration is obtained;
3. by using
Figure BDA00033125080000001210
And equation (13) yields the power p at that timemn；
4. Updating the dual vectors by using (14) and (15), if the dual vectors are converged, turning to the step 5, otherwise, returning to the step 3;
5.l＝l+1,
Figure BDA0003312508000000131
6. if l > lmaxOr the power converges, then the power p is outputmnOtherwise, the flow chart of the algorithm 1 is returned to the step 2 as shown in fig. 1.
In order to obtain a global optimal solution, an iterative algorithm of joint precoding and power allocation based on NOMA is provided: a specific algorithm of the NOMA based joint precoding and power allocation method, algorithm 2, is given below, as follows:
1. randomly allocating power to each user according to user gain
Figure BDA0003312508000000132
And rate of speed
Figure BDA0003312508000000133
The current iteration number is q, and q =1;
2. according to the power of the q-1 iteration
Figure BDA0003312508000000134
And the formula (6) obtains the precoding vector of each user at the q iteration
Figure BDA0003312508000000135
3. According to the precoding vector at the q-th iteration
Figure BDA0003312508000000136
And solving the second subproblem to obtain the power of each user in the q iteration
Figure BDA0003312508000000137
4. Substituting the power and the pre-coding vector obtained in the q iteration into a formula (2), calculating the velocity of each user, and calculating the sum velocity of the q iteration of the user
Figure BDA0003312508000000138
If it is
Figure BDA0003312508000000139
And if zeta is a convergence parameter, outputting the precoding vector and power of each user, otherwise, q = q +1, and returning to the step 2.
A detailed flowchart of the joint precoding and power allocation method based on NOMA is shown in fig. 2.
To highlight the performance advantage of the proposed method, the following simulation verification was done. The simulation parameters were set as follows, with 16 × 16 antennas, 600km satellite orbits, r0=0.01bit/s/Hz, without loss of generality, the product of the satellite antenna gain, the user antenna gain and the free space loss of the orbit height is 1, the Rice factor is 10dB, the number of multipaths is 5, and the maximum number of iterations q ismax=20. The non-orthogonal multiple access represents a joint precoding and power allocation method based on the non-orthogonal multiple access, namely the method is provided, the complete SIC represents complete serial interference elimination, the non-complete SIC, mu =0.01 represents incomplete interference elimination, and the orthogonal multiple access represents a MIMO joint precoding and power allocation method based on the orthogonal multiple access.
As can be seen from fig. 3, the joint precoding and power allocation methods based on complete SIC and non-complete SIC have better convergence and higher performance than the MIMO joint precoding and power allocation methods based on orthogonal multiple access. When complete SIC is considered, the influence of the pre-coding vector on the power is small, so that the sum rate tends to be stable after 1 iteration, and convergence is achieved; when the incomplete SIC is considered, the user power has influence on the design of precoding, the sum rate of the proposed non-orthogonal multiple access-based joint precoding and power distribution method is increased along with the increase of the number of iterations, and when the number of iterations is more than 12, the sum rate is stable, and the convergence is verified; the proposed method is able to better regulate inter-user power, and therefore the performance of the proposed method based on non-full SIC is slightly degraded compared to full SIC.
Fig. 4 depicts a graphical representation of performance as a function of signal to noise ratio. The gap between the non-orthogonal multiple access (star) and MIMO-based joint precoding and power allocation (triangle) approaches of orthogonal multiple access remains substantially constant as the signal-to-noise ratio increases. When the signal-to-noise ratio is 20dB, the performance of the non-orthogonal multiple access method is improved by about 33% compared with the orthogonal multiple access method. This is because the proposed non-orthogonal multiple access method can serve multiple users in each beam, and non-orthogonal multiple access has higher spectral efficiency than orthogonal multiple access. When non-complete successive interference cancellation is considered (circled lines), the proposed power allocation algorithm can effectively adjust the power of each user such that the system performance is slightly degraded under this condition.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (10)

1. A joint precoding and power allocation method based on NOMA is characterized by comprising the following steps:
determining the signal-to-interference-and-noise ratio of each user in a selected wave beam in a non-orthogonal multiple access mode, and determining the reachable rate of each user in the selected wave beam according to the signal-to-interference-and-noise ratio of each user;
the method comprises the steps of taking the reachable rate of each user in a selected beam as a target, considering beam power limitation and ensuring the minimum service quality of the user, and establishing a combined precoding and power distribution problem based on NOMA;
converting the joint precoding and power distribution problem based on NOMA into two sub-problems, wherein the first sub-problem is fixed power, and a precoding vector is optimized; the second sub-problem is to fix the precoding vector and optimize the power; and iteratively solving a global optimal solution based on the solving result of the subproblem, wherein the obtained global optimal solution is used as a precoding vector and power of each user.
2. The method of claim 1, wherein the SINR of each user is calculated as follows:
Figure FDA0003312507990000011
wherein the SINRmnFor user n in beam m,
Figure FDA0003312507990000012
for the signal strength of user n in beam m, WmnPrecoding vectors, p, for users n in a beam mmnFor the power of user N in beam m, NmIs the number of users in the beam m, WmiPrecoding vectors, p, for users i in beam mmiFor the power, σ, of user i in beam m2Is the Gaussian white noise power, μ is the non-perfect SIC factor.
3. The NOMA-based joint precoding and power allocation method of claim 2, wherein the achievable rate for each user in a beam is represented as:
Rmn＝log2(1+SINRmn) (2)
wherein R ismnThe achievable rate for user n in beam m.
4. The method of claim 1, wherein the NOMA-based joint precoding and power allocation problem is represented as follows:
Figure FDA0003312507990000021
wherein
Figure FDA0003312507990000022
Figure FDA0003312507990000023
WmnPrecoding vectors, p, for users n in a beam mmnIs the power of user N in beam m, N =1,2m；NmIs the number of users in the beam m, RmnReachable rate, p, for user n in beam mmIs the total power of the beam m, r0The minimum quality of service for the user.
5. The method of claim 2, wherein the first subproblem is represented by:
Figure FDA0003312507990000031
wherein
Figure FDA0003312507990000032
WmnPrecoding vector for user N in beam m, NmIs the number of users in beam m.
6. The method of claim 5, wherein the solving of the first sub-problem comprises:
converting the maximized SINR to the maximized SINR, as follows:
P1′：
Figure FDA0003312507990000033
wherein SLNRmnFor user n in beam m the signal to leakage noise ratio,
Figure FDA0003312507990000034
for the signal strength, p, of user i in beam mmiPower for user i in beam m;
the above problem is a generalized Rayleigh entropy problem, and the optimal solution for the precoding vector of user n in beam m is
Figure FDA0003312507990000035
Wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003312507990000036
，
i is a standard matrix, and I is a standard matrix,
Figure FDA0003312507990000037
is GmnTransposed matrix of pmnFor the power of user N in beam m, N =1,2m；NmIs the number of users in beam m.
7. A NOMA-based joint precoding and power allocation method according to claim 3, wherein the second sub-problem is represented as:
Figure FDA0003312507990000041
wherein
Figure FDA0003312507990000042
Achievable rate R for user n in beam mmnIs approximately represented by pmnIs the power of user N in beam m, N =1,2m；NmFor the number of users in the beam m, pmFor the total power of the beam m,
Figure FDA0003312507990000048
8. the method of claim 7, wherein the solving of the second sub-problem P2 comprises:
order to
Figure FDA0003312507990000043
Figure FDA0003312507990000044
And transforming the second sub-problem P2 into a convex optimization problem for the natural logarithm of the power of the user n in the wave beam m, solving a lower bound of the optimal power when the precoding vector is fixed by using a Lagrange dual method and a secondary gradient method, and obtaining the power of the user n in the wave beam m when the precoding vector is fixed by using an iteration method.
9. The method of claim 8, wherein obtaining power of user n in beam m with fixed precoding vector by using an iterative method comprises:
step 1: set the maximum number of iterations lmaxWith iteration number l =0, the initial value of the power of user n in beam m is randomly allocated
Figure FDA0003312507990000045
Step 2: set the dual vector to be non-negative, update alphamn，
Figure FDA0003312507990000046
Figure FDA0003312507990000047
The SINR value of the user n in the beam m in the ith iteration is obtained;
and step 3: using user n power in beam m at the first iteration
Figure FDA0003312507990000051
And the following formula obtains the power p of the user n in the beam m at this timemn，
Figure FDA0003312507990000052
Wherein the content of the first and second substances,
Figure FDA0003312507990000053
corresponding non-negative dual vectors of constraint C1 and C2 of formula (7), t is the iteration number of obtaining optimal dual variable by using a secondary gradient method, sigma2Is Gaussian white noise power, Hin、HijIs an intermediate parameter that is a function of,
Figure FDA0003312507990000054
Figure FDA0003312507990000055
Figure FDA0003312507990000056
is a waveSignal strength, W, of user i in bundle mmjThe precoding vector for user j in beam m,
Figure FDA0003312507990000057
the power of user j in beam m at the l-th iteration;
and 4, step 4: updating the dual vectors by using (14) and (15), if the dual vectors are converged, turning to the step 5, otherwise, returning to the step 3;
Figure FDA0003312507990000058
Figure FDA0003312507990000061
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00033125079900000612
and τtThe t-th iteration step length (x) when obtaining the optimal dual variable for the sub-gradient method+Is the maximum of x and 0;
and 5:
Figure FDA0003312507990000062
step 6: if l > lmaxOr the power converges, then the power p is outputmnOtherwise, returning to the step 2.
10. The NOMA-based joint precoding and power allocation method of claim 1, wherein the method of iteratively solving the global optimal solution based on the sub-problem solution results comprises:
step 1: randomly allocating power to each user according to user gain
Figure FDA0003312507990000063
Sum rate
Figure FDA0003312507990000064
The current iteration number is q, and q =1;
step 2: according to the power of the q-1 iteration
Figure FDA0003312507990000065
And the formula (6) obtains the precoding vector of each user in the q iteration
Figure FDA0003312507990000066
Figure FDA0003312507990000067
Wherein the content of the first and second substances,
Figure FDA0003312507990000068
and I is a standard matrix,
Figure FDA0003312507990000069
is GmnTransposed matrix of pmnFor the power of user N in beam m, N =1,2m；NmThe number of users in the beam m;
and 3, step 3: according to the precoding vector of the user n in the wave beam m at the q-th iteration
Figure FDA00033125079900000610
And solving the second subproblem to obtain the power of the user n in the wave beam m when each user iterates for the q times
Figure FDA00033125079900000611
And 4, step 4: substituting the power and the pre-coding vector obtained in the q iteration into a formula (2) to calculate the reachable rate of each user in the beam m, and calculating the sum rate of the user in the q iteration based on the reachable rate of each user
Figure FDA0003312507990000071
And the sum rate of q-1 iteration of each user is calculated according to the reachable rate of each user
Figure FDA0003312507990000072
If it is
Figure FDA0003312507990000073
Zeta is convergence parameter, then output
The precoding vector and the power of each user, otherwise, q = q +1, and the step 2 is returned;
Figure FDA0003312507990000074
Rmn＝log2(1+SINRmn) (2)
wherein R ismnThe achievable rate for user n in beam m.
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