A multi-data-stream beamforming technology method for a non-orthogonal multiple access communication network

Abstract

The present invention relates to the field of communication technologies, and discloses a multi-data-stream beamforming technology method for a non-orthogonal multiple access communication network, including the following steps: S1: Determine the number of antennas of the transmitter, users, the number of data streams, and the number of IRS passive devices; S2: Determine the received signals of the users and the signals after SIC decoding; S3: Decouple the original problem into 2 sub-problems, namely sub-problem 1 and sub-problem 2; S4: Introduce a surrogate function in sub-problem 1 to transform the non-convex SIC decoding rate constraint into a convex constraint; S5: Use the matrix lifting method in sub-problem 2 to transform the non-convex unit modulus constraint into a convex constraint. The present invention simultaneously considers the more practical scenarios of multi-antenna transmitters and multi-antenna users, which is more in line with the actual situation. In particular, the multi-antenna at the user side enables multiple data streams to be transmitted simultaneously, improving communication efficiency, and the introduction of IRS further improves the energy efficiency.

Description

Technical Field

[0001] The present invention relates to the field of communication technologies, and particularly to a multi-data stream beamforming technique method for a non-orthogonal multiple access communication network. Background Art

[0002] In recent years, intelligent reflecting surface (IRS)-assisted transmission has received extensive attention due to its superior performance in improving the spectral efficiency (SE) and energy efficiency (EE) of wireless communication networks. IRS is a planar array composed of a large number of low-cost passive reflecting elements, which can reflect incident electromagnetic waves while changing their amplitude and phase shift. With this new degree of freedom, IRS can create an additional reflecting link when the transmitter and receiver are blocked by obstacles. Compared with traditional relay technologies, IRS requires less energy consumption due to its almost passive characteristics. Therefore, IRS technology has been highly regarded by academia and industry and is considered a promising solution for future 6G networks.

[0003] Non-orthogonal multiple access (NOMA) has become one of the key technologies for future wireless communication networks due to its advantages such as high SE implementation, user fairness guarantee, and support for massive connections. The key idea of NOMA is to serve multiple users in the same resource block, where superposition coding (SC) and successive interference cancellation (SIC) are applied at the transmitter and receiver, respectively. Users with better channel conditions can eliminate in-channel interference. In current literature, the performance gain of NOMA over orthogonal multiple access (OMA) has been studied in different scenarios, such as cognitive radio and millimeter-wave communication.

[0004] Based on the advantages of NOMA and IRS, the combination of NOMA and IRS has recently been proposed as a promising solution to improve communication systems. Some recent research results such as [1]-[2] considered a simple scenario where one IRS serves two users in a downlink NOMA network. In [1], the transmission power was minimized by optimizing the beamforming vectors and IRS phase shifts. In [2], two phase shift designs, namely random phase shift and coherent phase shift, were analyzed.

[0005] In addition, many studies have considered IRS-assisted NOMA networks, where one IRS serves multiple users [3]-[7]. The problems studied currently can be divided into two categories. One is about the problem of minimizing the transmit power [3]-[4], and the other is about the problem of maximizing the sum rate [5]-[7]. For the transmit power minimization problem, the authors in [3] minimized the total transmit power by optimizing the beamforming vectors of each user and the phase shift design of the IRS in a downlink NOMA network with IRS assistance. [4] considered a single IRS-assisted downlink NOMA network and used reinforcement learning to design the beamforming vectors to minimize the transmit power at the BS. For the sum rate maximization problem, [5] optimized the sum rate maximization beamforming design for a downlink MISO IRS-assisted NOMA system. [6] discussed a multi-channel downlink communication IRS-NOMA framework that maximized the sum rate of multiple NOMA users served by one IRS by optimizing the resource allocation of each user and comprehensively considering channel allocation and decoding order. [7] considered an IRS-assisted uplink NOMA system where multiple NOMA users can only transmit data to the BS through the IRS.

[0006] There are also some works considering the multi-cluster system model, that is, dividing users into different clusters [8]-[9]. In [8], the authors discussed a downlink IRS-assisted NOMA network, where two types of users, named central users and cell-edge users, were assigned to different clusters. Each cluster has a central user, a cell-edge user, and an IRS serving all users. By jointly optimizing the beamforming vectors of each user and the phase shift design of the IRS, the transmit power of the BS was minimized. In [9], the authors considered a multi-cluster and multi-BS IRS-assisted NOMA network, where each cluster was served by its associated BS and one IRS served all clusters. The sum rate was maximized by jointly optimizing power allocation and phase shift.

[0007] However, all the above works considered multiple-input single-output (MISO). The research on beamforming design for IRS-assisted multiple-input multiple-output (MIMO) NOMA networks is still lacking. Therefore, how to design a multi-data stream beamforming technology method for non-orthogonal multiple access communication networks is a technical problem that needs to be solved urgently by those skilled in the art. Summary of the Invention

[0008] The purpose of the present invention is to provide a multi-data stream beamforming technology method for non-orthogonal multiple access communication networks to solve the problems raised in the above background technology.

[0009] To achieve the above purpose, the present invention provides the following technical solutions:

[0010] A multi-data stream beamforming technology method for a non-orthogonal multiple access communication network, comprising the following steps:

[0011] S1: Determine the number of antennas of the transmitter, users, the number of data streams, and the number of IRS passive devices;

[0012] S2: Determine the received signals of the users and the signals after SIC decoding;

[0013] S3: Decouple the original problem into 2 sub-problems, namely sub-problem 1 and sub-problem 2;

[0014] S4: Introduce a surrogate function in sub-problem 1 to transform the non-convex SIC decoding rate constraint into a convex constraint;

[0015] S5: Use the matrix lifting method in sub-problem 2 to transform the non-convex unit modulus constraint into a convex constraint, and use the difference of convex (d.c.) method and the subgradient method to transform the non-convex rank-one constraint into a convex constraint;

[0016] S6: Fix the irrelevant variables, perform iterative alternating optimization, and update the variables;

[0017] S7: The original problem finally converges to a finite value.

[0018] Preferably, the transmitted signal vector z of the transmitter in step S1 is determined by the following formula:

[0019]

[0020] where d j represents the transmitted signal, F j represents the precoding matrix of user j, and J represents the number of users;

[0021] User j receives the following signal, and its formula is:

[0022] X j = H j ΦG Z + a j (2)

[0023] where H j represents the channel matrix between the IRS and user j, the IRS phase shift matrix Φ = diag(θ1,..., θ N ), where θ = (β1e jω1 ,..., β N e jωN ), T where ω n ∈(0,2π] represents the phase shift range, β n ∈[0,1] represents the amplitude reflection coefficient, G ∈ C N×Trepresents the channel matrix between the transmitter and the IRS, represents the additive Gaussian noise at user j, represents the circularly symmetric complex Gaussian vector of the covariance matrix at user j, and I represents the identity matrix;

[0024] Assume that all elements of H j are zero-mean and complex Gaussian random variables with variance SIC is used to decode the superimposed coded signal received by the user. Assume that Then a fixed SIC decoding order is adopted, that is, the signal of user J is decoded first, and the signal of user 1 is decoded last. User k will decode all signals of k < j from the signals it has and delete the signals belonging to user j. If considering decoding the signal belonging to user j at user k, the remaining signal is:

[0025]

[0026] where the three terms on the right are the useful signal, interference, and noise respectively; then the corresponding achievable rate is:

[0027] where

[0028]

[0029] To minimize the total transmission power, we jointly optimize the multi-data-stream beamforming F j of the transmitter and the phase shift matrix Φ. Then the optimization problem is as follows:

[0030]

[0031] |Φ n，n | 2 = 1, 1 ≤ n ≤ N (6c);

[0032] where t j is the target rate of user j. In the formula, (6b) is the SIC decoding rate constraint at the user, and (6c) is the unit modulus constraint.

[0033] Preferably, sub-problem 1 in step S3 is the sub-problem of optimizing the multi-data-stream transmission beamforming of the transmitter, and sub-problem 2 is the sub-problem of optimizing the passive beamforming (phase shift matrix) of the IRS.

[0034] Preferably, sub-problem 1 in step S4 is:

[0035]

[0036] The proxy function expression is as follows:

[0037]

[0038] where \(A\in\mathbb{C}\) N×N , and \(A > 0\), \(f(\psi)=-\text{tr}(\psi A)+\ln|\psi|+N\), where \(N\) is a constant, \(\text{tr}()\) represents the trace of a matrix, and \(\psi\) is a positive definite matrix;

[0039] First, we use the following mean squared error (MSE) matrix to estimate \(d\) j ;

[0040] where \(Z\) k,j is a linear decoding matrix,

[0041]

[0042] For any positive definite matrix \(B\) k,j , according to the weighted minimum mean squared error (WMMSE) algorithm, we have

[0043]

[0044] Substituting (11) into (9), we have

[0045]

[0046] We obtain and After that, the constraint (7b) is equivalent to

[0047]

[0048] (14) is equivalent to

[0049]

[0050] where

[0051]

[0052] Let \(f\) j =\(\text{vec}(F\) j ), where \(\text{vec}()\) represents vectorization, and using the mathematical operation is equivalent to

[0053]

[0054] where

[0055]

[0056] Then, sub - problem 1 can be rewritten as the following second - order cone programming (SOCP) problem:

[0057]

[0058] Among them,

[0059]

[0060] Preferably, in step S5, sub - problem 2 is

[0061] Find Φ (23a)

[0062]

[0063] |Φ n，n | 2 ]> = 1, 1 ≤ n ≤ N (23c)

[0064] (23b) is equivalent to

[0065]

[0066] Among them,

[0067]

[0068] Using singular value decomposition (SVD), S j can be transformed into Then we have

[0069]

[0070] We replace the optimization variable Φ with θ = Diag(Φ), where Diag() takes the diagonal elements of a matrix to form a vector, and equivalently reformulate (26) as

[0071]

[0072] By defining (27) can be rewritten as

[0073]

[0074] Then, sub - problem 2 can be rewritten as the following problem:

[0075] Find Θ (29a)

[0076] s.t. (28) (29b)

[0077] Diag(Θ) = 1 N (29c)

[0078]

[0079] Rank(Θ) = 1 (29e)

[0080] We replace the unit modulus constraint (23c) with the constraint (29c). The rank-one constraint (29e) is a non-convex constraint. To handle it, we first rewrite (29e) into an equivalent form:

[0081] Tr(Θ)-λ max (Θ) = 0 (30)

[0082] Since the constraint (30) is in the d.c. form and thus non-convex, using the left-hand side of the constraint (30) as the objective function, we have

[0083]

[0084] s.t. (28) (31b)

[0085] Diag(Θ) = 1 N (31c)

[0086]

[0087] An iterative method is adopted to handle the non-convexity of (31a). For a feasible point Θ at the m-th iteration (m) we have

[0088]

[0089] where is the unit eigenvector corresponding to the largest eigenvalue λ max (Θ[[ID=4o]] (m) ). Therefore, the problem (29) at the (m + 1)-th iteration can be rewritten as the following problem:

[0090]

[0091] s.t. (28) (33b)

[0092] Diag(Θ) = 1 N (33c)

[0093]

[0094] Since the problem (33) is convex, it can be solved using CVX. Once Θ is obtained, we have

[0095]

[0096] Although the modulus of each element of

[0097]

[0098] Then we have

[0099] Φ = diag(θ) (36).

[0100] Preferably, in step S6, the irrelevant variables include {F j} and Φ, where is the multi - data - stream beamforming of the transmitter, and Φ is the phase - shift matrix of the IRS.

[0101] Preferably, in step S7, after replacing the original problem with a convex problem, there is a lower bound, and the overall algorithm finally converges to a finite value.

[0102] The present invention provides a multi - data - stream beamforming technology method for a non - orthogonal multiple access communication network. The multi - data - stream beamforming technology method for the non - orthogonal multiple access communication network has the following beneficial effects:

[0103] The solution proposed by the present invention has better performance, and at the same time considers more practical scenarios of multi - antenna transmitters and multi - antenna users, which is more in line with the actual situation. Especially, the multi - antenna at the user side enables multiple data streams to be transmitted simultaneously, thus greatly improving the communication efficiency, and the introduction of the IRS further improves the energy efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0104] Figure 1 It is a schematic flowchart of the multi - data - stream beamforming technology method for the non - orthogonal multiple access communication network according to the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0105] Embodiment:

[0106] As Figure 1 shown, the multi - data - stream beamforming technology method for the non - orthogonal multiple access communication network provided by the present invention includes the following steps:

[0107] S1: Determine the number of antennas of the transmitter, users, the number of data streams, and the number of passive devices of the IRS; the transmitted signal vector z of the transmitter in this step is determined by the following formula:

[0108]

[0109] where d j represents the transmitted signal, F j represents the precoding matrix of user j, and J represents the number of users;

[0110] User j receives the following signal, and its formula is:

[0111] X j = H j ΦGZ +a j (2)

[0112] where H j represents the channel matrix between the IRS and user j, and the IRS phase shift matrix Φ = diag(θ1,..., θ N ), where θ = (β1e jω1 ,..., β N e jωN ) T , where ω n ∈(0, 2π] represents the phase shift range, β n ∈[0, 1] represents the amplitude reflection coefficient, G ∈ C N×T represents the channel matrix between the transmitter and the IRS, represents the additive Gaussian noise at user j, represents the circularly symmetric complex Gaussian vector of the covariance matrix at user j, and I represents the identity matrix;

[0113] Assume that all elements of H j are zero-mean, and variance is complex Gaussian random variables. SIC is used to decode the superimposed coded signals received by the users. Assume Then a fixed SIC decoding order is adopted, that is, the signal of user J is decoded first, and the signal of user 1 is decoded last. User k will decode all signals of k < j from the signals it has and delete the signals belonging to user j. If considering decoding the signal belonging to user j at user k, the remaining signal is:

[0114]

[0115] where the three terms on the right are the useful signal, interference, and noise respectively; then the corresponding achievable rate is:

[0116] where

[0117]

[0118] To minimize the total transmission power, we jointly optimize the multi-data-stream beamforming F j of the transmitter and the phase shift matrix Φ. Then the optimization problem is as follows:

[0119]

[0120] Φ n，n || 2 = 1, 1 ≤ n ≤ N (6c);

[0121] where t jis the target rate for user j, where (6b) is the SIC decoding rate constraint at the user, and (6c) is the unit modulus constraint;

[0122] S2: Determine the received signal of the user and the signal after SIC decoding;

[0123] S3: Decouple the original problem into 2 sub-problems, namely sub-problem 1 and sub-problem 2;

[0124] Sub-problem 1 is the sub-problem of optimizing the multi-data-stream transmission beamforming of the transmitter. The formula for this sub-problem 1 is:

[0125]

[0126] The surrogate function expression is as follows:

[0127]

[0128] where, A ∈ C N×N , and A > 0, f(ψ) = -tr(ψA) + In|ψ| + N, N is a constant, tr() represents the trace of a matrix, and ψ is a positive definite matrix;

[0129] First, we use the following mean squared error (MSE) matrix to estimate d j ;

[0130] where Z k,j is the linear decoding matrix,

[0131]

[0132] For any positive definite matrix B k,j , according to the weighted minimum mean squared error (WMMSE) algorithm, we have

[0133]

[0134] Substituting (11) into (9), we have

[0135]

[0136] Obtaining and After that, the constraint (7b) is equivalent to

[0137]

[0138] (14) is equivalent to

[0139]

[0140] where,

[0141]

[0142] Let \(f\) j \(=\text{vec}(\mathbf{F}\) j ), where \(\text{vec}()\) represents vectorization and uses mathematical operations is equivalent to

[0143]

[0144] where

[0145]

[0146] Then, sub - problem 1 can be rewritten as the following SOCP problem:

[0147]

[0148] where

[0149]

[0150] Sub - problem 2 is the sub - problem of optimizing the IRS passive beamforming (phase - shift matrix), and the formula for this sub - problem 2 is:

[0151] Find \(\varPhi\) (23a)

[0152]

[0153] \(\vert\varPhi\) n，n \(\vert\) 2 \( = 1,1\leq n\leq N\) (23c)

[0154] (23b) is equivalent to

[0155]

[0156] where

[0157]

[0158] Using singular - value decomposition (SVD), \(\mathbf{S}\) j can be transformed into Then we have

[0159]

[0160] We replace the optimization variable \(\varPhi\) with \(\theta=\text{Diag}(\varPhi)\), where \(\text{Diag}()\) takes the diagonal elements of a matrix to form a vector, and equivalently reformulate (26) as

[0161]

[0162] By defining (27) can be rewritten as

[0163]

[0164] Then, sub - problem 2 can be rewritten as the following problem:

[0165] Find Θ (29a)

[0166] s.t. (28) (29b)

[0167] Diag(Θ) = 1 N (29c)

[0168]

[0169] Rank(Θ) = 1 (29e)

[0170] We replace the unimodular constraint (23c) with the constraint (29c). The rank - one constraint (29e) is non - convex. To handle it, we first rewrite (29e) into an equivalent form:

[0171] Tr(Θ) - λ max (Θ) = 0 (30)

[0172] Since the constraint (30) is in d.c. form and thus non - convex, using the left - hand side of the constraint (30) as the objective function, we have

[0173]

[0174] s.t. (28) (31b)

[0175] Diag(Θ) = 1 N (31c)

[0176]

[0177] Adopt an iterative method to handle the non - convexity of (31a). For a feasible point Θ at the m - th iteration (m) We have

[0178]

[0179] where is the unit eigenvector corresponding to the largest eigenvalue λ max (Θ (m) ). Therefore, the problem (29) at the (m + 1)-th iteration can be rewritten as the following problem:

[0180]

[0181] such that (28) (33b)

[0182] Diag(Θ) = 1 N (33c)

[0183]

[0184] Since problem (33) is convex, it can be solved using CVX. Once Θ is obtained, we have

[0185]

[0186] Although the modulus of each element of

[0187]

[0188] is very close to 1, we still need to recover the unit modulus through the following steps

[0189] Φ = diag(θ); (36)

[0190] S4: Introduce a surrogate function in sub-problem 1 to transform the non-convex SIC decoding rate constraint into a convex constraint;

[0191] S5: Use the matrix lifting method in sub-problem 2 to transform the non-convex unit modulus constraint into a convex constraint, and use the difference of convex (d.c.) method and the subgradient method to transform the non-convex rank-one constraint into a convex constraint;

[0192] S6: Fix the irrelevant variables, iterate and alternately optimize, update the variables. The irrelevant variables include {F j}, and Φ, where is the multi-data stream beamforming of the transmitter, and Φ is the phase shift matrix of the IRS;

[0193] S7: The original problem finally converges to a finite value. After replacing the original problem with a convex problem, there is a lower bound, and the overall algorithm finally converges to a finite value.

[0194] In summary, the proposed scheme of the present invention has better performance, and at the same time considers the more practical scenarios of multi-antenna transmitters and multi-antenna users, which is more in line with the actual situation. Especially, the multi-antenna at the user end enables multiple data streams to be transmitted simultaneously, thus greatly improving the communication efficiency, and the introduction of the IRS further improves the energy efficiency.

[0195] As described above, it is only the preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A multi-stream beamforming technology method for a non-orthogonal multiple access communication network, characterized by: The following steps are involved: S1: Determine the number of transmitters, user antennas, data streams, and IRS passive components. S2: Determine the user's received signal and the signal after SIC decoding; S3: Decouple the original problem into two sub-problems, namely sub-problem 1 and sub-problem 2; S4: Introduce a surrogate function in subproblem 1 to transform the non-convex SIC decoding rate constraint into a convex constraint; S5: In subproblem 2, use the matrix lifting method to transform the non-convex unit module constraint into a convex constraint, and use the convex difference method and subgradient method to transform the non-convex rank-one constraint into a convex constraint; S6: fix irrelevant variables, iterate and alternately optimize, and update variables; S7: The original problem eventually converges to a finite value; Among them, sub-problem 1 in step S3 is to optimize the transmitter multi-data stream transmit beamforming sub-problem, and sub-problem 2 is to optimize the IRS passive beamforming (phase shift matrix) sub-problem; Sub-problem 1 in step S4 is: The proxy function expression is as follows: Among them, A∈C N×N , and A>0, f(ψ)=-tr(ψA)+In|ψ|+N, N is a constant, tr() represents the trace of the matrix, and ψ is a positive definite matrix; First, we use the following mean squared error (MSE) matrix to estimate d j ; where Z k,j is the linear decoding matrix, For any positive definite matrix B k,j , according to the weighted minimum mean square error (WMMSE) algorithm, we have Substituting (11) into (9), we have get and Then, constraint (7b) is equivalent to (14) is equivalent to in, Let f j =vec(F j ), vec() means vectorization, using mathematical operations (15) is equivalent to in, Then, subproblem 1 can be rewritten as the following SOCP problem: in, In step S5, sub-problem 2 is FindΦ (23a) |F n，n | 2 =1.1≤n≤N (23c) (23b) is equivalent to in, Using singular value decomposition (SVD), S j Can be converted into Then we have We replace the optimization variable Φ with θ = Diag(Φ), where Diag() is a vector formed by taking the diagonal elements of the matrix, and equivalently reformulate (26) as By definition (27) can be rewritten as Then, sub-problem 2 can be rewritten as the following problem: FindΘ (29a) st(28) (29b) Diag(Θ)=1 N (29c) Θ≥0 (29d) Rank(Θ)=1 (29e) We use constraint (29c) to replace the unit modulus constraint (23c). The rank-one constraint (29e) is a non-convex constraint. To deal with it, we first rewrite (29e) into an equivalent form: Tr(Θ)-λ amx (Θ)=0 (30) Since constraint (30) is in dc form, it is non-convex. Using the left-hand side of constraint (30) as the objective function, we have st(28) (31b) Diag(Θ)=1 N (31c) Θ≥0 (31d) An iterative method is used to deal with the non-convexity of (31a). For a feasible point Θ at the mth iteration (m) We have in is about the maximum eigenvalue λ max (Θ (m) ), so the problem (29) at the m+1th iteration can be rewritten as the following problem: st(28) (33b) Diag(Θ)=1 N (33c) Θ≥0 (33d) Since problem (33) is convex, it can be solved using CVX. Once we get Θ, we have Although The modulus of each element of is very close to 1, but we still need to restore the unit modulus by the following steps Then we have Φ=diag(θ) (36) .

2. The multi-stream beamforming technology method for a non-orthogonal multiple access communication network according to claim 1, characterized in that: The transmission signal vector z of the transmitter in step S1 is determined by the following formula: where d j Indicates the signal that the transmitter wants to transmit to user j, F j represents the precoding matrix of user j, and J represents the number of users; User j receives the following signal, which is formulated as: X j =H j ΦG Z +a j (2) Among them H j represents the channel matrix between IRS and user j, and the IRS phase shift matrix Φ = diag(θ1, ..., θ N ), where θ=(β1e jω1 ,...,β N e jωN ) T , where ω n ∈(0,2π] represents the phase shift range, β n ∈[0,1] represents the amplitude reflection coefficient, G∈C N ×T represents the channel matrix between the transmitter and the IRS, represents the additive Gaussian noise at user j, represents the circularly symmetric complex Gaussian vector of the covariance matrix at user j, and I represents the identity matrix; Hypothesis H j All elements of are zero-mean and have a variance of Complex Gaussian random variables. SIC is used to decode the superimposed coded signals received by the users. Assume that Then a fixed SIC decoding order is adopted, that is, the signal of user J is decoded first and the signal of user 1 is decoded last. User k will decode all signals of k < j from the signals it has and delete the signals belonging to user j. If considering decoding the signal belonging to user j at user k, the remaining signals are: The three items on the right are useful signal, interference, and noise respectively; the corresponding achievable rate is: in In order to minimize the total transmit power, we perform multi-stream beamforming on the transmitter F j The optimization problem is as follows: |F n，n | 2 =1,1≤n≤N (6c); where t j is the target rate of user j, where (6b) is the SIC decoding rate constraint at the user, and (6c) is the unit modulus constraint.

3. The multi-stream beamforming technology method for a non-orthogonal multiple access communication network according to claim 1, characterized in that: In step S6, irrelevant variables include {F j } and Φ, where is the transmitter multi-stream beamforming and Φ is the phase shift matrix of the IRS.

4. The multi-stream beamforming technology method for a non-orthogonal multiple access communication network according to claim 1, characterized in that: In step S7, after the original problem is replaced by a convex problem, a lower bound exists and the overall algorithm eventually converges to a finite value.

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