Non-orthogonal active-passive collaborative beamforming design method based on beneficial interference

Abstract

The application provides a non-orthogonal active-passive cooperative beamforming design method based on beneficial interference, and belongs to the field of energy efficiency optimization of downlink wireless communication. In a conventional IRS-NOMA network, two potential inter-user interferences affect the performance of the system. On one hand, SIC cannot eliminate the interference from high-decoding-order users, and these signals are regarded as noise by the receiving users; on the other hand, when SIC eliminates the interference from low-decoding-order users, the interference signals are difficult to be completely detected and eliminated, and thus the residual interference affects the system performance. Based on this, the application provides two CI-assisted interference design schemes. Specifically, for scheme I, CI converts the interference from high-decoding-order users into user useful receiving information to utilize the interference that cannot be eliminated by the user receiving end. For scheme II, CI converts the interference from low-decoding-order users into user useful receiving information to eliminate the SIC process and improve the useful signal power of the user end.

Description

Technical Field

[0001] This invention belongs to the field of energy efficiency optimization in downlink wireless communication, and involves two design schemes to improve system energy efficiency by utilizing beneficial interference. Specifically, it refers to designing different beneficial interference alignment schemes to address the two types of interference defects existing in non-orthogonal multiple access technology, and adopting a method of jointly optimizing active beamforming of the base station and passive beamforming of the intelligent reflector, thereby maximizing the system energy efficiency. Background Technology

[0002] Non-orthogonal multiple access (NOMA) technology has become one of the key technologies in sixth-generation (6G) wireless communication systems due to its high spectral efficiency, massive connectivity, and strong user fairness. Unlike traditional orthogonal multiple access (OMA), NOMA utilizes the power domain to serve multiple users on the same resource block (time, frequency, or symbol). At the transmitting end, NOMA allocates power according to the channel conditions of each user and uses superposition coding (SC) technology to transmit multiple user information simultaneously. At the receiving end, NOMA employs continuous interference cancellation (SIC) technology to receive information from each user. Specifically, user information with poor channel conditions is first decoded, then removed, until the information the user expects to receive is decoded. It is worth noting that NOMA performance is closely related to the difference in channel gain between users; NOMA can only achieve better spectral efficiency gain than OMA when there is a significant difference in channel gain between users. To address this, the application of intelligent reflectors (IRS) can effectively leverage NOMA performance. By adjusting the reflection amplitude or phase shift of the reflecting elements, the IRS can dynamically control the channel transmission environment and intelligently adjust the channel gain differences between users.

[0003] However, inter-user interference in traditional IRS-NOMA networks is also a significant problem. On one hand, SiC (Self-Injection Interference) technology can only eliminate interference from low-decoding-order users; interference from high-decoding-order users still exists at the receiver, affecting user reception performance. On the other hand, the achievable rate of traditional NOMA users is based on perfect SiC, but in practical communication systems, it is difficult for traditional NOMA to achieve perfect SiC. Therefore, when SiC errors occur, users cannot completely eliminate interference from low-decoding-order users, and the residual interference signals will affect user reception performance and threaten the user's achievable rate.

[0004] Recently, beneficial interference precoding (CIP) technology has been recognized as an effective measure to address interference problems. In fact, CIP is a symbol-level precoding (SLP) technique. By utilizing channel state information (CSI) and transmitted symbol information, the CIP encoder can move the received signal away from the constellation points of the symbol information and into the beneficial interference region. In this way, harmful inter-user interference is transformed into beneficial information, considered as an additional source of useful signal power, thus improving the user's reception performance.

[0005] To address the two potential inter-user interference problems in IRS-NOMA networks, this invention introduces CIP to construct useful information from these two types of interference, thereby improving user reception performance and network energy efficiency. Summary of the Invention

[0006] In traditional IRS-NOMA networks, two potential inter-user interferences affect system performance. On the one hand, Silent Interference Processing (SIC) cannot eliminate interference from users with higher decoding order, and these signals are perceived as noise by the receiving user. On the other hand, when SIC eliminates interference from users with lower decoding order, the interference signal is difficult to completely detect and eliminate, thus the residual interference affects system performance. To address the problems of existing technologies, this invention provides a beamforming method for IRS-NOMA networks based on Cipher Interference Processing (CI). For the designed downlink multiple-input single-output (MISO) IRS-NOMA network, two schemes are proposed to utilize CI to beneficially process interference and minimize transmit power. Specifically, this invention provides two CI-assisted interference design schemes: Scheme I, CI transforms interference from users with higher decoding order into useful received information for the user, utilizing interference that the user receiver cannot eliminate. Scheme II, CI transforms interference from users with lower decoding order into useful received information for the user, eliminating the Silent Interference Processing (SIC) and increasing the useful signal power at the user end.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A non-orthogonal active-passive cooperative beamforming design method based on beneficial interference is proposed. First, the traditional IRS-NOMA system model is introduced, and the two types of interference present in the traditional IRS-NOMA model are analyzed. Second, corresponding CI-aided design schemes are proposed for each of these two types of interference, transforming the interference into useful received information for the user. Finally, the proposed optimization problem is solved. Specifically, the following steps are included:

[0009] The first step is to construct a traditional IRS-NOMA system model.

[0010] 1) This invention considers an IRS-assisted downlink NOMA network, wherein the IRS is equipped with N reflecting elements to adjust the phase shift of the incident signal, providing direct and reflected links for user communication. The base station has M antennas for simultaneously transmitting information for K single-antenna NOMA users. k This represents the k-th user. Furthermore, this invention assumes that the base station can obtain the CSI of each channel, and defines the base station to IRS, IRS to U... k and base station to U k The channels are respectively and Rice distribution is used here to simulate the channel between the base station and the IRS, specifically:

[0011]

[0012] Where β represents the path loss constant at a unit distance D0 = 1m; D0 represents the reference distance; d BI Indicates the distance between the base station and the IRS; α BI Indicates the path loss factor; Indicates the channel Rice factor; Indicates the Los path; This represents an NLos path that follows a Rayleigh distribution.

[0013] The Los path is represented as:

[0014]

[0015] Where, θ AoA It is the angle of arrival (AoA) at the IRS, elevation angle. It is the AoA azimuth at the IRS. It is the azimuth angle (AoD) at the base station.

[0016] Considering the IRS reflective element along the x-axis and y-axis, the IRS receiver array response is expressed as:

[0017]

[0018] The base station's transmit array response is:

[0019]

[0020] For the array response in (3), Where, N x N y These represent the number of units assigned to the IRS on the x-axis and y-axis, respectively. This indicates the NLos path.

[0021] For the channel h between the IRS and the user I,k This invention also employs the same channel model. However, considering the numerous obstacles and long distances in the direct link between the base station and the user, this invention uses a Rayleigh distribution to describe its channel h. k .

[0022] 2) The superimposed signal transmitted by the base station is represented as: in It is a unit power U k Information symbols, It's U k The corresponding active beamforming vector.

[0023] Then U k The received signal is represented as:

[0024]

[0025] in, The mean is 0 and the variance is σ. 2 Additive white Gaussian noise. It is the IRS phase shift diagonal matrix. It is the IRS phase shift vector. γ i ∈[0,2π) and a i ∈[0,1] represent the reflection phase shift and reflection amplitude of the i-th reflecting unit, respectively. In this invention, we assume a... i =1, the reflected signal can obtain the maximum reflection gain.

[0026] In IRS-NOMA networks, the SIC decoding order is related not only to the active beamforming of the base station but also to the passive beamforming of the IRS. To simplify the model, this invention uses O(k) to define U. k The decoding order, and set O(k) = k. With U k To clarify, in the IRS-NOMA network, except for U k Other users can be divided into two categories: the first category is defined as Users included in this category are called low-decoding-level users; the second category is correspondingly defined as... Users are referred to as high-decoding level users. Specifically, U k First, the information of lower-order users is decoded sequentially according to the SIC decoding order, and then eliminated one by one. Afterwards, the information of higher-order users is decoded as interference. To ensure the smooth execution of the SIC decoding order, the following power constraints must be met:

[0027]

[0028] in, U k The power of the user k information received by the receiver; U k The power of the user p information received by the receiver; U k The power of the user i information received by the receiver; U k The power of the user j information received by the receiver; H I,k =diag(h I,k );w i w j and w p They represent U respectively i U j and U p Active beamforming vector.

[0029] 3) According to NOMA, ultimately, U k Decodes k The obtained signal-to-interference-plus-noise ratio (SINR) is:

[0030]

[0031] Where, σ 2 This represents the power of additive white Gaussian noise.

[0032] In particular, in U K At the receiving end, SIC will eliminate all inter-user interference, therefore, U K The received signal-to-noise ratio (SNR) can be expressed as:

[0033]

[0034] In addition, U p , About U on the receiver k The SINR of a signal is represented as:

[0035]

[0036] According to Shannon's theory, U k The achievable rate is:

[0037]

[0038] The above discussion focuses on the traditional IRS-NOMA system model. From formula (7), it is easy to see that interference from high-decoding-order users limits the user's reception performance. On the other hand, the performance of the traditional IRS-NOMA discussed in the first step is based on perfect SiC, but in actual communication scenarios, perfect SiC is difficult to guarantee completely. Therefore, the interference remaining from imperfect SiC will affect the system performance. To address these two types of interference in the traditional IRS-NOMA system, this invention uses CI to convert them into useful received information for the user, thereby improving system performance. The specific design scheme is shown in the second and third steps:

[0039] The second step is to construct CI-assisted scheme I based on the traditional IRS-NOMA model constructed in the first step, and to list and solve the corresponding optimization problems.

[0040] 1) Scheme I: Use CI to eliminate interference from users at higher decoding levels.

[0041] In traditional IRS-NOMA, interference from low-decoding-order users can be eliminated using SiC, but interference from high-decoding-order users cannot, which affects the decoding reliability of the receiving user. To fully utilize the interference generated by these high-decoding-order users, the CI encoder can be designed as follows:

[0042]

[0043] in, It's U k Information symbols.

[0044] U k The noiseless received signal at that location can be expressed as:

[0045]

[0046] Through SIC, U k This can eliminate interference from users with lower decoding levels. Therefore, U p Receiver decoding U k The SINR of a signal can be expressed as

[0047]

[0048] According to the CI principle, U k The endpoint needs to meet the following beneficial interference constraints:

[0049]

[0050] in

[0051] Through the above design, U kTerminal about U k The SINR(7) of the signal is converted into SNR, which is expressed as:

[0052]

[0053] At the same time, the SIC decoding order constraint is updated to:

[0054]

[0055] It should be noted that in CI-assisted systems, instantaneous transmit power is expressed as... Therefore, the problem of minimizing transmit power under this scheme can be constructed as:

[0056]

[0057] The active beamforming vector w in P1 k , The phase shift vector θ of the IRS is highly coupled, making the problem difficult to solve directly. To resolve the coupling between variables, this invention decomposes the original problem P1 into two subproblems and uses the first-order Taylor approximation method to transform it into a convex subproblem for solution.

[0058] 2) Design an algorithm to solve P1:

[0059] 2.1) Fix the IRS phase shift vector θ and optimize the base station active beamforming vector w k .

[0060] In optimizing w k At that time, the IRS phase shift vector θ remains unchanged (using If we consider the given information (e.g., if we denote it as such), then constraint C4 can be disregarded. Therefore, the problem of optimizing the active beamformer can be expressed as:

[0061]

[0062] Here, C1 and C2 are non-convex quadratic programming constraints. To solve for this non-convexity, the present invention employs the first-order Taylor approximation method.

[0063] First, adjust the C1 structure and write it in the following form:

[0064]

[0065] Therefore, this invention defines a function. And perform a first-order Taylor expansion on it, the specific expansion is expressed as:

[0066]

[0067] in this way, F(w) in constraint (19) can be replaced k (19) is transformed into:

[0068]

[0069] It can be verified that (21) is a convex constraint.

[0070] For the non-convex constraint C2, the same transformation method is used. Performing a first-order Taylor expansion, we obtain its expansion formula:

[0071]

[0072] Therefore, C2 can be approximately transformed into:

[0073]

[0074] Ultimately, the problem of optimizing active beamforming sub-probes for base stations is transformed into a convex sub-probe problem:

[0075]

[0076] 2.2) Fixed base station active beamforming vector w k Optimize the IRS phase shift vector θ.

[0077] When optimizing θ, the active beamforming vector w k The value should remain unchanged. Since the objective function of minimizing transmit power is independent of θ, and considering that maximizing minimum SINR can more strictly satisfy all SINR constraints, there is room for reducing the transmit power. Therefore, the problem of minimizing transmit power is rewritten as the problem of maximizing minimum SINR, expressed as:

[0078]

[0079] in, C1, C2, and C3 are non-convex constraints.

[0080] For C1, we first express it as:

[0081]

[0082] Define function And by performing a first-order Taylor expansion, we obtain the expansion:

[0083]

[0084] Replacing the expression on the right side of inequality (26) with this, we obtain the convex constraint condition:

[0085]

[0086] Similar to the conversion of C1, C2 can be converted to:

[0087]

[0088] As for C3 It is a function of θ, and its first-order Taylor expansion can be expressed as:

[0089]

[0090] Therefore, C3 is transformed into:

[0091]

[0092] Finally, the IRS passive beamforming convex optimization problem is expressed as:

[0093]

[0094] 2.3) Design an alternating optimization algorithm.

[0095] Through the first-order Taylor approximation transformation shown in formulas (19) to (23) and formulas (26) to (31), the optimization problems of active beamforming (18) and passive beamforming (25) have been transformed into convex problems as shown in formulas (24) and (32), which can be solved using a convex optimization toolbox, such as CVX. Specifically, the present invention adopts the following alternating optimization algorithm:

[0096] 2.3.1) Initialize the base station active beamforming vector IRS phase shift vector Auxiliary variables The number of iterations n = 1;

[0097] 2.3.2) Update n = n + 1;

[0098] 2.3.3) Based on The optimal solution is obtained by solving (24) using CVX.

[0099] 2.3.4) Based on Using CVX to solve (32), the optimal solution θ is obtained. (n) ;

[0100] Update 2.3.5) and

[0101] 2.3.6) Repeat steps 2.3.2)-2.3.5) until the iteration converges or the number of iterations reaches the maximum value.

[0102] The third step is to construct CI-assisted scheme II based on the traditional IRS-NOMA model constructed in the first step, and to list and solve the corresponding optimization problems.

[0103] 1) Solution II: Use CI to eliminate the SIC process.

[0104] In practical applications, incorrect detection of each user information by the receiver can lead to SIC errors, resulting in additional interference, which will further affect subsequent SIC operations. Specifically, when U k Detect and eliminate from U j , When U is interfered with j The signal may be difficult to completely eliminate. And the remaining portion will damage the U... k This reduces decoding reliability and degrades the performance of the IRS-NOMA network, especially when there are a large number of legitimate users.

[0105] To completely eliminate the aforementioned SIC error, the present invention designs the CI encoder as follows:

[0106]

[0107] U k The noiseless received signal at the terminal can be expressed as:

[0108]

[0109] In this scheme, U k The beneficial interference constraint at the end is expressed as:

[0110]

[0111] in,

[0112] Through the above design, U k Terminal about U k The SINR(7) of the signal is expressed as:

[0113]

[0114] Therefore, the problem of minimizing the transmit power in Scheme II can be expressed as:

[0115]

[0116] 2) Design an algorithm to solve P2:

[0117] 2.1) Fix the IRS phase shift vector θ and optimize the base station active beamforming vector w k .

[0118] With the IRS phase shift vector θ fixed, the subproblem can be expressed as:

[0119]

[0120] Due to constraints C1 and C2, this problem is nonconvex. To solve this problem, we still use the first-order Taylor approximation method for convex transformation, then (38) can be reconstructed as follows:

[0121]

[0122] in, yes The first-order Taylor expansion of is expressed as:

[0123]

[0124] 2.2) Fixed base station active beamforming vector w k Optimize the IRS phase shift vector θ.

[0125] Similarly, the optimization problem of the IRS phase shifter can be approximately expressed as the problem of maximizing the minimum SINR, as follows:

[0126]

[0127] Where C1 and C2 are nonconvex constraints. Using the first-order Taylor approximation method, (41) can be transformed into:

[0128]

[0129] in, yes The first-order Taylor expansion of θ is expressed as:

[0130]

[0131] 2.3) Design an alternating optimization algorithm.

[0132] Through first-order Taylor approximation transformation, the optimization problems of active beamforming (38) and passive beamforming (41) have both been transformed into convex problems as shown in equations (39) and (42), which can be solved using a convex optimization toolbox, such as CVX. Specifically, the present invention adopts the following alternating optimization algorithm:

[0133] 2.3.1) Initialize the base station active beamforming vector IRS phase shift vector Auxiliary variables The number of iterations n = 1;

[0134] 2.3.2) Update n = n + 1;

[0135] 2.3.3) Based on The optimal solution is obtained by using CVX to solve (39).

[0136] 2.3.4) Based on Using CVX to solve (42), the optimal solution θ is obtained. (n) ;

[0137] Update 2.3.5) and

[0138] 2.3.6) Repeat steps 2.3.2)-2.3.5) until the iteration converges or the number of iterations reaches the maximum value.

[0139] This invention proposes two CI-assisted interference design schemes. Scheme I designs interference from high-decoding-order users to transform it into useful received information; Scheme II designs interference from low-decoding-order users to transform it into useful received information. To solve the optimization problems of the two schemes, the original problems P1 and P2 are decomposed into optimization subproblems for active beamforming and passive beamforming, respectively. When solving each subproblem, a first-order Taylor approximation method is used to transform it into a convex subproblem, which can then be solved directly using the CVX toolbox.

[0140] The beneficial effects of this invention are as follows: This invention proposes a CI-assisted non-orthogonal active-passive cooperative beamforming communication method. Under the action of the CI precoder, the two types of inter-user interference existing in the NOMA network are respectively processed in a beneficial way, which significantly improves the energy efficiency of the IRS-NOMA communication system and shows certain superior performance in terms of user rate. Attached Figure Description

[0141] Figure 1 This is a diagram of a downlink MISO wireless communication IRS-NOMA network system;

[0142] Figure 2 It is a graph showing the change in system transmission power as a function of the number of IRS reflective units N;

[0143] Figure 3 It is a graph showing how the system transmission power changes as a given user SINR threshold.

[0144] Figure 4 This is a graph showing the results of user achievable rates versus total transmission rates for each scheme under N=49 and Γ=3.

[0145] Figure 5This is a graph showing the system's transmitted power under different QPSK modulation phase combinations;

[0146] Figure 6 This is a comparison chart of power consumption in two-user, three-user, and four-user systems. Detailed Implementation

[0147] To better understand the above technical solution, the following detailed analysis of the results is provided in conjunction with the accompanying drawings and specific implementation methods.

[0148] The first step is to construct the IRS-NOMA system model.

[0149] Build Figure 1 The illustrated downlink MISO wireless communication IRS-NOMA system includes a base station and an IRS. The base station acts as a transmitter, sending confidential information to multiple single-antenna users, while the IRS assists the base station in information transmission.

[0150] The second step is to construct two CI-assisted solutions and list the optimization problems corresponding to each solution.

[0151] For the two types of interference present in the IRS-NOMA system, two CI-assisted schemes are constructed, and the optimizations of P1 and P2 are listed respectively.

[0152] The third step is to design an alternating optimization algorithm to solve the optimization problem.

[0153] 1) Scheme I: Fix the active beamforming vector w respectively k Given the phase shift vector θ of the IRS, P1 is decomposed into two subproblems (18) and (25). For the non-convex constraints in the two subproblems, the first-order Taylor approximation method is adopted to transform them into convex subproblems (24) and (32) respectively. Then, CVX can be used to solve (24) and (32) alternately to obtain the optimal solution.

[0154] 2) Scheme II: Maintain the active beamforming vector w k With the phase shift vector θ of the IRS unchanged, P2 is decomposed into two subproblems (38) and (41). For the non-convex constraints in the two subproblems, the first-order Taylor approximation method is adopted to approximate them as convex subproblems (39) and (42) respectively. Then, CVX is used to solve (39) and (42) alternately to obtain the optimal solution.

[0155] This implementation example verifies:

[0156] exist Figure 1 In the system, the maximum transmit power P of the base station is set. max =20dBm, noise power σ 2= -80dBm, number of users K=2, number of base station antennas and number of IRS reflector units M=3 and N=49 respectively, distance between base station and IRS is d BI =20m, the distance between the base station, IRS and user 1 is d B1 =d I1 =150m, the distance between the base station, IRS and user 2 is d B2 =d I2 =50m. Furthermore, this invention sets α... BI =2.5, α Bk =α Ik =2.8, β = -30dB, Γ k =3.

[0157] 1) Figure 2 The results show that as the number of IRS reflector units N increases, the system power consumption gradually decreases. This is mainly because increasing N provides greater freedom to the system, making the IRS configuration more flexible. Furthermore, from... Figure 2 The results show that Schemes I and II consume less power compared to the traditional NOMA and CI schemes. Compared to NOMA, this is because in Scheme I, CIP converts interference from high-decoding-order users into useful signals, eliminating inter-user interference in the network. In Scheme II, CIP converts interference from low-decoding-order users into useful signals, increasing the power of the useful signal received by the user. Both of these contribute to improved system performance. Compared to the CI scheme, we know that the CI scheme requires strict design of all interferences, which consumes a significant amount of power.

[0158] 2) Figure 3 The study investigated different Γ k The performance of each scheme is analyzed. Simulation results show that as Γ... k As the number of users increases, the power consumed by the system also gradually increases in order to meet the service quality requirements of each user. Figure 3 It also shows that Scheme I and Scheme II consume less power compared to traditional NOMA and CI schemes. Furthermore, Scheme II has an advantage over Scheme I. This is because NOMA allocates more power to users at lower decoding levels, which facilitates Scheme II. Next, Figure 4 This shows that at N=49, Γ k The graph shows the achievable speeds for each user in the system under a parameter setting of 3, where R1, R2, and R... sum These represent the transmission rates of U1, U2, and users, respectively. Observe. Figure 4It can be seen that the U1 rate of each scheme is a threshold set by the system. However, the U2 rates of Schemes I and II are higher than those of the traditional NOMA and CI schemes. In other words, Schemes I and II can achieve a better overall transmission rate than the traditional NOMA and CI schemes. Furthermore... Figure 3 , Figure 4 This demonstrates that the CI scheme sacrifices energy efficiency for a high transmission rate.

[0159] 4) Figure 5 The system performance was studied across ten time slots, with a different combination of modulation phases for user information in each slot. Specifically, the C1 phase combination was... C2 phase combination is C3 phase combination is C4 phase combination is C5 phase combination is C6 phase combination is C7 phase combination is C8 phase combination is C9 phase combination is C10 phase combination is Figure 5 The power consumed by the display system remains almost constant under different phase combinations, and Scheme I and Scheme II consistently maintain superior performance.

[0160] 5) To further verify the superior performance of the proposed scheme, simulations were also performed on three-user and four-user systems. In the two-user system, the distance between the base station, IRS, and users is d. B1 =d I1 =60m,d B2 =d I2 =30m. The distance between the base station, IRS and the user in a three-user system is d. B1 =d I1 =100m,d B2 =d I2 =60m,d B3 =d I3 =30m. The distance between the base station, IRS and users in a four-user system is d. B1 =d I1 =150m,d B2 =d I2 =100m,d B3 =d I3 =60m,d B4 =d I4 =30m. Simulation results show that as the number of users increases, the power consumption of the system also increases. Furthermore, Figure 6This further verifies that Scheme I and Scheme II always consume less power during communication, indicating that the two schemes proposed in this invention are beneficial to improving the energy efficiency of the system.

Claims

1. A non-orthogonal active-passive cooperative beamforming design method based on beneficial interference, characterized in that, The design method described above first proposes corresponding CI-aided design schemes based on the two types of interference present in the IRS-NOMA system model, determines the optimization problem, and transforms the interference into useful received information for the user; finally, it solves the proposed optimization problem. The two CI-assisted interference design schemes are as follows: Scheme I designs interference from high-decoding-level users to transform it into useful received information for the user; Scheme II designs interference from low-decoding-level users to transform it into useful received information for the user. To solve the optimization problem for both schemes, the original problem is... and It is decomposed into an optimization problem of active beamformers and an optimization problem of passive beamformers, respectively. Includes the following steps: The first step is to construct an IRS-NOMA system model; The second step is to construct CI-assisted scheme I based on the IRS-NOMA model built in the first step, and list and solve the corresponding optimization problems. Solution I: Use CI to eliminate interference from high-decoding-order users; To fully utilize the interference generated by high-decoding-order users, the CI encoder is designed as follows: （11） in, yes Information symbols; The noiseless received signal at that location can be expressed as: （12） Through SIC, It can eliminate interference from users with lower decoding levels; therefore, Decoding at the receiving end The SINR of a signal is represented as: （13） According to CI principle The endpoint needs to meet the following beneficial interference constraints: （14） in ; Based on the above design End of discussion The SINR (7) of the signal is converted into SNR, which is expressed as: （15） At the same time, the SIC decoding order constraint is updated to: （16） In a CI-assisted system, the instantaneous transmit power is expressed as: Therefore, the problem of minimizing transmit power under this scheme is constructed as follows: （17）； Includes the following steps: The first step is to construct an IRS-NOMA system model; The third step is to construct CI-assisted scheme II based on the IRS-NOMA model built in the first step, and list and solve the corresponding optimization problems. Solution II: Eliminate the SIC process using CI; To completely eliminate the aforementioned SIC error, the CI encoder is designed as follows: （33） The noiseless received signal at the terminal can be expressed as: （34） In this scheme, The beneficial interference constraint at the end is expressed as: （35） in, ; Based on the above design End of discussion The SINR(7) of the signal is expressed as: （36） Therefore, the problem of minimizing the transmit power in Scheme II can be expressed as: （37）。 2. The non-orthogonal active-passive cooperative beamforming design method based on beneficial interference according to claim 1, characterized in that, The original problem The problem is decomposed into two subproblems, and then transformed into a convex subproblem using the first-order Taylor approximation method. 1) Design an algorithm to solve the problem : 1.1) Fixed IRS phase shift vector Optimize the active beamforming vector of the base station ; In optimization At that time, the IRS phase shift vector Keep it unchanged (using) If the expression is not considered, then constraint C4 is disregarded; therefore, the problem of optimizing the active beamformer can be expressed as: （18） C1 and C2 are non-convex quadratic programming constraints; to solve for this non-convexity, the first-order Taylor approximation method is adopted. For the non-convex constraint C1, adjust the structure of C1 and write it in the following form: （19） Therefore, define a function And perform a first-order Taylor expansion on it, transforming (19) into: （21） For the non-convex constraint C2, using the same transformation method and performing a first-order Taylor expansion, C2 can be approximately transformed into: （23） Finally, the problem of optimizing the active beamforming sub-probe of the base station is transformed into the convex sub-probe problem shown in equation (24): （24） 1.2) Fixed base station active beamforming vector Optimize IRS phase shift vector ; optimization At that time, active beamforming vector Keeping the same, the problem of minimizing transmit power is rewritten as the problem of maximizing minimum SINR, expressed as: （25） in, C1, C2, and C3 are non-convex constraints; For C1, we first express it as: （26） Define function And by performing a first-order Taylor expansion, we obtain the convex constraint conditions: （28） Similar to the conversion of C1, C2 can be converted to: （29） As for C3 It is about The function is expanded using a first-order Taylor series, transforming C3 into: （31） Finally, the IRS passive beamforming convex optimization problem is expressed as: （32） 1.3) Design an alternating optimization algorithm; By transforming the problem by first-order Taylor approximation, the optimization problem of active beamforming (18) and the optimization problem of passive beamforming (25) have been transformed into convex problems as shown in equations (24) and (32), using the convex optimization toolbox.

3. The non-orthogonal active-passive cooperative beamforming design method based on beneficial interference according to claim 2, characterized in that, The alternating optimization algorithm in step 1.3) is as follows: 1.3.1) Initialize the base station active beamforming vector , IRS phase shift vector Auxiliary variables and number of iterations ; Update 1.3.2) ; 1.3.3) Based on The optimal solution is obtained by solving (24) using CVX. ; 1.3.4) Based on The optimal solution is obtained by solving (32) using CVX. ; Update 1.3.5 and ; 1.3.6) Repeat steps 1.3.2)-1.3.5) until the iteration converges or the number of iterations reaches the maximum value.

4. The non-orthogonal active-passive cooperative beamforming design method based on beneficial interference according to claim 1, characterized in that, Design an algorithm to solve : (1) Fixed IRS phase shift vector Optimize the active beamforming vector of the base station ; Fixed IRS phase shift vector The subproblem can be represented as: （38） Since constraints C1 and C2 are non-convex, to solve this problem, a first-order Taylor approximation method is used for convex transformation, and (38) is reconstructed as follows: （39） in, yes The first-order Taylor expansion; (2) Fixed base station active beamforming vector Optimize IRS phase shift vector ; Similarly, the optimization problem of the IRS phase shifter can be approximately expressed as the problem of maximizing the minimum SINR, as follows: （41） Where C1 and C2 are nonconvex constraints; using the first-order Taylor approximation method, (41) can be transformed into: （42） in, yes about The first-order Taylor expansion of is expressed as: （43） (3) Design an alternating optimization algorithm; Through the first-order Taylor approximation transformation, the optimization problem of active beamforming (38) and the optimization problem of passive beamforming (41) have both been transformed into convex problems as shown in equations (39) and (42), using the convex optimization toolbox.

5. The non-orthogonal active-passive cooperative beamforming design method based on beneficial interference according to claim 4, characterized in that, The specific steps of the alternating optimization algorithm in step (3) are as follows: (3.1) Initialize the base station active beamforming vector , IRS phase shift vector Auxiliary variables and number of iterations ; (3.2) Update ; (3.3) Based on The optimal solution is obtained by using CVX to solve (39). ; (3.4) Based on The optimal solution is obtained by solving (42) using CVX. ; (3.5) Update and ; (3.6) Repeat steps (3.2)-(3.5) until the iteration converges or the number of iterations reaches the maximum value.

6. A non-orthogonal active-passive cooperative beamforming design method based on beneficial interference according to claim 2 or 4, characterized in that, The first step, constructing the IRS-NOMA system model, involves the following steps: Consider an IRS-assisted downlink NOMA network, where the IRS is equipped with Each base station has a reflective element to adjust the phase shift of the incident signal, providing both direct and reflected links for user communication; the base station is equipped with... One antenna, used for A single-antenna NOMA user can transmit information simultaneously; Indicates the first One user, Furthermore, it is assumed that the base station can obtain the CSI of each channel, and that the base station to IRS and IRS to [other channels] are defined. and base station to The channels are respectively , and Here, Ricean distribution is used to simulate the channel between the base station and the IRS, specifically: （1） in, Indicates unit distance Path loss constant at 1m; Indicates a reference distance; Indicates the distance between the base station and the IRS; Indicates the path loss factor; Indicates the channel Rice factor; Indicates the Los path; This represents an NLos path that follows a Rayleigh distribution; The Los path is represented as: （2） in, It is the angle of arrival (AoA) at the IRS, elevation angle. It is the AoA azimuth at the IRS. It is the azimuth angle (AoD) at the base station; IRS reflective elements are divided into shaft and Considering the axis, the IRS receiver array response is expressed as: （3） The base station's transmit array response is: （4） For the array response in (3), , ;in, , These represent the IRS allocations to shaft and The number of units on the axis; Indicates an NLos path; For the channel between the IRS and the user The same channel model is also used; however, considering the numerous obstacles and long distances in the direct link between the base station and the user, a Rayleigh distribution is used to describe its channel. ; 2) The superimposed signal transmitted by the base station is represented as: ,in It has a unit power Information symbols, yes The corresponding active beamforming vector; but The received signal is represented as: （5） in, The mean is 0 and the variance is Additive white Gaussian noise; It is the IRS phase shift diagonal matrix. It is the IRS phase shift vector; and They represent the first The reflection phase shift and reflection amplitude of each reflection unit; To simplify the model, we adopt definition The decoding order, and setting ;by To clarify, in the IRS-NOMA network, except for Other users can be divided into two categories: the first category is defined as Users included in this category are called low-decoding-level users; the second category is correspondingly defined as... Users are referred to as high-decoding-order users; to ensure the smooth execution of the SIC decoding sequence, the following power constraints must be met: （6） in, express The receiver received the user Information power; express The receiver received the user Information power; express The receiver received the user Information power; express The receiver received the user Information power; ; , and They represent , and Active beamforming vector; 3) According to NOMA, ultimately, decoding The obtained signal-to-interference-plus-noise ratio (SINR) is: （7） in, This represents the power of additive white Gaussian noise; In particular, At the receiving end, SIC will eliminate all inter-user interference, therefore, The received signal-to-noise ratio (SNR) can be expressed as: （8） also, , About the receiver The SINR of a signal is represented as: （9） According to Shannon's theory, The achievable rate is: （10）。

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