Non-orthogonal multiple access-dual-functional radar joint beamforming and power allocation method

Abstract

The application relates to a non-orthogonal multiple access-dual-function radar combined beamforming and power distribution method and belongs to the wireless communication field. First, a base station adopts a NOMA technology to provide services for multiple communication users, and simultaneously utilizes superimposed NOMA signals to sense a target. In order to enhance the quality of a communication link, a RIS is deployed to provide a virtual line-of-sight link for the communication users. Then, an optimization function is established by taking the sum of the maximum system reachable sum rate and the target effective sensing power as a target, and the function is solved by optimization to guarantee sensing performance and communication performance. Finally, an alternating optimization algorithm is adopted to split the target problem to be solved into three subproblems and alternately solve the three subproblems, wherein continuous convex approximation and semi-positive definite relaxation technology are combined to optimize the active beamforming vector of the base station, the phase shift coefficient of the RIS and the power distribution coefficient among the users. The application has a simple implementation process, a wide application range and can improve the spectrum efficiency of a communication and sensing integrated system.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication and relates to a joint beamforming and power allocation algorithm for a dual-function radar-communication system (DFRC) assisted by a reconfigurable intelligent surface (RIS). Specifically, it relates to a method for joint beamforming and power allocation of a non-orthogonal multiple access-dual-function radar. Background Technology

[0002] Faced with the challenge of limited wireless network spectrum, future communication systems will need to explore the feasibility of coexisting with other electronic devices on the same frequency band. Traditionally, radar and communication operate as two independent systems, with radar used for target detection and tracking, and communication for information transmission. However, as wireless communication spectrum expands into higher frequency bands such as millimeter waves and terahertz, there will be significant overlap with the frequency bands occupied by traditional radar. Furthermore, communication and radar systems share significant similarities in hardware structure, thus creating the possibility for integrated sensing and communication (ISAC) joint design. As one of the potential key technologies for future Beyond 5G (B5G) and 6G wireless networks, ISAC utilizes shared waveforms, shared spectrum, and shared hardware to achieve collaborative processing of communication and sensing, further improving energy efficiency and spectrum efficiency.

[0003] In ISAC technology, compared to Radar and Communication Coexistence (RCC) systems, Dual-Function Radar-Communication Systems (DFRC) can perform both radar and communication functions on the same platform, achieving information sharing while reducing hardware costs, and have attracted widespread attention from scholars in recent years. However, mobile communication systems face the problem of low spectrum utilization. With continuous research, Non-Orthogonal Multiple Access (NOMA), as a technology that supports large-scale connections and enhances communication capabilities, has been introduced into ISAC systems. It can support multiple users in resource blocks such as time, frequency, and code domain. In NOMA communication networks, superimposed signals are transmitted from the transmitter, and Successive Interference Cancellation (SIC) is applied at the receiver to eliminate interference. Early research showed that NOMA can achieve significant performance improvements over Orthogonal Multiple Access in terms of summation rate, security rate, user fairness, and interruption probability.

[0004] Meanwhile, intelligent reflective surfaces (RIS) designed using a large number of low-cost passive reflective devices can be flexibly adjusted in terms of amplitude and phase of incident signals through programming to obtain an artificially controllable electromagnetic propagation environment. More importantly, RIS can introduce additional optimization degrees of freedom and virtual line-of-sight (LoS) links for the desired target. Therefore, deploying RIS is expected to significantly improve the performance of wireless communication. However, previous research on integrated communication and sensing technologies has often focused only on radar detection performance or communication service quality, without considering the trade-off between the two. Recently, a few studies have begun to introduce NOMA technology into RIS-assisted DFRC systems, forming RIS-assisted NOMA-DFRC systems. The aim is to use NOMA technology to enable DRFC systems to provide services to more users through power domain multiplexing, thereby alleviating system overload problems. However, this approach tends to focus more on improving radar sensing performance, so the communication performance of integrated communication and sensing is not satisfactory. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a method for joint beamforming and power allocation of non-orthogonal multiple access-dual-function radar.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for joint beamforming and power allocation of nonorthogonal multiple access-dual-function radar, comprising the following steps:

[0008] Step 1: Deploy a RIS-assisted NOMA-DFRC system with M reflector units to assist the dual-function base station in communicating with 2K single-antenna users and detecting N radar targets. The communication users are divided into K clusters, each containing one central user and one edge user.

[0009] Step 2: Design and solve the active beamforming vector w on the base station side. k The phase shift matrix Φ of the RIS and the power allocation coefficient α of the user. k The optimization problem, where the subscript k Indicates the index of the NOMA cluster;

[0010] Step 3: Initialize the active beamforming vector w k The phase shift matrix Φ of the RIS and the power allocation coefficient α of the user. k Set the maximum number of iterations I max subscript max This represents the maximum value and the convergence accuracy ε.

[0011] Step 4: Fix the phase shift matrix Φ of the RIS and the user power allocation coefficient α k Solve for the active beamforming vector w k ;

[0012] Step 5: Fix the active beamforming vector w k and user power allocation coefficient α k Solve for the RIS phase shift matrix Φ;

[0013] Step 6: Fix the active beamforming vector w k And the RIS phase shift matrix Φ, solve for the user power allocation coefficient α k ;

[0014] Step 7: Alternately iteratively optimize the active beamforming vector w k The phase shift matrix Φ of the RIS and the user power allocation coefficient α k This continues until the target value error is less than the threshold or the maximum number of iterations is reached.

[0015] Optionally, in step one, the system model is as follows:

[0016] Considering the downlink of a RIS-assisted NOMA-DFRC system, the base station is equipped with Q tThe system has 2K single-antenna communication users and N radar targets. The RIS is equipped with M reflective elements. Using NOMA technology, the 2K users are divided into K NOMA user clusters, each containing two users. For the k-th NOMA cluster, there is a central user U. k,c and a marginal user U k,e Let the set of all NOMA clusters be... A set consisting of N radar-detected targets

[0017] The base station transmits the following signals:

[0018]

[0019] in This represents the sum of the first to the Kth terms; s represents the active beamforming vector in the k-th NOMA cluster; k,c s k,e These represent the signals sent to the central user and edge user within the k-th NOMA cluster, respectively; subscript k,c , k,e Represents the central and peripheral users of the k-th cluster; α k The power allocation coefficient for the central user within the k-th NOMA cluster;

[0020] The received signal of the central user of the k-th cluster is:

[0021]

[0022] in These represent the equivalent baseband channels between the base station and the RIS, the RIS and the central user of the k-th cluster, and the base station and the central user of the k-th cluster, respectively. ∈ indicates belonging to; superscript H This represents the conjugate transpose; Φ = diag(φ) represents the RIS reflection coefficient matrix, where... Where β m ∈[0,1] and These represent the amplitude and phase of each passive reflector, respectively. `diag(·)` represents a diagonal matrix, where each diagonal element is the corresponding element `·`. `j` represents the imaginary unit, and the superscript... T Represents the transpose of a matrix; For U k,c The mean is 0 and the variance is 0. Additive Gaussian white noise, where ~ represents the distribution;

[0023] The received signal of the edge user of the kth cluster is

[0024]

[0025] in Let represent the equivalent baseband channels between the RIS and the edge user of the k-th cluster, and between the base station and the edge user of the k-th cluster, respectively. For U k,e The mean is 0 and the variance is 0. Additive white Gaussian noise; for ease of analysis, for any... Assumption

[0026] Optionally, in step two, the principle of the joint design beamforming method is as follows:

[0027] To achieve radar target detection, the covariance of the radar detection signal must meet the target detection requirements; based on the signal transmitted by the base station, in the target direction θ n The beamform of the upper sensing signal, i.e., the effective sensing power, is:

[0028] P(θ n ) = a H (θ n )Ra(θ n )

[0029] Where, θ n Represents the angle of the nth detected target; subscript n Indicates the target's index; Let λ be the transmission steering vector, and d be the wavelength and antenna spacing, respectively, with d = λ / 2; R represents the covariance matrix of the transmitted signal, defined as... E{·} represents the statistical expectation;

[0030] To achieve adaptive target localization, the sensing signal is in any two target directions θ z and θ p The cross-correlation on the x-axis is the lowest, and its cross-correlation is defined as:

[0031] C(θ z ,θ p )=|a H (θ z )Ra(θ p )|

[0032] Where z and p represent the index of the direction of the detected target, and z ≠ p. Represents the directions z and p of two different targets within the target set; |·| represents taking the absolute value;

[0033] U k,e decodes k,e The signal-to-interference-plus-noise ratio is:

[0034]

[0035] According to the NOMA principle, the central user of the k-th NOMA cluster first decodes the edge user signal using Successive Interference Cancellation (SIC) technology, thus U k,c Decoding signal s k,e The signal-to-interference-plus-noise ratio is:

[0036]

[0037] Considering a perfect SIC, then the central user U k,c Decoding its own signal s k,c The signal-to-interference-plus-noise ratio is:

[0038]

[0039] To ensure successful SIC decoding, the rate at which the central user decodes the edge user's signal must be no less than the rate at which the edge user decodes its own signal, i.e.:

[0040] R k,c→e =log2(1+SINR) k,c→e )≥R k,e =log2(1+SINR) k,e )

[0041] Where log2(·) represents the logarithmic function to the base 2; it is assumed that the base station has known the perfect channel state information;

[0042] The design of the RIS-assisted NOMA-DFRC system joint beamforming and power allocation algorithm can be expressed as maximizing the sum of the system's achievable rate and effective sensing power under constraints such as minimum user transmission rate, target correlation, and RIS phase shift. The optimization problem can be represented as:

[0043] P1:

[0044] stC1:R k,c→e ≥R k,e ,

[0045] C2:

[0046] C3:

[0047] C4:|P(θ z )-P(θ p )|≤P diff ,

[0048] C5:

[0049] C6:

[0050] C7:|Φ m,m |=1,

[0051] C8:0≤α k ≤1,

[0052] in Is seeking The maximum value and Φ and α k The value of R is given by P(·), which represents the index of the optimization problem, and R is given by R. k,e and R k,c ρ represents the rates of edge users and center users in the k-th cluster, respectively. c >0 and ρ r >0 is a regularization parameter that balances communication transmission performance and radar sensing performance; st stands for subject to, and C represents the constraint number. The minimum rate requirement for central and edge users within the k-th cluster is given by the superscript. min P represents the minimum value; diff For the power difference threshold in each direction, the subscript is... diff Indicates the name of the difference threshold identifier; ζ represents the mean square of the cross-correlation across all target directions, and ζ is the upper bound parameter of the cross-correlation; ||·|| represents the norm, P t This represents the total transmit power of the array antenna; Indicates the RIS unit number. This indicates that any value can be selected.

[0053] Optionally, the active beamforming vector w k The solution is:

[0054] First, fix the RIS diagonal matrix Φ and the power allocation coefficient α. k Solve for the active beamforming vector w k The original optimization problem can be expressed as:

[0055] P2:

[0056] stC1, C2, C3, C4, C5, C6

[0057] The optimization problem described above has a convex form and quadratic equality constraints, making it non-convex. The optimization problem is transformed into a convex problem by using continuous convex approximation and semidefinite relaxation techniques. Finally, Gaussian randomization is used to obtain a solution that satisfies the rank-one condition.

[0058] Optionally, the solution for the RIS diagonal matrix Φ is as follows:

[0059] Solve for w k Then, for a given active beamforming vector w k and power allocation coefficient α k The original optimization problem is transformed into the following problem for solution:

[0060] P3:

[0061] stC1, C2, C3, C7

[0062] The above optimization problem has a convex form and a modulo-1 constraint, so the optimization problem is non-convex. The above optimization problem is transformed into a convex problem by introducing an equivalent matrix and combining continuous convex approximation and semi-positive definite relaxation. Finally, the Gaussian randomization method is used to obtain the solution that satisfies the rank-1 condition.

[0063] Optionally, the power allocation coefficient α k The solution is:

[0064] After solving for the RIS diagonal matrix Φ, for a given active beamforming vector w k Given the diagonal matrix Φ of RIS, the original optimization problem is transformed into the following problem for solution:

[0065] P4:

[0066] stC1, C2, C3, C8

[0067] The optimization problem described above has a convex form, and the optimization problem is non-convex. The continuous convex approximation method is used to transform the optimization problem into a convex problem for solution.

[0068] This invention achieves beamforming and power allocation through a RIS-assisted NOMA-DFRC system. By optimizing the base station beamforming vector, the RIS phase shift matrix, and the user power allocation coefficients, the problem is expressed as a constrained optimization problem and solved using a combination of continuous convex approximation and semi-definite relaxation techniques, along with alternating optimization methods. The system uses superimposed NOMA signals for joint beamforming design, simultaneously performing target detection and user communication. This supports higher information rates while ensuring the system's detection capabilities, further enhancing the system's communication and sensing performance. Furthermore, by designing the power allocation coefficients among users, power domain reuse is achieved, further improving the spectral efficiency of the integrated communication and sensing system.

[0069] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0070] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0071] Figure 1 Schematic diagram of a NOMA-DFRC system model assisted by RIS;

[0072] Figure 2 The overall flowchart of the beamforming and power allocation method provided by the present invention;

[0073] Figure 3 This is a flowchart illustrating the specific implementation of the alternating iterative optimization algorithm in this invention. Detailed Implementation

[0074] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0075] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0076] The system environment intelligent reflector (RIS) assisted non-orthogonal multiple access (NOMA) dual-function radar-communication system (DFRC) model of the present invention is as follows: Figure 1As shown, the RIS-assisted DFRC system employs a dual-function radar-communication base station, which can perform radar and communication functions on the same platform. The base station is equipped with Q... t There are 2K single-antenna communication users and N radar targets, divided into K clusters, each containing one central user and one peripheral user. The RIS is equipped with M reflective elements, and the base station is assumed to be equipped with a uniform linear array. For ease of subsequent analysis, let the set consisting of all NOMA clusters be defined. A set consisting of N radar-detected targets

[0077] The base station transmits the following signals:

[0078]

[0079] in This represents the sum of the first to the Kth terms; s represents the active beamforming vector in the k-th NOMA cluster; k,c s k,e These represent the signals sent to the central user and edge user within the k-th NOMA cluster, respectively; subscript k,c , k,e Represents the central and peripheral users of the k-th cluster; α k Let be the power allocation coefficient for the central user within the k-th NOMA cluster.

[0080] The received signal of the central user of the k-th cluster is:

[0081]

[0082] in These represent the equivalent baseband channels between the base station and the RIS, the RIS and the central user of the k-th cluster, and the base station and the central user of the k-th cluster, respectively. ∈ indicates belonging to; superscript H This represents the conjugate transpose; Φ = diag(φ) represents the RIS reflection coefficient matrix, where... Where β m ∈[0,1] and These represent the amplitude and phase of each passive reflector, respectively. `diag(·)` represents a diagonal matrix, where each diagonal element is the corresponding element `·`. `j` represents the imaginary unit, and the superscript... T This represents the transpose of a matrix. For U k,c The mean is 0 and the variance is 0. The additive Gaussian noise is denoted by ~, which represents the distribution.

[0083] The received signal of the edge user of the k-th cluster is:

[0084]

[0085] in Let represent the equivalent baseband channels between the RIS and the edge user of the k-th cluster, and between the base station and the edge user of the k-th cluster, respectively. For U k,e The mean is 0 and the variance is 0. Additive Gaussian noise; for ease of analysis, for any Assumption

[0086] To achieve radar target detection, the covariance of the radar detection signal must meet the target detection requirements. Based on the signal transmitted from the base station, in the target direction θ... n The beamform of the upper sensing signal, i.e., the effective sensing power, is:

[0087] P(θ n ) = a H (θ n )Ra(θ n )

[0088] Where, θ n Represents the angle of the nth detected target; subscript n Indicates the target's index; Let λ be the transmission steering vector, and d be the wavelength and antenna spacing, respectively, with d = λ / 2; R represents the covariance matrix of the transmitted signal, defined as... E{·} represents the statistical expectation.

[0089] To achieve adaptive target localization, the sensing signal is in any two target directions θ z and θ p The cross-correlation on the x-axis should be as low as possible, and its cross-correlation is defined as:

[0090] C(θ z ,θ p )=|a H (θ z )Ra(θ p )|

[0091] Where z and p represent the index of the direction of the detected target, z≠p, z,p∈N represent two different target directions z and p within the set of detected targets; |·| represents taking the absolute value.

[0092] Meanwhile in U k,e decodes k,e The signal-to-interference-plus-noise ratio is:

[0093]

[0094] According to the NOMA principle, the central user of the k-th NOMA cluster first decodes the edge user signal using Successive Interference Cancellation (SIC) technology, and then U k,c Decoding signal s k,e The signal-to-interference-plus-noise ratio is:

[0095]

[0096] Considering a perfect SIC, then the central user U k,c Decoding its own signal s k,c The signal-to-interference-plus-noise ratio is:

[0097]

[0098] To ensure successful SIC decoding, the rate at which the central user decodes the edge user's signal must be no less than the rate at which the edge user decodes its own signal, i.e.:

[0099] R k,c→e =log2(1+SINR) k,c→e )≥R k,e =log2(1+SINR) k,e )

[0100] Where log2(·) represents the logarithmic function to the base 2; in addition, the paper assumes that the base station knows the perfect channel state information. In practice, the base station can use pilots to estimate the channel state information.

[0101] Therefore, we express the design of the RIS-assisted NOMA-DFRC system joint beamforming and power allocation algorithm as maximizing the sum of the system's achievable rate and effective sensing power under constraints such as minimum user transmission rate, target correlation, and RIS phase shift. The optimization problem is expressed as:

[0102] P1:

[0103] stC1:R k,c→e ≥R k,e ,

[0104] C2:

[0105] C3:

[0106] C4:|P(θ z )-P(θ p )|≤P diff ,

[0107] C5:

[0108] C6:

[0109] C7:|Φ m,m |=1,

[0110] C8:0≤α k ≤1,

[0111] in Is seeking The maximum value and Φ and α k The value of R is given by P(·), which represents the index of the optimization problem, and R is given by R. k,e and R k,c ρ represents the rates of edge users and center users in the k-th cluster, respectively. c >0 and ρ r >0 is a regularization parameter that balances communication transmission performance and radar sensing performance; st is an abbreviation for subject to, and C represents the constraint number. The minimum rate requirement for the central and edge users within the k-th cluster is given by the superscript. min P represents the minimum value; diff For the power difference threshold in each direction, the subscript is... diff Indicates the difference threshold name; ζ represents the mean square of the cross-correlation across all target directions, and ζ is the upper bound parameter of the cross-correlation; ||·|| represents the norm, P t This represents the total transmit power of the array antenna; Indicates the RIS unit number. This indicates that any value can be selected.

[0112] Considering that the objective function and constraints of the above optimization problem involve multiple coupled variables, the optimization problem is non-convex, and solving it presents certain challenges. Therefore, the following paper will present an iterative algorithm based on continuous convex approximation of alternating optimization algorithm combined with semidefinite relaxation technique to solve the above problem.

[0113] First, fix the RIS diagonal matrix Φ and the power allocation coefficient α. k Solve for the active beamforming vector w k The original optimization problem can be expressed as:

[0114] P2:

[0115] stC1, C2, C3, C4, C5, C6

[0116] The optimization problem described above involves convexity and quadratic equality constraints, making it non-convex. Therefore, a continuous convex approximation method is used to transform the optimization problem into a convex problem for solution. Specifically, when the phase shift coefficient of the RIS unit is fixed, the channel information is known, so let... To make this problem easier to solve, we first define variables. If k∈{1,2,...,K}, then Rank(W) k ) = 1, W k ≥0, where Rank(·) represents the rank; ≥ is a positive semi-definite sign. Based on mathematical operations, the rates of near-end users and far-end users in each NOMA cluster are rewritten as:

[0117]

[0118]

[0119] in

[0120]

[0121]

[0122]

[0123]

[0124] Tr(·) represents a trace.

[0125] Therefore, the objective function can be transformed into:

[0126]

[0127] Where f 2-1 (W1,W2...,W K ) = -log2G 2-1 f 2-2 (W1,W2...,W K )=-log2 G 2-2 f 2-3 (W1,W2...,W K )=-log2 G 2-3 f 2-4 (W1,W2...,W K )=-log2 G 2-4 Since the objective function is in convex form and exhibits non-convexity, a continuous convex approximation method is used to perform a first-order Taylor expansion on the third and fourth terms. d∈{2,4} means that the lower bound is taken:

[0128]

[0129]

[0130] Meanwhile, taking the logarithm of both sides of constraint C1 yields:

[0131]

[0132] Since the first and fourth terms of the above expression are non-convex, a continuous convex approximation method is used to process them. u∈{1,4}, where ^ denotes taking the upper bound, i.e.:

[0133]

[0134]

[0135] Therefore, constraint C1 is transformed into the following constraint; for ease of expression, we will use C... 2-1 express;

[0136]

[0137] Similarly, for C2 and C3, based on the result of the r-th iteration... It is processed using continuous convex approximation techniques, and... and This is represented by constraint C. 2-2 and C 2-3 :

[0138]

[0139]

[0140] Constraint C6 is transformed into the following constraint, using C 2-6 express:

[0141]

[0142] At the same time, the rank constraint Rank(W) must be satisfied. k Given that ) = 1, this newly added constraint can be addressed using a positive semidefinite relaxation technique, making the problem easier to handle. Since variables have already been introduced previously... Therefore, W exists. k If ≥0, denote this constraint as C. 2-7 Therefore, the optimization problem P2 is ultimately transformed into:

[0143]

[0144] stC 2-1 C 2-2 C 2-3 C4, C5, C2-6 C 2-7

[0145] Observing the optimization problem P2', both the objective function and constraints satisfy the convex function property, and it can be solved using the convex optimization tool CVX. However, the resulting W... k If the rank-one constraint is not satisfied, a Gaussian randomization method can be used to obtain a rank-one solution.

[0146] Solve for w k Then, for a given active beamforming vector w k and power allocation coefficient α k The original optimization problem can be transformed into the following problem for solution:

[0147] P3:

[0148] stC1, C2, C3, C7

[0149] The optimization problem described above has a convex form and a modulo-1 constraint, making it non-convex. Therefore, an equivalent matrix is ​​introduced. q∈{e,c}, where For ease of processing, we define e = [e1,...,e] M ] H ,in So It can be transformed into Define vector then Can be rewritten as definition It satisfies E≥0 and Rank(E)=1, therefore therefore

[0150] Similarly, by introducing a matrix back, Can be rewritten as Therefore, R in the objective function k,e and R k,c The change is as follows:

[0151]

[0152]

[0153] in

[0154]

[0155]

[0156]

[0157]

[0158] Let f 3-1 (E)=-log2G 3-1 f 3-2 (E)=-log2G 3-2 f 3-3 (E)=-log2G 3-3 f 3-4 (E)=-log2G 3-4 Using the idea of ​​continuous convex approximation, based on the result E of the r-th iteration... (r) , for f 3-2 (E) and f 3-4 (E) can be processed using its first-order Taylor expansion, denoted as... and

[0159]

[0160]

[0161] Therefore, the constraint terms C2 and C3 in the optimization subproblem P3 can be transformed into the following two equations, denoted as C 3-2 C 3-3 ;

[0162]

[0163]

[0164] Similarly, for the nonconvex terms of equation C1, according to the r-th iteration result E (r) We use a first-order Taylor expansion to handle this, denoted as This constraint is denoted as C. 3-1 That is:

[0165]

[0166]

[0167] in

[0168]

[0169]

[0170] Since the rank-one constraint is non-convex, the rank-one constraint can be relaxed using a positive semidefinite relaxation technique, thus the optimization problem P3 is equivalent to:

[0171] P3'

[0172] stC3-1 C 3-2 C 3-3

[0173] C 3-4 :E≥0

[0174] C 3-5 :E m+1,m+1 ==1,m=1,2,...M

[0175] Since the optimization problem P3' is a convex problem, it can be solved using the CVX toolbox; however, the solution usually fails to meet the rank-one requirement. Therefore, Gaussian randomization can be used to construct the corresponding rank-one solution.

[0176] After solving for the RIS diagonal matrix Φ, for a given active beamforming vector w k Given the diagonal matrix Φ of RIS, the original optimization problem can be transformed into the following problem to be solved:

[0177] P4:

[0178] stC1, C2, C3, C8

[0179] The optimization problem described above has a convex form, while the overall optimization problem is non-convex. Therefore, a continuous convex approximation method is used to transform the optimization problem into a convex problem for solution. Next, the objective function is processed, letting...

[0180]

[0181]

[0182]

[0183]

[0184] Because f 4-2 (α k In the objective function, for α k The behavior is nonconvex, based on the value of the r-th iteration. For f 4-2 (α k We approximate this using a first-order Taylor expansion, denoted as... Right now:

[0185]

[0186] Simultaneously, it was observed that the constraint condition C2 in the optimization problem has certainty regarding α. k It is nonconvex, and the constraints C1 and C3 themselves are related to α. k It exhibits convexity. Therefore, based on the value of the r-th iteration... The constraint C2 is approximated by a first-order Taylor expansion, denoted as C. 4-2 ,Right now:

[0187]

[0188] Based on the sub-problems of processing active beamforming vectors and RIS phase shift coefficients, optimization problem P4 is transformed into the following optimization problem:

[0189] P4':

[0190] stC1,C 4-2 C3, C8

[0191] The optimization problem P4' is a convex problem, which can be solved using the Convex Optimization Toolbox CVX.

[0192] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for joint beamforming and power allocation of non-orthogonal multiple access-dual-function radar, characterized in that: The method includes the following steps: Step 1: Deploy with A RIS-assisted NOMA-DFRC system with one reflector unit assists dual-function base stations in achieving [interoperability / cooperation]. Communication for a single-antenna user and Detection of radar targets, where communication users are divided into... There are 1 cluster, and each cluster contains one central user and one peripheral user; The system model is as follows: Considering the downlink of a RIS-assisted NOMA-DFRC system, the base station is equipped with 1 antenna, total Single-antenna communication users and The RIS is equipped with radar targets. A reflective element, using NOMA technology, to... User share There are N NOMA user clusters, each cluster consisting of two users, for the Nth... k Each NOMA cluster contains a central user. and a marginal user Let the set of all NOMA clusters be... ,Depend on A set of radar-detected targets ; The base station transmits the following signals: in Indicates the first to the last item Items and; Indicates the first Active beamforming vectors in a NOMA cluster; , They respectively represent the messages sent to the first Signals of central and edge users within a NOMA cluster; subscript , Indicates the first Central users and edge users of each cluster; For the first k Power allocation coefficients for central users within a NOMA cluster; No. The received signal of the central user of each cluster is: in , , These represent the base station and the RIS, and the RIS and the first... The central user of each cluster, the base station and the... The equivalent baseband channel of the central user of each cluster Indicates belonging to; superscript Indicates conjugate transpose; This represents the RIS reflection coefficient matrix, here ,in and These represent the amplitude and phase of each passive reflector element, respectively. This represents a diagonal matrix, where each diagonal element is a corresponding element. , Indicates the imaginary unit, superscript Represents the transpose of a matrix; for The mean is 0 and the variance is 0. Additive white Gaussian noise, The distribution is represented as follows; No. The received signal of each cluster's edge user is in , Representing RIS and the first The edge users of the cluster, the base station and the first Equivalent baseband channel for edge users of each cluster; for The mean is 0 and the variance is 0. Additive white Gaussian noise; for ease of analysis, for any... Assuming ; Step 2: Design and solve the active beamforming vector on the base station side. Phase shift matrix of RIS and the user's power allocation factor The optimization problem, where the subscript Indicates the index of the NOMA cluster; The principle of the joint design beamforming method is as follows: To achieve radar target detection, the covariance of the radar detection signal must meet the target detection requirements; based on the signal transmitted by the base station, in the target direction... The beamform of the upper sensing signal, i.e., the effective sensing power, is: in, Representing the Angle of the detected target; subscript n Indicates the target's index; For the launch guidance vector, and Let the wavelength and antenna spacing be respectively. ; The covariance matrix representing the transmitted signal is defined as follows: , Indicates statistical expectation; To achieve adaptive target localization, the sensing signal is in any two target directions. and The cross-correlation on the x-axis is the lowest, and its cross-correlation is defined as: in , The index indicates the direction of the detected target, and , Indicates the directions of two different targets within the set of detected targets. and ; Indicates taking the absolute value; Decoding The signal-to-interference-plus-noise ratio is: According to the NOMA principle, the first The central user of each NOMA cluster first decodes the edge user signals using Sequential Interference Cancellation (SIC) technology. Decoding signal The signal-to-interference-plus-noise ratio is: Considering a perfect SIC, then the central user Decoding its own signal The signal-to-interference-plus-noise ratio is: To ensure successful SIC decoding, the rate at which the central user decodes the edge user's signal must be no less than the rate at which the edge user decodes its own signal, i.e.: in Represents a logarithmic function to the base 2; assume the base station has known the perfect channel state information; The design of the RIS-assisted NOMA-DFRC system joint beamforming and power allocation algorithm can be expressed as maximizing the sum of the system's achievable rate and effective sensing power under constraints such as minimum user transmission rate, target correlation, and RIS phase shift. The optimization problem can be represented as: in Is seeking The maximum value and , and The value of , This indicates the sequence number of the optimization problem. and Representing the first The rates of edge users and center users in each cluster and Regularization parameters for balancing communication transmission performance and radar sensing performance; This is an abbreviation for "subject to". Represents the constraint number. , For the first Minimum rate requirements for central and edge users within a cluster, superscript Indicates the minimum value; For the power difference threshold in each direction, the subscript is... Indicates the name of the difference threshold identifier; This represents the mean square of the cross-correlation across all target directions. This is the upper bound parameter for cross-correlation; Indicates the norm. This represents the total transmit power of the array antenna; Indicates the RIS unit number. This indicates taking any option; Step 3: Initialize the active beamforming vector Phase shift matrix of RIS and the user's power allocation factor Set the maximum number of iterations. subscript Represents the maximum value and convergence accuracy. ; Step 4: Fix the phase shift matrix of RIS and user power allocation factor Solving for the active beamforming vector ; Step 5: Fix the active beamforming vector and user power allocation factor Solve the RIS phase shift matrix ; Step Six: Fix the active beamforming vector and RIS phase shift matrix Solve for the user power allocation coefficient ; Step 7: Alternately iteratively optimize the active beamforming vector Phase shift matrix of RIS and user power allocation coefficient This continues until the target value error is less than the threshold or the maximum number of iterations is reached.

2. The non-orthogonal multiple access-dual-function radar joint beamforming and power allocation method according to claim 1, characterized in that: The active beamforming vector The solution is: First, fix the RIS diagonal matrix. and power allocation factor Solving for the active beamforming vector The original optimization problem can be expressed as: The optimization problem described above has a convex form and quadratic equality constraints, making it non-convex. The optimization problem is transformed into a convex problem by using continuous convex approximation and semidefinite relaxation techniques. Finally, Gaussian randomization is used to obtain a solution that satisfies the rank-one condition.

3. The non-orthogonal multiple access-dual-function radar joint beamforming and power allocation method according to claim 2, characterized in that: The RIS diagonal matrix The solution is: Solve Then, for a given active beamforming vector and power allocation factor The original optimization problem is transformed into the following problem for solution: The above optimization problem has a convex form and a modulo-1 constraint, so the optimization problem is non-convex. The above optimization problem is transformed into a convex problem by introducing an equivalent matrix and combining continuous convex approximation and semi-positive definite relaxation. Finally, the Gaussian randomization method is used to obtain the solution that satisfies the rank-1 condition.

4. The non-orthogonal multiple access-dual-function radar joint beamforming and power allocation method according to claim 3, characterized in that: The power allocation coefficient The solution is: Solve for the RIS diagonal matrix Then, for a given active beamforming vector and RIS diagonal matrix The original optimization problem is transformed into the following problem for solution: The optimization problem described above has a convex form, and the optimization problem is non-convex. The continuous convex approximation method is used to transform the optimization problem into a convex problem for solution.

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