Joint optimization method of transmit beam and ris discrete phase shift matrix based on dual-function radar and communication system

Abstract

The application discloses a kind of based on the joint optimization method of transmitting beam and RIS discrete phase shift matrix of dual-function radar and communication system, the method includes the following steps: constructing intelligent reflecting surface assisted dual-function radar and communication system, under the constraint of sensing and communication, constructing the joint optimization problem of transmitting beam shaping vector and phase shift matrix;For beam shaping vector, based on dichotomous search algorithm, approximate optimal closed solution solving method is constructed using Lagrange dual decomposition method, global optimal solution is obtained;Quantize the discrete phase shift matrix of RIS, based on optimization minimization method, convert quadratic constraint quadratic programming into semi-definite relaxation problem for solving, complete the alternate optimization process of target problem solving.The application improves the radar detection performance of DRC system in the path loss serious environment by the deployment of RIS, jointly optimizes RIS phase shift matrix and beam shaping vector, and proposes RIS discrete phase shift design method to reduce hardware complexity, effectively improves the performance of DRC system.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and specifically to a joint optimization method for the transmit beam and RIS discrete phase shift matrix of a dual-function radar and communication system. Background Technology

[0002] With the rapid development of 5G mobile communication, the number of connected devices has increased dramatically, leading to a growing demand for spectrum resources. Dual-function radar and communication (DRC) systems integrate radar and communication systems into a single system, effectively reducing system power consumption, minimizing electromagnetic interference, and improving hardware sharing efficiency. However, a challenging issue is that DRC systems require the design of transmission waveforms capable of simultaneously performing data transmission and radar sensing tasks. Existing research often fails to consider the practical scenario where targets are located in congested areas, where path loss dominates all paths. In this situation, the echo signal received by the radar-assisted base station (BS) is weakened due to severe channel attenuation, severely limiting the performance of the DRC system.

[0003] Meanwhile, reconfigurable intelligent surface (RIS)-assisted wireless communication has attracted widespread attention for realizing intelligent and reconfigurable communication environments. RIS, by continuously or discretely adjusting the phase of its reflective elements, has the ability to enhance or suppress desired signals. Furthermore, RIS does not use any transmit RF chain, effectively reducing hardware and energy costs. In addition, RIS can be flexibly installed on building walls or ceilings to integrate with existing cellular and WiFi systems without requiring changes to the access point or user terminal hardware. Therefore, to mitigate severe channel fading problems, deploying RIS near the base station (BS) in a DRC system can be considered to provide additional transmission links, thereby effectively supporting radar detection and improving DRC system performance. While increasing RIS elements to improve system performance is a good approach, the presence of a large number of RIS reflective elements leads to a significant increase in hardware requirements. Therefore, an optimization method combining the transmit beam and the discrete phase-shift matrix of the RIS is urgently needed. Summary of the Invention

[0004] To overcome the defects and shortcomings of existing technologies, this invention provides a joint optimization method for the transmit beam and RIS discrete phase shift matrix based on a dual-function radar and communication system. By designing the deployment of RIS, the radar detection performance of the DRC system in environments with severe path loss is improved. The RIS phase shift matrix and beamforming vector are jointly optimized, and a RIS discrete phase shift design method is proposed to reduce hardware complexity.

[0005] The second objective of this invention is to provide a joint optimization system for the transmit beam and RIS discrete phase shift matrix based on a dual-function radar and communication system.

[0006] A third objective of this invention is to provide a storage medium.

[0007] A fourth objective of this invention is to provide a computing device.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] This invention provides a joint optimization method for the transmit beam and RIS discrete phase shift matrix based on a dual-function radar and communication system, comprising the following steps:

[0010] Construct a dual-function radar and communication system assisted by an intelligent reflector, and under the constraints of sensing and communication, construct a joint optimization problem of the transmit beamforming vector and phase shift matrix;

[0011] For beamforming vectors, based on the binary search algorithm and using the Lagrange dual decomposition method, an approximate optimal closed-form solution solution is constructed to obtain the global optimal solution;

[0012] The discrete phase shift matrix of RIS is quantized, and based on the optimization minimization method, the quadratic constraint quadratic programming is transformed into a semidefinite relaxation problem for solution, thus completing the alternating optimization process for solving the objective problem.

[0013] As a preferred technical solution, a dual-function radar and communication system assisted by an intelligent reflector is constructed. The system includes an intelligent reflector RIS, a radar target, a communication user, and a DRC base station. The DRC base station simultaneously sends radar detection waveforms to the radar target and sends communication symbols to the downlink communication user. The DRC base station is equipped with M antenna elements to complete the sensing task and serves a single antenna user. The intelligent reflector RIS with N reflective elements is deployed on the side of the building.

[0014] As a preferred technical solution, the signal received by the DRC base station is represented as follows:

[0015] y R =(G H VAV H G+B)wx+n r

[0016] Where x is the transmitted signal of the DRC base station, G represents the channel model between the DRC base station and the RIS, A represents the target response matrix of the RIS, B represents the target response matrix of the DRC base station parameters, V represents the diagonal effective phase shift matrix of the RIS, w is the beamforming vector of the DRC base station transmitter, and (·) HRepresents the transpose of a matrix;

[0017] The signal received by the user is represented as:

[0018]

[0019] in, It is the downlink channel between RIS and users. For the downlink channel between the DRC base station and the user, n c Noise received at the user's location;

[0020] As a preferred technical solution, under the constraints of sensing and communication, a joint optimization problem of the transmit beamforming vector and phase shift matrix is ​​constructed, specifically expressed as:

[0021]

[0022] stSNR c ≥η

[0023]

[0024] ||w|| 2 ≤P r

[0025] Where η is the SNR required by the user, P r v is the maximum transmit power of the radar base station transmitter. n Indicates the phase shift of RIS;

[0026] The signal-to-noise ratio received at the DRC base station is expressed as:

[0027]

[0028] Where G represents the channel model between the DRC base station and the RIS, A represents the target response matrix of the RIS, B represents the target response matrix of the DRC base station parameters, V represents the diagonal effective phase shift matrix of the RIS, and w is the beamforming vector of the DRC base station transmitter. H To represent the transpose of a matrix, Indicates the noise power at the DRC;

[0029] The signal-to-noise ratio received at the communication user's location is expressed as:

[0030]

[0031] in, The variance of the noise is represented. This represents the downlink channel between the RIS and the user. This indicates the downlink channel between the DRC base station and the user.

[0032] As a preferred technical solution, a Rayleigh fading channel model is adopted between the DRC base station and the intelligent reflector RIS, specifically expressed as follows:

[0033]

[0034] Among them, K R For Rayleigh factor, G LoS For the deterministic component of line-of-sight, G NLoS This refers to the non-line-of-sight Rayleigh fading component.

[0035] The deterministic component of sight distance is represented as:

[0036]

[0037] Where α is the large-scale channel gain, ψ is the random phase uniformly distributed in [0, 2π], and vector a t (θ) is related to the angle θ t The relevant DRC base station antenna array transmit response vector, vector a r (θ r ) is the receiver steering vector of the RIS;

[0038] The target response matrix of RIS is represented as:

[0039]

[0040] Where K is the target number, β k For complex path loss, vector a(θ) k ) is the turning vector of RIS.

[0041] As a preferred technical solution, based on the binary search algorithm, a method for finding the approximate optimal closed-form solution is constructed using the Lagrange dual decomposition method to obtain the global optimal solution, specifically including:

[0042] Define the following formula:

[0043] U = (G H VAV H G+B) H (G H VAV H G+B)

[0044]

[0045] Where G represents the channel model between the DRC base station and the RIS, A represents the target response matrix of the RIS, B represents the target response matrix of the DRC base station parameters, and V represents the diagonal effective phase shift matrix of the RIS. It is the downlink channel between RIS and users. This serves as the downlink channel between the DRC base station and the user.

[0046] Set the following parameters:

[0047]

[0048]

[0049]

[0050]

[0051]

[0052] The joint optimization problem is transformed into:

[0053]

[0054]

[0055] w H w≤P r

[0056] in, η is the SNR required by the user, P r Let be the maximum transmit power of the radar base station transmitter, and Re denote the real part of the matrix. Let w represent the first-order Taylor expansion of w, where w represents the transmitted beamforming vector. This indicates the noise power at the DRC. Represents the variance of the noise;

[0057] Solving the dual problem of the transformed joint optimization problem yields the optimal solution, specifically including:

[0058] The partial Lagrangian related to transmitter power constraints is defined as follows:

[0059]

[0060] Where λ is the Lagrange multiplier constrained by the transmitted signal power;

[0061] According to the duality theorem, the dual problem can be expressed as:

[0062]

[0063] stλ≥0

[0064] The dual function h(λ) is defined as follows:

[0065]

[0066]

[0067] The Lagrange function is expressed as:

[0068]

[0069] Where μ represents the Lagrange multiplier related to communication performance;

[0070] Optimal solution w opt Represented as:

[0071]

[0072] The optimal solution for the Lagrange multipliers related to communication performance is expressed as:

[0073]

[0074] As a preferred technical solution, the discrete phase shift matrix of RIS is quantized, and based on the optimization minimization method, the quadratic constrained quadratic programming is transformed into a semidefinite relaxation problem for solution, specifically including:

[0075] The joint optimization problem is transformed into:

[0076]

[0077] stv H ΦΦ H v+2Re(v H Φw H h2)+η1≥0

[0078]

[0079] in, It is a matrix A vector with diagonal elements, p = diag(vec(A) H ))vec(GBww H G H ), C = Tr(B H Bww H ), G represents the channel model between the DRC base station and the RIS, A represents the target response matrix of the RIS, B represents the target response matrix of the DRC base station parameters, V represents the diagonal effective phase shift matrix of the RIS, and w is the beamforming vector of the DRC base station transmitter. H V represents the transpose of a matrix, vec represents the matrix straightening operation, diag represents a diagonal matrix, and v n Indicates the phase shift of RIS;

[0080] The transformed joint optimization problem is solved using an optimization minimization algorithm. The optimization problem is expressed as:

[0081]

[0082] stv H ΦΦ H v+2Re(v H Φw H h2)+η1≥0

[0083]

[0084] Where Re represents the real part of the matrix, h1 represents the channel from RIS to the user, and h2 represents the channel from DRC to the user.

[0085] Introducing an auxiliary variable t transforms the optimization problem into a QCQP problem:

[0086]

[0087]

[0088]

[0089]

[0090] in, This means returning the elements of vector p into an N×N matrix. Indicates will The elements are returned to the matrix;

[0091] The QCQP problem is solved optimally using the interior-point method, yielding the following results: Then, the standard Gaussian randomization method is used to approximate the solution to the optimization problem, and through... The diagonal PSM is then obtained.

[0092] To achieve the second objective mentioned above, the present invention adopts the following technical solution:

[0093] This invention provides a joint optimization system for the transmit beam and RIS discrete phase shift matrix of a dual-function radar and communication system, comprising: a dual-function radar and communication system construction module, a joint optimization problem construction module, a global optimal solution solution module, and a semidefinite relaxation problem solution module;

[0094] The dual-function radar and communication system building module is used to build a smart reflector-assisted dual-function radar and communication system;

[0095] The joint optimization problem construction module is used to construct a joint optimization problem of the transmit beamforming vector and phase shift matrix under the constraints of sensing and communication.

[0096] The global optimal solution solving module is used to construct an approximate optimal closed solution solving method for the beamforming vector based on the binary search algorithm and using the Lagrange dual decomposition method to obtain the global optimal solution.

[0097] The semidefinite relaxation problem solving module is used to quantize the discrete phase shift matrix of RIS. Based on the optimization minimization method, it transforms the quadratic constraint quadratic programming into a semidefinite relaxation problem for solving, thus completing the alternating optimization process of solving the target problem.

[0098] To achieve the third objective mentioned above, the present invention adopts the following technical solution:

[0099] A computer-readable storage medium storing a program that, when executed by a processor, implements the aforementioned joint optimization method for the transmit beam and RIS discrete phase shift matrix based on a dual-function radar and communication system.

[0100] To achieve the fourth objective mentioned above, the present invention adopts the following technical solution:

[0101] A computing device includes a processor and a memory for storing processor-executable programs. When the processor executes the program stored in the memory, it implements the aforementioned joint optimization method of transmit beam and RIS discrete phase shift matrix based on a dual-function radar and communication system.

[0102] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0103] (1) This invention proposes a RIS-assisted DRC framework to address the spectrum scarcity problem and alleviate severe channel fading. Under the constraints of SINR service quality at the user, BS transmit power, and RIS phase shift modulus, this framework jointly optimizes the transmit beamforming vector of the BS and the passive reflection matrix of the RIS to maximize radar detection performance.

[0104] (2) The present invention describes the design problem as an optimization problem with a non-convex objective function and constraints, and uses the alternating optimization method to divide it into two sub-problems, which are solved effectively by binary search and QCQP respectively.

[0105] (3) This invention proposes a RIS discrete phase shift design method, which aims to address the problem that a large number of RIS elements may lead to a significant increase in hardware requirements, so as to realize the practical application of improving system performance by adding RIS elements. Attached Figure Description

[0106] Figure 1This is a flowchart illustrating the joint optimization method of the transmit beam and RIS discrete phase shift matrix based on a dual-function radar and communication system according to the present invention.

[0107] Figure 2 This is a schematic diagram of the architecture of the intelligent reflector-assisted dual-function radar and communication system of the present invention.

[0108] Figure 3 This is a schematic diagram illustrating the relationship between the radar signal-to-noise ratio and the number of reflecting elements in this invention. Detailed Implementation

[0109] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0110] Example 1

[0111] like Figure 1 As shown, this embodiment provides a joint optimization method for the transmit beam and RIS discrete phase shift matrix based on a dual-function radar and communication system, including the following steps:

[0112] Step 1: Construct a dual-function radar and communication system assisted by a smart reflector. Under the constraints of sensing and communication, construct a joint optimization problem of the transmit beamforming vector and phase shift matrix.

[0113] Consider a RIS-assisted dual-function radar and communication (DRC) system, such as... Figure 2 As shown, the system consists of a RIS (Radio Recognition Array), a radar target, communication users, and a DRC (Digital Radio Controlled Recognition) base station. The DRC base station simultaneously transmits radar detection waveforms to surrounding targets and communication symbols to downlink users. Assuming the radar target is located in a congested area dominated by path loss, the echo signal received by the base station is weak due to significant channel fading. To mitigate the severe channel fading problem, an RIS is deployed near the DRC base station to provide an additional transmission link to support both communication and radar detection tasks. Since radar sensing and communication tasks are coordinated using a unique integrated DRC base station, self-interference or mutual interference generated in conventional radar and communication systems will no longer exist. Without loss of generality, assume the DRC base station is equipped with M antenna elements to perform the sensing task and serves a single antenna user. The RIS with N reflective elements is deployed on the side of a building, maintaining good channel conditions with both the target and the user. Due to sparse propagation conditions, the direct echo signal between the DRC base station and the target is very small. Therefore, the signal received at the integrated DRC base station receiver can be written as:

[0114]

[0115] Where G is the channel model between the DRC base station and the RIS, A is the target response matrix of the RIS, B is the target response matrix of the DRC base station parameters, and x is the transmitted signal of the DRC base station. For the beamforming vector of the DRC base station transmitter, It follows a pattern with a mean of zero and a covariance matrix of... An independent and identically distributed complex Gaussian random process. Furthermore, (·) H This represents the transpose of a matrix. Let the diagonal effective phase shift matrix of RIS be expressed as... and γ n ∈[0,1] and θ n ∈[0,2π] represents the amplitude and phase shift reflection coefficient of the element labeled n. In practice, controlling the reflection amplitude and phase shift independently is costly. Therefore, for simplicity, each element is usually designed to maximize signal reflection, i.e., γ n =1, Furthermore, the phase shift of RIS is discrete. For further processing, we define a vector v = [v1,...,v...]. N ] T Considering that the integrated DRC base station is in a congested environment, a Rayleigh fading channel model is adopted between the DRC base station and the RIS, and its modeling is as follows:

[0116]

[0117] Where K R Rayleigh factor, For the deterministic component of sight distance, For the non-line-of-sight Rayleigh fading components, each term is a circularly symmetric complex Gaussian random variable with zero mean and unit variance. Specifically, the line-of-sight deterministic components are represented as:

[0118]

[0119] Where α is the large-scale channel gain, and ψ is a random phase uniformly distributed in [0, 2π]. For angle θ t The transmit response vector of the antenna array of the relevant DRC base station can be expressed as:

[0120]

[0121] Where d and λ are the element spacing and signal wavelength, respectively. Vector The receiver steering vector for the RIS is defined analogously to (4). Matrix This is the target response matrix of the RIS, which depends on the angle of arrival, target reflectivity, and velocity. The RIS can be viewed as a single-point MIMO radar; therefore, the expression for the target response matrix A is the same as that for a single-point MIMO radar, and can be defined as:

[0122]

[0123] Where K is the target number, β k This is the complex path loss, which includes the target's path loss, reflection coefficient, and complex radar crossover coefficient. (Vector) This is the RIS turning vector, as defined in (4). Matrix This is the target response matrix based on the DRC base station parameters. In the DRC system, it is recommended to use RIS to provide additional transmission links to support radar detection. It is assumed that the signal power caused by multiple reflections on the RIS is ignored due to severe path loss conditions. From (1), the signal-to-noise ratio received at the DRC base station is:

[0124]

[0125] in, This represents the noise power at the DRC.

[0126] On the other hand, the signal received by the user can be written as:

[0127]

[0128] in, For the channel between RIS and the user, n is the downlink channel between the DRC base station and the user. c The noise received at the user's location, obeying distributed, Let represent the noise power at the user's location. Since the user is in a congested area, path loss dominates across all paths, and therefore can be described using a Rayleigh distributed channel between the DRC base station and the user:

[0129]

[0130] Where α includes the path loss coefficient and the shadow fading coefficient, and has vector This is the downlink channel between the RIS and the user, and the parameters of the RIS can be defined using (8). According to the above formula, the signal-to-noise ratio at the user receiver can be expressed as:

[0131]

[0132] in, Noise power at the user's location;

[0133] Assume the integrated DRC base station transmits a signal with zero mean and zero unit variance to detect a target. Therefore, the transmitted beamforming vector satisfies the following constraints:

[0134] ||w|| 2 ≤P r (10)

[0135] Where P r This represents the maximum transmission power of the radar base station transmitter.

[0136] The objective of this embodiment is to maximize the radar's SNR by jointly designing the transmit beamforming vector w and the diagonal effective phase shift matrix (PSM) V, under sensing and communication constraints. The issues considered can be stated as follows:

[0137]

[0138] stSNR c ≥η (11b)

[0139]

[0140] ||w|| 2 ≤P r (11d)

[0141] Where η is the SNR required by the user, v n Indicates the phase shift of RIS. N is the specification of the RIS, meaning it has N reflecting elements. Constraint (11c) reflects the passive nature of the RIS, which does not amplify the incoming signal but only provides a phase shift. However, due to the coupling between the optimization variables V and w, and the non-convexity of the unity norm constraint in (11c), the above non-convex optimization problem cannot be solved directly.

[0142] Step 2: For the beamforming vector, based on the binary search algorithm and using the Lagrange dual decomposition method, design a low-complexity approximate optimal closed-form solution algorithm.

[0143] To obtain the optimal solution to the optimization problem in (11), an alternating optimization method is used. First, assume a fixed V and find the value of w that maximizes the signal-to-noise ratio of the radar. Then, optimize V while keeping w constant. First, find the optimal transmit beamforming vector w of the radar BS, while keeping the PSMV constant. Therefore, the joint optimization problem in step one can be expressed as:

[0144]

[0145]

[0146] w H w≤P r (12c)

[0147] Clearly, the above problem is a non-convex quadratic constraint quadratic programming (QCQP) problem, which makes it difficult to obtain the global optimal solution.

[0148] Based on the binary search algorithm and utilizing the Lagrange dual decomposition method, a low-complexity algorithm for finding the approximate optimal closed-form solution is presented. The following equation is defined:

[0149] U = (G H VAV H G+B) H (G H VAV H G+B) (13)

[0150]

[0151] and It can be observed that the objective function of (12) is a non-convex function, and the power constraint is also a non-convex constraint. Therefore, the above problem is a non-convex optimization problem. To solve this problem, the first-order Taylor approximation can be used to transform the non-convex optimization problem into a convex optimization problem. Let:

[0152]

[0153]

[0154] Where ζ represents the functional relationship, and w represents the transmitted beamforming vector;

[0155] (15) and (16) at point The first-order Taylor expansion of the vicinity can be expressed as:

[0156]

[0157]

[0158] Where Re represents the real part of the matrix, Let w be the first-order Taylor expansion; considering (17) and (18), the problem in (12) can be rewritten as:

[0159]

[0160] in Clearly, the optimization problem in (19) is a convex problem, satisfying the Slater condition, with zero duality. Solving its dual problem can replace the original dual problem to obtain the optimal solution. Therefore, the partial Lagrangian problem related to the transmitter power constraint is defined as:

[0161]

[0162] Where λ is the Lagrange multiplier constrained by the transmitted signal power. According to the duality theorem, the dual problem of (20) can be expressed as:

[0163]

[0164] The dual function h(λ) is defined as follows:

[0165]

[0166] It is worth noting that the problem in (22) is a quadratic programming problem with linear constraints, and its closed-form solution can be obtained. The Lagrangian function of problem (22) is expressed as:

[0167]

[0168] Here, μ represents the Lagrange multiplier related to communication performance. Since the Lagrange function mentioned earlier is a quadratic function of w, its minimum value at a certain point can be obtained, and the optimal solution w can be found. opt It can be represented as:

[0169]

[0170] Substituting (24) into (23), we obtain a quadratic function of μ. Based on the properties of a quadratic function, the optimal value of μ can be expressed as:

[0171]

[0172] Based on the preceding analysis, the problem in (22) can be effectively solved using the binary search algorithm:

[0173] Step 1. Initialize w to satisfy the following conditions. And w H w≤P r ;

[0174] Step 2. Assume w0 = w;

[0175] Step 3. Initialize 0≤λ l ≤λ u ;

[0176] Step 4. Order

[0177] Step 5. Calculate μ according to (25);

[0178] Step 6. Based on μ, calculate w according to (24);

[0179] Step 7. If Tr(ww) H )≤P r , let λ=λ1, otherwise, let λ=λ μ ;

[0180] Step 8. Determine |λ l -λ μ If |≤∈ is true, then proceed to Step 4; if true, proceed to Step 9.

[0181] Step9.Judge|SNR r (w)-SNR r If (w0)|≤∈ is not true, jump to Step2; if true, end the loop and output λ.

[0182] Step 3: Quantize the discrete phase shift matrix of RIS. Based on the optimization minimization method, transform the quadratic constrained quadratic programming (corresponding to the following formula (54)) into a semidefinite relaxation problem (corresponding to formula (55)) for solution, and complete the design of the alternating optimization algorithm for solving the target problem.

[0183] Building upon step two, further optimization of PSMV is performed. It's worth noting that increasing RIS elements to improve system performance is a good energy-saving solution. However, a large number of RIS elements leads to a significant increase in hardware requirements. Therefore, the phase shifts of the RIS elements are quantized to further reduce hardware complexity. Let... Quantization phase It can be represented as in B represents the phase shift resolution and the quantization bits.

[0184] After some mathematical operations, the optimization problem (11) can be transformed into:

[0185]

[0186]

[0187]

[0188] However, due to the constraints of the high power and unity norm of the objective function, the problem in (26) is difficult to solve. To solve this problem, the objective function in (26) needs to be restated as follows:

[0189]

[0190] Where Tr represents the trace operation of the matrix. Since A is a Hermitian matrix, then:

[0191] (vec((VAV H ) T )) T =(vec(VAV) H )) H (28)

[0192] Where vec represents the matrix straightening operation. According to And (28), the first part of (27) can be rewritten as:

[0193]

[0194] because have:

[0195]

[0196] Based on the characteristics of diagonal matrices, the right side of (30) can be rewritten as:

[0197]

[0198] in It is a matrix The vector of diagonal elements. According to (30) and (31), (29) can be transformed into:

[0199]

[0200] in,

[0201]

[0202] Similarly, the second part of the objective function (27) is transformed into:

[0203]

[0204] Where p = diag(vec(A) H ))vec(GBww H G H ), where diag represents a diagonal matrix and vec represents matrix straightening operation;

[0205] Step (a) originates from Tr(A) H B)=(vec(A)) H vec(B), step (b) originates from According to (32) and (34), the equivalent form of the objective function (27) can be expressed as:

[0206]

[0207] Where C = Tr(B) H Bww H ), where Tr represents the trace of the matrix.

[0208] Next, while making full use of the properties of the diagonal matrix V, through some mathematical operations, namely h H V = vdiag(h) H (26b) can be expressed as:

[0209]

[0210] in and h1 represents the RIS-to-user channel, and h2 represents the DRC-to-user channel. Using (36) and (35), the optimization problem in (26) can be re-expressed as:

[0211]

[0212]

[0213]

[0214] Clearly, solving the optimization problem in (37) is a challenging task, which can be addressed using the majorization minimization (MM) algorithm. The MM algorithm involves two steps: in the first step, a substitute function is found that locally approximates the objective function and its upper bound. In the second step, the substitute function is minimized.

[0215] To find the substitution function of (37), the following lemma 1 should be used.

[0216] Lemma 1: If f(x) is a convex function, then it satisfies

[0217]

[0218] Since the objective function of (37) is Since it is a quadratic convex function, therefore, by Lemma 1, we have

[0219]

[0220] in,

[0221]

[0222] However, due to the function Given a complex matrix and a complex vector, to apply the above inequality, the function can be represented using the complex real number convention. This is transformed into an equivalent problem with a real objective. First, we derive the equivalent formula for the objective function. Let... in and This describes the process of finding the real and imaginary parts of a complex function. It's worth noting that Q is a Hermitian matrix. Let... Arbitrary matrix Q and arbitrary vector The product can be expressed as:

[0223]

[0224] According to the properties of Hermitian matrices, we have:

[0225]

[0226] Furthermore, for any two vectors c H and The product of can be written in the following form:

[0227]

[0228] Substituting (41) into (43), we get

[0229]

[0230] Based on the properties of Hermitian matrices, it can be noted that the matrix The diagonal elements of the matrix are equal to zero. The values ​​at the symmetrical positions are opposite to each other. Therefore, we can obtain:

[0231]

[0232] According to (45), it can be known that If the value is a real number, then It can be represented as:

[0233]

[0234] Furthermore, (46) can be rewritten as:

[0235]

[0236] in and It is a positive definite symmetric matrix. Taking the derivative of (47), we get:

[0237]

[0238] Substituting (48) into (40), according to Lemma 1, we have:

[0239]

[0240] For further processing, assume... We can obtain:

[0241]

[0242] in

[0243] Based on the MM algorithm and (50), maximizing (37) is equivalent to maximizing the following function by discarding constant terms:

[0244]

[0245] in It is a matrix A vector of diagonal elements. Based on matrix operations and vector... Its characteristics include:

[0246]

[0247] Where Σ(p) represents the vector The elements are returned to a matrix of dimension N×N. Substituting (52) into (51), the optimization problem in (37) can be expressed as:

[0248]

[0249]

[0250]

[0251] To further process this, an auxiliary variable t is introduced, transforming problem (53) into a QCQP problem:

[0252]

[0253] in, Σ(p) represents the vector The elements are returned in an N×N matrix. Indicates will The elements are returned to the matrix. express The transpose of .

[0254] However, due to the unit norm constraint, the problem in (54) is difficult to solve. To solve this non-convex problem, the problem is transformed into an SDP problem and relaxed to an SDR problem. Therefore, the problem in (54) is rewritten, removing the first constraint, as follows:

[0255]

[0256] in Problem (55) is a convex optimization problem; therefore, the interior point method can be used to find the optimal solution. After obtaining... Then, the standard Gaussian randomization method is used to approximate the solution to the problem in (55), and through... The diagonal PSM is further obtained. Therefore, an alternating optimization algorithm can be proposed to solve the optimization problem in (11):

[0257] Input: a(θ), h1, φ, β, σ R , σ c , B, η, N, M, set threshold ∈.

[0258] Initialization: k = 0, phase shift of V is generated randomly.

[0259] Step 1. Based on V k Calculate and obtain U = (βG) H VAV H G+B) H (βG H VAV H G+B) and Then, w is obtained using the binary search algorithm. k+1 V k This represents V obtained after the (k-1)th iteration;

[0260] Step 2. Based on w k+1 , obtain and Then, calculate according to (55) Then, V is obtained using the Gaussian randomization method. k+1 , where w k+1 This represents the values ​​of w and V obtained after the k-th iteration. k+1 This represents V obtained after the k-th iteration;

[0261] Step 3. Based on the w obtained in Step 1 and Step 2 k+1 and V k+1 calculate judge If the condition is not met, proceed to Step 1; if the condition is met, proceed to the output.

[0262] Output: SNR r .

[0263] like Figure 2 As shown, the performance of the proposed method was verified in a dual-function radar and communication system, with the user signal-to-noise ratio and transmit power set to 10 dB and 3 W, respectively. Figure 3 As shown, the relationship between radar signal-to-noise ratio (SNR) and the number of reflecting elements is obtained. The SDP scheme replaces the binary search in Step 1 of the proposed algorithm with the common SDP solution. As can be seen from the figure, the method proposed in this invention, along with the SDP-based scheme, comprehensively considers the design of the beamforming vector and the RIS phase matrix. With the increase in reflecting elements, it consistently achieves a higher SINR than the traditional MRT and the case without RIS, effectively improving the transmission performance of radar and communication systems. It is worth noting that the method proposed in this invention has a very similar SINR to the SDP-based scheme, and the SDP scheme even has a higher value, but the SDP scheme has O((M 2 ) 3.5 The high complexity of the previous algorithm severely limited its practical application. The proposed scheme is based on binary search. In Step 1, each iteration only needs to update μ and w (i.e., the parameters proposed in Steps 5 and 6 of the previously proposed binary search algorithm). The computational complexity is determined by the number of internal and external iterations. Therefore, it can effectively reduce computational complexity and has superior overall performance.

[0264] Example 2

[0265] This invention provides a joint optimization system for the transmit beam and RIS discrete phase shift matrix of a dual-function radar and communication system, comprising: a dual-function radar and communication system construction module, a joint optimization problem construction module, a global optimal solution solution module, and a semidefinite relaxation problem solution module;

[0266] The dual-function radar and communication system building module is used to build a smart reflector-assisted dual-function radar and communication system;

[0267] The joint optimization problem construction module is used to construct a joint optimization problem of the transmit beamforming vector and phase shift matrix under the constraints of sensing and communication.

[0268] The global optimal solution solving module is used to construct an approximate optimal closed solution solving method for the beamforming vector based on the binary search algorithm and using the Lagrange dual decomposition method to obtain the global optimal solution.

[0269] The semidefinite relaxation problem solving module is used to quantize the discrete phase shift matrix of RIS. Based on the optimization minimization method, it transforms the quadratic constraint quadratic programming into a semidefinite relaxation problem for solving, thus completing the alternating optimization process of solving the target problem.

[0270] Example 3

[0271] This embodiment provides a storage medium, which may be a ROM, RAM, disk, optical disk, or other storage medium. The storage medium stores one or more programs. When the program is executed by the processor, it implements the joint optimization method of the transmit beam and RIS discrete phase shift matrix based on the dual-function radar and communication system of Embodiment 1.

[0272] Example 4

[0273] This embodiment provides a computing device, which may be a desktop computer, laptop computer, smartphone, PDA handheld terminal, tablet computer or other terminal device with display function. The computing device includes a processor and a memory. The memory stores one or more programs. When the processor executes the program stored in the memory, it implements the joint optimization method of transmit beam and RIS discrete phase shift matrix based on dual-function radar and communication system of embodiment 1.

[0274] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A joint optimization method for the transmit beam and RIS discrete phase shift matrix based on a dual-function radar and communication system, characterized in that, Includes the following steps: Construct a dual-function radar and communication system assisted by an intelligent reflector, and under the constraints of sensing and communication, construct a joint optimization problem of the transmit beamforming vector and phase shift matrix; For beamforming vectors, based on a binary search algorithm and utilizing the Lagrange dual decomposition method, a method for finding approximate optimal closed-form solutions is constructed to obtain the global optimal solution. Specifically, this includes: Define the following formula: ； ； Where G represents the channel model between the DRC base station and the RIS, A represents the target response matrix of the RIS, B represents the target response matrix of the DRC base station parameters, and V represents the diagonal effective phase shift matrix of the RIS. It is the downlink channel between RIS and users. This serves as the downlink channel between the DRC base station and the user. Set the following parameters: ， ； ； ； ； ； The joint optimization problem is transformed into: ； in, , For the SNR required by the user, Let be the maximum transmit power of the radar base station transmitter, and Re denote the real part of the matrix. Let w represent the first-order Taylor expansion of w, where w represents the transmitted beamforming vector. This indicates the noise power at the DRC. Represents the variance of the noise; Solving the dual problem of the transformed joint optimization problem yields the optimal solution, specifically including: The partial Lagrangian related to transmitter power constraints is defined as follows: ； in, Lagrange multipliers constrained by transmit signal power; According to the duality theorem, the dual problem can be expressed as: ； Among them, dual function Defined as: ； The Lagrange function is expressed as: ； in, Represents the Lagrange multipliers related to communication performance; Optimal solution Represented as: ； The optimal solution for the Lagrange multipliers related to communication performance is expressed as: ； The discrete phase shift matrix of RIS is quantized by transforming a quadratic constrained quadratic programming problem into a semidefinite relaxation problem based on an optimization minimization method. Specifically, this includes: The joint optimization problem is transformed into: ； ； ； in, It is a matrix A vector of diagonal elements. , , , G represents the channel model between the DRC base station and the RIS, A represents the target response matrix of the RIS, B represents the target response matrix of the DRC base station parameters, and V represents the diagonal effective phase shift matrix of the RIS. Let be the beamforming vector of the DRC base station transmitter, (·) H The expression represents the transpose of a matrix, vec represents the matrix straightening operation, and diag represents a diagonal matrix. Indicates the phase shift of RIS; The transformed joint optimization problem is solved using an optimization minimization algorithm. The optimization problem is expressed as: ； ； ； Where Re represents the real part of the matrix, h1 represents the channel from RIS to the user, and h2 represents the channel from DRC to the user. Introduce an auxiliary variable The optimization problem is transformed into a QCQP problem: ； in, , , , , , This means returning the elements of vector p to a dimension of . In the matrix, Indicates will The elements are returned to the matrix; The QCQP problem is solved optimally using the interior-point method, yielding the following results: Then, the standard Gaussian randomization method is used to approximate the solution to the optimization problem, and through... Further, the diagonal PSM is obtained; Complete the alternating optimization process for solving the objective problem.

2. The joint optimization method for the transmit beam and RIS discrete phase shift matrix based on a dual-function radar and communication system according to claim 1, characterized in that, A dual-function radar and communication system with intelligent reflector assistance is constructed. This system includes an intelligent reflector (RIS), a radar target, communication users, and a DRC base station. The DRC base station simultaneously transmits radar detection waveforms to the radar target and communication symbols to the downlink communication users. The DRC base station is equipped with… Each antenna element completes the sensing task and serves a single antenna user, possessing... The intelligent reflective surface RIS of the reflective element is deployed on the side of the building.

3. The joint optimization method for the transmit beam and RIS discrete phase shift matrix based on a dual-function radar and communication system according to claim 2, characterized in that, The signal received by the DRC base station is represented as follows: ； in, Let G represent the transmitted signal of the DRC base station, G represent the channel model between the DRC base station and the RIS, A represent the target response matrix of the RIS, B represent the target response matrix of the DRC base station parameters, and V represent the diagonal effective phase shift matrix of the RIS. Let be the beamforming vector of the DRC base station transmitter, (·) H Represents the transpose of a matrix; The signal received by the user is represented as: ； in, It is the downlink channel between RIS and users. This serves as the downlink channel between the DRC base station and the user. This refers to the noise received at the user's location.

4. The joint optimization method for the transmit beam and RIS discrete phase shift matrix based on a dual-function radar and communication system according to claim 1, characterized in that, Under the constraints of sensing and communication, the joint optimization problem of constructing the transmit beamforming vector and phase shift matrix is ​​specifically expressed as: ； ； ； ； in, For the SNR required by the user, This represents the maximum transmit power of the radar base station transmitter. Indicates the phase shift of RIS; The signal-to-noise ratio received at the DRC base station is expressed as: ； Where G represents the channel model between the DRC base station and the RIS, A represents the target response matrix of the RIS, B represents the target response matrix of the DRC base station parameters, and V represents the diagonal effective phase shift matrix of the RIS. Let be the beamforming vector of the DRC base station transmitter, (·) H Represents the transpose of a matrix. Indicates the noise power at the DRC; The signal-to-noise ratio received at the communication user's location is expressed as: ； in, The variance of the noise is represented. This represents the downlink channel between the RIS and the user. This indicates the downlink channel between the DRC base station and the user.

5. The joint optimization method for the transmit beam and RIS discrete phase shift matrix of a dual-function radar and communication system according to claim 3 or 4, characterized in that, A Rayleigh fading channel model is adopted between the DRC base station and the intelligent reflector RIS, specifically expressed as follows: ； in, Rayleigh factor, For the deterministic component of sight distance, This refers to the non-line-of-sight Rayleigh fading component. The deterministic component of sight distance is represented as: ； in, For large-scale channel gain, To distribute evenly in random phase, vector For angle The relevant DRC base station antenna array transmit response vector, vector This is the receiver steering vector for the RIS; The target response matrix of RIS is represented as: ； in, For the target number, For complex path loss, vector It is the turning vector of RIS.

6. A joint optimization system for the transmit beam and RIS discrete phase shift matrix based on a dual-function radar and communication system, characterized in that, The method for jointly optimizing the transmit beam and RIS discrete phase shift matrix of a dual-function radar and communication system as described in any one of claims 1-5 includes: a dual-function radar and communication system construction module, a joint optimization problem construction module, a global optimal solution solution module, and a semidefinite relaxation problem solution module. The dual-function radar and communication system building module is used to build a smart reflector-assisted dual-function radar and communication system; The joint optimization problem construction module is used to construct a joint optimization problem of the transmit beamforming vector and phase shift matrix under the constraints of sensing and communication. The global optimal solution solving module is used to construct an approximate optimal closed solution solving method for the beamforming vector based on the binary search algorithm and using the Lagrange dual decomposition method to obtain the global optimal solution. The semidefinite relaxation problem solving module is used to quantize the discrete phase shift matrix of RIS. Based on the optimization minimization method, it transforms the quadratic constraint quadratic programming into a semidefinite relaxation problem for solving, thus completing the alternating optimization process of solving the target problem.

7. A computer-readable storage medium storing a program, characterized in that, When the program is executed by the processor, it implements the joint optimization method of transmit beam and RIS discrete phase shift matrix based on dual-function radar and communication system as described in any one of claims 1-5.

8. A computing device, comprising a processor and a memory for storing a processor-executable program, characterized in that, When the processor executes the program stored in the memory, it implements the joint optimization method of the transmit beam and RIS discrete phase shift matrix based on the dual-function radar and communication system as described in any one of claims 1-5.

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