Waveform optimization method of difunctional radar system

Abstract

The invention relates to a waveform optimization method for a dual-function radar system, and the method comprises the following steps: obtaining parameters of the dual-function radar system, and building a communication model and a radar model of the dual-function radar system; calculating a direct component of the dual-function radar base station received by the user side and a reflection component of the intelligent reflection surface through a communication model, and calculating a signal to interference plus noise ratio according to the direct component and the reflection component; a target response matrix from the intelligent reflecting surface to the detection target is established through a radar model, and the radar model comprises a transmitting wave beam and a passive wave beam; the Cramer-Rao bound minimization of target angle information sensed by a dual-function radar system is taken as an optimization target, a signal to interference plus noise ratio is taken as a constraint, an optimization expression is established, a transmitting beam and a passive beam are alternately optimized, and an optimization result and the minimum Cramer-Rao bound are obtained. Compared with the prior art, the method has the advantages of low calculation complexity, high communication performance and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of communication and perception integration, and in particular to a waveform optimization method for a dual-function radar system. Background Art

[0002] At present, among the methods for realizing Integrated Sensing And Communications (ISAC), there are many studies on the Radar-Communication Coexistence (RCC) system. This system considers that the radar and communication systems are separate but radar detection and user communication share a spectrum. Therefore, the channel interference between them is more obvious and information exchange is difficult.

[0003] The Dual-Functional Radar-Communication (DFRC) system is an emerging technology that can better implement ISAC. It takes into account that radar and communication systems share the same spectrum and the same hardware platform, and can exchange information with each other. In addition, radar detection and user communication share dual-function waveforms, and the interference between them is relatively light. Compared with the RCC system, the DFRC system can better balance user communication and radar detection performance. However, the actual signal transmission environment is complex, and there are problems such as channel fading, communication blind spots, and obstacles that prevent direct signal transmission.

[0004] Current research on the DFRC system mainly focuses on issues such as radar detection probability, communication users and rates, and radar signal-to-noise ratio. There is relatively little research on the Cramér-Rao Bound (CRB) of the detection target angle. There is even less research on the CRB of the detection target angle when RIS is combined with DFRC systems to enhance radar detection while ensuring user communication.

[0005] In terms of CRB optimization algorithm, the successive approximation method is often used for unconstrained optimization, so it is difficult to guarantee the quality of downlink user communication, and the successive approximation method cannot always obtain the optimal solution to the CRB problem. Secondly, the Lagrange multiplier method can guarantee user communication needs, but the overall computational complexity is high.

[0006] Therefore, it is necessary to propose an optimization method for a dual-function radar system with low computational complexity and capable of ensuring user communication needs. Summary of the invention

[0007] The purpose of the present invention is to provide a waveform optimization method for a dual-function radar system in order to overcome the defects of the above-mentioned prior art, namely, high computational complexity and difficulty in ensuring communication quality.

[0008] The purpose of the present invention can be achieved by the following technical solutions:

[0009] A waveform optimization method for a dual-function radar system comprises the following steps:

[0010] Obtain dual-function radar system parameters and establish a communication model and radar model of the dual-function radar system;

[0011] Through the communication model, the direct component of the dual-function radar base station received by the user end and the reflected component of the intelligent reflector are calculated, and the signal-to-interference-noise ratio is calculated based on the direct component and the reflected component;

[0012] A target response matrix from the intelligent reflective surface to the detection target is established through a radar model, wherein the radar model includes a transmitting beam and a passive beam;

[0013] The optimization objective is to minimize the Cramer-Rao bound of the target angle information perceived by the dual-function radar system. The signal-to-interference-noise ratio is used as a constraint, and an optimization expression is established. The transmit beam and the passive beam are optimized alternately to obtain the optimization result and the minimum Cramer-Rao bound.

[0014] Furthermore, the calculation expression of signal to interference noise ratio is:

[0015]

[0016] In the formula, γ k is the signal-to-interference-noise ratio expression of the kth user, is the channel from the dual-function radar base station to the kth user terminal, is the channel from the smart reflector to the kth user end, Θ is the phase shift matrix of the smart reflector, G is the channel from the dual-function radar base station to the smart reflector, w k is the dual-function beamforming vector transmitted by the dual-function radar base station, is the variance of interference noise, and K is the total number of user terminals.

[0017] Furthermore, the channel from the dual-function radar base station to the intelligent reflective surface is a multipath fading channel, and the expression is:

[0018]

[0019] Where β is the strength ratio of the direct link to the multiple reflection links, is the direct component, G NLoS is the attenuation component, d1 is the distance between the dual-function radar base station and the smart reflecting surface, C0 is the path loss coefficient when the reference distance d0=1, α0 is the path loss index of the transmission link between the dual-function radar base station and the smart reflecting surface, and G is the channel from the dual-function radar base station to the smart reflecting surface.

[0020] Furthermore, the calculation expression of the target response matrix is:

[0021] A=αa(θ)a H (θ)

[0022]

[0023] Where A is the target response matrix, a(θ) is the steering vector with an angle of θ on the smart reflector, α is the channel coefficient, and a H (θ) is the conjugate transpose of a(θ), λ is the wavelength of the radar emission waveform, d is the array element spacing, and θ represents the DoA angle of the detected target relative to the RIS.

[0024] Furthermore, the optimized expression is:

[0025]

[0026] sttr(W)≤P0

[0027]

[0028] |[Θ] n,n |=1,n=1,...,N

[0029] In the formula, γ k is the signal to interference plus noise ratio expression of the kth user, Γ is the minimum signal to interference plus noise ratio required by the user, P0 is the total power budget, [Θ] n,n represents the diagonal elements of the smart reflector phase shift matrix θ, W is the dual-function waveform matrix, θ represents the DoA angle of the detected target relative to the RIS, and N is the number of RIS array elements.

[0030] Furthermore, the transmit beam and the passive beam are optimized alternately, specifically: determining the transmit beam to optimize the passive beam, and determining the passive beam to optimize the transmit beam, and the two are performed alternately.

[0031] Furthermore, the calculation expression for determining the transmit beam to optimize the passive beam is:

[0032]

[0033] In the formula, γ k is the signal to interference and noise ratio expression of the kth user, P0 is the total power budget, Γ is the minimum signal to interference and noise ratio required by the user, W k is the bifunctional waveform matrix, t is the optimization auxiliary variable, R C H YesR C The conjugate transpose of yes The conjugate transpose of H(θ) is the conjugate transpose of c(θ), yes is the conjugate transpose of , K is the number of communication users, and ≥ indicates the semi-positive definiteness of the matrix.

[0034] Furthermore, through the Shure complement, when determining the transmit beam to optimize the passive beam, the constraint condition is converted into a convex semidefinite constraint form; through the low-order Taylor expansion, when determining the passive beam to optimize the transmit beam, a lower bound function is established to constrain the passive beam.

[0035] Furthermore, the lower bound function implements the constraint by solving the maximum value, and the calculation expression is:

[0036]

[0037] In the formula, for The real part of [θ] n is the nth θ element, N is the number of RIS array elements, W k is a dual-function waveform matrix, is the interference noise variance, θ is the diagonal element of the phase shift matrix, is the channel from the dual-function radar base station to the kth user terminal, is the channel from the smart reflector to the kth user terminal, G is the channel from the dual-function radar base station to the smart reflector, and Γ is the minimum signal-to-interference-noise ratio required by the user.

[0038] Furthermore, the expression of the Cramer-Rao bound for the dual-function radar system to perceive target angle information is:

[0039]

[0040] Where CRB(θ) is the Cramer-Rao bound for the dual-function radar system to perceive target angle information, α is the channel coefficient, and R C H YesR C The conjugate transpose of yes The conjugate transpose of H (θ) is the conjugate transpose of c(θ), yes The conjugate transpose of , L is the length of the communication frame, R X is the radar covariance matrix, is the interference noise variance.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] 1) The present invention uses the Shure complement code and the signal-to-interference-noise ratio as constraints to alternately optimize the transmit beam and the passive beam, so as to obtain the minimum Cramer-Rao bound while ensuring the communication quality of the user end, so as to improve the performance of the dual-channel radar, reduce the mutual interference between the dual-channel radar detection and the user communication, and improve the communication performance of the dual-channel radar system.

[0043] 2) The present invention transforms the objective function and the constraint conditions through methods such as Schur's complement code and low-order Taylor expansion to reduce the computational complexity.

[0044] 3) The present invention provides a non-direct path between the dual-channel radar base station and the detection target through an intelligent reflective surface, thereby avoiding the influence of obstacles on radar detection, and at the same time enhancing the communication between the dual-channel radar base station and the user end, further improving the system performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Illustration of the RIS-assisted downlink DFRC radar and communications system.

[0046] Figure 2 It is a flow chart of the steps of the present invention.

[0047] Figure 3 This is the curve showing the change of the radar detection CRB value when the user signal-to-noise ratio increases.

[0048] Figure 4 This is the curve showing the change of the radar detection CRB value when the number of DFRC transmitting antennas increases.

[0049] Figure 5 This is the curve showing the change of the radar detection CRB value when the number of RIS array elements increases.

[0050] Figure 6 Iteration curve of CRB optimization algorithm for radar detection.

[0051] Explanation of the markings in the figure: 1. Dual-function radar base station, 2. Intelligent reflective surface, 3. Detection target, 4. User end. DETAILED DESCRIPTION

[0052] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0053] Example 1

[0054] This embodiment is based on Figure 1The RIS-assisted downlink DFRC system shown in the figure is illustrated, and the system includes a dual-function radar base station (DFRC-BS or BS) 1, a detection target 3 and a user terminal 4. The dual-function radar 1 transmits a radar detection waveform to the detection target 3, and simultaneously transmits a communication signal to the user terminal 4. In addition, the present invention considers that there are obstacles between the detection target 3 and the dual-function radar base station 1, so there is a serious channel fading problem in the direct path between the dual-function radar base station 1 and the detection target 3. In order to solve this problem, a smart reflecting surface (RIS) 2 is deployed to provide a non-direct path between the dual-function radar base station 1 and the detection target 3. The smart reflecting surface 2 is also used to enhance the communication between the dual-function radar base station 1 and the user terminal 4.

[0055] The present invention is a waveform optimization method for a dual-function radar system, comprising the following steps:

[0056] Obtain dual-function radar system parameters and establish a communication model and radar model of the dual-function radar system;

[0057] Through the communication model, the direct component of the dual-function radar base station received by the user end and the reflected component of the intelligent reflector are calculated, and the signal-to-interference-noise ratio is calculated based on the direct component and the reflected component;

[0058] A target response matrix from the intelligent reflective surface to the detection target is established through a radar model, wherein the radar model includes a transmitting beam and a passive beam;

[0059] The optimization objective is to minimize the Cramer-Rao bound of the target angle information perceived by the dual-function radar system. The signal-to-interference-noise ratio is used as a constraint, and an optimization expression is established. The transmit beam and the passive beam are optimized alternately to obtain the optimization result and the minimum Cramer-Rao bound.

[0060] like Figure 2 As shown, the specific steps are:

[0061] S1: The base station is equipped with M antennas and the users are K single-antenna users. In addition, N RIS panels are deployed, and the phase shift vector of the RIS panel is expressed as: And there and β n ∈[0,1] represents the phase shift and amplitude reflection coefficient, and the diagonal matrix Θ=diag(θ) is defined as the phase shift matrix of RIS, that is, the passive beam. Next, the channels in the model are introduced. The channels from DFRC base station to k-th user, DFRC base station to RIS, and RIS to k-th user are expressed as

[0062] S2: Establish communication model and radar model:

[0063] S21: Communication Model:

[0064] like Figure 1 As shown, each user receives the direct component from the DFRC-BS and the reflected component from the RIS, so that the dual-function beamforming vector transmitted by the BS and the user communication symbol are and Without loss of generality, we assume

[0065] Therefore, the signal received by k users is:

[0066]

[0067] In the formula, represents the interference noise received by the user. Since the radar sensing and communication tasks are coordinated by the integrated waveform transmitted by the dual-function radar (DFRC-BS), there is no self-interference or mutual interference generated in traditional radar and communication systems. Based on the above assumptions, the signal-to-noise ratio (SINR) received by the k-th user is:

[0068]

[0069] In this embodiment, the target is an irregular point at a certain distance from the DFRC-BS, and there is an obstacle between the dual-function radar (DFRC-BS) and the detection target, so there is no direct channel but only a cascade channel reflected by the RIS. The transceiver channel from the RIS to the detection target is represented by A, and the target response matrix can be written as A = αa(θ)a H (θ), in order to facilitate the DoA estimation of the target, let θ represent the DoA angle of the detected target relative to the RIS. The steering vector with an angle of θ on the RIS is

[0070]

[0071] where α is the channel coefficient, which is related to the radar cross section and the path loss of the RIS-target-RIS link, a H (θ) is the conjugate transpose of a(θ).

[0072] S22: Radar Model:

[0073] The expression of the radar model is:

[0074]

[0075] S3: Obtain the CRB analytical formula under the RIS-assisted DFRC system:

[0076]

[0077] is equivalent to:

[0078]

[0079] In the formula, R C (θ) = c(θ)c H (θ), c(θ) = G H Θa(θ), L is the length of the communication frame.

[0080] S4: In order to maximize the CRB of the estimated detection target angle information to reach the desired minimum value under the premise of ensuring the user communication quality, so as to meet the needs of downlink user communication and radar detection. The present invention proposes to jointly optimize the beamforming and phase shift matrix, and the expression of the optimization problem is:

[0081]

[0082] Where Γ is the SINR required by the user, P0 is the total power budget, [Θ] n,n Represents the diagonal elements of θ. Since the optimization target CRB(θ) is in fractional form, the solution complexity is high and has certain challenges, so it is converted into an easy-to-handle form. Equation (7) can be equivalently expressed as:

[0083]

[0084] It can be found that CRB(θ) as the optimization objective function has a non-convex structure and the optimization variable R X The optimization variable W described in equation (7) k There is still a gap, so next we need to turn to W again k Convex expression of .

[0085] S5: Joint transmit and passive beamformer design:

[0086] Since it is difficult to directly optimize equation (8), it is necessary to transform it into a tractable form. First, the objective function is transformed from a non-convex optimization problem to a convex optimization problem, and the optimization variable is transformed from the radar covariance matrix R X is converted to a bifunctional covariance matrix, but the W resulting from the conversion k The problem of coupling with the Θ variable and the rank-one constraint further complicates the problem. Therefore, the present invention jointly designs the joint transmission and passive beamformer, and adopts an alternating optimization method to minimize the CRB of the estimated detection target DoA while ensuring the user communication quality.

[0087] S51: Determine the passive beam Θ to optimize the transmit beam W

[0088] For any given Θ, equation (8) can be rewritten as:

[0089]

[0090] Formula (9) is obviously a non-convex optimization function, which can be rewritten by introducing the auxiliary variable t as follows:

[0091]

[0092] Through the theory of Schur's complement, the constraint in equation (10) can be transformed into a convex semidefinite constraint form such as equation (11), that is:

[0093]

[0094] in The radar covariance matrix is ​​related to the dual-function covariance matrix through matrix transformation:

[0095]

[0096] Its value becomes more accurate as the communication frame length of the dual-function base station increases:

[0097]

[0098] Through the above discussion and transformation, formula (10) is rewritten into an optimizable form:

[0099]

[0100] Due to the existence of rank(W k )=1, equation (14) cannot be solved well. Therefore, we use the semidefinite relaxation theorem (SDR) to relax it and transform the problem into a standard semidefinite regularization (SDP) problem. Then, we use the eigenvalue decomposition or Gaussian randomization method to get the solution closest to the original problem. The solution process can be implemented by the CVX tool in Matlab.

[0101] S52: Determine the transmit beam W to optimize the passive beam θ:

[0102] The intermediate variable c, R C , Respectively, and put into formula (9), it is expressed as follows: c = G H θa, R C =cc H =G H Θaa H Θ H G.

[0103] in Its vector expansion is as follows:

[0104]

[0105] In order to facilitate optimization, equation (9) is mathematically expressed as a non-convex expression related to Θ:

[0106]

[0107] Where G1 = GG H , A2=aa H , tr(·) represents the trace of the matrix.

[0108] A1 and A2 are both Hermitian matrices. According to the Kronecker multiplication and trace transformation We get formula (17):

[0109]

[0110] In the formula,

[0111]

[0112] In the formula, the symbol represents the Kronecker product of the matrix, and diag(·) represents the diagonal matrix of the matrix.

[0113] S53: Solving the lower bound function:

[0114] The optimized variable Θ in formula (18) is In the process, the user's communication needs cannot be directly constrained to This makes the optimization problem difficult, so we use the Minorize-Maximization algorithm, which is to find a lower bound of the optimization function through the low-order Taylor expansion of the function. It is required that the variable Θ in the lower bound function is constrained and can be directly optimized. We maximize the lower bound function to achieve our optimization goal.

[0115]

[0116] in, is a constant that is irrelevant to the optimization. To represent the real matrix we will Decomposition Order but can be written as:

[0117]

[0118] In the formula express The real part of express For the convenience of calculation, the real number matrix is ​​expressed as follows:

[0119]

[0120] in make is the tth iteration The real vector is reconstructed into an equivalent complex vector by manipulating real-valued functions and following basic operations on real and complex numbers:

[0121]

[0122] In the formula, is the vector reconstruction expression of q, is a signed real-valued product operation and This is a complex product operation, so in order to ensure that the value remains unchanged, By using the basic vector operations, we can get There unvec N×N (·) is the matrix reduction operation. Finally, the objective function that satisfies the above conditions is obtained by reducing the matrix:

[0123]

[0124]

[0125] To ensure the consistency between the optimization function and the constraints, we transform the objective function and constraints into the form of QCQP:

[0126]

[0127] Due to the constraints of formula (25), formula (25) is non-convex, so we convert it into the form of semidefinite programming:

[0128]

[0129] In the formula, The solution method of formula (26) is the same as that of formula (14), and finally we get The solution of θ is then approximated using Gaussian randomization.

[0130] Simulation experiment settings:

[0131] In this embodiment, the channel between the DFRC-BS and the RIS is a Rician channel model, that is, a multipath fading channel. The Rician channel model has a similar structure to the millimeter wave channel model and is represented as follows:

[0132]

[0133] β is the Rician factor, which represents the intensity ratio of the direct link to multiple reflection links. The larger β is, the greater the proportion of the direct component is. represents the fixed direct component, namely the Rayleigh fading component, G NLoS is the non-Rayleigh attenuation component, which follows a complex Gaussian distribution with a mean of 0 and a variance of 1. The path loss expression of the channel is:

[0134]

[0135] Where, L x is the path loss of the channel, d1 is the distance from DFRC-BS to RIS transmission link, C0 is the path loss coefficient when the reference distance d0=1, and α0 is the path loss index from DFRC-BS to RIS transmission link.

[0136] As shown in Table 1, this embodiment uses the following parameters for optimization:

[0137] Table 1 Dual-function radar system parameters

[0138]

[0139] In order to ensure the clear impact of a single variable, the simulation is carried out by controlling the variables, such as Figure 3 As shown in the figure, the change of radar detection CRB value when only the user's signal-to-interference-noise ratio increases. It can be seen that with the increase of the user's required signal-to-interference-noise ratio, the radar detection CRB will also increase, which represents the trade-off between multi-user communication and radar detection. With the assistance of RIS, the value of CRB changes less, indicating that the system has a higher degree of freedom with the assistance of RIS. It can also be seen that the user communication quality can be guaranteed under a certain CRB value.

[0140] like Figure 4 As shown in Figure 1, the relationship between the CRB of DoA estimation and the number of dual-function radar transmit antennas is evaluated. It can be seen from the figure that the proposed CRB minimization scheme achieves the lowest CRB in the entire range of antenna numbers. It can also be observed that the value of CRB tends to stabilize as the number of antennas M increases, indicating that transmit beamforming optimization is particularly important when the number of antennas increases.

[0141] like Figure 5 As shown in Figure 3, the change of radar detection CRB value when the number of RIS array elements increases. It can be seen that the CRB value gradually stabilizes with the increase of the number of RIS array elements, which shows the effectiveness of the RIS-assisted DFRC system.

[0142] like Figure 6As shown in the figure, based on the convergence of the alternating optimization algorithm, it can be seen that the algorithm converges after three iterations, thus verifying the effectiveness of the proposed algorithm. Next, the effectiveness of the joint transmission and passive beamforming design will be explained, that is, the change in CRB values ​​when the user signal-to-interference ratio increases, the number of RIS array elements increases, and the number of DFRC system transmitting antennas increases.

[0143] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A waveform optimization method for a dual-function radar system, characterized in that: The following steps are involved: Obtain dual-function radar system parameters and establish a communication model and radar model of the dual-function radar system; Through the communication model, the direct component of the dual-function radar base station received by the user end and the reflected component of the intelligent reflector are calculated, and the signal-to-interference-noise ratio is calculated based on the direct component and the reflected component; A target response matrix from the intelligent reflective surface to the detection target is established through a radar model, wherein the radar model includes a transmitting beam and a passive beam; The optimization objective is to minimize the Cramer-Rao bound of the target angle information perceived by the dual-function radar system. The signal-to-interference-noise ratio is used as a constraint, and an optimization expression is established. The transmit beam and the passive beam are optimized alternately to obtain the optimization result and the minimum Cramer-Rao bound.

2. The waveform optimization method of a dual-function radar system according to claim 1, characterized in that: The calculation expression of the signal to interference noise ratio is: In the formula, γ k is the signal-to-interference-noise ratio expression of the kth user, is the channel from the dual-function radar base station to the kth user terminal, is the channel from the smart reflector to the kth user end, Θ is the phase shift matrix of the smart reflector, G is the channel from the dual-function radar base station to the smart reflector, w k is the dual-function beamforming vector transmitted by the dual-function radar base station, is the variance of interference noise, and K is the total number of user terminals.

3. The waveform optimization method of a dual-function radar system according to claim 2, characterized in that: The channel from the dual-function radar base station to the intelligent reflector is a multipath fading channel, and the expression is: Where β is the strength ratio of the direct link to the multiple reflection links, is the direct component, G NLoS is the attenuation component, d1 is the distance between the dual-function radar base station and the smart reflecting surface, C0 is the path loss coefficient when the reference distance d0=1, α0 is the path loss index of the transmission link between the dual-function radar base station and the smart reflecting surface, and G is the channel from the dual-function radar base station to the smart reflecting surface.

4. The waveform optimization method of a dual-function radar system according to claim 1, characterized in that: The calculation expression of the target response matrix is: A=αa(θ)a H (i) Where A is the target response matrix, a(θ) is the steering vector with an angle of θ on the smart reflector, α is the channel coefficient, and a H (θ) is the conjugate transpose of a(θ), λ is the wavelength of the radar emission waveform, d is the array element spacing, and θ represents the DoA angle of the detected target relative to the RIS.

5. The waveform optimization method of a dual-function radar system according to claim 1, characterized in that: The optimization expression is: sttr(W)≤P0 |[I] n,n |=1,n=1,...,N In the formula, γ k is the signal to interference plus noise ratio expression of the kth user, Γ is the minimum signal to interference plus noise ratio required by the user, P0 is the total power budget, [Θ] n,n represents the diagonal elements of the smart reflector phase shift matrix θ, W is the dual-function waveform matrix, θ represents the DoA angle of the detected target relative to the RIS, and N is the number of RIS array elements.

6. The waveform optimization method of a dual-function radar system according to claim 1, characterized in that: The alternate optimization of the transmit beam and the passive beam specifically includes: determining the transmit beam to optimize the passive beam, and determining the passive beam to optimize the transmit beam, and the two are performed alternately.

7. The waveform optimization method of a dual-function radar system according to claim 6, characterized in that: The calculation expression for determining the transmit beam to optimize the passive beam is: R C (θ)=c(θ)c H (θ), c(θ)=G H Θa(θ), c(θ)=G H Θa(θ), In the formula, γ k is the signal to interference and noise ratio expression of the kth user, P0 is the total power budget, Γ is the minimum signal to interference and noise ratio required by the user, W k is the bifunctional waveform matrix, t is the optimization auxiliary variable, R C H YesR C The conjugate transpose of yes The conjugate transpose of H (θ) is the conjugate transpose of c(θ), yes The conjugate transpose of , K is the number of communication users, This indicates that the matrix is ​​positive semidefinite.

8. The waveform optimization method of a dual-function radar system according to claim 6, characterized in that: Through the Shure complement code, the constraint conditions are converted into convex semidefinite constraint form when determining the transmit beam to optimize the passive beam; through the low-order Taylor expansion, when determining the passive beam to optimize the transmit beam, a lower bound function is established to constrain the passive beam.

9. The waveform optimization method of a dual-function radar system according to claim 8, characterized in that: The lower bound function realizes the constraint by solving the maximum value, and the calculation expression is: |[θ] n |=1,n=1,...,N In the formula, for The real part of [θ] n is the nth θ element, N is the number of RIS array elements, W k is a dual-function waveform matrix, is the interference noise variance, θ is the diagonal element of the phase shift matrix, is the channel from the dual-function radar base station to the kth user terminal, is the channel from the smart reflector to the kth user terminal, G is the channel from the dual-function radar base station to the smart reflector, and Γ is the minimum signal-to-interference-noise ratio required by the user.

10. The waveform optimization method of a dual-function radar system according to claim 1, characterized in that: The expression of the Cramer-Rao bound for the dual-function radar system to perceive target angle information is: Where CRB(θ) is the Cramer-Rao bound for the dual-function radar system to perceive target angle information, α is the channel coefficient, and R C H YesR C The conjugate transpose of yes The conjugate transpose of H (θ) is the conjugate transpose of c(θ), yes The conjugate transpose of , L is the length of the communication frame, R X is the radar covariance matrix, is the interference noise variance.

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