Beam forming method integrating secret communication and perception

Abstract

The invention discloses a secret communication and perception integrated beam forming method. The method comprises the following steps: constructing a multi-cell multi-user MIMO system model based on secret ISAC; each base station transmits an information signal and a special radar signal through a uniform linear array, communicates with a communication user, realizes radar target perception, and calculates base station transmitting power and transmitting power budget; receiving the information signal and the special radar signal by each communication user through a channel, eliminating the interference of the special radar signal by a receiver of the communication user, and recovering the received signal through receiving beam forming to obtain an estimated signal; constructing an optimization problem model for minimizing the sum of the average power leakage beyond the angle of interest and the average weighted mean square error of the communication user information signal; a non-convex optimization problem model is decomposed into convex sub-problems by adopting a block coordinate descent method, and the optimal secret communication performance is realized by combining beamforming optimization. According to the invention, the reliability and confidentiality requirements of communication users can be met at the same time.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a beamforming method integrating secure communication and perception. Background Art

[0002] The deep integration of artificial intelligence, information technology, big data technology and mobile communication technology is driving the evolution of 5G to 6G in terms of technology and business. This future wireless network will be designed to support emerging applications such as drones, factory automation, autonomous driving and smart homes, which have higher demands on wireless networks in terms of reliability and low latency. At the same time, the overlap between wireless communication bands and traditional perception bands will increase. Wireless communication and wireless perception also show more and more similarities in signal processing, data processing and system design. With the advancement of ultra-large-scale antennas, smart reflectors, artificial intelligence and other technologies, perception technology will also be significantly promoted. Therefore, it is particularly important to explore new communication technologies to achieve joint optimization of system communication and perception performance.

[0003] ISAC (Integrated Sensing And Communication) technology achieves efficient operation of communication and perception functions synchronously by sharing hardware and spectrum resources. Single-station ISAC system is widely used in existing ISAC technology because it is easy to implement and does not require precise synchronization between base stations. However, in actual application scenarios, the interference problem of ISAC system in neighboring cells to communication users still exists, which may affect the accurate recovery of information signals. Therefore, it is necessary to consider how to achieve the effective operation of the broadcast channel of ISAC system with multiple cells and multiple users in actual interference environment;

[0004] In addition, current methods generally fail to fully consider the risk that the transmission beam may be exploited by eavesdroppers in the ISAC system. Although the base station has implemented the transmission beamforming technology, artificial noise is not incorporated into the transmission signal process. Therefore, eavesdroppers can still receive the information signal beam transmitted by the base station in a noisy environment, which poses a severe challenge to confidential communications.

[0005] Therefore, at present, there is a lack of a beamforming technology that integrates confidential communication and perception. In a multi-cell multi-user MIMO (Multiple-Input Multiple-Output) system model based on confidential ISAC, the transmit and receive beamforming are jointly optimized to meet the confidentiality requirements of ISAC while ensuring reliable communication for communication users and accurate perception of radar targets in the cell. Summary of the invention

[0006] In order to overcome the defects and shortcomings of the prior art, the present invention provides a beamforming method that integrates secure communication and perception, which can effectively improve the perception capability while meeting the communication needs, and formulates the beamforming method as a problem of maximizing the secure communication performance, while meeting the reliability and confidentiality requirements of communication users. By applying the block coordinate descent algorithm, the original non-convex optimization problem is simplified and effectively solved, and the iterative solution of the convex subproblem obtains a better overall suboptimal solution, which significantly improves the performance and computational efficiency.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] The present invention provides a beamforming method for integrating secure communication perception, comprising the following steps:

[0009] Construct a multi-cell multi-user MIMO system model based on confidential ISAC;

[0010] Each base station transmits information signals and dedicated radar signals through a uniform linear array, communicates with communication users in the cell and realizes radar target perception, and calculates the transmission power and transmission power budget of the base station;

[0011] The information signal and the dedicated radar signal transmitted by the base station are received by each communication user through the channel. The communication user's receiver eliminates the interference of the dedicated radar signal and recovers the received signal to obtain an estimated signal through receiving beamforming.

[0012] Construct an optimization problem model to minimize the sum of the average power leakage outside the angle of interest and the average weighted mean square error of the communication user information signal;

[0013] The block coordinate descent method is used to decompose the non-convex optimization problem model into convex sub-problems, and the optimal secure communication performance is achieved by combining beamforming optimization.

[0014] As a preferred technical solution, the construction of a multi-cell multi-user MIMO system model based on a confidential ISAC specifically includes:

[0015] In a multi-cell MIMO interference broadcast channel environment, each cell corresponds to a base station, and the base station has M k A uniform linear array of transmitting antennas serving cell k k The radar target perception is realized at the same time by the communication users of each cell, which interferes with the communication users of other cells and eavesdroppers. The receiver i of the i-th communication user in cell k k Features The root receiving antenna, the set of all users is expressed as:

[0016] I={i k∣k∈{1,2,…,K},i∈{1,2,…,I k}}

[0017] Wherein, K represents the total number of base stations.

[0018] As a preferred technical solution, each base station transmits information signals and dedicated radar signals through a uniform linear array, which is specifically expressed as follows:

[0019]

[0020] Among them, x k represents the transmission signal transmitted by base station k through a uniform linear array, Indicates that base station k transmits to communication user i k The information signal represents the transmit beamforming vector corresponding to the transmitted information signal, s k represents the dedicated radar signal transmitted by base station k, K represents the total number of base stations, and I k Indicates the total number of communication users in the cell.

[0021] As a preferred technical solution, the transmission power of base station k is:

[0022]

[0023] The transmit power budget of base station k is P k ,satisfy:

[0024]

[0025] where ‖·‖ represents the Euclidean norm of the vector, tr(·) is the trace of the matrix, and r(·) is the rank of the matrix.

[0026] As a preferred technical solution, the information signal and the dedicated radar signal transmitted by the base station are received by each communication user through the channel, and the communication user's receiver eliminates the interference of the dedicated radar signal. k The equivalent received signal is expressed as:

[0027]

[0028] in, Indicates that base station k transmits to communication user i k The information signal represents the transmit beamforming vector corresponding to the transmitted information signal, s k represents the dedicated radar signal transmitted by base station k, K represents the total number of base stations, and I k Indicates the total number of communication users in the cell, and Respectively represent the transmission distance from base station k and base station j to communication user receiver i k The channels between are represented by the channel matrix, Indicates receiver i k Noise, I represents the set of all communication users, each of which is equipped with a receiver;

[0029] The received signal is restored by receiving beamforming to obtain the estimated signal, which is specifically expressed as:

[0030]

[0031] in, Indicates receiving signal, represents the receive beamforming vector, Represents the estimated signal.

[0032] As a preferred technical solution, an optimization problem model is constructed to minimize the sum of the average power leakage outside the angle of interest and the average weighted mean square error of the communication user information signal, specifically including:

[0033] Set the range of the transmit beam pattern sensing angle θ to The uniform linear array steering vector is expressed as:

[0034]

[0035] Where d is the distance between two adjacent antennas, λ is the carrier wavelength, (·) T To take the transpose operation;

[0036] The transmit beam pattern gain of base station k in the θ direction is:

[0037]

[0038] Among them, |·| means taking the absolute value, E[·] means taking the mean operation, (·) H To take the conjugate transpose operation, Indicates that base station k transmits to communication user i k The information signal represents the transmit beamforming vector corresponding to the transmitted information signal, s k represents the dedicated radar signal transmitted by base station k, I k Indicates the total number of communication users in the cell,

[0039] Divide the transmit beam pattern gain angle range into M angles The community has N k Interesting angle

[0040] Minimize the average beam pattern gain over angles of no interest:

[0041]

[0042] The SINR constraint is converted into the communication item in the optimization objective, and the communication user i k Rate for:

[0043]

[0044] Where logdet(·) is the logarithm operation of the matrix determinant, I represents the identity matrix, and Respectively represent the transmission distance from base station k and base station j to communication user receiver i k The channels between are represented by the channel matrix, represents the covariance, I represents the set of all communication users;

[0045] The weighted sum rate of the multi-cell multi-user MIMO system based on confidential ISAC is expressed as:

[0046]

[0047] in, Represents each communication user i k Priority;

[0048] Initially set the objective function to Where 0≤μ≤1 is the coefficient for adjusting the weights of perception and communication indicators;

[0049] For minimizing the mean square error we obtain a minimum mean square error receiver:

[0050]

[0051] Estimated signal With information signal The mean square error is:

[0052]

[0053]

[0054] The corresponding minimum mean square error is:

[0055]

[0056] get:

[0057]

[0058] The weighted mean square error of the multi-cell multi-user MIMO system is:

[0059]

[0060] The optimization problem model for minimizing the sum of the average power leakage outside the angle of interest and the average weighted mean square error of the communication user information signal is constructed, which can be expressed as:

[0061]

[0062]

[0063] in, represents the weighted variable, and K represents the total number of base stations.

[0064] As a preferred technical solution, the block coordinate descent method is used to decompose the non-convex optimization problem into convex sub-problems, and the combined beamforming optimization is used to achieve the optimal secure communication performance, which specifically includes:

[0065] The block coordinate descent method is used to iteratively solve the problem. In each iteration, a part of the variables are fixed sequentially and the remaining variables are updated to minimize the objective function. The optimization problem model is decomposed into three convex sub-problems, which are specifically expressed as follows:

[0066] The optimal receive beamforming vector u is obtained by solving subproblem sp1:

[0067]

[0068] The optimal solution for the receive beamforming vector u is the minimum mean square error receiver, expressed as:

[0069]

[0070] The optimal weighted variable w is obtained by solving subproblem sp2:

[0071]

[0072] The optimal solution of the weighted variable w is obtained by the first-order optimality condition:

[0073]

[0074] The optimal transmit beamforming vector t and the covariance matrix R of the dedicated radar d By solving subproblem sp3, we get:

[0075]

[0076]

[0077] Solve subproblem sp3 using the standard solver.

[0078] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0079] In the multi-cell multi-user MIMO system based on confidential ISAC constructed by the present invention, each cell base station not only provides services for communication users in the cell, but also is responsible for sensing the surrounding environment, which is closer to the actual application scenario; each base station allocates communication and sensing power by optimizing the problem model, and simultaneously transmits information signals and dedicated radar signals, which can effectively improve the sensing ability while meeting the communication needs;

[0080] Since the dedicated radar signals of each base station are known a priori, communication users can eliminate the interference of these radar signals through SIC (Successive Interference Cancellation) technology after receiving the signal, thereby recovering the required information signal from the information signal interference within and between cells, while eavesdroppers will be affected by the interference of the dedicated radar signal;

[0081] The beamforming formulation is formulated as a problem of maximizing the performance of secure communications, while meeting the reliability and confidentiality requirements of communication users. By applying the block coordinate descent algorithm, the original non-convex optimization problem is simplified and effectively solved, and the convex subproblem is iteratively solved to obtain a better overall suboptimal solution, which significantly improves the performance and computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 A schematic diagram of the flow of the beamforming method for integrated secure communication and perception according to the present invention;

[0083] Figure 2 It is a schematic diagram of the architecture of a multi-cell multi-user MIMO system model based on a confidential ISAC according to the present invention;

[0084] Figure 3 It is a flowchart of the beamforming algorithm of the present invention. DETAILED DESCRIPTION

[0085] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0086] Example

[0087] like Figure 1 As shown, this embodiment provides a beamforming method integrating secure communication perception, including the following steps:

[0088] Step 1: Construct a multi-cell multi-user MIMO system model based on confidential ISAC;

[0089] like Figure 2 As shown in the figure, a multi-cell multi-user MIMO system based on confidential ISAC is constructed. In such a K-cell MIMO interference broadcast channel environment, each cell corresponds to a base station, and the base stations k, k = 1, 2, ..., K are equipped with M k The ULA (uniform linear array) of the transmitting antenna, serving cell k, I k The radar target perception is realized at the same time as the communication users of each cell k, which will also cause interference to the communication users and eavesdroppers in other cells. The receiver i of the i-th communication user in cell k k have Receiving antenna, the set of all users is I = {i k ∣k∈{1,2,…,K},i∈{1,2,…,I k}}.

[0090] Step 2: Each base station transmits information signals and dedicated radar signals through a uniform linear array (ULA) to communicate with communication users in the cell and realize radar target perception;

[0091] Conventional ISAC base station transmission signals are based on communication radar signals, that is, the communication signal is used as the radar waveform, and the perception function is realized by analyzing the communication signal. Different from the above scheme, this embodiment uses a dedicated radar signal to realize the perception function. In order to perform perception and communication at the same time, base station k transmits information signal To communication user i k ,i∈{1,2,…,I k}, whose mean is 0 and variance is 1, and the corresponding transmit beamforming vector of the information signal is At the same time, base station k transmits a priori known dedicated radar signal Its mean is 0 and and k are independent of each other, where the superscript (·) H is the conjugate transpose operation, E[·] represents the mean operation, C represents the complex number set, C x×y Represents the x×y complex matrix space.

[0092] Then the transmission signal transmitted by base station k through ULA is for:

[0093]

[0094] Note that, unlike the single beam transmission that carries the information signal, the present invention considers the dedicated radar signal s k General multi-beam transmission (i.e. of general rank). In particular, assuming This corresponds to a set radar signal beams, which can be The eigenvalue decomposition of is obtained, where r(·) is the rank of the matrix.

[0095] At this time, the transmission power of base station k is The transmit power budget of base station k is P k , then it satisfies where ‖·‖ represents the Euclidean norm of the vector and tr(·) is the trace of the matrix.

[0096] Step 3: The communication user receives the signal and eliminates the interference of the dedicated radar signal, and recovers the information signal under the signal interference within and between cells.

[0097] Base station j to communication user receiver i k The channels between Indicates that the receiver noise is additive white Gaussian noise and Right now Subject to mean 0 and covariance The complex Gaussian distribution of and k are independent of each other, where I represents the identity matrix.

[0098] The information signal and dedicated radar signal transmitted by the base station are received by each communication user through the channel. k It is known a priori that for communication user receiver i k For example, SIC technology can be used to eliminate the interference of dedicated radar signals to the receiver, and the communication user receiver i k Equivalent received signal for:

[0099]

[0100] Communication user receiver i k The received signal is formed by receiving beamforming. The estimated signal is recovered, and the corresponding receive beamforming vector is expressed as So the estimated signal recovered for:

[0101]

[0102] Step 4: Construct an optimization problem model to minimize the sum of the average power leakage outside the angle of interest and the average weighted mean square error of the communication user information signal.

[0103] The range of the transmit beam pattern sensing angle θ is d is the distance between two adjacent antennas (usually set to half a wavelength), λ is the carrier wavelength, and the ULA steering vector

[0104] Among them, the superscript (·) T To perform the transpose operation.

[0105] Therefore, the transmit beam pattern gain of base station k in the θ direction is:

[0106]

[0107] Here, |·| means taking the absolute value.

[0108] Divide the transmit beam pattern gain angle range into M angles Cell k has N k Interesting angle Since the location of potential eavesdroppers is unknown, in order to meet the needs of confidential communication, power leakage should be avoided while ensuring the communication quality, that is, SINR (Signal to Interference plus Noise Ratio) is less than the threshold, and the average beam pattern gain at uninteresting angles should be minimized:

[0109]

[0110] This also helps the base station allocate more power to perceive the angle of interest. In order to enable communication users to obtain better communication quality, the SINR constraint is converted into a communication item in the optimization target. At this time, communication user i k Rate for:

[0111]

[0112] Where logdet(·) is the logarithm operation of taking the determinant of the matrix.

[0113] Each communication user i k The priority of If we express it, the WSR (weighted sum rate) of the multi-cell multi-user MIMO system based on confidential ISAC is:

[0114]

[0115] Initially set the objective function to Where 0≤μ≤1 is the coefficient for adjusting the weights of perception and communication indicators. However, -WSR is not a convex or concave function;

[0116] Note that by minimizing the sum of the mean square errors we can obtain an MMSE (Minimum Mean Square Error) receiver:

[0117]

[0118] Estimated signal is easy to obtain With information signal MSE (Mean Square Error) for:

[0119]

[0120] The corresponding minimum mean square error is:

[0121]

[0122] Then we can get:

[0123]

[0124]

[0125] The second equal sign in the derivation of the above objective function transformation formula is derived from the famous Woodbury matrix identity (A+UCV) -1 =A -1 -A -1 U(C -1 +VA -1 U) -1 VA -1 The third equal sign is obtained by det(I+A1A2)=det(I+A2A1). So far, the transformation from weighted sum rate to mean square error function is realized, but it is obviously not a convex function either.

[0126] Consider user i k The weighted variable is Then the weighted mean square error of the system is:

[0127]

[0128] For weighted variables The above formula is a convex function. According to the basic theory of convex optimization, we can get Therefore and The two optimization objectives are equivalent. In view of the confidentiality of communication requirements, an optimization problem model is constructed to minimize the sum of the average power leakage outside the angle of interest and the average weighted mean square error of the communication user information signal, namely (p1):

[0129]

[0130] Step 5: Use the block coordinate descent method to decompose the non-convex optimization problem into convex sub-problems, and combine the beamforming optimization to achieve the optimal secure communication performance.

[0131] The optimization problem (p1) is a non-convex optimization problem due to the existence of WMSE, but it can be noted that WMSE is a convex function with respect to each of the optimization variables t, u and w, so the objective function is a convex function for each optimization variable.

[0132] like Figure 3 As shown, in order to solve the non-convex objective function, the block coordinate descent method is used to iteratively solve it. In each iteration, a part of the variables is sequentially fixed to update the remaining variables to minimize the objective function. The non-convex optimization problem (p1) is decomposed into three convex sub-problems:

[0133] The optimal receive beamforming vector u is obtained by solving subproblem (sp1):

[0134]

[0135] Obviously, the subproblem (sp1) is a convex problem with respect to the variable u and only The rest are fixed parameters, so the optimal solution for the receive beamforming vector u is the MMSE receiver mentioned above:

[0136]

[0137] The optimal weighted variable w is obtained by solving subproblem (sp2):

[0138]

[0139] For the optimization variable w, the subproblem (sp2) is convex and only The rest are fixed parameters. The optimal solution of the weighted variable w is obtained by the first-order optimality condition:

[0140] The optimal transmit beamforming vector t and the covariance matrix R of the dedicated radar d By solving the subproblem (sp3), we get:

[0141]

[0142]

[0143] For the remaining optimization variables t and R dFor example, the subproblem (sp3) is a convex problem, and the remaining optimization variables are fixed parameters. It can be effectively solved by standard solvers such as CVX. CVX is a convex optimization toolkit developed based on the MATLAB environment and can be used to solve linear programming, quadratic programming, semidefinite programming, and geometric programming problems.

[0144] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A beamforming method integrating secure communication and perception, characterized in that: The steps include: Construct a multi-cell multi-user MIMO system model based on confidential ISAC; Each base station transmits information signals and dedicated radar signals through a uniform linear array, communicates with communication users in the cell and realizes radar target perception, and calculates the transmission power and transmission power budget of the base station; The information signal and the dedicated radar signal transmitted by the base station are received by each communication user through the channel. The communication user's receiver eliminates the interference of the dedicated radar signal and recovers the received signal to obtain an estimated signal through receiving beamforming. Construct an optimization problem model to minimize the sum of the average power leakage outside the angle of interest and the average weighted mean square error of the communication user information signal; The block coordinate descent method is used to decompose the non-convex optimization problem model into convex sub-problems, and the optimal secure communication performance is achieved by combining beamforming optimization.

2. The beamforming method for integrated secure communication and perception according to claim 1, characterized in that: The construction of a multi-cell multi-user MIMO system model based on a confidential ISAC specifically includes: In a multi-cell MIMO interference broadcast channel environment, each cell corresponds to a base station, and the base station has M k A uniform linear array of transmitting antennas serving cell k k The radar target perception is realized at the same time by the communication users of each cell, which interferes with the communication users of other cells and eavesdroppers. The receiver i of the i-th communication user in cell k k Features The root receiving antenna, the set of all users is expressed as: I={i k |k∈{1,2,...,K},i∈{1,2,...,I k }} Wherein, K represents the total number of base stations.

3. The beamforming method for integrated secure communication and perception according to claim 1, characterized in that: Each base station transmits information signals and dedicated radar signals through a uniform linear array, which can be specifically expressed as: Among them, x k represents the transmission signal transmitted by base station k through a uniform linear array, Indicates that base station k transmits to communication user i k The information signal represents the transmit beamforming vector corresponding to the transmitted information signal, s k represents the dedicated radar signal transmitted by base station k, K represents the total number of base stations, and I k Indicates the total number of communication users in the cell.

4. The beamforming method for integrated secure communication and perception according to claim 3 is characterized in that: The transmission power of base station k is: The transmit power budget of base station k is P k ,satisfy: Here, ||·|| represents the Euclidean norm of the vector, tr(·) is the trace of the matrix, and r(·) is the rank of the matrix.

5. The beamforming method for integrated secure communication and perception according to claim 1, characterized in that: The information signal and the dedicated radar signal transmitted by the base station are received by each communication user through the channel. The communication user's receiver eliminates the interference of the dedicated radar signal. k The equivalent received signal is expressed as: in, Indicates that base station k transmits to communication user i k The information signal represents the transmit beamforming vector corresponding to the transmitted information signal, s k represents the dedicated radar signal transmitted by base station k, K represents the total number of base stations, and I k Indicates the total number of communication users in the cell, and Respectively represent the transmission distance from base station k and base station j to communication user receiver i k The channels between are represented by the channel matrix, Indicates receiver i k Noise, I represents the set of all communication users, each of which is equipped with a receiver; The received signal is restored by receiving beamforming to obtain the estimated signal, which is specifically expressed as: in, Indicates receiving signal, represents the receive beamforming vector, Represents the estimated signal.

6. The beamforming method for integrated secure communication and perception according to claim 1, characterized in that: Construct an optimization problem model to minimize the sum of the average power leakage outside the angle of interest and the average weighted mean square error of the communication user information signal, including: Set the range of the transmit beam pattern sensing angle θ to The uniform linear array steering vector is expressed as: Where d is the distance between two adjacent antennas, λ is the carrier wavelength, (·) T To take the transpose operation; The transmit beam pattern gain of base station k in the θ direction is: Among them, |·| means taking the absolute value, E[·] means taking the mean operation, (·) H To take the conjugate transpose operation, Indicates that base station k transmits to communication user i k The information signal represents the transmit beamforming vector corresponding to the transmitted information signal, s k represents the dedicated radar signal transmitted by base station k, I k Indicates the total number of communication users in the cell, Divide the transmit beam pattern gain angle range into M angles The community has N k Interesting angle Minimize the average beam pattern gain over angles of no interest: The SINR constraint is converted into the communication item in the optimization objective, and the communication user i k Rate for: Where logdet(·) is the logarithm operation of the matrix determinant, I represents the identity matrix, and Respectively represent the transmission distance from base station k and base station j to communication user receiver i k The channels between are represented by the channel matrix, represents the covariance, I represents the set of all communication users; The weighted sum rate of the multi-cell multi-user MIMO system based on confidential ISAC is expressed as: in, Represents each communication user i k Priority; Initially set the objective function to Where 0≤μ≤1 is the coefficient for adjusting the weights of perception and communication indicators; For minimizing the mean square error we obtain a minimum mean square error receiver: Estimated signal With information signal The mean square error is: The corresponding minimum mean square error is: get: The weighted mean square error of the multi-cell multi-user MIMO system is: The optimization problem model for minimizing the sum of the average power leakage outside the angle of interest and the average weighted mean square error of the communication user information signal is constructed, which can be expressed as: in, represents the weighted variable, and K represents the total number of base stations.

7. The beamforming method for integrated secure communication and perception according to claim 1, characterized in that: The block coordinate descent method is used to decompose the non-convex optimization problem into convex sub-problems, and the combined beamforming optimization achieves the optimal secure communication performance, including: The block coordinate descent method is used to iteratively solve the problem. In each iteration, a part of the variables are fixed sequentially and the remaining variables are updated to minimize the objective function. The optimization problem model is decomposed into three convex sub-problems, which are specifically expressed as follows: The optimal receive beamforming vector u is obtained by solving subproblem sp1: The optimal solution for the receive beamforming vector u is the minimum mean square error receiver, expressed as: The optimal weighted variable w is obtained by solving subproblem sp2: The optimal solution of the weighted variable w is obtained by the first-order optimality condition: The optimal transmit beamforming vector t and the covariance matrix R of the dedicated radar d By solving subproblem sp3, we get: Solve subproblem sp3 using the standard solver.

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