Beam forming optimization method of multi-target sensing and covert communication integrated system

Abstract

The invention discloses a beam forming optimization method of a multi-target sensing and covert communication integrated system, and belongs to the technical field of wireless communication. According to the method, an optimization problem which takes a minimum average Cramer-Rao bound as a target function and takes a communication rate demand, a transmitting power demand, a hidden demand and the like as constraints is constructed in a base station, a user, a plurality of detection targets and a monitor model. Firstly, the Cramer-Rao bound and the corresponding average Cramer-Rao bound are deduced, the detection performance of a monitor is analyzed, and a lower bound expression of the minimum detection error probability is given. The objective function and the constraint set of the constructed problem are non-convex, the objective function and the hidden constraint are simplified by applying a Schel complement method and analyzing monotonicity of hidden constraint and received signal energy, and then optimal beam forming is deduced. Meanwhile, according to the scheme provided by the invention, multi-target perception and covert communication can be realized at the same time, and the communication safety performance of the ISAC system is effectively enhanced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, in particular to a beamforming optimization method of a multi-target sensing and covert communication integrated system. BACKGROUND

[0002] With the rapid development of wireless communication technology, the sixth generation mobile communication technology (6G) has higher requirements for the sensing ability and covert communication performance of the communication system. The traditional communication system usually designs the sensing and covert communication functions independently, which leads to a large discount in the utilization rate of spectrum resources. The rapid development of the wireless communication industry leads to an increasingly crowded spectrum, and the urgent demand for additional spectrum resources makes the sensing and communication integration technology become a hot topic. Emerging sensing and communication integration (ISAC) is considered one of the potential key technologies for 6G mobile communication. The ISAC system can make sensing and communication mutually beneficial, for example, in the vehicle networking application scenario, it can use sensing to assist communication and use the echo signal for tracking, thereby obtaining the cooperation gain of the integrated system. However, in the ISAC system, the transmitter usually has a large transmission power in order to improve the accuracy of target detection, which also increases the risk of exposing the location information, which makes the ISAC system have certain communication security risks.

[0003] In previous studies, in order to solve this problem, physical layer security technology can be one of the solutions to improve the security performance of the ISAC system. However, from the perspective of physical layer security, the safety of the transmission content of the ISAC system is protected, which ignores the fact that if the transmission behavior of the transmitter is detected by a malicious node, it may be further tracked and monitored to expose the location information, so that the network still has certain security risks. In order to solve this problem, a more advanced wireless communication security transmission scheme, i.e. covert wireless communication technology, has attracted widespread attention from scholars at home and abroad in recent years. It is worth noting that in existing research, the target detection performance is usually designed to use the target detection mutual information and the target beam pattern as indicators to design the beamforming of the base station. However, neither the beam pattern nor the target detection mutual information can well quantify the target estimation performance in the ISAC system. Considering that CRLB is the lower bound of the variance of the unbiased estimator of the target, it has been widely used to measure the target estimation performance of the ISAC system in various ISAC scenarios. In addition, unlike general ISAC system scenarios, in the ISAC covert wireless communication system, the target estimation performance under the null hypothesis and the alternative hypothesis needs to be considered, and the system's covert performance also needs to be taken into account. Based on the above reasons, the present application proposes a beamforming optimization method of a multi-target sensing and covert communication integrated system. SUMMARY

[0004] The purpose of the present application is to provide a beamforming optimization method of a multi-target sensing and covert communication integrated system to solve the problems mentioned in the background art.

[0005] To achieve the above object, the present application adopts the following technical solutions:

[0006] A beamforming optimization method of a sensing and covert communication integrated system, specifically comprising the following steps:

[0007] S1, constructing a multi-target sensing and covert communication integrated system model: selecting a base station, a user, a monitor and a plurality of detection targets as the entity research objects of the multi-target sensing and covert communication integrated system model;

[0008] S2, deriving an analytical expression of the average Cramer-Rao bound and the minimum detection error probability of the monitor: deriving the Cramer-Rao bound expression according to the target's to-be-estimated quantity for the base station and analyzing the detection performance of the monitor to give the lower bound expression of the minimum detection error probability;

[0009] S3, constructing an optimization problem: taking the communication rate requirement, the transmission power requirement and the concealment requirement as constraints, constructing an optimization problem of minimizing the Cramer-Rao bound;

[0010] S4, simplifying the optimization problem: simplifying the objective function and the concealment constraint by applying the Schur complement method and analyzing the monotonicity of the concealment constraint and the received signal energy;

[0011] S5, solving the optimal beamforming: simplifying the optimization problem of minimizing the Cramer-Rao bound into a problem that can be directly solved by using convex optimization tools, and then determining the optimal beamforming.

[0012] Preferably, the S1 specifically comprises the following contents:

[0013] Assuming that the base station is equipped with a plurality of antennas, the user and the monitor are equipped with a single antenna; defining the transmission signal of the base station:

[0014] (1)

[0015] wherein, and represent the target detection signal and the communication signal of the base station, respectively, is a symbol index, L represents the total number of symbols in a communication block, and satisfies and ; represents the expectation of a random variable; represents the beamforming vector of the target detection signal, represents the beamforming vector of the communication signal; represents the null hypothesis, i.e. the base station only transmits the target detection signal; and represents the alternative hypothesis, i.e. the base station transmits the target detection signal and the communication signal simultaneously;

[0016] The user in the first The signal received per symbol period Represented as:

[0017] (2)

[0018] in, This represents the channel vector between the base station and the user; This indicates that the mean is zero and the variance is... Additive white Gaussian noise, i.e. ;

[0019] The monitor in the The signal received per symbol period Represented as:

[0020] (3)

[0021] in, This represents the channel vector between the base station and the monitor; This indicates that the mean is zero and the variance is... Additive white Gaussian noise, i.e. ;

[0022] The base station is in The echo signal received per symbol period Represented as:

[0023] (4)

[0024] in, This represents the channel vector from the base station to the target and back to the base station. , This is the transmission steering vector of the base station. Indicates the first The azimuth angle of the target. Indicates the first The complex amplitude of the nth target, which depends on the nth target. The scattering cross section of the target and the distance from the base station to the target; in addition, This indicates that the mean is zero and the variance is... Additive white Gaussian noise, i.e. .

[0025] Preferably, S2 specifically includes the following:

[0026] The Cramer-Rao boundary is used to measure the base station's sensitivity to target parameters. The estimated performance, of which, ;

[0027] make , , , ; otherwise, , denote the real and imaginary parts of ; the Fisher information matrix for estimating is given by

[0028] (5)

[0029] (6)

[0030] (7)

[0031] (8)

[0032] (9)

[0033] (10)

[0034] where denotes the column of the identity matrix, ;

[0035] The Cramér-Rao bound for N targets is the inverse of the Fisher information matrix, which is given by

[0036] (11)

[0037] where denotes the covariance matrix of the transmitted signals, which is given by

[0038] (12)

[0039] where ;

[0040] Since there are two covariance matrices of the transmitted signals, the average Cramér-Rao bound is adopted as the measure of the system's sensing performance, i.e.,

[0041] (13)

[0042] In covert communication, the monitor decides whether the base station transmits covert information to the user according to the observed sample sequence ; the monitor performs binary hypothesis testing to distinguish between the null hypothesis and the alternative hypothesis; the total detection error probability of the monitor is given by the false alarm error probability and the missed alarm error probability composition, wherein and respectively represent the decision of the monitor that the base station does not send information to the user and the base station sends information to the user; therefore, the total detection error probability of the monitor is:

[0043] (14)

[0044] wherein, represents the prior probability of the base station only transmitting the probe signal for target sensing, represents the prior probability of the base station transmitting the target probe signal and the communication signal at the same time; in the covert wireless communication, the monitor minimizes its total detection error probability ; while the monitor uses the likelihood ratio test to minimize its total detection error probability, the corresponding likelihood ratio function is as follows:

[0045] (15)

[0046] wherein, and respectively represent the likelihood function under and , and , ; wherein, , ;

[0047] The lower bound of the detection error probability is used to measure the detection performance of the monitor, and the corresponding lower bound expression is represented as:

[0048] (16)

[0049] wherein, , is the Kullback-Leibler divergence from to ; The expression of is: ; in order to meet the concealment performance requirement of the system, in the covert wireless communication, is used as the concealment constraint of the system, wherein, is an arbitrarily small number to determine the level of concealment performance; in combination with equation (16), the concealment constraint is represented as:

[0050] (17).

[0051] Preferably, the S3 specifically comprises the following contents:

[0052] Jointly optimize the beamforming of the base station target probe signal Beamforming of communication signals with base stations The constructed optimization problem needs to satisfy the communication rate constraint, the maximum transmit power constraint and the concealment constraint requirement, with the objective function of minimizing the average Cramer-Rao bound; the corresponding optimization problem is as follows:

[0053]

[0054]

[0055]

[0056] (18)

[0057] wherein, represents the average communication rate of the user, represents the communication rate threshold satisfied, represents the maximum transmit power.

[0058] Preferably, the S4 specifically comprises the following contents:

[0059] Firstly, the minimum is equivalent to minimizing , is a diagonal weight matrix; by using the method of Schur complement, introduce , , , ; the objective function is converted into:

[0060] (19)

[0061] The inequality constraint and are added;

[0062] Secondly, for the concealment constraint C3 in the optimization problem, it is verified that is a monotonically increasing function about in ; the concealment constraint C3 is rewritten as:

[0063] (20)

[0064] wherein, is the solution of the equation .

[0065] Preferably, the S5 specifically comprises the following contents:

[0066] The objective function, the concealment constraint and the communication rate constraint of the optimization problem are still non-convex, and for the optimization problem, define , , , , and , and and ; rewrite the optimization problem as:

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074] (21)

[0075] The optimization problem (21) has a convex objective function and a convex constraint set, and is solved by using a convex optimization tool to obtain optimal beamforming.

[0076] Compared with the prior art, the application provides a beamforming optimization method of a multi-target perception and covert communication integrated system, which has the following beneficial effects:

[0077] (1) In the multi-target perception and covert wireless communication system, the application derives the Fisher information matrix and the corresponding analytical expression of the average Cramer-Rao bound, analyzes the detection performance of the monitor, and gives the lower bound expression of the minimum detection error probability.

[0078] (2) The scheme proposed by the application can simultaneously realize multi-target perception and covert communication, effectively enhancing the communication security performance of the ISAC system.

[0079] (3) The objective function and the constraint set of the problem constructed by the application are non-convex, and it is usually difficult to directly solve them. By using the Schur complement method and analyzing the monotonicity of the concealment constraint and the received signal energy, the objective function and the concealment constraint are simplified, and the optimization problem is effectively solved based on the semi-definite relaxation method. BRIEF DESCRIPTION OF DRAWINGS

[0080] Figure 1 A system schematic diagram of a beamforming optimization method of a multi-target perception and covert communication integrated system proposed by the application.

[0081] Figure 2 An algorithm flowchart of a beamforming optimization method of a multi-target perception and covert communication integrated system according to the present application.

[0082] Figure 3 A relationship diagram of the average maximum transmit power and the symbol length in Embodiment 1 of a beamforming optimization method of a multi-target perception and covert communication integrated system according to the present application. and the covert level parameter and the communication rate requirement .

[0083] Figure 4 A relationship diagram of the average maximum transmit power and the symbol length in Embodiment 1 of a beamforming optimization method of a multi-target perception and covert communication integrated system according to the present application. and the average maximum transmit power and the symbol length .

[0084] Figure 5 A relationship diagram of the average maximum transmit power and the signal transmit power and the communication rate threshold in Embodiment 1 of a beamforming optimization method of a multi-target perception and covert communication integrated system according to the present application. and the signal transmit power and the communication rate threshold .

[0085] Figure 6 A relationship diagram of the beam pattern and the angle and the average maximum transmit power in Embodiment 1 of a beamforming optimization method of a multi-target perception and covert communication integrated system according to the present application. and the average maximum transmit power DETAILED DESCRIPTION

[0086] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, not all the embodiments.

[0087] Embodiment 1

[0088] Referring to Figures 1-2 , a beamforming optimization method of a multi-target perception and covert communication integrated system, specifically comprising the following steps:

[0089] S1, constructing a multi-target perception and covert communication integrated system model: selecting a base station, a user, a monitor and a plurality of detection targets as the entity research objects of the communication system model;

[0090] The multi-target perception and covert communication integrated system model mentioned in S1 specifically includes the following contents:

[0091] It is assumed that the base station is equipped with multiple antennas, and the user and the monitor are equipped with a single antenna; the transmit signal of the base station is defined as

[0092] (1)

[0093] wherein, and denote the target probe signal and the communication signal of the base station, respectively, is the symbol index, L denotes the total number of symbols within one communication block, and satisfies and ; denotes the expectation of a random variable; denotes the beamforming vector of the target probe signal, denotes the beamforming vector of the communication signal; denotes the null hypothesis, i.e., the base station only transmits the target probe signal; and denotes the alternative hypothesis, i.e., the base station simultaneously transmits the target probe signal and the communication signal;

[0094] The signal received by the user at the i-th symbol period is denoted as:

[0095] (2)

[0096] wherein, denotes the channel vector between the base station and the user; denotes the additive white Gaussian noise with mean zero and variance , i.e., ;

[0097] The signal received by the monitor at the i-th symbol period is denoted as:

[0098] (3)

[0099] wherein, denotes the channel vector between the base station and the monitor; denotes the additive white Gaussian noise with mean zero and variance , i.e., ;

[0100] The echo signal received by the base station at the i-th symbol period is denoted as:

[0101] (4)

[0102] wherein, denotes the channel vector from the base station to the target and then to the base station, , ​​​​​​a transmit steering vector of the base station, denotes an azimuth angle of the th target, denotes a complex amplitude of the th target, which depends on the scattering cross section of the th target and the distance from the base station to the target; in addition, denotes an additive white Gaussian noise with mean zero and variance , i.e. .

[0103] S2, deriving an analytical expression of the average Cramer-Rao bound and the minimum detection error probability of the monitor: according to the estimated quantity of the target to the base station, the Cramer-Rao bound expression is derived and the detection performance of the monitor is analyzed, and the lower bound expression of the minimum detection error probability is given.

[0104] The analytical expression of the average Cramer-Rao bound and the lower bound expression of the minimum detection error probability mentioned in S2, specifically includes the following contents:

[0105] The Cramer-Rao bound is used to measure the estimation performance of the base station on the target parameter , wherein ;

[0106] Let , , , ; in addition, , respectively represent the real part and the imaginary part of ; the Fisher information matrix for estimating is represented as:

[0107] (5)

[0108] (6)

[0109] (7)

[0110] (8)

[0111] (9)

[0112] (10)

[0113] wherein denotes the th column of the unit matrix, ;

[0114] The Cramer-Rao bound of the N targets is the inverse matrix of the Fisher information matrix, which is represented as:

[0115] (11)

[0116] wherein, denotes the covariance matrix of the transmitted signal, which is expressed as:

[0117] (12)

[0118] wherein,

[0119] Since there are two kinds of covariance matrices of the transmitted signal, the average Cramer-Rao bound is used as the scale to measure the system sensing performance, i.e.:

[0120] (13)

[0121] In covert communication, the monitor makes a decision on whether the base station transmits covert information to the user according to the observed sample sequence ; the monitor performs binary hypothesis testing to distinguish H0: the base station does not transmit information to the user H1: the base station transmits information to the user ; the total detection error probability of the monitor consists of the false alarm error probability and the missed alarm error probability , wherein, and respectively represent the decision of the monitor that the base station does not transmit information to the user and the decision of the monitor that the base station transmits information to the user; therefore, the total detection error probability of the monitor is:

[0122] (14)

[0123] wherein, denotes the prior probability of the base station transmitting only the probe signal for target sensing, denotes the prior probability of the base station transmitting both the target probe signal and the communication signal; in covert wireless communication, the monitor minimizes its total detection error probability ; while the monitor uses the likelihood ratio test to minimize its total probe error probability, and the corresponding likelihood ratio function is as follows:

[0124] (15)

[0125] wherein, and respectively represent the likelihood function under and , and , ; wherein, , ​

[0126] The expression derived directly from formula (15) for the minimum total detection error probability of the monitor contains an incomplete gamma function, which is not conducive to subsequent covert transmission design. Therefore, the present application uses a lower bound of the detection error probability to measure the detection performance of the monitor. The corresponding lower bound expression can be expressed as:

[0127] (16)

[0128] wherein, , is the Kullback-Leibler divergence from to . The expression of is: .

[0129] In order to meet the covert performance requirements of the system, the is generally used as the covert constraint of the system in covert wireless communication, wherein is an arbitrarily small number to determine the level of covert performance. Integrating formula (16), the covert constraint can be expressed as:

[0130] (17)

[0131] S3, constructing an optimization problem: taking the communication rate requirement, the transmission power requirement and the covert requirement as constraints, constructing a minimum Cramer-Rao bound optimization problem;

[0132] The construction of the optimization problem mentioned in S3 specifically includes the following contents:

[0133] Jointly optimizing the beamforming of the base station target detection signal and the beamforming of the base station communication signal , taking the minimum average Cramer-Rao bound as the objective function, the optimization problem constructed needs to meet the communication rate constraint, the maximum transmission power constraint and the covert constraint requirement; the corresponding optimization problem is as follows:

[0134]

[0135]

[0136]

[0137] (18)

[0138] wherein, indicates the average communication rate of the user, indicates the communication rate threshold that needs to be met, Pmaxdenotes the maximum transmit power.

[0139] S4, Simplify the optimization problem: Simplify the objective function and the concealment constraint by applying the method of Schur complement and analyzing the monotonicity of the concealment constraint and the received signal energy.

[0140] The simplification of the optimization problem mentioned in S4 specifically includes the following:

[0141] First, minimize Equivalently minimize , is a diagonal weighting matrix. By the method of Schur complement, introduce , , , . The objective function is transformed to:

[0142] (19)

[0143] Further, add inequality constraints and .

[0144] Secondly, for the concealment constraint C3 in the optimization problem, it can be verified that is a monotonically increasing function of in . Therefore, the concealment constraint C3 can be rewritten as:

[0145] (20)

[0146] where is the solution of equation .

[0147] S5, Solve the optimal beamforming: Simplify the minimization of the Cramer-Rao bound optimization problem into a problem that can be directly solved by convex optimization tools, and then determine the optimal beamforming.

[0148] The solving of the optimal beamforming mentioned in S5 specifically includes the following:

[0149] The objective function, concealment constraint and communication rate constraint of the optimization problem are still non-convex. For this optimization problem, define , , , and , and and . Then the optimization problem can be rewritten as:

[0150]

[0151]

[0152]

[0153]

[0154]

[0155]

[0156]

[0157] (21)

[0158] This optimization problem has a convex objective function and a convex constraint set, so it can be solved by using convex optimization tools to find the optimal beamforming.

[0159] To show the correctness and effectiveness of the above derivation, simulation results will be provided to verify the performance of the proposed algorithm and evaluate the impact of different values of system parameters on system performance. Assume that the base station is a uniform linear antenna array (ULA) and the target is a point target. In addition, the positions of the base station, user, monitor and two targets are respectively in the three-dimensional coordinate system , , and and . The signal attenuation at a reference distance of 1 m is -30 dB, and the path attenuation factors from the base station to the user and from the base station to the monitor are both 3.

[0160] If not specified, the remaining system parameters are set as follows: the number of antennas of the base station is , , , the angles of the two targets are , .

[0161] Figure 3 The relationship between the concealment level parameter and the communication rate requirement is given, where , , and the symbol length . From Figure 3 , it can be obtained that decreases with the increase of the concealment level parameter , because when As the communication rate requirement increases, the concealment constraint is easier to satisfy, so that the system can allocate more resources for communication and sensing, and the sensing performance of the system will be better. From Figure 3 It can also be observed that, As the communication rate requirement increases, the communication signal transmit power increases, the target detection signal power decreases, resulting in the sensing performance of the system will be worse.

[0162] Figure 4 The relationship between the average maximum transmit power and the symbol length is given, where is the communication rate requirement, is the concealment level parameter. From , it can be obtained that the value of Figure 4 decreases as the average maximum transmit power increases, because as the average maximum transmit power increases, both the sensing signal power and the communication signal power increase, and the sensing performance of the system will be better. In addition, it can also be observed from that the value of Figure 4 decreases as the symbol length increases. Although the larger the symbol length is, the more difficult the concealment constraint is to satisfy, from the perspective of extracting the echo signal, the larger the symbol length is, the more beneficial to target sensing, so is inversely proportional to .

[0163] Figure 5 The relationship between the average maximum transmit power and the signal transmit power and the communication rate threshold is given, where the concealment level parameter , . From Figure 5 , it can be seen that as the average maximum transmit power increases, both the sensing signal power and the communication signal power increase. This shows that in this system, increasing the transmit power can effectively improve the target sensing performance and the communication performance.

[0164] Figure 6 The relationship between the beam pattern and the angle and the average maximum transmit power is given, where the concealment level parameter , the communication rate requirement , . From Figure 6 , it can be seen that the beam patterns all focus their main lobes​​​ and This is because the target is located and However, due to the existence of communication rate constraint and concealment constraint, the beam pattern shows random fluctuations in its sidelobe region. In addition, the beam pattern value increases with the increase of the average maximum transmit power, and increasing the transmit power can effectively improve the target perception performance and concealment communication performance.

Claims

1. A method for beamforming optimization of a multi-target perception and covert communication integrated system, characterized in that, Specifically comprising the following steps: S1, constructing a multi-target perception and covert communication integrated system model: selecting a base station, a user, a monitor and multiple detection targets as the entity research objects of the multi-target perception and covert communication integrated system model; S2, deriving an analytical expression of the average Cramer-Rao bound and the minimum detection error probability of the monitor: deriving the Cramer-Rao bound expression according to the to-be-estimated quantity of the target for the base station and analyzing the detection performance of the monitor to give the lower bound expression of the minimum detection error probability; S3, constructing an optimization problem: taking the communication rate requirement, the transmission power requirement and the concealment requirement as constraints, constructing an optimization problem of minimizing the Cramer-Rao bound; S4, simplifying the optimization problem: simplifying the objective function and the concealment constraint by applying the Schur complement method and analyzing the monotonicity of the concealment constraint and the received signal energy; S5, solving the optimal beamforming: simplifying the optimization problem of minimizing the Cramer-Rao bound into a problem that can be directly solved by using a convex optimization tool, and then determining the optimal beamforming.

2. The beamforming optimization method of a multi-target perception and covert communication integrated system according to claim 1, wherein, The S1 specifically comprises the following contents: Assume that the base station is equipped with multiple antennas, and the user and the monitor are equipped with a single antenna; define the transmission signal of the base station as: （1） wherein and denote a target probe signal and a communication signal of the base station, respectively, is a symbol index, L denotes a total number of symbols within one communication block, and satisfies and ; denotes an expectation of a random variable; denotes a beamforming vector of the target probe signal, denotes a beamforming vector of the communication signal; denotes a null hypothesis, i.e. the base station transmits only the target probe signal; and denotes an alternative hypothesis, i.e. the base station transmits both the target probe signal and the communication signal; The signal received by the user at the first symbol period is represented as: ​ （2） wherein denotes a channel vector between the base station and the user; denotes additive white Gaussian noise with zero mean and variance , i.e. ; The monitor receives a signal at the first symbol period is represented as: （3） wherein denotes the channel vector between the base station and the monitor; denotes additive white Gaussian noise with zero mean and variance , i.e. ; The base station receives an echo signal in the first symbol period The echo signal received by the base station in the first symbol period is represented as: （4） in, This represents the channel vector from the base station to the target and back to the base station. , This is the transmission steering vector of the base station. Indicates the first The azimuth angle of the target. Indicates the first The complex amplitude of the nth target, which depends on the nth target. The scattering cross section of the target and the distance from the base station to the target; in addition, This indicates that the mean is zero and the variance is... Additive white Gaussian noise, i.e. .

3. The beamforming optimization method of a multi-target perception and covert communication integrated system according to claim 2, wherein, The S2 specifically comprises the following contents: Using the Cramér-Rao bound to measure the base station's estimation performance on a target parameter, wherein ; and ; and Let , , , ; otherwise, , denote the real and imaginary parts of , respectively; the Fisher information matrix for estimating is given by: （5） （6） （7） （8） （9） （10） wherein represents the first column of the identity matrix , ; The Cramer-Rao bound of the N targets is the inverse matrix of the Fisher information matrix, which is expressed as: （11） wherein denotes the covariance matrix of the base station transmit signal, which is expressed in terms of the transmit signal as （12） wherein ; Since there are two kinds of covariance matrices of the transmission signal, the average Cramer-Rao bound is adopted as the scale for measuring the perception performance of the system, that is: （13） In covert communication, a monitor decides whether the base station transmits covert information to the user according to the sample sequence observed by the monitor ; the monitor performs binary hypothesis testing to distinguish between the hypothesis that the base station transmits information to the user and the hypothesis that the base station does not transmit information to the user; the total detection error probability of the monitor consists of the false alarm error probability and the missed alarm error probability , where and represent the decision of the monitor that the base station does not transmit information to the user and the decision of the monitor that the base station transmits information to the user, respectively; therefore, the total detection error probability of the monitor is （14） where denotes the prior probability that the base station transmits only a probing signal for target awareness, denotes the prior probability that the base station transmits both a target probing signal and a communication signal; in covert wireless communication, the monitor minimizes its total detection error probability ; while the monitor uses likelihood ratio detection to minimize its total probing error probability, the corresponding likelihood ratio function is given by （15） wherein and represent the likelihood function under and respectively, and , ; wherein , ; Measuring the performance of a monitor using a lower bound on the probability of a detection error The corresponding lower bound expression is given by （16） in, , yes arrive Kullback-Leibler divergence; The expression is: To meet the system's concealment requirements, covert wireless communication employs... As a hidden constraint of the system, among which... It is an arbitrarily small value to determine the level of concealment performance; the comprehensive formula (16) represents the concealment constraint as follows: （17）。 4. The beamforming optimization method of a multi-target perception and covert communication integrated system according to claim 3, wherein, The S3 specifically comprises the following contents: Joint optimization of base station target detection signal beamforming and base station communication signal beamforming The optimization problem constructed takes the average Cramer-Rao bound as the objective function, needs to meet the communication rate constraint, the maximum transmission power constraint and the concealment constraint requirement; the corresponding optimization problem is as follows: （18） wherein, represents an average communication rate of the user, represents a communication rate threshold that is satisfied, represents a maximum transmit power.

5. The beamforming optimization method of a multi-target perception and covert communication integrated system according to claim 4, wherein, The S4 specifically comprises the following contents: First, minimize Equivalence minimization , is a diagonal weighting matrix; by using the method of the Schur complement, introduce , , , ; the objective function is converted to: （19） Inequality constraints are added and ; Secondly, for the hidden constraint C3 in the optimization problem, it is verified that is a monotonically increasing function with respect to In ; The hidden constraint C3 is rewritten as: （20） wherein is the solution of the equation .

6. The beamforming optimization method of a multi-target perception and covert communication integrated system according to claim 5, wherein, The S5 specifically comprises the following contents: The objective function, the hidden constraints, and the communication rate constraints of the optimization problem are still non-convex, for which the optimization problem is defined as , , , and , and and ; Rewrite the optimization problem as: （21） The optimization problem (21) has a convex objective function and a convex constraint set, and the convex optimization tool is used to solve the optimal beamforming.

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