CN115441906B - Cooperative game-based cooperative MIMO radar communication integrated system power distribution method - Google Patents
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- H—ELECTRICITY
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- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/0413—MIMO systems
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- H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
- H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
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- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks
Abstract
The invention discloses a cooperative MIMO radar communication integrated system power distribution method based on cooperative game, and belongs to the field of communication. The power distribution method of the collaborative MIMO radar communication integrated system is provided, wherein the target detection probability is used as a radar performance evaluation index and the communication mutual information is used as a communication performance evaluation index under the Neyman-Pearson criterion. In the method, a radar subsystem and a communication subsystem are regarded as two parties of a game, and the optimization problem based on Nash bargaining solution is established in consideration of the limitation of the total power of the system. According to the cooperative game theory, the Nash bargaining solution obtained by using the iterative NBS algorithm meets the properties of pareto optimal property, fairness and the like. The iterative NBS algorithm may adjust whether the system performance is more prone to radar or communication by negotiating a point of rupture.
Description
Technical Field
The invention belongs to the field of signal processing, relates to the problem of power distribution of a cooperative MIMO radar communication integrated system, and is suitable for designing the MIMO radar subsystem and the antenna transmitting power of the MIMO communication subsystem in the cooperative integrated system.
Background
In previous studies, radar and communication generally operated independently, and in recent years, many expert scholars have focused on radar communication integrated systems. The radar system and the communication system have many similarities, such as in hardware, and the radio frequency parts of the radar system and the communication system are similar, so that signals are radiated to space through an antenna and then processed at a receiving end, and the antenna, the transmitter, the receiver and the like have the common possibility. The difference between the two is reflected in signal processing, the information of the radar is from the target, and the information of the communication is from the transmitter. Thus, radar and communication systems have a foundation for integration.
In recent years, research on commercial 5G technology and 6G technology and development of millimeter wave radar provide fertile soil for development of radar communication integration. Through extensive research and verification, the existing research classifies radar communication integrated systems into the following three types: (1) a radar communication coexistence system, (2) a cooperative radar communication coexistence system, and (3) a dual-function radar communication integration system. Radar communication in a radar communication coexistence system shares resources, but radar and communication systems are separately designed. The present invention is based on a collaborative coexistence system that utilizes paths that would otherwise be considered interference in the coexistence system to help improve system performance. The radar and the communication system in the dual-function integrated system share the same hardware platform, and the same platform can realize radar and communication functions at the same time, so that the dual-function integrated system has high integration.
In the communication field, MIMO (Multiple Input Multiple Out) technology is widely used in the 4G age, and the key technology of 5G is a massive MIMO antenna array and beam forming technology. At present, millimeter wave radar is rapidly developed in the fields of automobile auxiliary driving, security inspection, medical detection and the like due to the maturity of millimeter wave technology. Similar to communication, millimeter wave technology brings about higher bandwidth, but transmission loss is high, and millimeter wave and massive MIMO technologies are combined with complementary advantages. The MIMO technology can improve the accuracy of target parameter estimation and the target detection capability. The MIMO technology can improve the channel capacity, improve the channel reliability and reduce the bit error rate in the field of communication application.
The problem of power allocation has been an important issue in studying various types of systems. The MIMO systems considered in this patent are all split antenna MIMO systems, and current MIMO radars are divided into co-located antenna MIMO radars and split antenna MIMO radars. The multi-angle target detection can be realized for the split antenna MIMO radar, and the target detection performance is improved. The patent considers the problem of power distribution under the condition of limited total power of radar and communication, designs by taking the overall performance of the optimized radar and the communication as a target, and provides an algorithm for realizing the optimal overall performance in the pareto sense.
Current applications to game theory focus on collaborative and non-collaborative games. In the radar field, gaming theory is often used to study MIMO radar different antennas, interaction process between different base radars, interaction process between radar and jammers, cooperation and antagonism between radar and targets, etc. In the communication field, how to reasonably and fairly distribute the resources of each system is often researched by adopting cooperative game, and finally, the optimization of the overall performance is realized. The game theory provides a brand new view angle and model, and provides an efficient solution for solving complex problems such as non-convex multi-objective optimization problems.
Therefore, aiming at the problem of power distribution optimization of integrated transmitting antennas of cooperative MIMO radar communication, the invention provides a cooperative game model, and under the condition of limited total power of a system, the invention provides an iterative Nash Bargaining Solution (NBS) algorithm to realize the optimization problem of radar and communication overall performance.
Disclosure of Invention
The invention provides a power distribution method of a cooperative MIMO radar communication integrated system, which uses target detection probability as a radar performance evaluation index and uses communication mutual information quantity as a communication performance evaluation index under the Neyman-Pearson criterion by combining cooperative game knowledge. In the method, a radar subsystem and a communication subsystem are regarded as two parties of a game, and the optimization problem based on Nash bargaining solution is established in consideration of the limitation of the total power of the system. According to the cooperative game theory, the Nash bargaining solution obtained by using the iterative NBS algorithm meets the properties of pareto optimal property, fairness and the like. The iterative NBS algorithm may adjust whether the system performance is more prone to radar or communication by negotiating a point of rupture.
The technical scheme of the invention is that the cooperative MIMO radar communication integrated system power distribution method based on cooperative game comprises the following steps:
step 1: let MIMO radar have N R Multiple receiving antennas M R Multiple transmit antennas, MIMO communication with N C Multiple receiving antennas M C A plurality of transmit antennas, and each antenna location is known to radar and communications; let the total emission power of the cooperative integrated system beThe total transmit power of the radar is +.>M-th radar transmitting antennaThe transmission power of (c) is denoted as E R,m The total transmit power of the communication is +.>The transmission power of the m' th communication transmission antenna is E C,m′ The radar transmit power allocation weight is defined as η R ，
Step 2: defining the observed value of the received signal of the MIMO radar end as a vector r R The observed value of the received signal of the MIMO communication terminal is vector r C ：
wherein URt and UR Representing a radar-radar channel matrix, a block diagonal matrix comprising target reflection coefficients, fading coefficients, respectively, U Ct and UC Block diagonal matrix s representing a communication-radar channel matrix, each containing target reflection coefficients and fading coefficients Rt and sR Radar signal vector s representing reflected and direct paths through the target Ct and sC A communication signal vector representing the reflected and direct paths through the object, U Rt and UR A block diagonal matrix representing a radar-communication channel matrix, U, comprising target reflected channel gain, direct path channel gain, respectively Ct and UC A communication-communication channel matrix is represented, comprising a block diagonal matrix of channel gains for the target reflection and channel gains for the direct path, respectively, and />Radar signal vectors representing the reflected and direct paths of the object received by the communication receiver, < >> and />A communication signal vector, w, representing the target reflected and direct paths received by the communication receiver R Representing an additive Gaussian white noise vector with zero mean and a covariance matrix of Q R ，w C Representing an additive Gaussian white noise vector, obeying zero mean and covariance matrix of Q C ；
Step 3: defining the assumption of the existence of a target asThe assumption that the target does not exist is +.>Establishing a hypothesis testing problem to obtain a log-likelihood ratio, and writing detection statistics into the log-likelihood ratio:
step 4: generally, the NP criterion specifies a false alarm probability P FA Below a certain value alpha f Under the condition of (1), calculating the maximum detection probability and giving the false alarm probability alpha f Carrying out detection statistics to obtain radar target detection probability P D ：
The function Q (·) represents a complementary distribution function,sigma is the detection statistic T R Standard deviation of (1)/(c)>Representing mathematical expectations for solving for random variables; also because of->The expression ≡is proportional to the two, use +.>To represent the detection probability P D In the case of a change in (a),
wherein the parameter alpha m,m′ ，β m,m′ ，γ m,m′ Related to target reflection coefficients, radar and communication transmit signals, time delays;
step 5: according to the definition of the mutual information quantity, the communication mutual information quantity MI is calculated as follows:
wherein The method comprises radar transmitting power, radar transmitting signals, reflection coefficients, target time delay and target estimation error items, wherein the received signals of different communication receivers are mutually independent and uncorrelated at different observation moments under the assumption that the communication received signals are Gaussian signals with zero mean value, and the time delay estimation error of a communication receiving end is in a reasonable range, so that the method meets the following requirements>The corresponding element is much smaller than Q C Will be->Is approximately toThe angle matrix, using the diagonal matrix algorithm, the mutual information quantity MI can be written as:
it can be seen that χ m,m′,n′,k Communication signal vector with communication receiving endThe direct path channel gain is related to the target reflected channel gain; due to the cooperation of radar communication, the channel gain and the direct path access gain reflected by the target can be obtained by a preprocessing mode, and the phi is obtained by the method n′,m,k The channel gain after target reflection is obtained by a preprocessing mode and is influenced by time delay estimation errors;
step 6: based on the knowledge of the cooperative game in the game theory, there is a unique and fair Nash bargaining solutionIt can be obtained by maximizing the nash product:
E R,m ,E C,m′ ≥0
wherein the negotiating breaking point isAnd solving by adopting an iterative NBS algorithm.
The iterative NBS algorithm provided by the invention is suitable for the mutual cooperation between the radar and the communication subsystem, communication signals can be accurately decoded at a radar receiving end, and target reflection coefficients and channel gains of the radar and the communication can be obtained through preprocessing. Under the limitation of the total power of the system, the optimal overall performance of the radar and the communication is realized, and whether the overall performance is more focused on the radar or the communication can be realized by adjusting the negotiating breaking point. The proposed iterative NBS algorithm focuses on the overall performance of the system, can realize pareto optimal, and has higher precision compared with a genetic algorithm. Therefore, the method provided by the invention is an efficient and effective method for solving the problem of power distribution of the collaborative MIMO radar communication integrated system.
Drawings
Fig. 1 shows a distribution diagram of the transmitting/receiving antenna position of the cooperative integrated system.
Fig. 2 is a graph of iteration number versus transmit power using an iterative NBS algorithm.
FIG. 3 is a graph of target detection probability and mutual information quantity under NSGA-II algorithm and iterative NBS algorithm.
Fig. 4 is a graph showing the change of target detection probability and communication mutual information quantity with signal-to-interference-noise ratio SCNR under the iterative NBS algorithm, the trisection search nash equalization algorithm, the uniform distribution method and the random distribution method.
Fig. 5 is a diagram showing overall performance of the system according to SCNR under the iterative NBS algorithm, the three-way search nash equalization algorithm, the uniform distribution method, and the random distribution method.
Detailed Description
Defining the signal transmitted by the mth radar transmitting antenna asBy s R,m (T) represents a radar transmission signal, T s The time sampling interval is denoted, K (k=1, 2,..k) for different sampling samples, s for the communication end C,m′ (t) represents a communication transmission signal, the transmission signal of the communication transmission antenna being represented as +.>Considering that both radar and communication signals have been normalized, < >>According to the radar receiving signal model, at kT s Time, N (n=1,) N R ) The received signal of each radar receiving antenna is represented as
wherein ζRt,nm and ζCt,nm′ Representing the target reflection coefficient at different paths. Similarly ζ R,nm and ζC,nm′ Representing radar fading coefficients under different paths, tau Rt,nm and τCt,nm′ Representing the time delay of reflection by the target under different paths, τ R,nm and τC,nm′ Representing the time delay of the direct path under different paths. w (w) R,n [k]Gaussian white noise signals, noise zero mean values of different paths are independently distributed in the same way.
Information such as antenna position, transmit signal, transmit power, etc. of the cooperative integrated system is shared among the radar and the communication. The communication signal can be accurately decoded and reconstructed by using the communication information at the radar receiving end. The target reflection coefficient of the radar may be known by preprocessing.
The observation vector of the nth receiving antenna of the MIMO Lei Daduan at different moments can be expressed as r R,n ＝(r R,n [1],...,r R,n [K]) T The observation vector of the MIMO radar end can be written as
wherein
Diag {.cndot } represents the block diagonal matrix, w R Is an additive Gaussian white noise vector, the mean value is zero and the covariance matrix is Q R ，
At the radar receiving end, if the radar task is to detect whether a target exists, the hypothesis test problem is expressed as
Assuming that the target is not present, the vector r is observed at this time R Is written as the probability density function of (2)
Assuming that the target is present, the vector r is observed at this time R Is written as the probability density function of (2)
Accordingly, the log-likelihood ratio is expressed as
Find AND r in equation (7) R The related terms, resulting in a detection statistic expressed as
In the general radar detection problem, the judgment can be carried out only through the received signal, the prior probability and the cost are not known in advance, and the Neyman-Pearson criterion is adopted as the main judgment criterion. In general, the Neyman-Pearson criterion specifies that the false alarm probability is below a certain value α f The maximum detection probability is calculated. Because the false alarm probability and the detection probability are often increased at the same time, and the actual requirement is that the lower the false alarm probability is, the higher the detection probability is, the maximum detection probability under the premise of giving the maximum acceptable false alarm probability can be calculated. The false alarm probability is expressed as
wherein Indicating that there is actually a target present. The detection probability is expressed as
Bringing the detection statistics into (9) to obtain
Where beta represents the detection threshold and,
β＝σQ -1 (α f )+μ 0 (12)
therefore, the target detection probability of the radar is expressed as
wherein
The standard Gaussian complementary distribution function Q (-) is known to be a monotonically decreasing function when the argument is greater than zero, thus P D And (Q) -1 (α f )+(μ 0 -μ 1 ) /sigma) is inversely proportional to the area greater than zero. Suppose Q -1 (α f ) The value of (a) is greater than (mu) 0 -μ 1 ) /σ (this assumption is generally true in actual simulation signal selection).
Further will (mu) 0 -μ 1 ) Sigma spread, can be obtainedAnd->Can be obtained by
wherein
At kT s Time, N '(N' =1, 2,) N C ) The received signals of the individual communications may be expressed as
wherein ζCt,n′m′ and ζRt,n′m Representing the channel gain reflected by the target at different channels. Zeta type R,n′m and ζC,n′m′ Indicating the direct path channel gain at different channels, and />Representing the time delay through the reflection of the target under different channels, and />Representing the time delay of the direct path under the different channels. w (w) C,n′ [k]The Gaussian white noise signal received by the communication receiving end is zero-mean and is independently and uniformly distributed.
In the cooperative integrated system, the antenna positions, the transmission signals and the transmission power of the radar and the communication are all known through cooperation. The communication receiving end can estimate the target position by using the target echo signal of the radar, so that the signal interference of the radar on the communication direct reaching path and the target reflection path is eliminated.
The observation vector of the nth receiving antenna of the MIMO communication end at different moments is expressed as r C,n′ ＝(r C,n′ [1],...,r C,n′ [K]) T The observation vector of the MIMO communication end can be written as
wherein UCt 、U C 、U Rt 、U R Definition of (d) and U Ct 、U C 、U Rt 、U R Similarly to this, the process of the present invention,definition of (c) and s Ct 、s C 、s Rt 、s R Similarly. w (w) C For obeying mean to be zero and covariance matrix to be Q C Is a white gaussian noise signal of (c),
at the MIMO communication receiving end, the cooperative sharing radar position can eliminate direct wave interference of the radar at the communication receiving end, and further eliminate interference of radar target echo according to the estimation result of the target position. Assuming that the target position to be estimated is θ= (x, y), the communication transmission signal is a gaussian signal, and the communication reception signal r C The probability density function of (2) can be expressed as
Where a is the covariance matrix of the matrix,
the patent adopts an ML estimation method, ML estimation of the target position,
wherein Is an estimate of the target location. The estimated value of the target position affects the time delay of radar and communication through the target reflection path, and the estimated error n of the target parameter estimation is assumed Ct,n′m′ and nRt,n′m Obeying Gaussian distribution, the estimated time delay is obtained as
The parameter estimation of the target at the communication end can be used for eliminating the target echo interference of the radar transmitting signal at the communication end, and the communication signal reflected by the target can also be utilized. Echo signalTime delay ∈>Replaced by estimated time delay->Obtain->Estimate of +.>To simplify the analysis, assume an estimate of the reflection of the communication signal by the targetError count->Can be ignored. Because of the estimation error, the communication received signal can be written as
wherein
wherein Representation s R,m (t) biasing t. The amount of mutual information can be written as
wherein
Since the communication received signal is a gaussian signal with a mean value of zero, the received signals of different communication receivers are independent and uncorrelated at different moments. For different N 1 and N2 ，k 1 and k2 ，Assume again that the time delay estimation error n of arrival at the communication receiving end via the target reflection Ct,n′m′ and nRt,n′m Within a reasonable range, make +.>Is much smaller than Q C Is described. Therefore, can be +.>Approximately as a diagonal matrix. Further using the diagonal matrix algorithm, the mutual information quantity can be expressed as
wherein
According to the theory of cooperative game, a cooperative game model is established, the game participants comprise a radar and a communication party,the policy set of radar is +.>The policy set of communication is->The symbol x represents a cartesian product. Representing the utility function u of the radar with a reduced radar detection probability (see (15)) R (E R ,E C ) The utility function of the communication expressed by the simplified communication mutual information quantity (see formula (25)) is u C (E R ,E C )。
The power allocation problem is how to allocate the transmit power of the radar and communication systems under the total power constraint to achieve fairness. Defining the negotiating breaking point asNash product is->The optimization problem can be described as
Solves the problems ofSee iterative NBS algorithm proposed by the present invention.
The steps for the iterative NBS algorithm are as follows:
initializing: initial valueLagrangian multiplier->Step size s t Iterative step length k 1 The iteration number n=0, the convergence factor epsilon > 0.
Step 1: when the number of iterations is n+1The updated formula of (2) is
Step 2: when the number of iterations is n+1The updated formula of (2) is
Step 3: if obtained in steps 1 and 2Beyond the feasible region, i.e.)>Updating ∈with orthogonal projection operator>The orthogonal projection operator P is
P＝I n -A T (AA T ) -1 A
wherein In Represented as an n-order unit array,updating the formula to
wherein If none of the above areas exceeds the feasible area, the method proceeds to step 4.
Step 4: when the number of iterations is n+1Updating the formula to
wherein
Step 5: if it isAnd->Let n=n+1, re-enter step 1,2,3,4.
The algorithm ends: and obtaining the optimal power distribution.
Three simulation examples and comparison curves are given for the power distribution method based on the cooperative game.
The simulation parameters were set as follows: the system antennas are assumed to be in a two-dimensional cartesian coordinate system and are each 70 km from the origin of coordinates. Consider the MIMO radar to have M R =2 transmit antennas, positions (70, 0) km and (-70, 0) km, N R =3 receiving antennas, positions (66,24) km, (-54,45) km and (-12, -69) km; consider MIMO communication with M C =2 transmit antennas, located at (0,70) km and (0, -70) km, N C =3 receive antennas, positions (-24,66) km, (-45,64) km and (69, -12) km; the coordinates of the target position to be estimated are (50, 30) meters, and the antenna position and the target position are shown in fig. 1. The MIMO radar transmit signal is a single gaussian pulse signal,f Δ =125 hz, t=0.01 s. The transmit signals for MIMO communications employ orthogonal frequency division multiplexing signals,T′＝0.01s，Δf＝125Hz，N f =6. Covariance matrix->The signal clutter noise ratio is->Total power of transmitting antenna of cooperative integrated system>Kilowatt, scnr= -6dB.
In simulation 1, the convergence condition is set as phaseThe difference between the power of two adjacent iterations is 10 -5 The dimensions of the tile are such that,to negotiate the breaking point. As shown in fig. 2, it can be derived that the transmit power tends to stabilize after about 25 iterations.
In simulation 2, the optimal individual coefficient paretoFraction of the NSGA-II algorithm is 0.8, the population size is 100, the maximum genetic algebra generation is 200, the stop algebra GenLimit is 200, the fitness function deviation TolFun is 1e-100, the obtained pareto boundary is shown as fig. 3 (a), the theoretical pareto boundary is not obtained by the NSGA-II algorithm relative to the NBS algorithm, and the result obtained by the NBS algorithm is superior to the NSGA-II algorithm. When pareto fraction was modified to 0.7, fig. 3 (b) was obtained, and it can be seen that the agreement was reached when the point of the negotiating fracture was (0, 0), and the theoretical pareto optimum was reached, and when the point of the negotiating fracture was (1, 0), the NSGA-II algorithm was still inferior to the result obtained by the NBS algorithm.
In the simulation 3, under analysis of different SCNR, the NE algorithm based on three-point search, the iterative NBS algorithm (negotiating the breaking point (1, 0)), the uniform distribution and the random distribution are adopted, and under four power distribution methods, the radar detection probability and the communication mutual information quantity change. With the random allocation method in fig. 4, better detection performance than the uniform allocation, iterative NBS algorithm can be obtained when the SCNR is less than-2 dB, but the communication performance is poor. The uniform distribution and iterative NBS algorithm can obtain similar detection probability, but the mutual information amount obtained by the iterative NBS algorithm is far higher than that of other methods. And comparing the binary search NE algorithm with the iterative NBS algorithm, wherein the radar detection performance obtained by the binary search NE algorithm is far superior to that of the iterative NBS algorithm when the SCNR is smaller than 0dB, but the iterative NBS algorithm is better in the communication mutual information quantity diagram. Along with the continuous increase of SCNR, the interference signal strength of the radar is weakened, and at the moment, good target detection performance can be achieved without too much radar power. The increase of SCNR improves the cooperation benefit brought by the iterative NBS algorithm, and the system distributes more power to the communication terminal, so that the performance of the communication terminal is optimal on the premise of optimal target detection probability. Figure 5 shows the impact of different allocation algorithms on the overall performance of the system. Fig. 5 shows that the overall performance of the system obtained by using the iterative NBS algorithm is superior to the rest of the algorithms at different SCNRs. The iterative NBS algorithm mainly takes the overall performance as a main part, and the algorithm sacrifices part of radar detection probability under the simulation scene of the invention so as to obtain the optimal overall performance of the system. The algorithm proposed by the patent can provide reference for a system designer, and an iterative NBS algorithm is adopted when overall performance is considered.
Claims (1)
1. A cooperative MIMO radar communication integrated system power distribution method based on cooperative game, the method includes:
step 1: let MIMO radar have N R Multiple receiving antennas M R Multiple transmit antennas, MIMO communication with N C Multiple receiving antennas M C A plurality of transmit antennas, and each antenna location is known to radar and communications; let the total emission power of the cooperative integrated system beThe total transmit power of the radar is +.>The transmit power of the mth radar transmit antenna is denoted as E R,m The total transmit power of the communication is +.>The transmission power of the m' th communication transmission antenna is E C,m′ The radar transmit power allocation weight is defined as η R ，
Step 2: defining the observed value of the received signal of the MIMO radar end as a vector r R The observed value of the received signal of the MIMO communication terminal is vector r C ：
wherein URt and UR Representing a radar-radar channel matrix, a block diagonal matrix comprising target reflection coefficients, fading coefficients, respectively, U Ct and UC Representing a communication-radar channel matrix, a block diagonal matrix comprising target reflection coefficients, fading coefficients, s Rt and sR Radar signal vector s representing reflected and direct paths through the target Ct and sC A communication signal vector representing the reflected and direct paths through the object, U Rt and UR A block diagonal matrix representing a radar-communication channel matrix, U, comprising target reflected channel gain, direct path channel gain, respectively Ct and UC A communication-communication channel matrix is represented, comprising a block diagonal matrix of channel gains for the target reflection and channel gains for the direct path, respectively, and />Radar signal vectors representing the reflected and direct paths of the object received by the communication receiver, < >> and />A communication signal vector, w, representing the target reflected and direct paths received by the communication receiver R Representing an additive Gaussian white noise vector with zero mean and a covariance matrix of Q R ，w C Representing an additive Gaussian white noise vector, obeying zero mean and covariance matrix of Q C ；
Step 3: defining the assumption of the existence of a target asThe assumption that the target does not exist is +.>Establishing a hypothesis testing problem to obtain a log-likelihood ratio, and writing detection statistics into the log-likelihood ratio:
step 4: NP criterion specifies false alarm probability P FA Below a certain value alpha f Under the condition of (1), calculating the maximum detection probability and giving the false alarm probability alpha f Carrying out detection statistics to obtain radar target detection probability P D ：
Function ofRepresenting a standard gaussian complementary distribution function, +.>Sigma is the detection statistic T R Standard deviation of (1)/(c)>Representing mathematical expectations for solving for random variables; and because ofThe ratio of the two is proportional toTo represent the detection probability P D In the case of a change in (a),
wherein the parameter alpha m,m′ ，β m,m′ ，γ m,m′ Related to target reflection coefficients, radar and communication transmit signals, time delays;
step 5: according to the definition of the mutual information quantity, the communication mutual information quantity MI is calculated as follows:
wherein ,the method comprises radar transmitting signals, reflection coefficients, target time delay and target estimation error items;
wherein ,ζRt,n′m Representing the channel gain of the radar channel reflected by the target,indicating the time delay under the radar channel through the reflection of the target,/->Representation s R,m (t) bias the t, s R,m (t) represents a radar-transmitted signal,n Rt,n′m representing the estimation error, T, of the target parameter estimation s Representing a time sampling interval; k represents different sample samples, k=1, 2,;
assuming that the communication receiving signals are Gaussian signals with zero mean value, the receiving signals of different communication receivers are mutually independent and uncorrelated at different observation moments, and the time delay estimation error of the communication receiving end is within a reasonable range, thereby meeting the requirements ofThe corresponding element is much smaller than Q C Will be->Approximating a diagonal matrix, using a diagonal matrix algorithm, the mutual information quantity MI is:
wherein ,χm,m′,n′,k Related to the following four parameters: communication signal vector of communication receiving end and />Direct path channel gain, reflected channel gain via target; due to the cooperation of radar communication, the channel gain and the direct path access gain reflected by the target can be obtained by a preprocessing mode, and the phi is obtained by the method n′,m,k The warp of (3)The channel gain of the target reflection is obtained by a preprocessing mode and is influenced by a time delay estimation error;
step 6: based on the knowledge of the cooperative game in the game theory, there is a unique and fair Nash bargaining solutionIt can be obtained by maximizing the nash product:
wherein the negotiating breaking point isAnd solving by adopting an iterative NBS algorithm.
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