CN115441906A - Cooperative MIMO radar communication integrated system power distribution method based on cooperative game - Google Patents

Cooperative MIMO radar communication integrated system power distribution method based on cooperative game Download PDF

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CN115441906A
CN115441906A CN202210873425.8A CN202210873425A CN115441906A CN 115441906 A CN115441906 A CN 115441906A CN 202210873425 A CN202210873425 A CN 202210873425A CN 115441906 A CN115441906 A CN 115441906A
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朱竣泽
何茜
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University of Electronic Science and Technology of China
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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 cooperative MIMO radar communication integrated system is characterized in that under the Neyman-Pearson criterion, the target detection probability is used as a radar performance evaluation index, and the communication mutual information quantity is used as a communication performance evaluation index. In the method, a radar subsystem and a communication subsystem are regarded as two cooperative game parties, the total power limitation of the system is considered, and an optimization problem based on Nash bargaining solution is established. According to the cooperative game theory, the Nash bargaining solution obtained by utilizing the iterative NBS algorithm meets the properties of pareto optimality, fairness and the like. The iterative NBS algorithm can adjust whether system performance is more prone to radar or communication by negotiating the point of failure.

Description

Cooperative MIMO radar communication integrated system power distribution method based on cooperative game
Technical Field
The invention belongs to the field of signal processing, relates to the power distribution problem of a cooperative MIMO radar communication integrated system, and is suitable for designing the antenna transmitting power of an MIMO radar subsystem and an MIMO communication subsystem in the cooperative integrated system.
Background
In the past research, radar and communication generally work independently, and in recent years, many experts and scholars focus on radar and communication integrated systems. Radar systems and communication systems have many similarities, for example, in hardware, radio frequency parts of the two systems are similar, signals are radiated to the space through an antenna and then processed at a receiving end, and the antenna, a transmitter, a receiver and the like have common possibility. The difference of the two is reflected in signal processing, information of radar comes from a target, and information of communication comes from a transmitter. Therefore, radar and communication systems have a basis for achieving integration.
In recent years, the commercial 5G technology and the research of 6G technology and the development of millimeter wave radar provide fertile soil for the development of radar communication integration. Through extensive research and verification, the existing research divides radar communication integrated systems into the following three categories: the system comprises (1) a radar communication coexistence system, (2) a cooperative radar communication coexistence system and (3) a dual-function radar communication integrated system. The radar communication in the radar communication coexistence system shares resources, but the radar and communication systems are designed separately. The present invention is based on a cooperative 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 simultaneously realize radar and communication functions, so that the dual-function integrated system has high integration.
In the field of communications, as early as the 4G era, MIMO (Multiple Input Multiple Out) technology is widely used, and the key technology of 5G is massive MIMO antenna array and beam forming technology. At present, due to the maturity of millimeter wave technology, millimeter wave radars are rapidly developed in the fields of automobile auxiliary driving, security inspection, medical detection and the like. Similar to communication, millimeter wave technology brings higher bandwidth, but transmission loss is high, and combining millimeter wave and massive MIMO technology can complement advantages. The MIMO technology can improve the precision of target parameter estimation and the target detection capability. The MIMO technology applied in the communication field can improve the channel capacity, improve the reliability of the channel and reduce the error rate.
The power allocation problem has been an important issue in the research of various types of systems. The MIMO system that this patent was considered is the split antenna MIMO system, and present MIMO radar divide into common antenna MIMO radar and split antenna MIMO radar. The multi-angle target detection can be realized for the MIMO radar with the split antennas, and the target detection performance is improved. The method considers the power distribution problem under the condition that the total power of the radar and the communication is limited, 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 meaning.
Current applications to gaming theory focus on cooperative gaming and non-cooperative gaming. In the field of radar, game theory is often used for researching the mutual influence process between different antennas of the MIMO radar and different base radars, the mutual influence process between the radar and jammers, the cooperation and confrontation between the radar and targets, and the like. In the field of communication, cooperative game is often adopted to study how to reasonably and fairly distribute resources of each system to finally realize the optimal overall performance. The game theory provides a brand-new visual angle and a model, and provides an efficient solution for solving complex problems such as a non-convex multi-target optimization problem and the like.
Therefore, aiming at the problem of optimizing the power distribution of the communication integrated transmitting antenna of the cooperative MIMO radar, the invention provides a cooperative game model, and provides an iterative Nash locking Solution (NBS) algorithm to realize the optimization problem of the overall performance of the radar and the communication under the condition that the total power of the system is limited.
Disclosure of Invention
The invention provides a power distribution method of a cooperative MIMO radar communication integrated system, which combines cooperative game knowledge and takes target detection probability as a radar performance evaluation index and communication mutual information quantity as a communication performance evaluation index under a Neyman-Pearson criterion. In the method, a radar subsystem and a communication subsystem are regarded as two cooperative game parties, the total power limitation of the system is considered, and an optimization problem based on Nash bargaining solution is established. According to the cooperative game theory, the Nash bargaining solution obtained by utilizing the iterative NBS algorithm meets the properties of pareto optimality, fairness and the like. The iterative NBS algorithm can adjust whether system performance is more prone to radar or communication by negotiating the point of failure.
The technical scheme of the invention is that a 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 A receiving antenna, M R One transmitting antenna, MIMO communication has N C A receiving antenna, M C Transmitting antennas, each antenna position being known for both radar and communication; the total transmitting power of the integrated system is
Figure BDA0003758369780000021
The total transmitting power of the radar is
Figure BDA0003758369780000022
The transmission power of the mth radar transmission antenna is denoted as E R,m Total transmission power of the communication is
Figure BDA0003758369780000023
The m' th communication transmitting antenna has the transmitting power of E C,m′ The radar transmission power distribution weight is defined as eta R ，
Figure BDA0003758369780000024
Step 2: defining the observed value of the MIMO radar end receiving signal as a vector r R The observed value of the MIMO communication terminal receiving signal is a vector r C ：
Figure BDA0003758369780000031
Figure BDA0003758369780000032
wherein URt and UR Representing a radar-radar channel matrix, comprising a block diagonal matrix of target reflection coefficients, fading coefficients, respectively, U Ct and UC A block diagonal matrix s representing a communication-radar channel matrix and including a target reflection coefficient and a fading coefficient respectively Rt and sR Representing the warp of a targetRadar signal vector of the direct and direct paths, s Ct and sC Representing vectors of communication signals, U, reflected and direct paths through the object Rt and UR Representing a radar-communication channel matrix, comprising a block diagonal matrix of target reflection channel gains, direct path channel gains, respectively, U Ct and UC A block diagonal matrix representing a communication-communication channel matrix containing channel gains for target reflections, and direct path channel gains, respectively,
Figure BDA0003758369780000033
and
Figure BDA0003758369780000034
representing the radar signal vectors received by the receiving end of the communication via the target reflection and direct path,
Figure BDA0003758369780000035
and
Figure BDA0003758369780000036
vector of communication signals, w, representing reflected and direct paths through the target received at the receiving end of the communication R Represents an additive white Gaussian noise vector with a mean of zero and a covariance matrix of Q R ，w C Representing an additive white Gaussian noise vector, obeying a zero mean and having a covariance matrix of Q C ；
And step 3: the assumption defining the existence of the target is
Figure BDA0003758369780000037
The assumption that the target does not exist is
Figure BDA0003758369780000038
Establishing a hypothesis test problem to obtain a log-likelihood ratio, and writing the detection statistics as:
Figure BDA0003758369780000039
and 4, step 4: in general, NP criteria specify false alarm profilesRate P FA Below a certain value alpha f In the case of (2), the maximum detection probability is calculated, giving a false alarm probability α f And introducing the detection statistic to obtain the radar target detection probability P D ：
Figure BDA00037583697800000310
The function Q (-) represents a complementary distribution function,
Figure BDA00037583697800000311
σ is the detection statistic T R Standard deviation of (2), operator
Figure BDA00037583697800000315
Expressing the mathematical expectation of solving random variables; and because of
Figure BDA00037583697800000313
Oc indicates that the two are in direct proportion, indicated by
Figure BDA00037583697800000314
To represent the detection probability P D In the case of a change in the state of the art,
Figure BDA0003758369780000041
wherein the parameter alpha m,m′ ，β m,m′ ，γ m,m′ Relative to target reflection coefficient, radar and communication emission signals, time delay;
and 5: according to the mutual information quantity definition, the communication mutual information quantity MI is calculated as:
Figure BDA0003758369780000042
wherein
Figure BDA0003758369780000043
Comprising radar hairThe method comprises the steps of transmitting power, radar transmitting signals, reflection coefficients, target time delay and target estimation error items, assuming that communication receiving signals are Gaussian signals with the mean value of zero, at different observation moments, the receiving signals of different communication receivers are independent and uncorrelated, assuming that the time delay estimation error of a communication receiving end is in a reasonable range, and meeting the requirement that the time delay estimation error of the communication receiving end is in the reasonable range
Figure BDA0003758369780000044
Is much smaller than Q C Each element of (1) will
Figure BDA0003758369780000045
Approximated as a diagonal matrix, using the diagonal matrix algorithm, the mutual information MI can be written as:
Figure BDA0003758369780000046
can see chi m,m′,n′,k Communication signal vector with communication receiving end
Figure BDA0003758369780000047
The direct path channel gain is related to the target reflection channel gain; channel gain via target reflection and direct path gain via pre-processing means, psi, due to radar communication cooperation n′,m,k The channel gain reflected by the target in the system is obtained in a preprocessing mode and is influenced by time delay estimation errors;
step 6: based on cooperative game knowledge in game theory, there is a unique and fair Nash bargained solution
Figure BDA0003758369780000048
Can be obtained by maximizing the nash product:
Figure BDA0003758369780000049
Figure BDA00037583697800000410
Figure BDA00037583697800000411
E R,m ,E C,m′ ≥0
wherein the point of failure is negotiated as
Figure BDA00037583697800000412
And (5) solving by adopting an iterative NBS algorithm.
The iterative NBS algorithm provided by the invention is suitable for mutual cooperation between the radar and the communication subsystem, communication signals can be accurately decoded at a radar receiving end, and the target reflection coefficient and channel gain of the radar and the communication can be obtained through preprocessing. Under the condition that the total power of the system is limited, the radar and communication overall performance is optimal, and whether the overall performance emphasizes radar or communication can be realized by adjusting negotiation breaking points. The iterative NBS algorithm emphasizes the overall performance of the system, can realize pareto optimality, 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 cooperative MIMO radar communication integrated system.
Drawings
Fig. 1 shows a distribution diagram of the positions of the transmitting and receiving antennas 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 showing the relationship between the target detection probability and the mutual information amount under the NSGA-II algorithm and the iterative NBS algorithm.
Fig. 4 is a graph of the variation of the target detection probability and the communication mutual information amount with the signal-to-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 graph showing the overall performance of the system varying with SCNR under the iterative NBS algorithm, the trisection search Nash equilibrium algorithm, the uniform distribution method and the random distribution method.
Detailed Description
Defining the signal transmitted by the m-th radar transmitting antenna as
Figure BDA0003758369780000051
By s R,m (T) denotes a radar transmission signal, T s Denotes the time sampling interval, with K (K =1, 2.., K) denoting the different sampling samples, and s for the communication end C,m′ (t) represents a communication transmission signal, and a transmission signal of a communication transmission antenna is represented as
Figure BDA0003758369780000052
Considering that both radar and communication signals have been normalized,
Figure BDA0003758369780000053
according to a model of the radar received signal, at kT s Time, nth (N =1,., N) R ) The received signal of each radar receiving antenna is represented as
Figure BDA0003758369780000054
wherein ζRt,nm and ζCt,nm′ Representing the reflection coefficient of the target for different paths. Similarly, ζ R,nm and ζC,nm′ Representing the radar fading coefficients, tau, under different paths Rt,nm and τCt,nm′ Representing the time delay, τ, of reflections off the target under different paths R,nm and τC,nm′ Representing the time delay of the direct path under the different paths. w is a R,n [k]Gaussian white noise signals, noise of different paths is zero-mean and independently and uniformly distributed.
The antenna position, the transmitting signal, the transmitting power and other information of the cooperative integrated system are mutually shared between the radar and the communication. And the communication signal can be decoded and reconstructed more accurately by using the communication information at the radar receiving end. The target reflection coefficient of the radar can be known by means of preprocessing.
The observation vector of the nth receiving antenna at the MIMO radar end at different time can represent r R,n ＝(r R,n [1],...,r R,n [K]) T The observation vector of the MIMO radar end can be written as
Figure BDA0003758369780000061
wherein
Figure BDA0003758369780000062
Figure BDA0003758369780000063
Figure BDA0003758369780000064
Figure BDA0003758369780000065
Figure BDA0003758369780000066
Figure BDA0003758369780000067
Figure BDA0003758369780000068
Figure BDA0003758369780000069
Figure BDA00037583697800000610
Diag {. Is } representation BlockDiagonal matrix, w R Is an additive white Gaussian noise vector with a mean of zero and a covariance matrix of Q R ，
Figure BDA00037583697800000611
At the radar receiving end, if the radar task is to detect the presence of a target, then the hypothesis testing problem is expressed as
Figure BDA00037583697800000612
Figure BDA00037583697800000613
Assuming that the target does not exist, the observation vector r is then R Is written as
Figure BDA00037583697800000614
Figure BDA00037583697800000615
Assuming that an object exists, the observation vector r is then R Is written as
Figure BDA00037583697800000616
Accordingly, the log-likelihood ratio is expressed as
Figure BDA0003758369780000071
The sum r is found in formula (7) R Related terms, resulting in detection statistics expressed as
Figure BDA0003758369780000072
In a general radar detection problem, judgment can be performed only through a received signal, the prior probability and the cost cannot be known in advance, and a Neyman-Pearson criterion is adopted as a main judgment criterion at this time. In general, the Neyman-Pearson criterion specifies that the false alarm probability is below a certain value α f And calculating the maximum detection probability. Because the false alarm probability and the detection probability are usually 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 can be calculated on the premise of giving the maximum acceptable false alarm probability. The false alarm probability is expressed as
Figure BDA0003758369780000073
wherein
Figure BDA0003758369780000074
Indicating that there is actually a target present. The detection probability is expressed as
Figure BDA0003758369780000075
Bringing the detection statistic into (9)
Figure BDA0003758369780000076
Where beta represents the detection threshold and where,
β＝σQ -1 (α f )+μ 0 (12)
thus, the target detection probability of a radar is expressed as
Figure BDA0003758369780000077
wherein
Figure BDA0003758369780000078
It is known that the standard Gaussian complement distribution function Q (-) is a monotonically decreasing function when the argument is greater than zero, and thus P D And (Q) -1 (α f )+(μ 0 -μ 1 ) /σ) is inversely proportional to the region greater than zero. Suppose Q -1 (α f ) A value of greater than (mu) 0 -μ 1 ) σ (in actual simulation signal selection, this assumption generally holds).
Will further (mu) 0 -μ 1 ) Spread out by
Figure BDA0003758369780000079
And is
Figure BDA0003758369780000081
Can obtain
Figure BDA0003758369780000082
wherein
Figure BDA0003758369780000083
At kT s Time, N '(N' =1, 2., N) C ) The received signal of a communication can be expressed as
Figure BDA0003758369780000084
wherein ζCt,n′m′ and ζRt,n′m Representing the channel gain reflected by the target for different channels. ζ represents a unit R,n′m and ζC,n′m′ Representing the direct path channel gain at different channels,
Figure BDA0003758369780000085
and
Figure BDA0003758369780000086
representing the time delay of the reflection off the target under different channels,
Figure BDA0003758369780000087
and
Figure BDA0003758369780000088
representing the time delay of the direct path under different channels. w is a C,n′ [k]The Gaussian white noise signals received by the communication receiving end are zero-mean and independently distributed.
In the cooperative integrated system, the antenna positions, the transmission signals and the transmission power of the radar and the communication are known through cooperation. The communication receiving end can estimate the target position by using the target echo signal of the radar, thereby eliminating the signal interference of the radar to the communication direct path and the target reflected path.
The observation vectors of the n' th receiving antenna at different time at the MIMO communication end are represented as r C,n′ ＝(r C,n′ [1],...,r C,n′ [K]) T The observation vector of the MIMO communication terminal can be written as
Figure BDA0003758369780000089
wherein UCt 、U C 、U Rt 、U R Definition of (2) and U Ct 、U C 、U Rt 、U R In a similar manner to the above-described embodiments,
Figure BDA00037583697800000810
definition of (1) and s Ct 、s C 、s Rt 、s R Similarly. w is a C Subject to mean of zero and covariance matrix of Q C The white gaussian noise signal of (a) is,
Figure BDA00037583697800000811
at MIMO communication receiving end, the direct wave interference of the communication receiving end radar can be eliminated by cooperatively sharing the radar positionAnd further eliminating the interference of the 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 Can be expressed as
Figure BDA0003758369780000091
Wherein A is a covariance matrix and A is a covariance matrix,
Figure BDA0003758369780000092
Figure BDA0003758369780000093
the patent adopts ML estimation method, ML estimation of the target position,
Figure BDA0003758369780000094
wherein
Figure BDA0003758369780000095
Is an estimate of the target location. The estimated value of the target position influences the time delay obtained by radar and communication through a target reflection path, and the estimation error n of the target parameter estimation is assumed Ct,n′m′ and nRt,n′m Obeying a Gaussian distribution, the estimated delay is
Figure BDA0003758369780000096
The parameter estimation of the target at the communication end can be used for eliminating the target echo interference from radar transmission signals at the communication end, and communication signals reflected by the target can also be utilized. Echo signal
Figure BDA0003758369780000097
Time delay in
Figure BDA0003758369780000098
Substitution by estimated time delay
Figure BDA0003758369780000099
To obtain
Figure BDA00037583697800000910
Is estimated value of
Figure BDA00037583697800000911
To simplify the analysis, the estimation error of the reflection of the communication signal by the target is assumed
Figure BDA00037583697800000912
Can be omitted. Due to estimation errors, the communication reception signal can be written as
Figure BDA00037583697800000913
wherein
Figure BDA00037583697800000914
wherein
Figure BDA00037583697800000915
Denotes s R,m (t) calculating a partial derivative of t. The amount of mutual communication information can be written as
Figure BDA00037583697800000916
wherein
Figure BDA00037583697800000917
Since the communication reception signal is a gaussian signal with a mean value of zero, the reception signals of different communication receivers are independent and uncorrelated with each other at different times. For different N 1 and N2 ，k 1 and k2 ，
Figure BDA0003758369780000101
Further assume that the time delay estimation error n arriving at the receiving end of the communication via the target reflection Ct,n′m′ and nRt,n′m Within a reasonable range, so that
Figure BDA0003758369780000102
Are much smaller than Q C Each element of (a). Thus, can be connected
Figure BDA0003758369780000103
Approximated as a diagonal matrix. Further using the diagonal matrix algorithm, the amount of mutual information can be expressed as
Figure BDA0003758369780000104
wherein
Figure BDA0003758369780000105
According to the cooperative game theory, a cooperative game model is established, game participants comprise two parties of radar and communication,
Figure BDA0003758369780000106
the strategy set of the radar is
Figure BDA0003758369780000107
The strategy set of communication is
Figure BDA0003758369780000108
Symbol x represents a cartesian product. The utility function u of the radar is expressed by the simplified radar detection probability (see equation (15)) R (E R ,E C ) The utility function of the communication is represented as u by the simplified mutual traffic information quantity (see equation (25)) C (E R ,E C )。
The power allocation problem is how to allocate the transmit power of the radar and communication systems to achieve fairness under total power constraints. Defining negotiation failure point as
Figure BDA0003758369780000109
Nash product is
Figure BDA00037583697800001010
The optimization problem can be described as
Figure BDA00037583697800001011
Means for solving the problems
Figure BDA00037583697800001012
See the iterative NBS algorithm proposed by the present invention.
The steps for the iterative NBS algorithm are as follows:
initialization: initial value
Figure BDA00037583697800001013
Lagrange multiplier
Figure BDA00037583697800001014
Step length s t Step size k of iteration 1 The number of iterations n =0, the convergence factor epsilon > 0.
Step 1: when the number of iterations is calculated as n +1
Figure BDA0003758369780000111
Is updated by the formula
Figure BDA0003758369780000112
Figure BDA0003758369780000113
Step 2: calculating the number of iterationsWhen n +1
Figure BDA0003758369780000114
Is updated by the formula
Figure BDA0003758369780000115
Figure BDA0003758369780000116
And 3, step 3: if obtained in steps 1 and 2
Figure BDA0003758369780000117
Beyond the feasible domain, i.e.
Figure BDA0003758369780000118
Updating with orthogonal projection operators
Figure BDA0003758369780000119
The orthogonal projection operator P is
P＝I n -A T (AA T ) -1 A
wherein In Is expressed as a unit matrix of order n,
Figure BDA00037583697800001110
update the formula to
Figure BDA00037583697800001111
wherein
Figure BDA00037583697800001112
If no, go to step 4.
And 4, step 4: when the number of iterations is calculated as n +1
Figure BDA00037583697800001113
Update the formula to
Figure BDA0003758369780000121
wherein
Figure BDA0003758369780000122
And 5: if it is
Figure BDA0003758369780000123
And is provided with
Figure BDA0003758369780000124
Let n = n +1 and re-enter step 1,2,3,4.
And (4) finishing the algorithm: and obtaining the optimal power distribution.
Three simulation examples and comparison curves are given for the cooperative game based power distribution method.
The simulation parameters are set as follows: the system antennas are assumed to be in a two-dimensional cartesian coordinate system and are each 70 kilometers from the origin of coordinates. Consider that MIMO radar has M R =2 transmitting antennas located at (70, 0) km and (-70, 0) km, with N R =3 receiving antennas, positions are (66, 24) km, (-54, 45) km and (-12, -69) km; consider that MIMO communication has M C =2 transmitting antennas, located at (0, 70) km and (0, -70) km, having 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 transmits signals which are single Gaussian pulse signals,
Figure BDA0003758369780000125
f Δ =125hz, t =0.01s. The transmission signal of MIMO communication employs an orthogonal frequency division multiplexing signal,
Figure BDA0003758369780000126
T′＝0.01s，Δf＝125Hz，N f and (6). Covariance matrix
Figure BDA0003758369780000127
Signal to clutter noise ratio of
Figure BDA0003758369780000128
Total power of transmitting antenna of cooperative integrated system
Figure BDA0003758369780000129
Kilowatts, SCNR = -6dB.
In simulation 1, the convergence condition is set to be 10 as the difference between the powers of two adjacent iterations -5 The number of the tiles is such that,
Figure BDA00037583697800001210
to negotiate the break point. As shown in fig. 2, it can be concluded that the transmit power tends to stabilize after about 25 iterations.
In simulation 2, the optimal individual coefficient pareto frame using the NSGA-II algorithm is 0.8, the population size popup size is 100, the maximum genetic Generations are 200, the stop algebra stalgenlimit is 200, the fitness function deviation TolFun is 1e to 100, and the resulting pareto boundary is as shown in fig. 3 (a). Modifying the pareto fraction to 0.7, results in fig. 3 (b), which shows that the theoretical pareto optimum has been achieved for agreement at the negotiation breaking point (0, 0), and that the results obtained using the NSGA-II algorithm are still inferior to the results obtained using the NBS algorithm at the negotiation breaking point (1, 0).
In the simulation 3, under different SCNRs, changes of radar detection probability and communication mutual information amount are analyzed by adopting an NE algorithm based on three-section searching, an iterative NBS algorithm (negotiation cracking points (1, 0)), uniform distribution and random distribution under four power distribution methods. In fig. 4, when the SCNR is less than-2 dB, the random allocation method can obtain better detection performance than the uniform allocation and iterative NBS algorithm, but the communication performance is poor. The uniform distribution and iterative NBS algorithm can obtain similar detection probability, but the iterative NBS algorithm obtains much higher mutual information amount than other methods. Comparing the three-division search NE algorithm with the iterative NBS algorithm, the radar detection performance obtained by the three-division search NE algorithm is far better than that of the iterative NBS algorithm when the SCNR is less than 0dB, but the iterative NBS algorithm is better in a communication mutual information quantity graph. With the increasing of the 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 cooperative gain brought by the iterative NBS algorithm, and the system distributes more power to the communication end, thereby ensuring that the performance of the communication end is optimal on the premise of optimal target detection probability. Figure 5 shows the effect of different allocation algorithms on the overall performance of the system. Fig. 5 shows that the overall performance of the system obtained by the iterative NBS algorithm is better than that of the rest of the algorithms under different SCNRs. The iterative NBS algorithm is mainly based on overall performance, and under the simulation scene of the invention, the algorithm sacrifices partial radar detection probability to obtain the optimal overall performance of the system. The algorithm proposed by the patent can provide a reference for a system designer, and an iterative NBS algorithm is adopted when the overall performance is considered.

Claims (1)

1. A 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 A receiving antenna, M R A plurality of transmitting antennas, MIMO communication having N C A receiving antenna, M C A plurality of transmit antennas, each antenna location being known for radar and communications; the total transmitting power of the integrated system is
Figure FDA0003758369770000011
The total transmitting power of the radar is
Figure FDA0003758369770000012
The transmission power of the mth radar transmission antenna is denoted as E R,m Total transmission power of communication of
Figure FDA0003758369770000013
Transmission power of m' th communication transmitting antennaA rate of E C,m′ The radar transmission power distribution weight is defined as eta R ，
Figure FDA0003758369770000014
Step 2: defining the observed value of the MIMO radar end receiving signal as a vector r R The observed value of the received signal of the MIMO communication end is a vector r C ：
Figure FDA0003758369770000015
Figure FDA0003758369770000016
wherein URt and UR Representing a radar-radar channel matrix, comprising a block diagonal matrix of target reflection coefficients, fading coefficients, respectively, U Ct and UC A block diagonal matrix s representing a communication-radar channel matrix and including a target reflection coefficient and a fading coefficient respectively Rt and sR Representing the radar signal vector, s, reflected by the target and directed path Ct and sC Representing vectors of communication signals, U, reflected and direct paths through the object Rt and UR Representing a radar-communication channel matrix comprising a block diagonal matrix of target reflection channel gains, direct path channel gains, respectively, U Ct and UC A block diagonal matrix representing a communication-communication channel matrix containing channel gains for target reflections, direct path channel gains, respectively,
Figure FDA0003758369770000017
and
Figure FDA0003758369770000018
representing a radar signal vector received by a communication receiving end via a target reflection and a direct path,
Figure FDA0003758369770000019
and
Figure FDA00037583697700000110
vector of communication signals, w, representing reflected and direct paths through a target received at a receiving end of the communication R Represents an additive white Gaussian noise vector with a mean of zero and a covariance matrix of Q R ，w C Representing an additive white Gaussian noise vector obeying a zero mean and a covariance matrix of Q C ；
And 3, step 3: the assumption defining the existence of the target is
Figure FDA00037583697700000111
The assumption that the target does not exist is
Figure FDA00037583697700000112
Establishing a hypothesis test problem to obtain a log-likelihood ratio, and writing the detection statistics as:
Figure FDA00037583697700000113
and 4, step 4: in general, the NP criterion specifies a false alarm probability P FA Below a certain value alpha f In the case of (2), the maximum detection probability is calculated, giving a false alarm probability α f And substituting detection statistic to obtain radar target detection probability P D ：
Figure FDA0003758369770000021
The function Q (-) represents the complementary distribution function,
Figure FDA0003758369770000022
σ is the detection statistic T R Standard deviation of (1), operator
Figure FDA0003758369770000023
Expressing the mathematical expectation of solving random variables; and because
Figure FDA0003758369770000024
A value of-
Figure FDA0003758369770000025
To represent the detection probability P D In the case of a change in the state of (c),
Figure FDA0003758369770000026
wherein the parameter alpha m,m′ ，β m,m′ ，γ m,m′ Related to target reflection coefficient, radar and communication emission signals, time delay;
and 5: according to the mutual information quantity definition, the communication mutual information quantity MI is calculated as:
Figure FDA0003758369770000027
wherein
Figure FDA0003758369770000028
The method comprises radar transmitting power, radar transmitting signals, reflection coefficients, target time delay and target estimation error items, and assumes that communication receiving signals are Gaussian signals with the mean value of zero, so that the receiving signals of different communication receivers are independent and uncorrelated at different observation moments, and the time delay estimation error of a communication receiving end is assumed to be in a reasonable range, thereby meeting the requirement of the communication receiving end
Figure FDA0003758369770000029
Is much smaller than Q C Will be each element of
Figure FDA00037583697700000210
Approximately as a diagonal momentArray, using the diagonal matrix algorithm, the mutual information MI can be written as:
Figure FDA00037583697700000211
can see chi m,m′,n′,k Communication signal vector with communication receiving end
Figure FDA00037583697700000212
The direct path channel gain is related to the target reflection channel gain; channel gain via target reflection and direct path gain via pre-processing means, psi, due to radar communication cooperation n′,m,k The channel gain reflected by the target is obtained in a preprocessing mode and is influenced by a time delay estimation error;
step 6: based on cooperative game knowledge in game theory, there is a unique and fair Nash bargained solution
Figure FDA0003758369770000031
Can be obtained by maximizing the nash product:
Figure FDA0003758369770000032
Figure FDA0003758369770000033
Figure FDA0003758369770000034
wherein the point of failure is negotiated as
Figure FDA0003758369770000035
And (5) solving by adopting an iterative NBS algorithm.
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