CN115459817B - Power distribution method of cooperative MIMO radar communication integrated system based on non-cooperative game - Google Patents

Power distribution method of cooperative MIMO radar communication integrated system based on non-cooperative game Download PDF

Info

Publication number
CN115459817B
CN115459817B CN202210865380.XA CN202210865380A CN115459817B CN 115459817 B CN115459817 B CN 115459817B CN 202210865380 A CN202210865380 A CN 202210865380A CN 115459817 B CN115459817 B CN 115459817B
Authority
CN
China
Prior art keywords
communication
radar
power
mimo
game
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202210865380.XA
Other languages
Chinese (zh)
Other versions
CN115459817A (en
Inventor
何茜
朱竣泽
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
University of Electronic Science and Technology of China
Original Assignee
University of Electronic Science and Technology of China
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by University of Electronic Science and Technology of China filed Critical University of Electronic Science and Technology of China
Priority to CN202210865380.XA priority Critical patent/CN115459817B/en
Publication of CN115459817A publication Critical patent/CN115459817A/en
Application granted granted Critical
Publication of CN115459817B publication Critical patent/CN115459817B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • 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
    • H04B7/0426—Power distribution
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/391—Modelling the propagation channel
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • 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 power distribution method of a cooperative MIMO radar communication integrated system based on a non-cooperative game, and belongs to the field of communication. Provided is a power distribution method for a collaborative MIMO radar communication integrated system, wherein the target detection probability is used as an MIMO radar performance evaluation index, and the communication mutual information quantity is used as an MIMO communication performance evaluation index. In the method, a radar subsystem and a communication subsystem are regarded as two non-cooperative game parties, a power distribution multi-objective optimization problem based on the non-cooperative game is established, and the limitation of the total power of the system is considered. Searching Nash equilibrium points of radar and communication under the non-cooperative game, wherein the Nash equilibrium points are solutions of power allocation optimization problems, and are obtained through an iteration NE algorithm. The invention also considers the overall performance of the system, and provides an iterative NE algorithm based on three-part search to find the optimal radar and communication power distribution scheme on the premise of realizing the optimal performance of each of the radar subsystem and the communication subsystem.

Description

Power distribution method of cooperative MIMO radar communication integrated system based on non-cooperative game
Technical Field
The invention belongs to the field of communication; the method aims at the power distribution problem of the collaborative MIMO radar communication integrated system and is used for designing the MIMO radar subsystem and the antenna transmitting power of the MIMO communication subsystem in the collaborative integrated system.
Background
Research on radar communication integrated systems originates in military applications and can be traced back to the 70 s of the 19 th century. For fighter planes, ships and other fighter platforms with limited space, load and energy sources, various independent electronic systems can greatly drag and slow the fighter rhythm. The radar communication integrated technology integrates the radar system and the communication system, reduces the weight of equipment, reduces the cost, reduces the electromagnetic scattering area, simultaneously makes the equipment difficult to detect, and simultaneously reduces the system power consumption.
The existing research classifies radar communication integrated systems into the following three categories: (1) a dual-function radar communication integrated system, (2) a radar communication coexistence system, and (3) a cooperative radar communication coexistence system. The dual-function radar communication integrated system has the characteristic of high integration, the radar and the communication system share the same hardware platform at the receiving end or the transmitting end, and integrated signals can be designed to realize two functions of the radar and the communication. Radar and communication in a coexistence system are designed separately and share limited spectrum resources, power resources or other resources. In the traditional coexisting system, various interference suppression methods are mostly adopted to suppress interference signals at a receiving end, and a plurality of resources are consumed for suppressing interference. The estimated target information is utilized at the communication end, the interference of the radar is restrained in a cooperative mode, and the information of a target reflection path of the communication transmitting end is effectively utilized; on the radar side, the cooperation between the radar and the communication enables the communication to assist the radar in target detection.
The radar and communication contemplated by the present invention are both multiple-input multiple-output (MIMO) systems. From the communication perspective, the loss of the power of the receiving antenna is serious because the frequency band of the signal is continuously improved, and the MIMO technology, the large-scale MIMO and the beam forming technology are adopted to generate stronger signals to overcome the loss, so that the signal strength of the receiving end is improved. The MIMO technique can also improve the spatial diversity gain, spatial multiplexing gain, waveform diversity gain, etc. of the radar system. The MIMO technology can effectively improve the system capacity in the field of communication application.
Power is an important resource of radar and communication systems, and research on power allocation problem has been an important subject in the radar and communication fields. The MIMO systems considered by the invention are all split antenna MIMO systems, the channel gains of different paths under the split antennas are different, and the antennas with good channel states can better improve the system performance by distributing more power. The patent considers the power distribution problem under the condition of limited total power of the radar and the communication, designs by taking the performance of each of the optimized radar and the communication as a target, and the optimization problem is a multi-target optimization problem. For the single-objective optimization problem, there is only one general optimal solution, but in the multi-objective optimization problem, the targets are constrained mutually, and there is no possibility that one solution can reach the optimal performance of all targets.
Game theory, which is one of the standard analytical tools in economics, is now applied in the fields of biology, computer science, radar and communications, etc., which is used to understand and predict various behaviors of individuals and to study corresponding strategies. Game theory is often used in the radar field to study the interaction process between each transmitting antenna of MIMO radar, between different bases of multi-base radar, the interaction process between radar and jammer, the antagonism between radar and target, etc., and the optimized parameters may be power, radar waveform, etc. The application of the game theory in the communication field is concentrated in the fields of unmanned aerial vehicle communication networks, satellite communication networks, cognitive radio networks and the like from the current investigation, and the distribution strategy of a Nash equilibrium research system of non-cooperative games is often adopted. In the above fields, various non-convex multi-objective optimization problems are more or less considered, and the game theory provides a brand new view angle and model, so that an efficient solution is provided for solving the complex problems.
Therefore, aiming at the problem of power distribution optimization of integrated transmitting antennas of cooperative MIMO radar communication, the invention provides a non-cooperative game model, provides an iterative Nash Equibrium (NE) algorithm to solve the problem of multi-objective optimization on radar and communication performance under the condition of limited total power of a system, and also provides an iterative NE algorithm based on three-component search to determine the distribution weight of radar and communication power in consideration of the optimal overall performance of the system. The iterative NE algorithm provided by the invention can be obtained in limited iterations based on the iterative NE algorithm of three-part search.
Disclosure of Invention
The invention provides a power distribution method of a collaborative MIMO radar communication integrated system, which takes target detection probability as an MIMO radar performance evaluation index and takes communication mutual information quantity as an MIMO communication performance evaluation index by combining game theory knowledge. In the method, a radar subsystem and a communication subsystem are regarded as two non-cooperative game parties, a power distribution multi-objective optimization problem based on the non-cooperative game is established, and the limitation of the total power of the system is considered. According to the non-cooperative game theory, searching Nash equilibrium points of radar and communication under the non-cooperative game, wherein the Nash equilibrium points are solutions of power allocation optimization problems, and the Nash equilibrium points are obtained through an iterative NE algorithm. The invention also considers the overall performance of the system, and provides an iterative NE algorithm based on three-part search to find the optimal radar and communication power distribution scheme on the premise of realizing the optimal performance of each of the radar subsystem and the communication subsystem.
The technical scheme of the invention is a cooperative MIMO radar communication integrated system power distribution method based on non-cooperative game, which comprises the following steps:
step 1: let MIMO radar have N R Multiple receiving antennas and M R Multiple transmit antennas, MIMO communication with N C Multiple receiving antennas and M C And determining the antenna positions of the transmitting antennas. The total transmitting power of the system isThe total transmit power of the MIMO radar is +.>The transmitting power of the m-th radar transmitting antenna is E R,m The total transmit power of the MIMO communication is +.>The transmission power of the m' th communication transmission antenna is E C,m′ The radar transmit power allocation weight of the system is defined as eta R ，/>
Step 2: establishing a MIMO radar and MIMO communication receiving end signal model of a cooperative integrated system; the observed value of the received signal of the MIMO radar end can be written as a vector r R Receiving signals at MIMO communication endThe observations can be written as vectors r C ：
Wherein U is Rt 、U Ct 、U R 、U C 、U Rt 、U Ct 、U R 、U C Representing a channel matrix, s Rt 、s R 、Representing radar signal vectors s Ct 、s C 、/>Representing the communication signal vector, w 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: constructing a binary hypothesis testing problem, the target existence hypothesis is thatTarget absence assumption +.>Calculating the log-likelihood ratio to obtain an optimal detector:
step 4: given the false alarm probability alpha f Calculating the radar target detection probability P D ：
The function Q (-) represents the right-tail function of the normal distribution,σ 2 to detect statistics T R Variance of (1)/(c)>Representing mathematical expectations; also because of->The oc represents proportional; can use->Representing the probability of detection P D In the course of the variation of (a),
wherein the parameter alpha m,m′ ，β m,m′ ，γ m,m′ Related to the target reflection coefficient, the transmitted signal, the time delay;
step 5: calculating the communication mutual information quantity MI:
wherein the method comprises the steps ofError items introduced for target parameter estimation at the communication end; if the communication receiving signals are Gaussian signals with the mean value of zero, the receiving signals of different communication receivers are independent and uncorrelated; the time delay estimation error of radar and communication reaching the communication receiving end through target reflection is set within a reasonable range, and the +.>The corresponding element is much smaller than Q C Is described. The mutual information quantity MI can be further simplified into
Wherein χ is m,m′,n′,k Related to communication channel gain, communication signal and time delay, ψ n′,m,k Is a term for introducing estimation errors of target parameters;
step 6: according to non-cooperative game knowledge in the game theory, searching for specific implementation of radar and communication optimal strategies in the single game process, wherein the single optimal strategy can be found through the following problems:
the only argument in the first problem is the radar power strategy E R The communication power strategy is known, only the communication power strategy is considered in the second problem, the radar power strategy is known, the initialization power of the radar and the communication is given, the solution of the two problems is calculated as the respective strategy selection of the radar and the communication for the first game, the radar and the communication power obtained by the first game are used as the known quantity for the second game, and the optimal strategy of the radar and the communication for the second game is calculated; the above process is carried out until convergence, and the final Nash equilibrium is obtained; the Nash equilibrium point is calculated by an iterative NE algorithm;
step 7: when considering the overall performance of the system, the following optimization problem can be established:
wherein ω represents the normalized weight;
step 8: writing the optimization problem in the step 6 into a two-step optimization problem for step solving, wherein the two-step optimization problem is written as follows:
the problem (A) is to use a three-part searching algorithm to continuously reduce the interval to find the optimal power distribution weight eta R In the three-point search algorithm, the radar detection probability and the communication mutual information quantity under different power allocation weights need to be calculated, so that the optimal radar and communication power allocation scheme needs to be obtained by solving the problem (B), namely, the Nash equilibrium point is found by adopting the iteration NE algorithm in the step 5.
The iterative NE algorithm provided by the invention is suitable for power distribution weight eta R Under the known condition, the optimal performance of the radar and the communication is realized, nash equilibrium points are found after limited iterations, and the calculation complexity is low. The proposed iterative NE algorithm based on the three-part search is more focused on the overall performance of the system, and compared with a conventional exhaustive search method, the computational complexity is greatly reduced. Therefore, the method provided by the invention is an effective and rapid 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 at η R When=0.4, the transmission power is plotted against the number of iterations.
FIG. 3 is a graph of radar power allocation weights versus target detection probability and mutual information amount under iterative NE algorithm and uniform allocation.
FIG. 4 is a graph of radar power allocation weights versus overall system performance for an iterative NE algorithm, uniform allocation.
Fig. 5 is an iterative process of radar power allocation weight left value in a three-part search iterative NE algorithm.
Detailed Description
For convenience of description, the following definitions are first made:
bold lower case letter represents vector, bold upper case letter tableDisplay matrix (.) * Is conjugated ( T Is transposed ( H For conjugate transpose, diag {.cndot } represents the block diagonal matrix, I is the unit matrix, det (. Cndot.) represents the determinant of the matrix,representing mathematical expectations +.>Representation s R,m (t) deriving the bias for t, the symbol x representing the Cartesian product,
defining the signal transmitted by the mth radar transmitting antenna asWherein s is R,m (T) represents a radar transmission signal, T s Representing the sampling interval, the samples taken at different times are represented by K (k=1, 2, K) represents M '(M' =1,) M C ) The transmission signal of the individual communication transmission antennas is denoted +.>s C,m′ And (t) represents a communication transmission signal. The radar and communication signals are normalized>At kT s Time, the first n (n＝1,...,N R ) The received signal of each radar receiving antenna is represented as
Wherein ζ Rt,nm And zeta Ct,nm′ Respectively representing the target reflection coefficient under the n channels from the radar transmitting end m to the radar receiving end and the target reflection coefficient under the n channels from the communication transmitting end m' to the radar receiving end. Similarly ζ R,nm And zeta C,nm′ Respectively representing radar fading coefficient under mn channel and radar fading coefficient under m' n channel, τ Rt,nm And τ Ct,nm′ Represented by the time delay through the target reflection under the mn channel and the time delay through the target reflection under the m' n channel, respectively, τ R,nm And τ C,nm′ Represented as the time delay of the direct path under the mn channel and the time delay of the direct path under the m' n channel, respectively. w (w) R,n [k]The method is characterized in that the method is used for receiving Gaussian white noise signals by a radar receiving end, and each path of noise is zero-mean and independently distributed.
A cooperative system means that the information of the antenna position, the transmitted signal, the transmitted power, etc. of the radar and the communication are shared with each other. 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.
Definition of MIMO Lei Daduan n The observation vector of the individual receiving antennas is denoted r R,n ＝(r R,n [1],…,r R,n [K]) T . Therefore, the observation vector of the received signal at the MIMO radar side can be written as
Wherein the method comprises the steps of
Additive white gaussian noise vector w R Is zero and the covariance matrix is Q R ，
The hypothesis testing problem may be written as
At the position ofUnder the assumption, the observation vector r R The probability density function of (2) can be expressed as
At the position ofUnder the assumption, the observation vector r R The probability density function of (2) can be expressed as
The log-likelihood ratio can be written as
After the formula (7) is simplified, only four terms and r can be found R The influence of the rest items is ignored in the correlation, and the detection statistic can be obtained as
Based on Neyman-Pearson criterion, it is assumed that the false alarm probability satisfies P FA ≤α f If T R Greater than threshold betaHold true, otherwise->This is true. The threshold value beta is defined by the false alarm probability P FA And (5) determining. False alarm probability P FA And T is R Is used in the relation of (a),
the threshold beta satisfies
β＝σQ -1 (α f )+μ 0 (10)
Therefore, the target detection probability of the radar is expressed as
Wherein the method comprises the steps of
Further willExpansion, get->And->Can be obtained by
Wherein the method comprises the steps of
Similar to the MIMO radar receiving model, at kT s Time, N '(N' =1, 2,) N C ) The received signals of the communication receivers can be written as
Wherein ζ Ct,n′m′ And zeta Rt,n′m The channel gain of the target reflection under the channel from the communication transmitting end m ' to the communication receiving end n ' and the channel gain of the target reflection under the channel from the radar transmitting end m to the communication receiving end n ' are represented. Zeta type R,n′m And zeta C,n′m′ Representing the direct path channel gain under the mn ' channel and the direct path channel gain under the m ' n ' channel,and->Expressed as time delay through target reflection under n'm channel and time delay through target reflection under n'm channel, respectively, +.>Andrepresented as the time delay of the direct path under the n'm channel and the time delay of the direct path under the n'm channel, respectively. w (w) C,n′ [k]The method is characterized by comprising the steps of receiving a zero-mean and independent and uniformly distributed Gaussian white noise signal for a communication receiving end.
At the communication end, the antenna position, the transmission signal and the transmission power of the radar 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 defining the nth' receiving antenna of the MIMO communication end is denoted as r C,n′ ＝(r C,n′ [1],...,r C,n′ [K]) T The observation vector of the received signal of the MIMO communication terminal can be written as
Wherein U is Ct 、U C 、U Rt 、U R Definition of (d) and U Ct 、U C 、U Rt 、U R Similarly to this, the process is carried out,definition of (c) and s Ct 、 s C 、s Rt 、s R Similarly. w (w) C Representing an additive gaussian white noise vector, obeying zero mean and a covariance matrix of Q C ，
At the communication receiving end, the radar position is shared by utilizing cooperation between the radar and the communication, so that direct wave interference of the radar can be eliminated, and interference of radar target echo can be eliminated according to an 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. Communication reception signal r C The probability density function of (2) can be expressed as
Where a is the covariance matrix received with information,
ML estimation of the target position is as follows
Wherein the method comprises the steps ofIs an estimate of the target location. The estimated value of the target position affects the time taken by the radar and communication to travel the target reflection pathDelay, estimation error n of assumed target parameter estimation Ct,n′m′ And n Rt,n′m Obeying Gaussian distribution, the estimated time delay is obtained as
The communication received signal can be written as due to the existence of estimation error
Wherein the method comprises the steps of
Thus, the amount of mutual information can be expressed as
Wherein H (r' C ) For the edge entropy of the image,for conditional entropy, < >>
Assuming that 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 with each other. For different N 1 And N 2 Different observation times k 1 And k 2 ，Assume again that the estimated error n of the time delay with respect to radar and communication arriving at the communication receiver via reflection from the target Ct,n′m′ And n Rt,n′m Within a reasonable range, make +.>The corresponding element is much smaller than Q C Is described. Thus (S)>May be approximated as a diagonal matrix. Using the focusing matrix algorithm, the mutual information quantity is further simplified into
Wherein the method comprises the steps of
According to the non-cooperative game theory, a non-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 utility function of the radar is u R (E R ,E C ) Represented by a simplified radar detection probability (see equation (13)), the utility function of the communication is u C (E R ,E C ) Represented by a simplified amount of mutual information (see formula (23)).
The best strategy for radar and communication is denoted BR r 、BR c ：
Wherein BR is r (E C ) Representing the radar's most significantThe optimal strategy response specifically means that the radar makes the most favorable strategy selection for the radar according to the power distribution strategy of the communication, and accords with the maximization of the benefit of the radar party. Similarly, BR c (E R ) Representing the best policy response of the communication, which selects the most favorable policy for the communication according to the power allocation policy at the radar side, so that the benefit of the current communication is maximized. In practical practice, E C And E is R Both communication and radar power allocation strategies are employed at a previous time.
In a complete information static game, both the radar and the communication continuously change their own optimal strategies, and finally an equilibrium point is reached, at which neither the radar nor the communication has the reason to change their own strategies to change their own performance, which is called as reaching a Nash equilibrium point in the game. Nash equalization can be interpreted as "in the case of only two-player gaming, in the case of a particular radar and communication strategy scenario, its strategy is already optimal for communication in the case of a known radar strategy, and for radar, the radar strategy is already optimal in the case of a known communication strategy, and both radar and communication have no reason to change their own strategies again in search of superior performance".
To find the Nash equilibrium point, we want to find it by simulating the process of both radar and communication gaming. First according to radar and communication optimal strategy BR r ,BR c In the course of finding a single game, the radar and communication optimal strategy is specifically implemented, and finding an optimal strategy can be solved by the following problems:
calculation problemAnd problem->As the respective policy choices for radar and communication first game. The radar and communication power obtained in the first game are taken as known quantities in the second game, and the optimal strategy of the radar and communication in the second game is calculated. The above process is performed until convergence, and final nash equalization can be obtained. Solve the problems->And problem->And the process of realizing Nash equilibrium is shown in the iterative NE algorithm provided by the invention.
The steps for the iterative NE algorithm are as follows:
initializing: initial valueLagrangian multiplier lambda (0) Lagrangian multiplier κ (0) Step size s t Game times n' =0, single game iteration times n=0, convergence factor epsilon > 0.
Step 1: counting the number of iterations of a single game as n+1The updated formula of (2) is
Step 2: counting the number of iterations of a single game as n+1The updated formula of (2) is
Step 3: if obtained in step 1Beyond the feasible region, i.e.)>Updating with projection algorithmThe projection algorithm is realized by a least square method to obtain +.>For updating->The method is realized by the following specific formula:
wherein S is R Representing all possible domains of radar power. Similarly, if step 2 results inThe feasible domain is exceeded and also updated with least squares. If none of the above areas exceeds the feasible area, the method proceeds to step 4.
Step 4: lambda when the number of single game iterations is n+1 is calculated (n+1) And kappa (kappa) (n+1) Updating the formula to
Step 5: if it isAnd->Let n=n+1, re-enter step 1,2,3,4. Otherwise, step 6 is entered.
Step 6: order theIf->And->Let n '=n' +1, re-enter steps 1,2,3,4,5.
The algorithm ends: and obtaining the optimal power distribution.
The iterative NE algorithm implements the optimal radar and communication power allocation strategy under specific radar power allocation weights. If the overall performance of the system is to be optimized, the following optimization problems are established:
the optimization problem is a non-convex optimization problem, and can be written into a two-step optimization problem to solve step by step. The two-step optimization problem is written as:
the above problem can be solved with an iterative NE algorithm for a three-way search, the steps for the iterative NE algorithm for a three-way search are as follows:
initializing: initial value left=0, right=1, convergence accuracy θ.
Step 1: taking eta R =tfel, calculating the optimal power allocation by using iterative NE algorithm, and calculating the overall system performance, denoted as F (left), which is P D (E R ,E C )+ωMI(E R ,E C )。
Step 2: taking eta R =right, the optimal power allocation is calculated with an iterative NE algorithm,and the overall performance of the system was determined and noted as F (right).
Step 3: taking mid 1= (left r+right)/2, calculating the optimal power distribution by using an iterative NE algorithm, and obtaining the overall performance of the system, and marking as F (mid 1).
Step 4: taking mid 2= (mid 1+ right)/2, calculating the optimal power distribution by using an iterative NE algorithm, and calculating the overall performance of the system, and marking as F (mid 2).
Step 5: if F (mid 1) > F (mid 2), right=mid 2 is taken. If F (mid 1) < F (mid 2), take tfel mdil=1.
Step 6: if |left-right| > θ, step 1,2,3,4,5 is re-entered.
The algorithm ends: obtaining radar power allocation weight eta for optimizing overall performance R And a corresponding power allocation strategy.
Three simulation examples and comparison curves are given for a non-cooperative game-based power distribution method.
The simulation parameters were set as follows: each transmit antenna and receive antenna of a MIMO radar and MIMO communication is assumed to be in a two-dimensional cartesian coordinate system, with a distance coordinate system origin of 70 km. Consider the MIMO radar to have M R =2 transmit antennas, the transmit antenna positions are (70, 0) km and (-70, 0) km, N R =3 receive antennas, the receive antenna positions being (66,24) km, (-54,45) km and (-12, -69) km; MIMO communication with M C =2 transmit antennas, the transmit antenna positions being (0,70) km and (0, -70) km, N C =3 receive antennas, the receive antenna positions are (-24,66) km, (-45,64) km and (69, -12) km. Assume that the target position coordinates are located at (50, 30) meters, as shown in FIG. 1. The MIMO radar transmit signal is a frequency-extended single gaussian pulse signal,f Δ =125 hz, t=0.01 s. The transmitting signal of MIMO communication adopts OFDM signal, +.>T′＝0.01s，Δf＝125Hz，N f =6. SynergismVariance matrix->The signal clutter to noise ratio isDefine the total power of the system->SCNR＝-6dB。
In simulation 1, a transmission power allocation weight η is set R =0.4, the convergence condition is that the difference between the powers of two adjacent iterations is 10 -5 A tile. As shown in fig. 2, it can be derived that the radar and communication converge through three iterations, which means that a nash equalization has been achieved. Since the channel conditions of radar emission 1 and communication emission 1 through target reflection are better, and in the cooperative integrated system, the communication also assists the radar in target detection, radar emission 1 and communication emission 1 are allocated more power than radar emission 2 and communication emission 2.
In simulation 2, an iterative NE algorithm and a uniform power distribution strategy are adopted, and the radar target detection probability obtained by the two methods is shown in figure 3. It can be seen that the performance of the iterative NE algorithm is better than that of the uniform distribution method, and the weight η is distributed along with the power R The probability of radar detection increases, although communication can assist the radar in target detection, the probability of radar detection is more affected by radar power, independent of the algorithm employed. Similarly, the algorithm affects the communication performance as shown in fig. 3. At eta R When=0, the total communication power is the largest, and the communication end performance is the best. With eta R The total power distributed by the communication terminal is continuously reduced, and the amount of communication mutual information is also reduced. When eta R When the total communication power is 0, the radar signal does not carry communication information, so that the communication performance cannot be improved, and the algorithm does not bring any improvement. As can be seen in fig. 4, the system performance is a function of η R The increase of (1) is firstly increased and then decreased, the system overall performance is greatly improved by adopting an iterative NE algorithm, and in eta R When= 0.4844The overall performance of the system is maximized.
In simulation 3, the iterative process of applying the ternary search algorithm is shown in fig. 5. Left in the trisection lookup represents eta R Is defined by the lower bound of η R By continuously reducing eta R Determination of eta by the range of possible values R . Taking θ=0.01, it means that the accuracy of the search is one percent, |left-right| < 0.01, the accuracy requirement is met and the iteration is stopped. For a sequence without monotonicity, the sequence length is n and is convex, the time complexity of the three-way search is O (2 log 3 (n)). Using the simulation results of FIG. 5 to represent η R The precision of (2) is 0.01, the precision can be achieved by only 12 iterations, if adopting a poor search rule, 100 different eta are calculated R The same accuracy can be obtained.

Claims (1)

1. A cooperative MIMO radar communication integrated system power distribution method based on non-cooperative game, the method includes:
step 1: let MIMO radar have N R Multiple receiving antennas and M R Multiple transmit antennas, MIMO communication with N C Multiple receiving antennas and M C Determining the positions of the transmitting antennas; the total transmitting power of the system isThe total transmit power of the MIMO radar is +.>The transmitting power of the m-th radar transmitting antenna is E R,m The total transmit power of the MIMO communication is +.>The transmission power of the m' th communication transmission antenna is E C,m′ The radar transmit power allocation weight of the system is defined as eta R ，/>
Step 2: establishing a MIMO radar and MIMO communication receiving end signal model of a cooperative integrated system; the observed value of the received signal of the MIMO radar end can be written as a vector r R The observed value of the received signal of the MIMO communication terminal can be written as a vector r C ：
Wherein U is Rt 、U Ct 、U R 、U C Representing a channel matrix, s Rt 、s R 、Representing radar signal vectors s Ct 、s C 、/> Representing the communication signal vector, w 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: constructing a binary hypothesis testing problem, the target existence hypothesis is thatTarget absence assumption +.>Calculating the log-likelihood ratio to obtain an optimal detector:
step 4: given the false alarm probability alpha f Calculating the radar target detection probability P D ：
Function Q () represents the right-tail function of a normal distribution,σ 2 to detect statistics T R Variance of (1)/(c)>Representing mathematical expectations; also because of->The oc represents proportional; can use->Representing the probability of detection P D In the course of the variation of (a),
wherein the parameter alpha m,m′ ，β m,m′ ，γ m,m′ Related to the target reflection coefficient, the transmitted signal, the time delay;
step 5: calculating the communication mutual information quantity MI:
wherein the method comprises the steps ofError items introduced for target parameter estimation at the communication end; i is a unit array, and if the communication receiving signals are Gaussian signals with the mean value of zero, the receiving signals of different communication receivers are mutually independent and uncorrelated; the time delay estimation error of radar and communication reaching the communication receiving end through target reflection is set within a reasonable range, and the +.>The corresponding element is much smaller than Q C Is a component of the formula (I);
n Rt,n′m representing the estimation error of the target parameter estimation,representation s R,m (t) biasing t, wherein s R,m (T) represents a radar transmission signal, T s Representative of the sampling interval, samples taken at different times are denoted by K, k=1, 2.Representing the time delay, ζ, of reflection from a target under an n'm channel Rt,n′m The channel gain of the radar transmitting end m to the radar receiving end n' reflected by the target is represented;
using the diagonal matrix algorithm, the amount of mutual information MI is further reduced to:
wherein χ is m,m′,n′,k Related to communication channel gain, communication signal and time delay, ψ n′,m,k Is a term for introducing estimation errors of target parameters;
step 6: according to non-cooperative game knowledge in the game theory, searching for specific implementation of radar and communication optimal strategies in the single game process, wherein the single optimal strategy can be found through the following problems:
the only argument in the first problem is the radar power strategy E R The communication power strategy is known, only the communication power strategy is considered in the second problem, the radar power strategy is known, the initialization power of the radar and the communication is given, the solution of the two problems is calculated as the respective strategy selection of the radar and the communication for the first game, the radar and the communication power obtained by the first game are used as the known quantity for the second game, and the optimal strategy of the radar and the communication for the second game is calculated; the above process is carried out until convergence, and the final Nash equilibrium is obtained; the Nash equilibrium point is calculated by an iterative NE algorithm;
step 7: when considering the overall performance of the system, the following optimization problem can be established:
wherein ω represents the normalized weight;
step 8: writing the optimization problem in the step 6 into a two-step optimization problem for step solving, wherein the two-step optimization problem is written as follows:
(A)(B)/>
s.t.0≤η R ≤1
the problem (A) is to use a three-part searching algorithm to continuously reduce the interval to find the optimal power distribution weight eta R In the three-point search algorithm, the radar detection probability and the communication mutual information quantity under different power allocation weights need to be calculated, so that the optimal radar and communication power allocation scheme needs to be obtained by solving the problem (B), namely, the Nash equilibrium point is found by adopting the iteration NE algorithm in the step 5.
CN202210865380.XA 2022-07-21 2022-07-21 Power distribution method of cooperative MIMO radar communication integrated system based on non-cooperative game Active CN115459817B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210865380.XA CN115459817B (en) 2022-07-21 2022-07-21 Power distribution method of cooperative MIMO radar communication integrated system based on non-cooperative game

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210865380.XA CN115459817B (en) 2022-07-21 2022-07-21 Power distribution method of cooperative MIMO radar communication integrated system based on non-cooperative game

Publications (2)

Publication Number Publication Date
CN115459817A CN115459817A (en) 2022-12-09
CN115459817B true CN115459817B (en) 2023-08-01

Family

ID=84296147

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210865380.XA Active CN115459817B (en) 2022-07-21 2022-07-21 Power distribution method of cooperative MIMO radar communication integrated system based on non-cooperative game

Country Status (1)

Country Link
CN (1) CN115459817B (en)

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR20130104369A (en) * 2012-03-13 2013-09-25 삼성전자주식회사 Method for determining transmitting power in the mimo system based on cooperative transmitting
CN106199579A (en) * 2016-06-22 2016-12-07 中国人民解放军信息工程大学 Distributed MIMO radar target tracking precision method for joint optimization of resources
CN108717180A (en) * 2018-07-05 2018-10-30 南京航空航天大学 A kind of radar network power distribution method based on Stackelberg game
CN109743774A (en) * 2019-03-14 2019-05-10 杭州电子科技大学 A kind of power distribution method for realizing safety of physical layer transmission based on non-cooperative game
CN110133635A (en) * 2019-04-03 2019-08-16 电子科技大学 A kind of method of cooperation MIMO radar and communication system calculating target positioning and mutual information
CN111323773A (en) * 2020-02-20 2020-06-23 南京航空航天大学 Networking radar power and bandwidth joint optimization distribution method based on radio frequency stealth
CN112272064A (en) * 2020-09-29 2021-01-26 电子科技大学 Detection probability and mutual information calculation method of cooperative MIMO radar

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20090286471A1 (en) * 2008-05-14 2009-11-19 Jun Ma Method for Allocating Power to Source and Relay Stations in Two-Hop Amplify-and-Forward Relay Multi-Input-Multi-Output Networks
KR101527110B1 (en) * 2009-04-13 2015-06-16 삼성전자주식회사 Apparatus and method for power control in distributed multiple input multiple output wireless communication system

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR20130104369A (en) * 2012-03-13 2013-09-25 삼성전자주식회사 Method for determining transmitting power in the mimo system based on cooperative transmitting
CN106199579A (en) * 2016-06-22 2016-12-07 中国人民解放军信息工程大学 Distributed MIMO radar target tracking precision method for joint optimization of resources
CN108717180A (en) * 2018-07-05 2018-10-30 南京航空航天大学 A kind of radar network power distribution method based on Stackelberg game
CN109743774A (en) * 2019-03-14 2019-05-10 杭州电子科技大学 A kind of power distribution method for realizing safety of physical layer transmission based on non-cooperative game
CN110133635A (en) * 2019-04-03 2019-08-16 电子科技大学 A kind of method of cooperation MIMO radar and communication system calculating target positioning and mutual information
CN111323773A (en) * 2020-02-20 2020-06-23 南京航空航天大学 Networking radar power and bandwidth joint optimization distribution method based on radio frequency stealth
CN112272064A (en) * 2020-09-29 2021-01-26 电子科技大学 Detection probability and mutual information calculation method of cooperative MIMO radar

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
Non-Cooperative Game Theoretic Power Allocation Strategy for Distributed Multiple-Radar Architecture in a Spectrum Sharing Environment;CHENGUANG SHI等;《IEEE Access》;全文 *
分布式MIMO 雷达目标定位与功率分配研究;孙斌;《中国博士学位论文全文数据库》;全文 *
合作式MIMO 雷达通信一体化系统的 检测与互信息增益;王珍等;《信号处理》;第36卷(第10期);全文 *
非再生中继合作下的OFDM 系统功率分配研究;陈雁等;《第十三届信息论学术年会论文集》;全文 *

Also Published As

Publication number Publication date
CN115459817A (en) 2022-12-09

Similar Documents

Publication Publication Date Title
Fa et al. Reduced-rank STAP algorithms using joint iterative optimization of filters
Lehmann et al. Evaluation of transmit diversity in MIMO-radar direction finding
US8553797B2 (en) Channel information prediction system and channel information prediction method
CN109738856B (en) Noise suppression Capon active target DOA estimation method based on time reversal
Fascista et al. A Pseudo Maximum likelihood approach to position estimation in dynamic multipath environments
Khawar et al. Beampattern analysis for MIMO radar and telecommunication system coexistence
US8462869B2 (en) Channel information prediction system and channel information prediction method
Dontamsetti et al. A distributed MIMO radar with joint optimal transmit and receive signal combining
CN106909779A (en) MIMO radar Cramér-Rao lower bound computational methods based on distributed treatment
Luo et al. RIS-aided integrated sensing and communication: Joint beamforming and reflection design
CN109683151A (en) Tenth of the twelve Earthly Branches rooting MUSIC angle estimating method under non-uniform noise environment based on matrix completion
Feng et al. Jointly iterative adaptive approach based space time adaptive processing using MIMO radar
CN106788655A (en) The relevant robust ada- ptive beamformer method of the interference of unknown mutual coupling information under array mutual-coupling condition
He et al. Joint beamforming and power allocation between a multistatic MIMO radar network and multiple targets using game theoretic analysis
CN113360841B (en) Distributed MIMO radar target positioning performance calculation method based on supervised learning
Du et al. Multi-user and multi-target dual-function radar-communication waveform design: Multi-fold performance tradeoffs
Wang et al. A dual-function radar-communication system empowered by beyond diagonal reconfigurable intelligent surface
CN108037487B (en) Distributed MIMO radar transmitting signal optimization design method based on radio frequency stealth
CN112272064B (en) Detection probability and mutual information calculation method of cooperative MIMO radar
Zhang et al. Communications-inspired sensing: a case study on waveform design
CN115459817B (en) Power distribution method of cooperative MIMO radar communication integrated system based on non-cooperative game
CN110146854B (en) Robust anti-interference method for FDA-MIMO radar
da Silva et al. Multi-Static ISAC in Cell-Free Massive MIMO: Precoder Design and Privacy Assessment
Sridhar et al. Spatiotemporal-MIMO channel estimator and beamformer for 5G
US11764857B2 (en) Systems and methods for multiple signal reception using receiver diversity

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant