CN112272064A - Detection probability and mutual information calculation method of cooperative MIMO radar - Google Patents

Detection probability and mutual information calculation method of cooperative MIMO radar Download PDF

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CN112272064A
CN112272064A CN202011048149.9A CN202011048149A CN112272064A CN 112272064 A CN112272064 A CN 112272064A CN 202011048149 A CN202011048149 A CN 202011048149A CN 112272064 A CN112272064 A CN 112272064A
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CN112272064B (en
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何茜
王珍
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Nanjing Zhongboda Electronic Technology Co ltd
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University of Electronic Science and Technology of China
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/10—Monitoring; Testing of transmitters
    • H04B17/101—Monitoring; Testing of transmitters for measurement of specific parameters of the transmitter or components thereof
    • H04B17/103—Reflected power, e.g. return loss
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/40—Means for monitoring or calibrating
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/40—Means for monitoring or calibrating
    • G01S7/4004—Means for monitoring or calibrating of parts of a radar system
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/309—Measuring or estimating channel quality parameters
    • H04B17/364—Delay profiles
    • 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

Abstract

The invention discloses a method for calculating mutual information and detection probability of a cooperative MIMO radar communication integrated system, belongs to the technical field of radar communication integration, and particularly relates to calculation of target detection problems and mutual information in radar communication integration. The mutual information of the communication end of the integrated MIMO system and the target detection probability of the radar end are obtained through calculation, and the mutual information and the target detection probability of the communication end of the integrated MIMO system can be used for evaluating the performance of the cooperative MIMO radar communication integrated system. According to the method, the MIMO radar system and the MIMO communication system are not considered to be interference of the other signal, but are utilized cooperatively, so that the performances of the two parties can be improved.

Description

Detection probability and mutual information calculation method of cooperative MIMO radar
Technical Field
The invention belongs to the technical field of radar communication integration, and particularly relates to target detection problems and mutual information calculation in radar communication integration.
Background
With the development of electronic technology, radar communication integration is a necessary trend in both military and civil fields. For example, unmanned fighters in military field need to complete tasks such as aerial reconnaissance and battlefield environment monitoring, and timely transmit acquired data back to the ground. In an intelligent traffic system in the civil field, an intelligent vehicle needs to communicate with other vehicles or a fusion center while sensing the surrounding traffic environment, and all of the intelligent vehicles need to have the functions of radar and communication at the same time. In an integrated system, a single antenna has been difficult to meet the requirement due to the complex environment to be monitored and the heavy communication task. Multiple-input Multiple-output (MIMO) technology has shown significant advantages in both radar systems and communication systems, and has also received attention from researchers in integrated research. Therefore, the research on the performance of the MIMO radar communication integrated system is of great significance.
Target detection is one of the main functions of the radar system, and is often a task that needs to be completed by the radar end in an integrated system, so that many documents use detection performance as an index for measuring the performance of the radar system. Mutual information of communication systems is used as an important index for measuring the quality of communication channels, and is also often used as a performance metric of a communication end in an integrated system. The larger the mutual information, the larger the corresponding channel capacity. Therefore, in the radar communication integrated system, the performance of the integrated system can be evaluated by selecting the detection performance and the mutual information.
The coexistence of radar and communication systems is an important task for integrated research, and has attracted the attention of students. In view of the conventional research situation, the research on the coexistence integration system can be roughly classified into three types. The first type is that mutual interference between two systems is reduced by means of reasonably designing a transmitting waveform and the like at a transmitting end. The second type is to remove the interference between two systems at the receiving end by using successive interference cancellation and other techniques. The third type is that two systems cooperate to utilize the other system to assist in completing the tasks of the system, for example, document 1(M Bica, Kuanwen Huang, U Mitra, et al, orthogonal radio wave design in joint radio and cellular communication systems [ C ]//2015IEEE Global communication Conference (GLOBECOM), 2015: 1-7.), document 2(M Bica, V Koivun. delay evaluation method for correlating radio and wireless communication systems [ C ]/2017 IEEE radio communication (radio Conf), 2017: 1557) and document 3 (chemical shift, coupling wave, Fei Wang, et al, Low probability-section OFDM) communication system 2019, for estimating the performance of a Radar in consideration of the radio communication system [ C ]/, and radio communication system 19. for estimating the performance of a Radar in a Radar system [ C ]/(radio communication), and for estimating the performance of a radio-radio communication system [ 10 ] using a radio communication system and radio communication system [ C ]/(radio communication system 19). Therefore, in the integrated system, the radar system and the communication system do not use the signals transmitted from each other as interference, but use them cooperatively, so that the performance of both systems can obtain gain.
Disclosure of Invention
The invention aims at solving the technical problem of the prior art that a performance calculation method for bringing performance gain to an MIMO radar communication integrated system by considering cooperation is obtained, and Mutual Information (MI) of a communication end and target detection probability of a radar end are calculated.
The technical scheme of the invention is a method for calculating mutual information and detection probability of a cooperative MIMO radar communication integrated system, which comprises the following steps:
step 1: at the receiver of the communication end, the nth ', N' ═ 1, …, N is obtainedCkT received by a communication receiversReceived signal r of timeC,n′[k]Comprises the following steps:
Figure BDA0002708672300000021
wherein
Figure BDA0002708672300000022
And
Figure BDA0002708672300000023
respectively representing echo signals of a target reflection path and a direct path corresponding to the communication transmitting signal,
Figure BDA0002708672300000024
respectively representing echo signals of a target reflection path and a direct path corresponding to the radar transmission signal; w is aC,n'[k]Represents the clutter plus noise component at time k; mCAnd NCNumber of transmitters and receivers, M, respectively, of communication terminalsRThe number of transmitters at the radar end; m, M ═ 1, …, MRA radar transmitter and M', M ═ 1, …, MCThe transmission signals of the communication transmitters are respectively sR,m(kTs) And sC,m′(kTs)，ER,mAnd EC,m′Representing the transmission power, TsFor a sampling period, K, K is 1, …, K represents a time sequence number;
Figure BDA0002708672300000025
Figure BDA0002708672300000026
and
Figure BDA0002708672300000027
it indicates the time delay of the corresponding path,
Figure BDA0002708672300000028
and
Figure BDA0002708672300000029
is the corresponding target reflection coefficient;
step 2: arranging K time samples received by the nth' receiver of the communication end into a vector rC,n′；
Figure BDA00027086723000000210
Wherein [. ]]TThe transpose is represented by,
Figure BDA00027086723000000211
Figure BDA00027086723000000212
Figure BDA0002708672300000031
Figure BDA0002708672300000032
Figure BDA0002708672300000033
Figure BDA0002708672300000034
Figure BDA0002708672300000035
Figure BDA0002708672300000036
wC,n′＝[wC,n′[1],…,wC,n′[K]]Tdiag {. } represents block diagonalization;
Figure BDA0002708672300000037
and
Figure BDA0002708672300000038
delay signals respectively representing the respective transmission signals;
and step 3: communication terminal NCThe K time samples received by the receiver are arranged into a vector rC
Figure BDA0002708672300000039
Wherein the content of the first and second substances,
Figure BDA00027086723000000310
Figure BDA00027086723000000311
Figure BDA00027086723000000312
and assume vector wCObeying a zero mean covariance matrix of QCComplex gaussian random distribution;
and 4, step 4: determining covariance matrix C of received communication signal for maximum likelihood estimation
Figure BDA00027086723000000313
Wherein, (.)HWhich represents the transpose of the conjugate,
Figure BDA00027086723000000314
an autocorrelation matrix representing the received direct communication signal,
Figure BDA00027086723000000315
a cross-correlation matrix representing the received direct communication signal and the communication signal reflected by the target,
Figure BDA00027086723000000316
autocorrelation matrix, Q, of a communication signal representing reflections of a targetCA covariance matrix representing clutter plus noise;
and 5: according to the formula
Figure BDA00027086723000000317
Obtaining the unknown position theta of the radar target (x, y)TIs expressed as
Figure BDA00027086723000000318
Step 6: derived by means of estimation
Figure BDA00027086723000000319
Calculating a time delay estimate for a communication signal reflected by a target and a time delay estimate for a radar signal
Figure BDA0002708672300000041
Figure BDA0002708672300000042
Wherein
Figure BDA0002708672300000043
And
Figure BDA0002708672300000044
respectively indicating the positions of the m ' th communication transmitting station, the m ' th radar transmitting station and the n ' th communication receiving station, c indicates the speed of light, nCt,n′m′And nRt,n′mRepresenting the estimation error, which can be assumed to follow a gaussian distribution. Radar echo signal
Figure BDA0002708672300000045
Is contained in
Figure BDA0002708672300000046
Can be replaced by an estimate
Figure BDA0002708672300000047
To obtain
Figure BDA0002708672300000048
Is expressed as
Figure BDA0002708672300000049
Obtaining direct radar signals by using signal information and position information shared by radar
Figure BDA00027086723000000410
And 7: eliminating radar signal interference in communication receiving signals to obtain communication receiving signal vector of
Figure BDA00027086723000000411
Wherein the content of the first and second substances,
Figure BDA00027086723000000420
representing the residual after the radar interference is removed,
Figure BDA00027086723000000413
Figure BDA00027086723000000414
Figure BDA00027086723000000415
denotes sR,m(t) derivative with respect to t, sR,m(t) denotes a radar emission signal sR,m(kTs) A continuous-time expression form of (a);
and 8: according to the formula
Figure BDA00027086723000000416
Computing mutual information of the communication system, where det (-) represents determinant, log (-) represents logarithm base 2, I is unit matrix,
Figure BDA00027086723000000417
Figure BDA00027086723000000418
expressing the mathematical expectation;
and step 9: at the receiver of the radar end of the integrated system, the nth, N is 1, …, NRkT received by radar receiversReceived signal r of timeR,n[k]：
Figure BDA00027086723000000419
Wherein the content of the first and second substances,
Figure BDA0002708672300000051
and
Figure BDA0002708672300000052
the first four terms respectively represent target reflection path and direct path echo signals corresponding to the radar transmission signals,
Figure BDA0002708672300000053
and
Figure BDA0002708672300000054
representing target reflected path and direct path echo signals, w, corresponding to the communicated transmitted signalR,n[k]Represents the clutter plus noise component at time k; n is a radical ofRIs the number of receivers on the radar side, tauRt,nm，τR,nm，τCt,nm′And τC,nm′Then the delay, ζ, of the corresponding path is indicatedRt,nmAnd ζCt,nm′Is the corresponding target reflection coefficient;
step 10: arranging K time samples received by the nth receiver of the radar end into a vector rR,n
rR,n＝[rR,n[1],…,rR,n[K]]T＝URt,nsRt,n+UR,nsR,n+UCt,nsCt,n+UC,nsC,n+wR,n，
Wherein U isRt,n＝Diag{uRt,n[1],…,uRt,n[K]}，
Figure BDA0002708672300000055
UR,n＝Diag{uR,n[1],…,uR,n[K]}，
Figure BDA0002708672300000056
UCt,n＝Diag{uCt,n[1],…,uCt,n[K]}，
Figure BDA0002708672300000057
UC,n＝Diag{uC,n[1],…,uC,n[K]}，
Figure BDA0002708672300000058
sRt,n＝[sRt,n[1]T,…,sRt,n[K]T]T，
Figure BDA0002708672300000059
sR,n＝[sR,n[1]T,…,sR,n[K]T]T，
Figure BDA00027086723000000510
sCt,n＝[sCt,n(1)T,…,sCt,n(K)T]T，
Figure BDA00027086723000000511
Figure BDA00027086723000000512
wR,n＝[wR,n[1],…,wR,n[K]]T；
Step 11: connecting the radar end NRThe K time samples received by the receiver are arranged into a vector rR
Figure BDA00027086723000000513
Wherein
Figure BDA00027086723000000514
Figure BDA00027086723000000515
Figure BDA00027086723000000516
And assume a noise vector wRObeying a zero mean covariance matrix of QRComplex gaussian random distribution;
step 12: calculating a detection statistic T according toR
Figure BDA0002708672300000061
Step 13: obtaining a distribution of detection statistics from the equation
Figure BDA0002708672300000062
Wherein H1Indicating the presence of a target in the detection cell, H0Indicating that no target is present in the detection unit,
Figure BDA0002708672300000063
is shown in H0Let T beRObey mean value of mu0Variance is σ2The distribution of the gaussian component of (a) is,
Figure BDA0002708672300000064
is shown in H1Let T beRObey mean value of mu1Variance is σ2(ii) a gaussian distribution of;
step 14: obtaining a detection threshold beta according to the following formula
β＝σQ-1(PFA)+μ0
Wherein P isFARepresenting the false alarm probability, Q (-) represents the complementary distribution function of the standard Gaussian distribution, and the expression is
Figure BDA0002708672300000065
Step 15: obtaining radar target detection probability of integrated MIMO system by the following formula
Figure BDA0002708672300000066
Further, μ in said step 130，μ1The calculation method of sigma is as follows:
Figure BDA0002708672300000067
Figure BDA0002708672300000068
Figure BDA0002708672300000069
re {. is said to take the real part of a complex number.
The mutual information of the communication ends of the integrated MIMO system and the target detection probability of the radar end are obtained through calculation in the steps, and the mutual information and the target detection probability of the radar end can be used for evaluating the performance of the cooperative MIMO radar communication integrated system. According to the method, the MIMO radar system and the MIMO communication system are not considered to be interference of the other signal, but are utilized cooperatively, so that the performances of the two parties can be improved.
Drawings
Fig. 1 is a schematic structural diagram of a cooperative MIMO radar communication integrated system.
Fig. 2 is a schematic diagram of radar target detection probabilities of the cooperative MIMO radar communication integrated system calculated under different α.
Fig. 3 is a schematic diagram of communication mutual information of the cooperative MIMO radar communication integrated system calculated under different α.
Detailed Description
For convenience of description, the following definitions are first made:
[·]Tshowing transposition, (.)HFor conjugate transpose, Diag {. is } for block diagonalization, Re {. is } for taking the real part of a complex number,
Figure BDA0002708672300000071
it is a mathematical expectation that H (-) is the difference entropy, det (-) represents the determinant, and log (-) represents the base-2 logarithm.
A cooperative MIMO radar communication integrated system is provided, wherein a radar end is provided with MRA transmitter and NRA receiver, a communication end has MCA transmitter and NCThe receiver, all the transmitters and receivers are separated single antenna. M (M is 1, …, M)R) The position of the radar transmitter is
Figure BDA0002708672300000072
N (N is 1, …, N)R) The position of the radar receiver is
Figure BDA0002708672300000073
M '(M' 1, …, M)c) The location of the communication transmitter is
Figure BDA0002708672300000074
N '(N' 1, …, N)C) The position of the communication receiver is
Figure BDA0002708672300000075
M (M is 1, …, M)R) A radar transmitter and M '(M' 1, …, M)C) The transmission signals of the communication transmitters are respectively
Figure BDA0002708672300000076
And
Figure BDA0002708672300000077
wherein ER,mAnd EC,m′Representing the transmission power, TsFor the sampling period, K (K ═ 1, …, K) denotes a time index. The detection unit that determines whether the target exists is located at (x, y) in two-dimensional cartesian coordinates. A schematic diagram of a cooperative MIMO radar communication integration system is shown in fig. 1.
At the communication end of the integrated system, the nth '(N' is 1, …, N)C) A communication receiver is at kTsThe received signal of the moment is modeled as
Figure BDA0002708672300000078
Wherein the first four terms respectively represent a target reflection path and a direct path corresponding to the communication emission signal and a target reflection path and a direct path corresponding to the radar emission signal,
Figure BDA0002708672300000079
and
Figure BDA00027086723000000710
it indicates the time delay of the corresponding path,
Figure BDA00027086723000000711
and
Figure BDA00027086723000000712
for the corresponding target reflection coefficient, wC,n′[k]Representing the clutter plus noise component at time k. Let r beC,n′＝[rC,n′[1],…,rC,n′[K]]TThe total communication received signal vector can be written as
Figure BDA00027086723000000713
Wherein
Figure BDA00027086723000000714
The diagonal element of which is
Figure BDA00027086723000000715
Vector in formula (2)
Figure BDA00027086723000000716
By adopting
Figure BDA00027086723000000717
Similar definition is made. Signal vector in formula (2)
Figure BDA0002708672300000081
Wherein
Figure BDA0002708672300000082
Other signal vectors in equation (2)
Figure BDA0002708672300000083
Is defined in a manner of
Figure BDA0002708672300000084
Like. Assuming a clutter plus noise vector at the communication end
Figure BDA0002708672300000085
Obeying a zero mean covariance matrix of QCA Gaussian distribution of (a), wherein wC,n′＝[wC,n′[1],…,wC,n′[K]]T。
Similarly, for the radar system, let N (N ═ 1, …, NR) A radar receiver is located at kTsThe received signal of the moment is modeled as
Figure BDA0002708672300000086
Wherein the first four terms respectively represent a target reflection path and a direct path corresponding to a radar emission signal and a target reflection path and a direct path corresponding to a communication emission signal, and tauRt,nm，τR,nm，τCt,nm′And τC,nm′Then the delay, ζ, of the corresponding path is indicatedRt,nmAnd ζCt,nm′For the corresponding target reflection coefficient, wR,n[k]Representing the clutter plus noise component at time k. Defining the observation vector of the nth radar receiver as rR,n＝[rR,n[1],…,rR,n[K]]TThe total radar received signal vector can be written as
Figure BDA0002708672300000087
In the formula
Figure BDA0002708672300000088
And is
Figure BDA0002708672300000089
Vector U in equation (6)R，UCt，UCBy mixing with URtSimilar definition is made. Signal vector
Figure BDA00027086723000000810
Wherein
Figure BDA00027086723000000811
Other signal vectors s in equation (6)R sCt sCIs defined by the formula and sRtSimilarly. The clutter plus noise vector is
Figure BDA00027086723000000812
In the above formula wR,n＝(wR,n[1],…,wR,n[K])TAnd assume wRObeying a zero mean covariance matrix of QRA gaussian distribution of (a).
The invention adopts the following steps to calculate the mutual information of the communication end and the detection probability of the radar end of the cooperative MIMO radar communication integrated system:
step 1: the signal model (2) of the communication end obtains the received signal of the communication end of the integrated system,
Figure BDA00027086723000000813
step 2: determining covariance matrix C of received communication signal for maximum likelihood estimation
Figure BDA00027086723000000814
Wherein the content of the first and second substances,
Figure BDA00027086723000000815
an autocorrelation matrix representing the received direct communication signal,
Figure BDA00027086723000000816
a cross-correlation matrix representing the received direct communication signal and the communication signal reflected by the target,
Figure BDA00027086723000000817
autocorrelation matrix, Q, of a communication signal representing reflections of a targetCA covariance matrix representing clutter plus noise;
and step 3: according to the formula
Figure BDA0002708672300000091
Obtaining the unknown position theta of the radar target (x, y)TIs expressed as
Figure BDA0002708672300000092
And 4, step 4: derived by means of estimation
Figure BDA0002708672300000093
Calculating a time delay estimate for a communication signal reflected by a target and a time delay estimate for a radar signal
Figure BDA0002708672300000094
Figure BDA0002708672300000095
Wherein c represents the speed of light, nCt,n′m′And nRt,n′mRepresenting the estimation error, which can be assumed to follow a gaussian distribution. Radar echo signal
Figure BDA0002708672300000096
Is contained in
Figure BDA0002708672300000097
Substitution to estimated value
Figure BDA0002708672300000098
Can obtain
Figure BDA0002708672300000099
Is expressed as
Figure BDA00027086723000000910
Obtaining direct radar signals by using signal information and position information shared by radar
Figure BDA00027086723000000911
And 5: eliminating radar signal interference in communication receiving signals to obtain communication receiving signal vector of
Figure BDA00027086723000000912
Wherein the content of the first and second substances,
Figure BDA00027086723000000921
representing the residual after the radar interference is removed,
Figure BDA00027086723000000914
Figure BDA00027086723000000915
Figure BDA00027086723000000916
denotes sR,m(t) derivative with respect to t, sR,m(t) denotes a radar emission signal sR,m(kTs) A continuous-time expression form of (a);
step 6: according to the formula
Figure BDA00027086723000000917
Calculating mutual information of the communication system, I is an identity matrix,
Figure BDA00027086723000000918
and 7: the signal model (6) of the radar end is used for obtaining the receiving signal of the radar end of the integrated system,
Figure BDA00027086723000000919
and 8: according to the formula
Figure BDA00027086723000000920
Computing a detection statistic TR。
And step 9: the distribution of the detection statistics is obtained from
Figure BDA0002708672300000101
Wherein H1Indicating the presence of a target in the detection cell, H0Indicating that no target is present in the detection unit,
Figure BDA0002708672300000102
is shown in H0Let T beRObey mean value of mu0Variance is σ2The distribution of the gaussian component of (a) is,
Figure BDA0002708672300000103
is shown in H1Let T beRObey mean value of mu1Variance is σ2The distribution of the gaussian component of (a) is,
Figure BDA0002708672300000104
Figure BDA0002708672300000105
step 10: obtaining a detection threshold beta according to the following formula
β＝σQ-1(PFA)+μ0 (19)
Wherein P isFARepresenting false alarm probability, Q (-) represents the complementary distribution function of the standard Gaussian distribution, the tableHas the formula of
Figure BDA0002708672300000106
Step 11: obtaining radar target detection probability of integrated MIMO system by the following formula
Figure BDA0002708672300000107
Working principle of the invention
The cooperation of the two systems mainly refers to information sharing, for example, the antenna positions of the two systems are shared with the other system, the radar transmitting signals are shared with the communication system, and the radar receiving end can decode and reconstruct the communication signals more accurately by utilizing the information shared by the communication system. The cooperative integrated system can not only utilize the target echo of the traditional radar, but also utilize the target echo carried by the communication signal to complete the radar task. Therefore, due to the information sharing, the cooperative integrated system can be equivalent to a system in which an active MIMO radar and a passive MIMO radar are mixed, which is called an active and passive mixed MIMO radar system for short. On the other hand, because the transmitting signal and the antenna position of the radar end of the cooperative integrated system are shared with the communication end, the communication receiving end can accurately obtain the radar target parameters by utilizing the shared information, and further, on the basis of traditional communication information extraction, the communication quality is further improved by utilizing the communication signal reflected by the radar target
Assuming that the communication transmission signal is a Gaussian signal with known distribution, r can be obtained according to the communication receiving signal model (2)CProbability density function of
Figure BDA0002708672300000108
Wherein r isCHas a covariance matrix of
Figure BDA0002708672300000111
From this, the likelihood function can be obtained as
Figure BDA0002708672300000112
The maximum likelihood estimate of the target position then results in
Figure BDA0002708672300000113
Using the estimate of the target position, the estimate of the time delay of the communication signal reflected by the target and the estimate of the time delay of the radar signal may be expressed as
Figure BDA0002708672300000114
And
Figure BDA0002708672300000115
the delay estimation result can be further written as
Figure BDA0002708672300000116
Wherein n isCt,n′m′And nRt,n′mRepresenting the estimation error, which can be assumed to follow a gaussian distribution.
Radar echo signal of equation (2)
Figure BDA0002708672300000117
Is contained in
Figure BDA0002708672300000118
Substitution to estimated value
Figure BDA0002708672300000119
Can obtain
Figure BDA00027086723000001110
Is expressed as
Figure BDA00027086723000001111
This estimate can be used to cancel the target echo from the radar transmitted signal. Because the radar signal and the antenna position of the cooperative system are shared with the communication system, the direct signal from radar transmission of the communication receiving end
Figure BDA00027086723000001112
May also be eliminated. Prior to the elimination of the radar Signal, the following approximation was obtained using the method in the literature (A.R. Chiriyath, B.Paul, G.M. Jacyna, and D.W.Bliss, "Inner bases on performance of radar and communication co-existence," IEEE Transactions on Signal Processing, vol.64, No.2, pp.464-474, Jan 2016.)
Figure BDA00027086723000001113
According to the formula (28), after eliminating the interference of the radar signal in the formula (2), the vector of the communication received signal can be obtained as
Figure BDA00027086723000001114
From equation (29), an observation vector r can be foundC' in
Figure BDA00027086723000001115
And
Figure BDA00027086723000001116
all contain useful information of communication signals, the communication mutual information of the integrated system can be calculated as
Figure BDA00027086723000001117
Assuming that the radar task is to detect whether a target exists in the detection unit of interest, the assumption of the target existence in the detection unit is recorded as H according to the radar received signal model of formula (6)1If the target does not exist, H is assumed0Then the detection problem can be described as
Figure BDA0002708672300000121
To simplify the analysis, consider the case where the communication signal has been decoded and reconstructed, and assume that the target reflection coefficient ζ can be made by preprocessing or the likeRt,nmAnd ζCt,nm′It is known that in equation (31), except for the noise wRThe other terms are known, so that the received signal r is given two hypothesesRAre all Gaussian distributed, and the probability density function is respectively
Figure BDA0002708672300000122
And
Figure BDA0002708672300000123
deriving a derived log-likelihood ratio function of
Figure BDA0002708672300000124
At the right end of the equation (34), the terms other than the first two are all the same as rRThe irrelevant quantity, neglecting the influence of the items, can obtain the detection statistic as
Figure BDA0002708672300000125
Visible detection statistic T from the above equationRIs a received signal rRBecause of the linear combination at H0Hypothesis sum H1Let's assume lower rRAre all Gaussian distributed, and T is not known under two assumptionsRAre respectively distributed as
Figure BDA0002708672300000126
Wherein
Figure BDA0002708672300000127
According to false alarm probability PFADefinition of (1)
Figure BDA0002708672300000128
The detection threshold beta can be obtained as
β＝σQ-1(PFA)+μ0, (39)
In the above formula, Q (-) represents a complementary distribution function of a standard Gaussian distribution expressed by
Figure BDA0002708672300000131
The radar target detection probability of the integrated MIMO system can be calculated as follows
Figure BDA0002708672300000132
The simulation results of the communication mutual information and the radar target detection probability of the cooperative MIMO radar communication integrated system are shown in fig. 2 and 3, wherein the simulation parameters are set as follows:
suppose that the communication system has M C2 transmitting antennas and NC3 receiving antennas, transmitting station positions of (70,0) km and (-70,0) km, receiving station positions of (65,24) km, (-54,50) km and (-12, -69) km, respectively, number of transmitting antennas and receiving antennas of the MIMO radar systemThe number of antennas is M R2 and NRThe transmitter positions are (0,70) km and (0, -70) km, and the receiver positions are (-41,57) km, (-28, -64) km and (69,7) km, respectively, for 3. Assume that the radar target detection unit is located at (0.5,0.3) km. The OFDM signal transmitted by the communication system can be expressed as
Figure BDA0002708672300000133
Wherein a ism′[n]Representing data symbols, pT′(T) a rectangular pulse of unit amplitude and width T', Δ f being the frequency spacing between two subcarriers, NfRepresenting the number of subcarriers with a pulse width T'. Let Δ f be 125Hz, NfT' is 6, 0.01 s. Assuming that the transmission power of each communication transmission signal is the same, i.e.
Figure BDA0002708672300000134
The clutter and noise of the communication end are white Gaussian distribution, and the covariance matrix is expressed as
Figure BDA0002708672300000135
The radar system transmits a frequency-extended Gaussian monopulse signal, represented as
Figure BDA0002708672300000136
Wherein f isΔRepresenting the frequency spacing between radar transmitted signals, and T is the pulse width. Let fΔ125Hz and T0.01 s. The transmission power of each radar transmission signal being the same, i.e.
Figure BDA0002708672300000137
Clutter and noise at the radar end are in white Gaussian distribution, and a covariance matrix is expressed as
Figure BDA0002708672300000138
The total transmitting power of the cooperative MIMO radar communication integrated system is represented as E, the proportion distributed to the radar end is set as alpha, and then M is obtainedRER＝Eα、MCECE (1- α). Defining a signal to clutter plus noise ratio as
Figure BDA0002708672300000139
Let E equal to 104、SCNR＝5dB。
Fig. 2 shows the radar target detection probability with a curve in two scenarios. The first scenario (cooperation) takes into account the fact that the radar cooperates with the communication system, i.e. the received signal model r described by equation (6) is usedR. The second scenario (non-cooperative) considers the situation that the radar in the integrated MIMO system performs target detection in the traditional mode without cooperation with the communication system, that is, the received signal model is rR＝URtsRt+URsR+wR. As can be seen from the figure, the target detection probability P of the cooperative integrated systemDP of an always-on-one system compared to a non-cooperative systemDAnd larger, the cooperation is indeed helpful for improving the target detection performance of the radar.
FIG. 3 is the same as the simulation parameters of FIG. 2, assuming that the communication signal is a correlation matrix of
Figure BDA00027086723000001310
White gaussian distribution. Fig. 3 shows a graph of the mutual communication information as a function of a for both scenarios. The first scenario (cooperation) considers the cooperation between MIMO communication and MIMO radar system in the integrated system, and the communication system estimates the target parameters and utilizes the communication target echo, i.e. the received signal model r described by formula (2) is adoptedC. The second scenario (non-cooperative) considers that the MIMO communication system in the integrated system does not cooperate with the MIMO radar and communicates in the conventional manner, i.e. using a received signal model
Figure BDA0002708672300000141
As can be seen from the figure, the mutual information of the cooperation situation is always larger than that of the non-cooperation scene, which shows that the cooperation with the radar system is helpful for improving the communication mutual information.

Claims (2)

1. A method for calculating mutual information and detection probability of a cooperative MIMO radar communication integrated system comprises the following steps:
step 1: on-lineAt the receiver of the signal end, the N ', N' ═ 1, …, N is obtainedCkT received by a communication receiversReceived signal r of timeC,n′[k]Comprises the following steps:
Figure FDA0002708672290000011
wherein
Figure FDA0002708672290000012
And
Figure FDA0002708672290000013
respectively representing echo signals of a target reflection path and a direct path corresponding to the communication transmitting signal,
Figure FDA0002708672290000014
and
Figure FDA0002708672290000015
respectively representing echo signals of a target reflection path and a direct path corresponding to the radar transmission signal; w is aC,n'[k]Represents the clutter plus noise component at time k; mCAnd NCNumber of transmitters and receivers, M, respectively, of communication terminalsRThe number of transmitters at the radar end; m, M ═ 1, …, MRA radar transmitter and M', M ═ 1, …, MCThe transmission signals of the communication transmitters are respectively sR,m(kTs) And sC,m′(kTs)，ER,mAnd EC,m′Representing the transmission power, TsFor a sampling period, K, K ═ 1., K denotes a time sequence number;
Figure FDA0002708672290000016
Figure FDA0002708672290000017
and
Figure FDA0002708672290000018
it indicates the time delay of the corresponding path,
Figure FDA0002708672290000019
and
Figure FDA00027086722900000110
is the corresponding target reflection coefficient;
step 2: arranging K time samples received by the nth' receiver of the communication end into a vector rC,n′；
Figure FDA00027086722900000111
Wherein [. ]]TThe transpose is represented by,
Figure FDA00027086722900000112
Figure FDA00027086722900000113
Figure FDA00027086722900000114
Figure FDA00027086722900000115
Figure FDA00027086722900000116
Figure FDA00027086722900000117
Figure FDA00027086722900000118
Figure FDA0002708672290000021
wC,n′＝[wC,n′[1],...,wC,n′[K]]Tdiag {. } represents block diagonalization;
Figure FDA0002708672290000022
and
Figure FDA0002708672290000023
delay signals respectively representing the respective transmission signals;
and step 3: communication terminal NCThe K time samples received by the receiver are arranged into a vector rC
Figure FDA0002708672290000024
Wherein the content of the first and second substances,
Figure FDA0002708672290000025
Figure FDA0002708672290000026
Figure FDA0002708672290000027
and assume vector wCObeying a zero mean covariance matrix of QCComplex gaussian random distribution;
and 4, step 4: determining covariance matrix C of received communication signal for maximum likelihood estimation
Figure FDA0002708672290000028
Wherein, (.)HWhich represents the transpose of the conjugate,
Figure FDA0002708672290000029
an autocorrelation matrix representing the received direct communication signal,
Figure FDA00027086722900000210
showing and connectingA cross-correlation matrix of the received communication signal and the reflected communication signal of the target,
Figure FDA00027086722900000211
autocorrelation matrix, Q, of a communication signal representing reflections of a targetCA covariance matrix representing clutter plus noise;
and 5: according to the formula
Figure FDA00027086722900000212
Obtaining the unknown position theta of the radar target (x, y)TIs expressed as
Figure FDA00027086722900000213
Step 6: derived by means of estimation
Figure FDA00027086722900000214
Calculating a time delay estimate for a communication signal reflected by a target and a time delay estimate for a radar signal
Figure FDA00027086722900000215
Figure FDA00027086722900000216
Wherein
Figure FDA00027086722900000217
And
Figure FDA00027086722900000218
respectively indicating the positions of the m ' th communication transmitting station, the m ' th radar transmitting station and the n ' th communication receiving station, c indicates the speed of light, nCt,n′m′And nRt,n′mRepresenting the estimation error, which can be assumed to follow a gaussian distribution. Radar echo signal
Figure FDA0002708672290000031
Is contained in
Figure FDA0002708672290000032
Can be replaced by an estimate
Figure FDA0002708672290000033
To obtain
Figure FDA0002708672290000034
Is expressed as
Figure FDA0002708672290000035
Obtaining direct radar signals by using signal information and position information shared by radar
Figure FDA0002708672290000036
And 7: eliminating radar signal interference in communication receiving signals to obtain communication receiving signal vector of
Figure FDA0002708672290000037
Wherein the content of the first and second substances,
Figure FDA0002708672290000038
representing the residual after the radar interference is removed,
Figure FDA0002708672290000039
Figure FDA00027086722900000310
Figure FDA00027086722900000311
denotes sR,m(t) derivative with respect to t, sR,m(t) denotes a radar emission signal sR,m(kTs) A continuous-time expression form of (a);
and 8: according to the formula
Figure FDA00027086722900000312
Computing mutual information of the communication system, where det (-) represents determinant, log (-) represents logarithm base 2, I is unit matrix,
Figure FDA00027086722900000313
Figure FDA00027086722900000314
expressing the mathematical expectation;
and step 9: at the receiver of the radar end of the integrated system, the nth, N is 1, …, NRkT received by radar receiversReceived signal r of timeR,n[k]：
Figure FDA00027086722900000315
Wherein the content of the first and second substances,
Figure FDA00027086722900000316
and
Figure FDA00027086722900000317
the first four terms respectively represent target reflection path and direct path echo signals corresponding to the radar transmission signals,
Figure FDA00027086722900000318
and
Figure FDA00027086722900000319
representing target reflected path and direct path echo signals, w, corresponding to the communicated transmitted signalR,n[k]Represents the clutter plus noise component at time k; n is a radical ofRIs the number of receivers on the radar side, tauRt,nm，τR,nm，τCt,nm′And τC,nm′Then the delay, ζ, of the corresponding path is indicatedRt,nmAnd ζCt,nm′Is the corresponding target reflection coefficient;
step 10: arranging K time samples received by the nth receiver of the radar end into a vector rR,n
rR,n＝[rR,n[1],...,rR,n[K]]T＝URt,nsRt,n+UR,nsR,n+UCt,nsCt,n+UC,nsC,n+wR,n，
Wherein U isRt,n＝Diag{uRt,n[1],...,uRt,n[K]}，
Figure FDA0002708672290000041
UR,n＝Diag{uR,n[1],...,uR,n[K]}，
Figure FDA0002708672290000042
UCt,n＝Diag{uCt,n[1],...,uCt,n[K]}，
Figure FDA0002708672290000043
UC,n＝Diag{uC,n[1],...,uC,n[K]}，
Figure FDA0002708672290000044
sRt,n＝[sRt,n[1]T,...,sRt,n[K]T]T，
Figure FDA0002708672290000045
sR,n＝[sR,n[1]T,...,sR,n[K]T]T，
Figure FDA0002708672290000046
sCt,n＝[sCt,n(1)T,...,sCt,n(K)T]T，
Figure FDA0002708672290000047
Figure FDA0002708672290000048
wR,n＝[wR,n[1],...,wR,n[K]]T；
Step 11: connecting the radar end NRThe K time samples received by the receiver are arranged into a vector rR
Figure FDA0002708672290000049
Wherein
Figure FDA00027086722900000410
Figure FDA00027086722900000411
Figure FDA00027086722900000412
And assume a noise vector wRObeying a zero mean covariance matrix of QRComplex gaussian random distribution;
step 12: calculating a detection statistic T according toR
Figure FDA00027086722900000413
Step 13: obtaining a distribution of detection statistics from the equation
Figure FDA00027086722900000414
Wherein H1Indicating the presence of a target in the detection cell, H0Indicating that no target is present in the detection unit,
Figure FDA00027086722900000415
is shown in H0Let T beRObey mean value of mu0Variance is σ2The distribution of the gaussian component of (a) is,
Figure FDA00027086722900000416
is shown in H1Let T beRObey mean value of mu1Variance is σ2(ii) a gaussian distribution of;
step 14: obtaining a detection threshold beta according to the following formula
β＝σQ-1(PFA)+μ0
Wherein P isFARepresenting the false alarm probability, Q (-) represents the complementary distribution function of the standard Gaussian distribution, and the expression is
Figure FDA0002708672290000051
Step 15: obtaining radar target detection probability of integrated MIMO system by the following formula
Figure FDA0002708672290000052
2. The method as claimed in claim 1, wherein μ in step 13, the method for calculating mutual information and detection probability of cooperative MIMO radar communication integrated system0，μ1The calculation method of sigma is as follows:
Figure FDA0002708672290000053
Figure FDA0002708672290000054
Figure FDA0002708672290000055
re {. is said to take the real part of a complex number.
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