Quantized-based target velocity estimation and performance evaluation method for MIMO radar communication system

Abstract

This invention belongs to the field of radar-communication integration technology, and specifically relates to the calculation of target velocity estimation methods and parameter estimation performance bounds (Cramer-Rao bounds) in radar-communication integrated signal processing. It discloses a quantization-based MIMO radar-communication system target velocity estimation and performance evaluation method, further reducing the number of sample transmissions and lowering communication pressure. This scheme performs maximum likelihood estimation of the Doppler frequency, then performs multi-bit quantization on the Doppler frequency estimate, and then transmits the quantized Doppler frequency estimate to a fusion center. Finally, the fusion center uses the received quantized signal to estimate the target velocity and calculate the Cramer-Rao bound. This invention is applicable to radar-communication integrated systems.

Description

Technical Field

[0001] This invention belongs to the field of radar-communication integration technology, and specifically relates to the calculation of the target velocity estimation method and parameter estimation performance boundary Cramer-Rao boundary (CRB) in radar-communication integrated signal processing. Background Technology

[0002] With the development and popularization of wireless technology and the increasing application demands, the development of integrated radar and communication systems has become an inevitable trend, such as in automotive systems or 6G communication networks. Through cooperation between the radar and communication ends, an integrated system can simultaneously perform radar and communication tasks. MIMO (Multiple Input Multiple Out) technology, as a multi-antenna transceiver technology, was initially applied in the field of communications. The receiver combines different received signals from the same data stream to recover the original signal, giving the communication system spatial diversity gain, reducing multipath fading, and improving channel reliability. Later, MIMO technology was applied to the radar field, becoming known as MIMO radar. Compared to traditional radar, MIMO radar achieves multi-angle observation of targets through distributed antennas, increasing the accuracy of target detection and parameter estimation. Therefore, introducing MIMO technology into integrated radar and communication systems not only gives the communication end spatial diversity gain and increases channel capacity but also improves the performance of the radar system, offering many advantages.

[0003] Target velocity parameter estimation, as one of the main functions of the radar end in a radar-communication integrated system, can be achieved using the maximum likelihood (ML) estimation method. Maximum likelihood estimation is an asymptotically optimal method. When the received signal has additive noise, and the signal-to-noise ratio is sufficiently high, the mean square error of maximum likelihood estimation can approximately reach the Cramer-Rao bound (CRB). Therefore, to evaluate the parameter estimation performance of the integrated system, the Cramer-Rao bound is used as an evaluation metric. The Cramer-Rao bound is the minimum achievable variance of any unbiased estimator. The closer the variance of the estimator is to the Cramer-Rao bound, the better the performance of the estimation method.

[0004] In various radar-communication integrated system applications, receivers are typically deployed over a wide geographical area. Each local sensor, after receiving a signal, sends its local measurement results to a fusion center. The fusion center then performs further signal processing, forming a distributed network that allows local sensors to process their local measurement results more conveniently, economically, and efficiently. Typically, to reduce communication overhead, the local receiver first quantizes the measurement results from each local sensor before sending the quantized values ​​to the fusion center. Therefore, discussing the impact of quantization on the performance of radar-communication integrated systems is crucial.

[0005] Reference 1 (S. Zhu, F. Xi, S. Chen and A. Nehorai. A low-complexity MIMO dualfunction radar communication system via one-bit sampling. 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 8223-8227, 2021) studied the impact of one-bit quantization on radar target parameter estimation in an integrated radar communication system.

[0006] Reference 2 (D.Ma, N.Shlezinger, T.Huang, Y.Liu and YCEldar. Bit constrained communication receivers in joint radar communications systems. 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 8243-8247, 2021) proposes a communication signal detection strategy for integrated radar and communication systems based on low-precision quantization.

[0007] Reference 3 (Z.Cheng,S.Shi,Z.He and B.Liao. Transmit sequence design for dual-function radar-communication system with one-bit DACs.IEEE Transactions on Wireless Communications,20(9):5846-5860,2021) studies the transmission sequence design of a dual-function integrated system equipped with one-bit quantization under the condition of required radar target positioning performance.

[0008] The quantization of sample data in the above literature all uses 1-bit quantization, and the object of quantization is the direct quantization of the received signal of the integrated system. Although it can reduce the amount of data communication to a certain extent, the effect is limited. Summary of the Invention

[0009] The technical problem to be solved by this invention is to propose a quantization-based method for target velocity estimation and performance evaluation of MIMO radar communication systems, thereby further reducing the number of sample transmissions and lowering communication pressure.

[0010] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0011] A quantized target velocity estimation and performance evaluation method for MIMO radar communication systems is applied to an integrated radar communication system, which includes M... R One radar transmitter, M C One communication transmitter and N radar receivers, M R M C Both N and N are integers greater than or equal to 2;

[0012] The method includes the following steps:

[0013] S1. Arrange the signal sample values ​​received by the nth radar receiver in order to form the received signal vector r. n Where n = 1, ..., N, and N represents the total number of radar receivers;

[0014] S2. Calculate the received signal vector r n The log-likelihood function;

[0015] S3, according to r n Calculating the Doppler frequency f using the log-likelihood function nm Maximum likelihood estimation

[0016] S4. The Doppler frequency f nm Maximum likelihood estimation The input is quantized using a quantizer to obtain the quantized value q. f,m ;

[0017] S5. Quantize the output values ​​q of all quantizers. f,nm The signal q is constructed sequentially. f :

[0018]

[0019] S6, send signal q f The data is transmitted to the fusion center, where it is arranged in sequence to form a signal y. f :

[0020]

[0021] S7. The fusion center calculates the maximum likelihood estimate of the Doppler frequency. variance Then calculate the quantization value q. f,nm The conditional probability distribution function;

[0022] S8, Calculate signal y fLikelihood function:

[0023] S9, according to signal y f The likelihood function is used to calculate the estimated value of the velocity parameter θ of the moving target:

[0024] S10. Repeat steps S1-S9, based on the estimated... Calculate the root mean square error:

[0025]

[0026] Where num represents the number of repetitions;

[0027] S11, Order Calculate the matrix

[0028]

[0029] in, and The Doppler frequency f nm For the target velocity component v x ,v y The derivative;

[0030] S12. Assume the quantized Doppler frequency is d. nm , thus obtaining matrix J f The ij-th element of (f) is:

[0031]

[0032] Where, when n = n' and m = m', otherwise and

[0033]

[0034] S13, According to the formula CRB was calculated f Corresponding to CRB f The diagonal elements are the target velocity v. x ,v y The Clameros boundary, in which

[0035]

[0036]

[0037]

[0038] Furthermore, in step S1, the signal sample values ​​received by the nth radar receiver are arranged in order to form the received signal vector r. n Specifically, it includes:

[0039] r n =[r n [1],r n [2],…,r n [K] T =μ R,n +μ C,n +w n ,

[0040] Where, r n [k] represents the state of the nth radar receiver in kT. s M received at any time R One radar transmitter and M C All signal values ​​transmitted by a communication transmitter, [·] T Indicates transpose;

[0041]

[0042] and T represents the transmission power of the m-th radar transmitter and the m'-th communication transmitter. s The sampling interval is k (k = 1, ..., K), the sampling number is k, and the total number of samples is K. and This represents the time delay corresponding to the signal path received by the nth radar receiver from the mth radar transmitter and the m'th communication transmitter; and This represents the target reflection coefficient corresponding to the signal paths received by the nth radar receiver from the mth radar transmitter and the m'th communication transmitter; and Indicates the Doppler frequency of the corresponding signal path; w n [k] represents the clutter plus noise of all signal paths received by the nth radar receiver, and E{·} represents the expected value, (·) * To represent the conjugate of a complex number, Represents the Dirac function; This represents the variance of clutter plus noise;

[0043] Where, μ R，n =[μ R，n，1 μ R，n，2 , ..., μ R，n，K ] T , μ C，n=[μ C，n，1 ,μ C，n，2 ,…,μ C，n，K ] T , w n =[w n [1], w n [2]..., w n [K] T

[0044] Furthermore, in step S2, the calculation of the received signal vector r n The log-likelihood function specifically includes:

[0045]

[0046] Here, det(·) represents calculating the determinant of a matrix. I is the identity matrix, and θ is the velocity parameter of the moving target to be estimated. If the moving target moves at (v... x ,v y If the velocity of the motion is θ, then θ can be expressed as θ = [v] x ,v y ] T ;(·) H Indicates conjugate transpose; v x v y These represent the velocity components on the x-axis and y-axis, respectively.

[0047] Furthermore, in step S3, the step based on r n Calculating the Doppler frequency f using the log-likelihood function nm Maximum likelihood estimation Specifically, it includes:

[0048]

[0049] Among them, f nm for:

[0050]

[0051] M R M C These represent the total number of radar transmitters and radar communication transmitters, respectively.

[0052] Furthermore, in step S4, the Doppler frequency f is... nm Maximum likelihood estimation The input is quantized using a quantizer to obtain the quantized value q. f,nm Specifically, it includes:

[0053]

[0054] in, For the output of the quantizer, D=2 b γ is the number of quantized values, b is the number of quantized bits, γ0, γ1, ..., γ D This is the quantizer threshold.

[0055] Furthermore, in step S7, the maximum likelihood estimate of the Doppler frequency is calculated. variance Specifically, it includes:

[0056]

[0057] in, Re{·} denotes taking the real part of a complex number;

[0058] The calculated quantization value q f,nm The conditional probability distribution function specifically includes:

[0059]

[0060] in, The quantization value is d. nm Quantization threshold, d nm This represents the result after Doppler frequency quantization, with values ​​ranging from 0, 1, ..., D-1, where D is the number of quantized values. Ω(·) represents the cumulative distribution function of the standard Gaussian distribution, defined as:

[0061]

[0062] The beneficial effects of this invention are:

[0063] This method involves performing maximum likelihood estimation on the Doppler frequency, followed by multi-bit quantization of the Doppler frequency estimate. The quantized Doppler frequency estimate is then transmitted to the fusion center, where the received quantized signal is used to estimate the target velocity and calculate the Cramer-Rao bound. Compared to existing technologies that directly quantize the received signal of the integrated system with 1 bit, this method further reduces the number of samples that need to be transmitted, thus alleviating the communication burden. Attached Figure Description

[0064] Figure 1 This is a flowchart of the target velocity estimation and performance evaluation method for a quantization-based MIMO radar communication system in the embodiment.

[0065] Figure 2 When the quantization bit count is 9, v is calculated under different SCNR values. x and v y A schematic diagram of RMSE and RCRB;

[0066] Figure 3Based on the Doppler frequency quantization method, v is calculated under different SCNRs when the number of quantization bits b is different. x and v y A schematic diagram of RCRB. Detailed Implementation

[0067] This invention aims to propose a quantization-based method for target velocity estimation and performance evaluation in MIMO radar communication systems, further reducing the number of sample transmissions and alleviating communication pressure. This scheme involves performing maximum likelihood estimation on the Doppler frequency, then performing multi-bit quantization on the Doppler frequency estimate, transmitting the quantized Doppler frequency estimate to a fusion center, and finally using the received quantized signal to estimate the target velocity and calculate the Cramer-Rao bound.

[0068] For ease of description, we first define the following:

[0069] (·) T For transpose, (·) H For the conjugate transpose, E{·} denotes the mathematical expectation, det(·) denotes the determinant of a matrix, and Re{·} denotes taking the real part of a complex number.

[0070] Consider a MIMO radar-communication integrated system that includes M R One transmitter and N radar receivers, and M C The m-th communication transmitter (m = 1, ..., M) R ) radar transmitters, the m'th (m'=1,...,M) C The nth communication transmitter and the nth (n=1,...,N) radar receiver are located in a two-dimensional Cartesian coordinate system, with coordinates as follows: At time kT, the m-th radar transmitter and the m'-th communication transmitter s The transmitted signals are respectively and Where T s The sampling interval is k (k = 1, ..., K), the sampling number is k, and the total number of samples is K. and Let m represent the transmission power of the m-th radar transmitter and the m'-th communication transmitter, considering the speed (v) x v y Imagine a moving target whose velocity is deterministically unknown, assuming the target appears at a known position (x, y) during the observation interval. The nth radar receiver operates at time kT. s The received signal can be modeled as

[0071]

[0072] in and This represents the time delay corresponding to the signal path received by the nth radar receiver from the mth radar transmitter and the m'th communication transmitter; and This indicates that the known target reflection coefficients have been preprocessed; and Indicates the Doppler frequency of the corresponding signal path; w n [k] represents the clutter plus noise along the signal path received by the nth radar receiver, and This represents the variance of clutter plus noise.

[0073] For convenience, and Represented as:

[0074]

[0075] Define an unknown parameter vector θ = [v] containing the velocity of the target to be estimated. x ,v y ] T Doppler frequency f nm The parameter vector to be estimated is θ, which is the target velocity v. x ,v y Functions:

[0076]

[0077] Where λ represents the carrier wavelength. This indicates the location of the corresponding radar or communication transmitter.

[0078] The signal sample values ​​received by the nth (n = 1, ..., N) radar receiver are arranged in order to form the received signal vector r. n for

[0079] r n =[r n [1],r n [2],…,r n [K] T =μ R,n +μ C,n +w n

[0080] Where μ R,n =[μ R,n,1 ,μ R,n,2 ,…,μ R,n,K ] T , μ C，n =[μ C，n，1 μ C，n，2, ..., μ C，n，K ] T , w n =[w n [1], w n [2]..., w n [K] T .

[0081] Therefore, we can obtain r n Satisfy the following distribution

[0082]

[0083] Among them, C n The covariance matrix is ​​represented as...

[0084] In a MIMO radar-communication integrated system, the two systems share information to help each other better complete their tasks. For the radar receiver, using the target echo carried by the signal in the communication system and the target echo from the traditional radar can better accomplish the task of target velocity estimation. Assuming that in the MIMO radar-communication integrated system, the radar end knows the target echo from the communication end, and the radar end also knows the target echo it has received, then r... n The log-likelihood function is

[0085]

[0086] Due to the Doppler frequency f nm Since the Doppler frequency is a function of the parameter θ to be estimated, maximum likelihood estimation can be performed at each local receiver. The estimated Doppler frequency values ​​are then quantized and transmitted to the fusion center. This reduces the number of samples that need to be transmitted and alleviates the communication burden. Based on the above equation, f can be obtained. nm The maximum likelihood estimate is

[0087]

[0088] After completing the maximum likelihood estimation of the Doppler frequency, the Doppler frequency estimate is... After quantization, the data is sent to the fusion center. Here, we assume the transmission channel is ideal and neglect losses such as fading during transmission. The received observation vector y received by the fusion center... f for

[0089]

[0090] With a sufficient number of time samples, the Doppler frequency It can be approximated by the mean being f nm variance is The Gaussian distribution, i.e.

[0091]

[0092] in That is, the Doppler frequency. According to reference 4 (S. Kay, "Fundamentals of Statistical Signal Processing: Estimation Theory," Prentice-Hall, Englewood Cli_s, NJ, 1993), the CRB is known to be...

[0093]

[0094] and

[0095] according to The distribution of d nm =0,1,…,D-1,q f,nm The probability distribution function is

[0096]

[0097] Where Ω(·) represents the cumulative distribution function of the standard Gaussian distribution, defined as

[0098]

[0099] Therefore, the received observation vector y at the fusion center f The likelihood function is

[0100]

[0101] Based on the above formula, the maximum likelihood estimate of the parameter vector θ can be obtained as follows:

[0102]

[0103] make

[0104]

[0105] According to the chain rule, CRB can be obtained as follows:

[0106]

[0107] Calculate matrix

[0108]

[0109] in and The Doppler frequency fnm For the target velocity v x ,v y The derivative;

[0110] Calculate matrix J f The formula for the ij-th element of (f) is:

[0111]

[0112] Matrix J is obtained f The ij-th element of (f) is:

[0113]

[0114] Where, when n = n' and m = m', otherwise and

[0115]

[0116] Based on the above principles, the flowchart of a quantization-based MIMO radar communication system target velocity estimation and performance evaluation method provided in this embodiment of the invention is as follows: Figure 1 As shown, it includes the following steps:

[0117] Step 1: Arrange the signal sample values ​​received by the nth radar receiver in order to form the received signal vector r. n ;

[0118] r n =μ R,n +μ C,n +w n

[0119] Step 2, calculate r n The log-likelihood function;

[0120]

[0121] Step 3, based on r n Calculating the Doppler frequency f using the log-likelihood function nm Maximum likelihood estimation

[0122]

[0123] Step 4: Take the f obtained in step 3 nm Maximum likelihood estimation The input is quantized using a quantizer to obtain the quantized value q. f,nm ,

[0124]

[0125] in For the output of the quantizer, D=2 b γ is the number of quantized values, b is the number of quantized bits, γ0, γ1, ..., γ D This is the quantizer threshold;

[0126] Step 5: Quantize the output values ​​q of all quantizers. f,nm q are formed in sequence f ;

[0127]

[0128] Step 6: Take the q obtained in step 5 f The data is transmitted to the fusion center, where it is arranged in sequence to form a signal y. f ;

[0129]

[0130] Step 7: Calculate the Doppler frequency estimate. variance

[0131]

[0132] in,

[0133] Calculate q f,nm Conditional probability distribution function:

[0134]

[0135] in The quantization value is d. nm Quantization threshold, d nm This represents the result after Doppler frequency quantization, with values ​​ranging from 0, 1, ..., D-1, where D is the number of quantized values. Ω(·) represents the cumulative distribution function of the standard Gaussian distribution, defined as:

[0136]

[0137] Step 8: Calculate y using the following formula. f Likelihood function:

[0138]

[0139] Step 9: Obtain the estimated value of θ using the following formula;

[0140]

[0141] Step 10: Repeat steps 1 to 9, based on the estimated... The RMSE (root mean square error) is calculated as follows:

[0142]

[0143] Where num represents the number of repetitions;

[0144] Step 11, Order

[0145]

[0146] Calculate the matrix

[0147]

[0148] in and The Doppler frequency f nm For the target velocity v x ,v y The derivative;

[0149] Step 12: Assume the quantized Doppler frequency is d. nm , thus obtaining matrix J f The ij-th element of (f) is:

[0150]

[0151] Where, when n = n' and m = m', otherwise and

[0152]

[0153] Step 13: According to the formula:

[0154]

[0155] CRB was calculated f Corresponding to CRB f The diagonal elements are the target velocity v. x ,v y The lower realm of Clameros, among which

[0156]

[0157]

[0158]

[0159] Simulation experiment:

[0160] This experiment verifies the correctness of the target velocity estimation and Cramer-Rao boundary calculation based on Doppler frequency quantization in the target velocity estimation and performance evaluation method of the MIMO radar communication system of this invention.

[0161] The experimental parameters are set as follows:

[0162] Consider a target located at (150, 130)m, and assume there is M. R = 3 radar transmitters, M C =3 communication transmitters and N=4 radar receivers are uniformly distributed within the range [0, 2π) angle, the antenna is located 70km away from the origin of the coordinate system, and the target moves at a speed of (25, 20) km / h.

[0163] In the simulation, the radar transmitter uses a frequency-spread single Gaussian pulse signal: Where f Δ It is the frequency offset between adjacent radar transmitted signals, let f Δ =500hz, T=0.01s, K=22;

[0164] The communication transmitter uses orthogonal frequency division multiplexing (OFDM) signals as follows: Where a m' [n represents the data symbol, p] T' (t) is a rectangular pulse with unit amplitude and width T', Δf is the frequency interval between the two subcarriers, and N f This represents the number of subcarriers, with a pulse width of T'. Let Δf = 125 Hz, N f =6, T'=0.01s.

[0165] SCNR is defined as Where E is the total transmit power of the system. Using a dynamic range of [-γ] max γ max The quantizer based on the Doppler frequency quantization method has a dynamic range of F. max =250Hz.

[0166] Figure 1 This refers to the calculation of v under different SCNR conditions when the quantization bit number b is 9. x v y The RMSE and RCRB (the square root of the Cramer-Rao bound, i.e., the value after taking the square root of the Cramer-Rao bound) show that RMSEs decrease as SCNR increases. When SCNR reaches 5dB, RMSEs are close to RCRBs, proving the correctness of the Cramer-Rao bound derived based on the Doppler frequency quantization method.

[0167] Figure 2This refers to the value of v calculated under different SCNR values ​​when the number of quantization bits b is different. x v y The RCRBs are presented, and to illustrate the performance of distributed parameter estimation, the performance of centralized processing (CP) is also given. It can be seen that as the number of quantization bits b increases, the RCRBs become smaller, indicating that the larger the number of quantization bits, the higher the estimation accuracy. When the number of quantization bits b reaches 11, the performance of speed estimation based on quantization Doppler is very close to that of centralized processing.

[0168] Finally, it should be noted that the above embodiments are merely preferred embodiments and are not intended to limit the present invention. It should be pointed out that those skilled in the art can make various modifications, equivalent substitutions, and improvements without departing from the spirit and scope of the claims, and all such modifications, substitutions, and improvements should be included within the scope of protection of the present invention.

Claims

1. A method for target velocity estimation and performance evaluation of a quantized MIMO radar communication system, applied to a radar communication integrated system, the radar communication integrated system comprising M R radar transmitters, M C communication transmitters and N radar receivers, M R , M C , N are integers greater than or equal to 2; characterized in that, The method comprises the following steps: S1, arrange the signal sample values received by the nth radar receiver in order to form a received signal vector r n , wherein n = 1, …, N, and N represents the total number of radar receivers; S2, compute the log-likelihood function of the received signal vector r n of the received signal vector r; S3. According to r n The log-likelihood function is calculated for Doppler frequency f nm The maximum likelihood estimate of the Doppler frequency f S4, the maximum likelihood estimate of the Doppler frequency f nm input quantizer to obtain a quantized value q f,nm ;​ S5, quantized values q output by all quantizers are summed f,nm The signal q is formed in sequence f : S6, the signal q f is transmitted to the fusion center, which orders the received data to form the signal y f : S7. The fusion center calculates a maximum likelihood estimate of the Doppler frequency of the variance Then the conditional probability distribution function of the quantized value q f,nm is calculated; S8, compute signal y f Likelihood function of: S9. Calculate the estimate of the motion target velocity parameter θ from the likelihood function of the signal y f ​ S10, repeating steps S1-S9, based on the estimated Root mean square error is calculated: Wherein, num is the number of repetitions; S11, let matrix wherein and is the Doppler frequency f nm derivative of the target velocity component v x v y ; S12, suppose the quantized Doppler frequency value is d nm , the ijth element of matrix J f (f) is: wherein when n = n' and m = m', then Otherwise and S13, according to the formula The CRB is calculated f The diagonal elements of the CRB f corresponding to the target speed v x v y Cramer-Rao bound, where 2. The quantization-based MIMO radar communication system target velocity estimation and performance evaluation method of claim 1, wherein, In step S1, the signal sample values received by the nth radar receiver are arranged in order to form a received signal vector r n , and specifically comprises: r n = [r n [1], r n [2],..., r n [K]] T = μ R,n + μ C,n + w n , where r n [k] is the value of all signals transmitted by M s radar transmitters and M R communication transmitters received by the nth radar receiver at the kT C [k] = [r T denotes the transpose. and Pm,m'is the transmit power of the mth radar transmitter and the m'th communication transmitter, T s is the sampling interval, k (k = 1,..., K) is the sampling index, and K is the total number of samples; and denotes the time delay corresponding to the signal path of the mth radar transmitter and the m'th communication transmitter received by the nth radar receiver; and denotes the target reflection coefficient corresponding to the signal path of the mth radar transmitter and the m'th communication transmitter received by the nth radar receiver; and denotes the Doppler frequency corresponding to the signal path; W n [k] is the clutter plus noise of all signal paths received by the nth radar receiver, and E{·} denotes the mathematical expectation of (·) * denotes the conjugate of a complex number, denotes the Dirac function; denotes the variance of the clutter plus noise; wherein μ R，n = [μ R，n，1 , μ R，n，2 ,..., μ R，n，K ] T , μ C,n = [μ C,n,1 , μ C,n,2 ,..., μ C,n,K ] T , w n = [w n [1], w n [2]…, w n [K]] T .

3. The quantization-based MIMO radar communication system target velocity estimation and performance evaluation method of claim 2, wherein, In step S2, the calculation receives a log-likelihood function of the signal vector r n , specifically comprising: where det( ) denotes the determinant of a matrix, I is an identity matrix, and θ is a velocity parameter of the moving object to be estimated. If the moving object moves at a velocity of (v x ,v y ), then θ is expressed as θ = [v x ,v y ] T ; (·) H denotes the conjugate transpose; v x , v y denote velocity components in the x-axis and y-axis, respectively.

4. The quantization-based MIMO radar communication system target velocity estimation and performance evaluation method of claim 3, wherein, In step S3, the log-likelihood function of r n is used to calculate the maximum likelihood estimate of the Doppler frequency f nm In step S3, the log-likelihood function of r Specifically includes: wherein f nm is: M R , M C are the total number of radar transmitters, respectively radar communication transmitters.

5. The quantization-based MIMO radar communication system target velocity estimation and performance evaluation method of claim 2, wherein, In step S4, the maximum likelihood estimate of the Doppler frequency f nm is determined The input quantizer is quantized to obtain a quantized value q f,nm , specifically comprising: wherein D = 2 for quantizer output b is the number of quantization values, b is the number of quantization bits, γ0, γ1,..., γ D is the quantizer threshold.

6. The quantization-based MIMO radar communication system target velocity estimation and performance evaluation method of claim 2, wherein, In step S7, the maximum likelihood estimate value of the Doppler frequency is calculated of the variance Specifically includes: wherein Re{•} denotes taking the real part of a complex number; The calculated quantization value q f,nm The conditional probability distribution function, specifically comprising: wherein denotes the quantization value d nm denotes the quantization threshold for d nm denotes the quantized result of the Doppler frequency, taking values 0, 1, …, D-1, where D is the number of quantization values, and Ω(·) denotes the cumulative distribution function of the standard Gaussian distribution, defined as:

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