MIMO radar long-distance weak target detection based on low-bit quantization B-Rao

Abstract

The invention belongs to the field of large-scale MIMO radar signal detection, and relates to an algorithm for carrying out target detection on a long-distance weak signal under a low-bit quantization condition. The method specifically comprises the following steps: S1, setting a radar system model, setting multiple-input multiple-output of a large-scale MIMO radar, and setting a clutter covariance matrix to obey inverse Wishart distribution; s2, transmitting and receiving at the same time by each antenna to obtain a radar echo signal, and performing low-bit quantization processing on the received signal; s3, designing a Bayesian thought and a traditional Rao detector algorithm to be combined with a B-Rao detection algorithm; and S4, according to a particle swarm algorithm, performing multiple iterations to obtain an appropriate quantization threshold value so as to improve the detection performance. Under the condition that a large amount of echo data is obtained by a large-scale MIMO radar, a low-bit sampling method is introduced, the data processing amount is reduced, after low-bit sampling, an algorithm combining the Bayesian thought and a traditional detector is introduced, and compared with the single use of the traditional detector, the detection performance is effectively improved while the operation cost is reduced.

Description

Technical Field

[0001] The present invention belongs to the field of MIMO radar target detection, and in particular is an adaptive detector technology for weak targets under low-bit quantization conditions, based on Bayesian thinking and combined with traditional Rao test. Background Art

[0002] When using Multiple-Input Multiple-Output (MIMO) radar to detect long-range, weak signals, the numerous antenna elements and subsequent sampling of the echo signals naturally create a massive amount of received signal data, increasing the workload required for data processing. In real-world conditions, coupled with the influence of environmental and device noise, overcoming hardware limitations and improving detection performance become key issues.

[0003] Centralized MIMO radar maximizes spatial resources and offers greater design freedom. Compared to distributed MIMO radar, centralized MIMO radar utilizes waveform diversity technology during its design to scan the entire airspace, resulting in a high target search rate, especially in low signal-to-noise ratio environments, which can improve target detection and parameter estimation performance.

[0004] Typically, measured signals are analog signals. Analysis requires conversion to computer-readable digital signals. In theory, the closer the quantization bit count is to infinite, the more accurately the continuous-time signal can be restored. However, during algorithm design, increasing the number of quantization bits leads to increased computer system operating costs and reduced efficiency, creating significant challenges for practical quantization design. Compared to traditional analog-to-digital conversion techniques, low-bit sampling reduces excessive consumption of system resources. Under appropriate algorithmic conditions, low-bit sampling can also achieve the same effect. For target detection, the detection problem is modeled as a binary hypothesis testing problem, and the noise covariance matrix is ​​modeled as a random matrix. Existing detection technologies suffer from limitations such as a dependence of the covariance matrix on training data and inaccurate covariance matrix estimation due to a small number of samples. Therefore, this paper leverages the principles of traditional Rao detection technology, combined with Bayesian techniques and prior information, to develop a novel Bayesian detector that achieves performance gains under low-bit sampling conditions, ultimately improving signal detection performance. Summary of the Invention

[0005] (1) Technical problems solved

[0006] In view of the deficiencies of the prior art, the present invention provides a detector based on the combination of Bayesian and Rao tests in a low-bit situation, which solves the problems raised in the above background technology.

[0007] (2) Technical solution

[0008] In order to achieve the above-mentioned purpose, the present invention specifically adopts the following technical solutions:

[0009] A method for optimizing quantizer design under low-bit sampling data conditions by combining Bayesian thinking and utilizing the traditional Rao test principle to ultimately improve detection performance includes the following steps:

[0010] S1, the radar target detection problem is modeled as a binary hypothesis testing problem. The MIMO radar system uses a uniform linear array arrangement of transmitting and receiving antennas, and uses a centralized MIMO radar. t Transmitting antennas, N r The target to be detected is a long-range, static target. The interference data matrix between different pairs of transmitting and receiving antennas is defined as a random matrix with an inverse complex Wishart distribution as the prior distribution. The inverse complex Wishart distribution is the conjugate prior distribution of the covariance matrix, which means that in a Bayesian framework, the likelihood of the observed data follows a multivariate normal distribution, a property suitable for adaptive detection.

[0011] x(t) represents the baseband signal at the target position, and its expression is as follows:

[0012]

[0013] Where s(·) represents the signal of the far-field transmitting antenna. c represents the baseband frequency. d(·) represents the time it takes for the signal transmitted from the transmitting antenna to reach the target location. Indicates the location of the transmitting antenna. Θ 0 Indicates the target location.

[0014] Represents the echo signal, and the expression is as follows:

[0015]

[0016] By sampling the echo signal and quantizing it by q bits, the obtained signal can be expressed as:

[0017]

[0018] S2, quantizes the echo signal under low-bit conditions to reduce the amount of data samples.

[0019] Determine whether a reflective target exists and construct a binary hypothesis testing problem:

[0020]

[0021] In the case of H0, only noise exists. In the case of H1, noise and target exist at the same time, β≠0.

[0022] According to the set signal model, Uq [·] represents q-bit quantization of the data in brackets. The noise obeys the normal distribution. Covariance matrix Obey the inverse Wishart distribution, is the degree of freedom. The higher the degree of freedom, the closer the covariance prior matrix is ​​to a positive definite matrix, and the higher the reliability of the prior information. is the prior covariance matrix structure.

[0023] Quantify the observed PMF:

[0024]

[0025] Here is set is the known covariance matrix, g n and h n are the real and imaginary parts of the element to be detected. R (n) = β R g n -β I h n ,θ I (n) = β R h n +β I g n , Λ represents the difference between the echo signal and the theoretical estimated signal, in addition, |·| represents the determinant of the matrix; tr[·] represents the trace of the matrix. When x=b i When I i (x) represents the element indicator function is 1, otherwise it is 0.

[0026] S3, construct the B-Rao test quantity.

[0027] The traditional Rao test is used for derivation. The traditional Rao test formula is as follows:

[0028]

[0029] Here, the parameter Θ is defined as:

[0030]

[0031] Among them, Θ r =[β R ,β I ] T is a two-dimensional vector, β=β R +jβ I .

[0032] , represents the value of Θ under the assumption H0.

[0033] The joint probability density function (PMF) of the quantized data Y under the assumption is:

[0034]

[0035] So, let the likelihood function be:

[0036]

[0037] Calculate the partial derivatives of the real and imaginary parts of the likelihood function:

[0038]

[0039] Given The function f(z) has its formal partial derivative defined as:

[0040]

[0041] Where z = z R +jz I ,z R ∈R and z I ∈R are the real and imaginary parts of z respectively. So The first-order partial derivative of β is defined as:

[0042]

[0043] For the Fisher information matrix with β as parameter, it is defined as follows:

[0044]

[0045] For the information matrix The expression after block division is as follows:

[0046]

[0047] Cross terms:

[0048]

[0049] When the target amplitude and the clutter covariance are independent under the H0 assumption (i.e., β r = 0 when there is no coupling), then

[0050]

[0051] because so

[0052]

[0053] Using Bayesian thinking, we need to get The maximum a posteriori estimate of The maximum a posteriori probability density function of :

[0054]

[0055] After taking the logarithm of the above formula, Taking the derivative and setting the result equal to 0, we get Get the maximum a posteriori probability estimate:

[0056]

[0057] use The maximum a posteriori estimate, the partial derivative of the likelihood function with respect to the reflection coefficient, and the Fisher information matrix are obtained, and the Bayesian Rao detector formula under low-bit quantization conditions is comprehensively derived:

[0058]

[0059] S4, use PSO algorithm to design the quantization threshold.

[0060] For echo signal quantization, the quantization threshold set for q-bit quantization can be expressed as: If q-bit quantization is required, 2 q +1 bit quantization threshold.

[0061]

[0062] α is the corresponding asymptotic pdf, represents a chi-square distribution with 2 degrees of freedom, Noncentral chi-square distribution with 2 degrees of freedom. λ(τ) represents the noncentrality parameter:

[0063]

[0064] Given false alarm probability of radar system Determine the detection threshold η,

[0065]

[0066] in, represents the inverse chi-square cumulative distribution function.

[0067] Detection probability P d It is expressed as follows:

[0068]

[0069] τ is a controllable variable. The quantization threshold is one of the key factors affecting the detection probability. There is always τ0=-∞, τ 2q =+∞.

[0070]

[0071] Using the particle swarm algorithm to find the optimal estimate of τ, q -1 dimensional space to scatter particles to find the optimal position. Each particle has two vectors, the position vector τ i and velocity vector v i There are two considerations for finding the best position of particles: the initial best position ζ i and the global optimal position ξ i The two positions are guided by two learning factors c1 and c2 respectively. r1 and r2 are random numbers that obey uniform distribution. Through multiple iterations, when the i+1 iteration is completed, all the optimal positions ζ of the scattered particles are compared. i , taking the maximum value is the optimal solution.

[0072]

[0073] (3) Beneficial effects

[0074] Compared with the existing technology, the present invention provides a new adaptive target detection algorithm under the condition of large-scale MIMO long-distance weak targets, which performs low-bit quantization processing on the echo signal and then uses the B-Rao algorithm for detection. It has the following beneficial effects:

[0075] This method quantizes the echo signals collected by MIMO radar with different bit numbers, namely 1, 2, and 3 bits. This reduces system cost, improves computational efficiency, and reduces data volume for large-scale signals. Target detection is then performed on the quantized signals. A reasonable quantization threshold is designed for the quantizer. Using Bayesian thinking, the maximum a posteriori (MAP) estimate of the covariance matrix is ​​derived from the probability density function of the covariance matrix. This is then substituted into the traditional detector expression to ultimately determine the detection probability, forming the B-Rao detector. Compared to conventional detector MLE methods, using the Bayesian approach to obtain the MAP estimate of the covariance matrix improves accuracy. This method has promising applications in radar target detection for long-range weak signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 This is a flowchart of a method for removing motion noise from millimeter-wave radar signals based on total variation of the present invention; DETAILED DESCRIPTION

[0077] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0078] Example

[0079] like Figure 1 As shown, an embodiment of the present invention proposes a MIMO radar target detection algorithm based on Bayesian generalized likelihood ratio and Rao detector under low-bit conditions, including the following steps:

[0080] In S1, the radar system is set to a massive MIMO millimeter-wave radar system with multiple antennas transmitting and receiving simultaneously. The target simulation condition is a long-range weak target signal. The system clutter is set to have a clutter covariance matrix that follows an inverse Wishart distribution.

[0081] After setting the radar system parameters, the target detection problem is modeled as a binary hypothesis testing problem. The MIMO radar system uses a uniform linear array arrangement of transmitting and receiving antennas, and a centralized MIMO radar. t Transmitting antennas, N r The target to be detected is a long-range static target. The interference data matrix between different transmitting and receiving antenna pairs is defined as a random matrix. Since the prior distribution is set to the inverse complex Wishart distribution, which is the conjugate prior distribution of the covariance matrix, this means that in the Bayesian framework, the likelihood of the observed data follows a multivariate normal distribution. This property is suitable for adaptive detection.

[0082] x(t) represents the baseband signal at the target position, and its expression is as follows:

[0083]

[0084] Where s(·) represents the signal of the far-field transmitting antenna. c represents the baseband frequency. d(·) represents the time it takes for the signal transmitted from the transmitting antenna to reach the target location. Indicates the location of the transmitting antenna. Θ 0 Indicates the target location.

[0085] Represents the echo signal, and the expression is as follows:

[0086]

[0087] By sampling the echo signal and quantizing it by q bits, the obtained signal can be expressed as:

[0088]

[0089] S2, quantizes the echo signal under low-bit conditions to reduce the amount of data samples.

[0090] Determine whether a reflective target exists and construct a binary hypothesis testing problem:

[0091]

[0092] In the case of H0, only noise exists. In the case of H1, noise and target exist at the same time, β≠0.

[0093] According to the set signal model, U q [·] represents q-bit quantization of the data in brackets. The noise obeys the normal distribution. Covariance matrix Obey the inverse Wishart distribution, is the degree of freedom. The higher the degree of freedom, the closer the covariance prior matrix is ​​to a positive definite matrix, and the higher the reliability of the prior information. is the prior covariance matrix structure.

[0094] Quantify the observed PMF:

[0095]

[0096] Here is set is the known covariance matrix, g n and h n are the real and imaginary parts of the element to be detected. R (n) = β R g n -β I h n ,θ I (n) = β R h n +β I g n , Λ represents the difference between the echo signal and the theoretical estimated signal, in addition, |·| represents the determinant of the matrix; tr[·] represents the trace of the matrix. When x=b i When I i (x) represents the element indicator function is 1, otherwise it is 0.

[0097] S3, construct the B-Rao test quantity.

[0098] The traditional Rao test is used for derivation. The traditional Rao test formula is as follows:

[0099]

[0100] Here, the parameter Θ is defined as:

[0101]

[0102] Among them, Θ r =[β R ,β I ] T is a two-dimensional vector, β=β R +jβ I .

[0103] , represents the value of Θ under the assumption H0.

[0104] The joint probability density function (PMF) of the quantized data Y under the assumption is:

[0105]

[0106] So, let the likelihood function be:

[0107]

[0108] Calculate the partial derivatives of the real and imaginary parts of the likelihood function:

[0109]

[0110] Given The function f(z) has its formal partial derivative defined as:

[0111]

[0112] Where z = z R +jz I ,z R ∈R and z I ∈R are the real and imaginary parts of z respectively. So The first-order partial derivative of β is defined as:

[0113]

[0114] For the Fisher information matrix with β as parameter, it is defined as follows:

[0115]

[0116] For the information matrix The expression after block division is as follows:

[0117]

[0118] Cross terms:

[0119]

[0120] When the target amplitude and the clutter covariance are independent under the H0 assumption (i.e., β r = 0 when there is no coupling), then

[0121]

[0122] because so

[0123]

[0124] Using Bayesian thinking, we need to get The maximum a posteriori estimate of The maximum a posteriori probability density function of :

[0125]

[0126] After taking the logarithm of the above formula, Taking the derivative and setting the result equal to 0, we get Get the maximum a posteriori probability estimate:

[0127]

[0128] use The maximum a posteriori estimate, the partial derivative of the likelihood function with respect to the reflection coefficient, and the Fisher information matrix are obtained, and the Bayesian Rao detector formula under low-bit quantization conditions is comprehensively derived:

[0129]

[0130] S4, use PSO algorithm to design the quantization threshold.

[0131] For echo signal quantization, the quantization threshold set for q-bit quantization can be expressed as: If q-bit quantization is required, 2 q +1 bit quantization threshold.

[0132]

[0133] α is the corresponding asymptotic pdf, represents a chi-square distribution with 2 degrees of freedom, Noncentral chi-square distribution with 2 degrees of freedom. λ(τ) represents the noncentrality parameter:

[0134]

[0135] Given false alarm probability of radar system Determine the detection threshold η,

[0136]

[0137] in, represents the inverse chi-square cumulative distribution function.

[0138] Detection probability P d It is expressed as follows:

[0139]

[0140] τ is a controllable variable. The quantization threshold is one of the key factors affecting the detection probability. There is always τ0=-∞, τ 2q =+∞.

[0141]

[0142] Using the particle swarm algorithm to find the optimal estimate of τ, q -1 dimensional space to scatter particles to find the optimal position. Each particle has two vectors, the position vector τ i and velocity vector v i There are two considerations for finding the best position of particles: the initial best position ζ i and the global optimal position ξ i The two positions are guided by two learning factors c1 and c2 respectively. r1 and r2 are random numbers that obey uniform distribution. Through multiple iterations, when the i+1 iteration is completed, all the optimal positions ζ of the scattered particles are compared. i , taking the maximum value is the optimal solution.

[0143]

[0144] This method uses a large-scale MIMO millimeter-wave radar system to transmit and receive multiple signals simultaneously, thus generating radar transmission and reception signals with a large data scale. The method of the present invention mainly targets the case of large data volume and long-distance weak signals, and performs quantized sampling of different low bits on the received signal to reduce the data volume. At the same time, in order to ensure detection efficiency, an algorithm combining Bayesian and traditional RAO ​​detectors is used for detection. Compared with the traditional low-bit detection using RAO detectors, the addition of Bayesian ideas can be combined with prior probabilities, setting the clutter covariance matrix to obey the inverse Wishart distribution that can reflect environmental information, thereby improving detection probability and performance, while ensuring the CFAR characteristics. The design of the quantizer is optimized, and the detection threshold is improved by the particle swarm algorithm. And as the number of bits increases, the detection effect also improves. In actual scenarios, it helps large-scale MIMO radars to detect long-distance weak targets and improve detection performance.

[0145] Finally, it should be noted that the above content is only a preferred embodiment of the invention and does not limit the scope of the invention. Even if the present invention is fully described based on the above embodiments, professional and technical personnel still have the right to adjust the technical solutions described in each embodiment or implement equivalent substitutions for some technical features. As long as they are based on the core spirit and basic principles of the present invention, any form of modification, equivalent substitution, and optimization and improvement are included in the scope of protection of the present invention.

Claims

1. A target detection algorithm combining Bayesian and traditional Rao detectors under the condition of measuring long-range weak targets by massive MIMO radar, characterized by: The specific steps include: S1: When performing simulations on a radar system using massive MIMO multi-transmitter and multi-receiver technology and measuring signals from distant weak targets, it is necessary to first set the clutter covariance matrix to follow an inverse Wishart distribution. This distribution, as the conjugate prior distribution of the covariance matrix of the multidimensional normal distribution, can reflect prior information about the environment. S2: Perform low-bit quantization sampling on the echo signal first to reduce the amount of data processing, which is equivalent to compression processing and reduces hardware costs. S3: Combining Bayesian thinking with traditional Rao detectors. Bayesian thinking utilizes the factor of prior probability. The covariance matrix obeys the inverse Wishart prior distribution that can reflect environmental information. According to the traditional Rao detector formula and the joint density probability formula, a B-Rao detector suitable for low-bit quantization conditions is obtained. S4: For different bit numbers, appropriate threshold conditions are required. Therefore, a suitable quantizer is designed. Using the PSO particle swarm algorithm, through multiple iterations, the appropriate threshold conditions are finally obtained to detect whether the target exists in the data, thereby improving detection performance.

2. The target detection method according to claim 1, wherein the B-Rao algorithm is introduced after low-bit quantization for long-range weak target detection under MIMO radar conditions, characterized in that: The radar echo signal formula for long-range weak target signals is: Among them, f c represents the baseband frequency. d(·) represents the time it takes for the signal transmitted from the transmitting antenna to reach the target location. represents the location of the transmitting antenna, Indicates the location of the receiving antenna. Θ 0 Indicates the target location, Represents a clutter signal that obeys Gaussian white noise.

3. The target detection method according to claim 1, wherein the B-Rao algorithm is introduced after low-bit quantization for long-range weak target detection under MIMO radar conditions, characterized in that: By sampling the echo signal and quantizing it by q bits, the obtained signal can be expressed as: It is necessary to determine whether the reflective target exists and construct a binary hypothesis testing problem: H0: H1: Where β represents the target amplitude. Indicates taking the real part of the signal, Indicates taking the imaginary part of the signal. q [·] indicates quantized sampling of the signal.

4. The target detection method according to claim 1, wherein the B-Rao algorithm is introduced after low-bit quantization for long-range weak target detection under MIMO radar conditions, characterized in that: The joint probability density function (PMF) of the quantitative data Y under the assumption: Among them, F i,n [·] represents the joint probability density function, I i [·] represents an indicator function.

5. The method for removing motion noise from millimeter-wave radar signals based on total variation according to claim 1, characterized in that: τ is a controllable variable. The quantization threshold is one of the key factors affecting the detection probability. There is always τ0 = -∞. Among them, β1 represents the true value of β under the assumption H1.

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