CN113189556B - MIMO radar moving target detection method under composite Gaussian clutter environment - Google Patents

Abstract

The invention discloses a MIMO radar moving target detection method in a composite Gaussian clutter environment, belongs to the technical field of signal processing, and particularly relates to a method for detecting a moving target object in the composite Gaussian clutter environment by using a supervised learning method. The detection method can effectively detect the moving target object in the complex Gaussian clutter environment, and the detector has controllable calculation complexity, smaller calculation amount and higher detection precision compared with the traditional GLRT detector.

Description

MIMO radar moving target detection method under composite Gaussian clutter environment

Technical Field

The invention belongs to the technical field of signal processing, and particularly relates to a method for detecting a moving target object in a complex Gaussian clutter environment by using a supervised learning method.

Background

Multiple Input Multiple output (Multiple Out) radar can bring performance gain in target detection. In the detection process, the radar receives not only the target echo, but also clutter in the environment. In many scenarios, clutter may be modeled as a complex gaussian distribution, which is the product of a slowly varying texture component and a rapidly varying speckle component.

GLRT is a traditional statistical method for solving the problem of radar detection with unknown parameters, which requires estimation of the unknown parameters to achieve detection. The accuracy of the estimation significantly affects the final detection performance, and accurate parameter estimation also implies large computational complexity.

Compared with statistical methods, the learning-based method is data-driven, and has the great characteristic that the detection task can be completed within controllable complexity. In document 1(m. -p. jarbo-animals, m. rosa-zurrea, r. gil-Pita, and f. lopez-Ferreras, "Study of two error functions to approximate the new-Pearson detector using superior leaving mechanisms," IEEE transaction Signal Processing, vol.57, No.11, pp.4175-4181, nov.2009.), the authors consider a learning-based method as the NP detector. In document 2(W.Jiang, A.M.Haimovich, and O.Simeone, "End-to-End learning of fashion generation and detection for radio systems," in 201953^rdIn the Asilomar Conference on Signals, Systems, and computers, pacific Grove, CA, USA: IEEE, nov.2019, pp.1672-1676), authors propose a method to jointly design transmit waveforms and detectors in radar Systems using end-to-end learning. Therefore, it is necessary to solve the MIMO radar moving target detection problem in the complex gaussian clutter environment by using supervised learning.

Disclosure of Invention

The invention aims at solving the technical problem of the deficiency of the background technology and obtains a method for realizing MIMO radar moving target detection by using a fully connected neural network (FCN) within controllable time complexity in a composite Gaussian clutter environment.

The technical scheme of the invention is a MIMO radar moving target detection method under a composite Gaussian clutter environment, which comprises the following steps:

step 1: arranging signal sampling values received by N receivers into a line in sequence aiming at an MIMO radar system to form a received signal r;

wherein the content of the first and second substances,

η_n＝[η_n1,...,η_nM]^T

ζ_n＝[ζ_n1,...,ζ_nM]^T

S＝Diag{S₁,...,S_N}

S_n＝[s_n[1],...,s_n[K]]^T

s_n[k]＝[s_n1[k],...,s_nM[k]]^T

s_nm[k]＝s_m(kT_s-τ_nm)

A＝Diag{A₁,...,A_N}

A_n＝[a_n[1],...,a_n[K]]^T

a_n[k]＝[a_n1[k],...,a_nM[k]]^T

G＝Diag{g₁,...,g_N}

the position of the Cell (CUT) to be detected is (x)₀,y₀) If the target object is present, it is assumed that it does not leave the unit to be detected within the observation interval, and its velocity is (v)_x,v_y) (ii) a M is the number of transmitting antennas of the MIMO radar system, and N is the number of receiving antennas of the MIMO radar system; the transmitted signal of the m-th transmitting antenna is at kT_sSampled value of time being

Wherein E_mFor transmitting signal power, T_sFor the sampling time interval, k is the number of samples, s_mIndicating a transmission signal,. indicates a Hadamard product, and the distance between the mth transmission antenna and the target object is d_tmThe distance between the nth receiving antenna and the target object is d_rn，P₀Is when d is_tm＝d_rnRatio of received power to transmitted power at 1 time, τ_nmRepresenting the time delay, ζ, of the corresponding path_nmReflection coefficient of target object representing corresponding path, f_nmDoppler shift representing the corresponding path, c_n[k]Representing clutter plus noise; clutter plus noise vector c_nObey a composite Gaussian distribution, which can be expressed as

Wherein the texture component b_nA speckle component g being a non-negative random variable_nIs a complex Gaussian vector of K-dimensional zero-mean space white with a variance of Σ₀；

Step 2: constructing a detection problem:

H₀:r＝Gb

H₁:r＝(S⊙A)(η⊙ζ)+Gb

wherein H₀Signal model representing the absence of target, H₁A signal model representing the presence of a target;

converting the above detection problem into a binary classification problem

Wherein ε is the label of the binary detection problem, and ε 0 is equivalent to H₀With ε ═ 1 equivalent to H₁；

And step 3: generating data and corresponding labels according to a received signal model to form a training set and a test set;

and 4, step 4: constructing a fully-connected neural network with a specific structure, wherein a hidden layer uses a linear correction unit (ReLU) as an activation function, and an output layer uses a sigmoid activation function; initializing trainable parameters of the network by utilizing a method for initializing the Hocamamine;

and 5: training a network by utilizing a loss function, wherein the used loss function is a cross entropy loss function;

where φ is the set of trainable network parameters, P is the number of training samples, ε^(p)Is the label of the p-th training data, z^(p)Is the output of the fully-connected neural network corresponding to the p-th training data sample; adam is used as an optimizer in the training process; qth of a network trainable parameterThe secondary iteration is:

wherein the content of the first and second substances,

for training loss L_φThe gradient of (epsilon, z) to phi is set to phi^(q-1)Value of (a)^(q)Learning rate is more than 0; a preset value delta is given, when the absolute value of a training error is smaller than delta, training iteration is stopped, and an optimized FCN network parameter phi is obtained at the moment^*(ii) a Based on a given false alarm probability P for NP detection_faDetermining threshold gamma by using data of label corresponding epsilon 0 in training data_FCN；

Step 6: inputting the test data into the fully-connected neural network to obtain corresponding output z, and connecting z with threshold gamma_FCNComparing to obtain the final detection result

The detection probability is calculated as follows:

where num (e ═ 1) is the number of data items corresponding to the label of e ═ 1 in the test data,

the number of data which can be correctly judged by the FCN in the test data with the label of epsilon being 1;

and 7: and detecting the moving target object in the composite Gaussian clutter environment by adopting the trained fully-connected neural network.

The detection method can effectively detect the moving target object in the complex Gaussian clutter environment, and the detector has controllable calculation complexity, smaller calculation amount and higher detection precision compared with the traditional GLRT detector.

Drawings

Fig. 1 is a schematic diagram of an FCN with a number of hidden layers D-2.

FIG. 2 shows P for FCN and GLRT detectors at different antenna counts_dSchematic representation.

FIG. 3 is a graph of the P of the FCN and GLRT detectors under the shape parameters of the different clutter texture components_dSchematic representation.

Detailed Description

For convenience of description, the following definitions are first made:

()^Tis a transposition of^HRe {. is a conjugate transpose, Re {. is an actual part, Im {. is an imaginary part, Diag {. represents a block diagonal array, a represents a Hadamard product, Tr {. is a trace of a matrix, and | is an absolute value.

Consider a MIMO radar system having M transmit antennas and N receive antennas, where the M (M1.., M) th radar transmit antenna is located in (x) cartesian coordinates in two dimensions_tm,y_tm) The N-th radar receiving antenna is located at (x ═ 1.., N.)_rn,y_rn). The transmitting signal of the mth radar transmitting antenna is at kT_sSampled value of time being

Wherein the content of the first and second substances,

E_mfor transmitting signal power, T_sIs the sampling interval. The coordinate of CUT is (x)₀,y₀). If the target object exists, it is assumed that it does not leave the CUT within the observation interval and at a velocity (v)_x,v_y) And (4) moving. Therefore, for radar systems, at kT_sThe signal received by the nth receiving antenna at the moment is

In the first row of the above formula, d_tmFor the distance of the m-th transmitting antenna to the target object, d_rnIs the distance, P, between the nth receiving antenna and the target object₀Is when d is_tm＝d_rnRatio of received signal strength to transmitted signal strength at 1, τ_nmIs the time delay, ζ, of the (n, m) th path_nmIs the target object reflection coefficient for the (n, m) th path (assuming no known determination), f_nmIs the Doppler shift of the (n, m) th path, c_n[k]Is clutter plus noise. In the second line of the above-mentioned formula,

η_n＝[η_n1,...,η_nM]^T (2)

ζ_n＝[ζ_n1,...,ζ_nM]^T (4)

s_n[k]＝[s_n1[k],...,s_nM[k]]^T (5)

s_nm[k]＝s_m(kT_s-τ_nm) (6)

a_n[k]＝[a_n1[k],...,a_nM[k]]^T (7)

the signal received by the nth receiving antenna is

Wherein, the first and the second end of the pipe are connected with each other,

S_n＝[s_n[1],...,s_n[k]]^T (10)

A_n＝[a_n[1],...,a_n[k]]^T (11)

c_n＝[c_n[1],...,c_n[K]]^T (12)

hypothesis spur plus noise vector c_nObey a composite Gaussian distribution, which can be expressed as

Wherein the texture component b_nA speckle component g, which is a non-negative random variable (assumed unknown)_nIs a K-dimensional space white zero-mean Gaussian vector with a covariance matrix of ∑₀。

All signals received by the radar receiving end are

Wherein the content of the first and second substances,

S＝Diag{S₁,...,S_N} (17)

A＝Diag{A₁,...,A_N} (18)

G＝Diag{g₁,...,g_N} (19)

the binary detection problem is established as shown below

FCN is utilized to solve the detection problem. The above detection problem is considered as a binary classification problem as follows

Wherein ε is the label of the binary class, ε 0 is equivalent to H₀With ε ═ 1 equivalent to H₁. And generating data and corresponding labels according to the received signal model to form a training set and a test set. Constructing an FCN with the number of hidden layers D ═ 2 as shown in fig. 1, the hidden layers use ReLU as the activation function, and the output layers use sigmoid function as the activation function.

The trainable parameters of the network are initialized using a method for initializing He Cacamme. In training the network, the following cross entropy function is used as a loss function

Where P is the total number of training data, z^(p)Is the network output corresponding to the P (P ═ 1.. multidata., P) th training data, epsilon^(p)Is the label for the p-th training data and phi is the set of trainable parameters of the network. In an iterative process, we use an Adam optimizer.

The process of the q parameter iterative updating is

Wherein the content of the first and second substances,

is a training loss L_φThe gradient of (epsilon, z) to the parameter phi is phi ═ phi^(q-1)Value of (a)^(q)Learning rate > 0. When the training error is less than a given value delta, the training is iteratedStop

|L_φ(ε,z)|＜δ (25)

After training is finished, obtaining a network optimization parameter phi^*. Based on a given false alarm probability P for NP detection_faWe calculate the threshold γ using the data labeled with e ═ 0 in the training data_FCN。

In the testing stage, test data is input into the trained network to obtain an output z, and the output and a threshold gamma are used_FCNComparing to obtain the final decision result

The detection probability is calculated as follows

Wherein num (epsilon is 1) is the number of data with corresponding label epsilon being 1 in the test data,

the number of data that can be correctly decided by the FCN in the test data labeled with 1.

Working principle of the invention

FCN is essentially a parametric equation f_φ(. it inputs through D hidden layers

Mapping to output

Y_dRepresents the number of neurons in the D (D ═ 1., D +1) th layer. The d-th layer output of FCN is

Wherein phi is_d＝{W_d,b_dIs the trainable parameter set of level d, including the weights

And bias

ρ_d(. cndot.) is an activation function. The set of all trainable parameters of the FCN is

Initializing phi by using the method of initializing He Cacame, i.e. W_dEach element in (1) is zero mean and variance is 2/Y_d-1Gaussian distribution of b_dIs a zero vector. After initialization, h is₀＝[Re{r^T},Im{r^T}]^TAs an input of the FCN, where r is a received signal of N receiving ends. After D hidden layer processes, the output layer generates output z epsilon (0,1) to represent the posterior probability of the existence of the target object. Final decision result

By combining the output with a threshold gamma_FCNAnd (4) comparing to obtain.

Regarding moving target detection of FCN in the case of complex gaussian clutter, we performed simulations in both cases. The simulation parameters are set as follows:

the coordinate of CUT is (x)₀,y₀) (0.12,0.15) km, if the target object exists, its velocity is (v)_x,v_y) (20,20) m/s. Assuming that all antennas are located on a circle 3km from the origin, the angle of the mth transmitting antenna is

The angle of the N-th (N ═ 1.. multidot.n) receiving antenna is

The m-th transmitting antenna transmits signals of

Where T is 0.1ms, f_m10 m/T. Energy of the transmitted signal is E_m＝E＝10¹⁴The total number of time samples is K120. Clutter plus noise obeying a K distribution, i.e. clutter texture component b_nObey to the gamma distribution

Where Γ (·) is the Euler gamma equation, θ_nIs the shape parameter, κ_nIs a scale parameter, let θ be for simplicity and without loss of generality_n＝θ，κ_nK ═ k. Clutter speckle component g_nThe covariance matrix of₀The (i, j) th element is ρ^i-jAnd ρ is set to 0.95. Let the target object reflection coefficients of all paths take the same value, i.e.. zeta_nmζ. Signal to noise and noise ratio (SCNR) is defined as

We generated 50000 training data and 4000 test data between-22 dB to 5dB SCNR, each containing half of the data-corresponding label e 0 and half of the data-corresponding label e 1. False alarm probability is set to P_fa＝0.01。

In fig. 2, we compare the detection performance of the FCN and GLRT detectors at different numbers of receiving antennas, and set θ to 5 and κ to 0.2. First, consider the case where the number of transmit antennas M is 2 and the number of receive antennas N is 2, where the number of hidden layers in FCN is 2(FCN M2N2D2), the number of neurons per layer is 100 and 20, and the GLRT detector uses the simplex method (GLRT M2N2), the confidence-domain method (GLRT-region M2N2), and the class, respectivelyNewton's method (GLRT quasi-Newton M2N2) was used for velocity estimation. As can be seen from the figure, the FCN detector performs well in the GLRT detector in a given SCNR range, and the FCN gets P under a certain SCNR_dThe time used was 5500 times shorter than for a GLRT detector based on the simplex method, 13500 times shorter than for a GLRT detector based on the confidence domain method, and 11344 times shorter than for a GLRT detector based on the Newtonian-like method. Another result that can be observed from the graph is that among the three GLRT detectors, the GLRT detector based on the simplex method is superior to the other two GLRT detectors in both detection performance and calculation time. Therefore, in the simulations that follow, we only consider a GLRT detector based on the simplex method. In the second scenario, we increase the number of receiving antennas to N equal to 4, where the number of FCN hidden layers is D equal to 3(FCN M2N2D3), and the number of nodes in each layer is 200,100, and 20, respectively. In the third scenario, the number of MIMO radar receiving antennas is N-6, the number of FCN hidden layers is D-4 (FCN M2N6D4), and the number of nodes in each layer is 300, 200,100, 20. As can be seen from the figure, in both scenarios, the detection performance of FCN is better than that of GLRT detector and the running time is shorter than that of GLRT detector.

In fig. 3, we compare the detection performance of the FCN and GLRT detectors at different clutter texture component shape parameters θ. First, let θ be 5 and FCN have D2 hidden layers, each layer containing 100 and 20 neurons. As can be seen from the figure, the detection effect of FCN (FCN θ is 5, D is 2) is better than that of GLRT detector (GLRT θ is 5). Next, let θ be 1.5, FCN has D be 3 hidden layers, each layer contains 100, 100, and 20 neurons, and under this setting, detection performance of FCN (FCN θ is 1.5, D is 3) is also better than that of GLRT (GLRT θ is 1.5). In the third scenario, let θ be 0.5, FCN have D be 4 hidden layers, each layer contains 200,100, 100,20 neurons, and it can be seen from the figure that when SCNR is less than-19 dB, GLRT (GLRT θ is 0.5) has better detection performance than FCN (FCN θ is 0.5, D is 4), and when SCNR is greater than-19 dB, FCN has better detection performance. This may be because when the SCNR is low, the FCN cannot obtain advantages from the data, and the GLRT detector still has advantages brought by the statistical model, whereas when the SCNR is high, in the test phase, the performance of both detectors is improved, and for the FCN, in the training phase, the performance gain brought by high-quality data is also obtained, so when the SCNR is high, the FCN performance is better.

Claims (1)

1. A MIMO radar moving target detection method under a complex Gaussian clutter environment comprises the following steps:

step 1: arranging signal sampling values received by N receivers into a line in sequence aiming at an MIMO radar system to form a received signal r;

wherein the content of the first and second substances,

r_n＝[r_n[1],...,r_n[K]]^T

＝(S_n⊙A_n)(η_n⊙ζ_n)+c_n

η_n＝[η_n1,...,η_nM]^T

ζ_n＝[ζ_n1,...,ζ_nM]^T

S＝Diag{S₁,...,S_N}

S_n＝[s_n[1],...,s_n[K]]^T

s_n[k]＝[s_n1[k],...,s_nM[k]]^T

s_nm[k]＝s_m(kT_s-τ_nm)

A＝Diag{A₁,...,A_N}

A_n＝[a_n[1],...,a_n[K]]^T

a_n[k]＝[a_n1[k],...,a_nM[k]]^T

G＝Diag{g₁,...,g_N}

the position of the Cell (CUT) to be detected is (x)₀,y₀) If the target object is present, it is assumed that it does not leave the unit to be detected within the observation interval, and its velocity is (v)_x,v_y) (ii) a M is the number of transmitting antennas of the MIMO radar system, and N is the number of receiving antennas of the MIMO radar system; the transmitted signal of the m-th transmitting antenna is at kT_sSampled value of time being

Wherein E_mFor transmitting signal power, T_sFor the sampling time interval, k is the number of samples, s_mIndicating a transmission signal,. indicates a Hadamard product, and the distance between the mth transmission antenna and the target object is d_tmThe distance between the nth receiving antenna and the target object is d_rn，P₀Is when d is_tm＝d_rnRatio of received power to transmitted power at 1, τ_nmRepresenting the time delay, ζ, of the corresponding path_nmReflection coefficient of target object representing corresponding path, f_nmDoppler shift representing the corresponding path, c_n[k]Representing clutter plus noise; clutter plus noise vector c_nObey a composite Gaussian distribution, which can be expressed as

Wherein the texture component b_nA speckle component g being a non-negative random variable_nIs a complex Gaussian vector of K-dimensional zero-mean space white with a variance of Σ₀；

Step 2: constructing a detection problem:

H₀:r＝Gb

H₁:r＝(S⊙A)(η⊙ζ)+Gb

wherein H₀Signal model representing the absence of target, H₁A signal model representing the presence of a target;

converting the above detection problem into a binary classification problem

r＝ε(S⊙A)(η⊙ζ)+Gb,

Wherein ε is the label of the binary detection problem, and ε 0 is equivalent to H₀With ε ═ 1 equivalent to H₁；

And step 3: generating data and corresponding labels according to a received signal model to form a training set and a test set;

and 4, step 4: constructing a fully-connected neural network with a specific structure, wherein a hidden layer uses a linear correction unit (ReLU) as an activation function, and an output layer uses a sigmoid activation function; initializing trainable parameters of the network by utilizing a method for initializing the Hocamamine;

and 5: training a network by utilizing a loss function, wherein the used loss function is a cross entropy loss function;

where φ is the set of trainable network parameters, P is the number of training samples, ε^(p)Is the label of the p-th training data, z^(p)Is the output of the fully-connected neural network corresponding to the p-th training data sample; adam is used as an optimizer in the training process; the qth iteration of the trainable parameters of the network is:

wherein the content of the first and second substances,

for training loss L_φThe gradient of (epsilon, z) to phi is phi ═ phi^(q-1)Value of (a)^(q)Learning rate is more than 0; a preset value delta is given, when the absolute value of a training error is smaller than delta, training iteration is stopped, and an optimized FCN network parameter phi is obtained at the moment^*(ii) a Based on a given false alarm probability P for NP detection_faDetermining threshold gamma by using data of label corresponding epsilon 0 in training data_FCN；

Step 6: inputting the test data into the fully-connected neural network to obtain corresponding output z, and connecting z with threshold gamma_FCNComparing to obtain the final detection result

The detection probability is calculated as follows:

wherein num (epsilon is 1) is the number of data with corresponding label epsilon being 1 in the test data,

the number of data which can be correctly judged by the FCN in the test data with the label of epsilon being 1;

and 7: and detecting the moving target object in the composite Gaussian clutter environment by adopting the trained fully-connected neural network.

Images