A MIMO radar imaging evaluation method based on scattering information

Abstract

The present invention discloses a MIMO radar imaging evaluation method based on scattering information, including: establishing a mathematical model of a surface target with two dimensions in range and azimuth; establishing a detection system model of a single pixel point of a MIMO radar to obtain an echo signal of a certain antenna; and writing the echo signal received from a certain antenna in a matrix form; generalizing to obtain an echo signal of a surface target composed of multiple pixels; performing two-step preprocessing of the echo signal in range and azimuth at the receiving end; performing matched filtering of the echo using a baseband signal in the range direction to obtain a matched filtering result in a discrete form; performing matched filtering in the azimuth direction using a weighted vector to obtain a two-dimensional observation data matrix; and obtaining the scattering information of the surface target, wherein the greater the amount of scattering information, the better the imaging effect. The present invention defines the scattering information in the MIMO radar as the mutual information between the scattering characteristics and the observation data after matching, and uses the scattering information as a performance indicator to better evaluate the imaging effect.

Description

Technical Field

[0001] The present invention belongs to the technical field of information acquisition and processing, relates to a multiple-input multiple-output (MIMO) radar technology, and specifically relates to a MIMO radar imaging evaluation method based on scattering information. Background Art

[0002] Radar, as a milestone invention in the field of radio, can detect and locate targets in all weather conditions, all day and at long distances. Early radars had low resolution, so they observed the detected objects as point targets. With the update and development of technology, radar resolution units have reached smaller sizes, much smaller than the detected targets. Therefore, imaging targets has become a new task for radar.

[0003] The commonalities between radar detection systems and communication systems have promoted the development of radar communication integration. At present, many communication theories and technologies have been well applied in radar systems. For example, MIMO radar, which is a combination of MIMO technology in communication and digital array technology in radar, has been widely used in practice. In the 1970s, MIMO technology greatly improved communication performance in the field of wireless communications. Later, Fishler et al. proposed the concept of MIMO radar and introduced this technology into radar systems.

[0004] Woodward and Davies used the inverse probability method and mutual information to study the problem of radar detection target distance, and introduced probability theory and information theory methods into radar detection systems. In the 1950s, Linfoot et al. introduced Shannon information theory into the sampling imaging system, and used the amount of information as an indicator for evaluating the quality of the optical system. In 1983, Frost first proposed the use of information theory methods in SAR imaging problems. Subsequent scholars also studied the distance-direction information of MIMO radar systems based on information theory. Although information theory has made important contributions to radar research, there are relatively few studies on the issue of radar imaging performance evaluation indicators based on information theory. Radar imaging is to restore its scattering coefficient based on the measured value of the scattering field of the imaging unit, and the scattering coefficient carries useful information. Mutual information can be understood as the reduction of the prior uncertainty of the target. Therefore, it is very reasonable to introduce scattering information as an evaluation indicator of imaging performance in the radar imaging system with mutual information as the link. At present, there is no theoretical analysis study on the application of information theory to the performance of MIMO radar imaging systems. Therefore, based on the existing research results, it is of great significance to study the MIMO radar imaging evaluation method based on scattering information. Summary of the invention

[0005] Purpose of the invention: The present invention provides a MIMO radar imaging evaluation method based on scattering information, which converts the MIMO radar imaging problem into a scattering information calculation problem for each pixel point on a surface target, and defines the scattering information as the mutual information between the scattering characteristics and the matched observation data. The scattering information reflects the amount of information contained in the resulting image, and is used to evaluate the quality of the imaging system, providing theoretical guidance for system designers.

[0006] Technical solution: The MIMO radar imaging evaluation method based on scattering information described in the present invention comprises the following steps:

[0007] S1: The entire detection area is taken as the radar detection object, and a mathematical model of the surface target with two dimensions, range and azimuth, is established by sampling the detection area;

[0008] S2: Establish a single pixel detection system for MIMO radar and obtain the echo signal of a certain antenna through one-way delay;

[0009] S3: Define the delay vector of the radar transmitting orthogonal signal, write the echo signal in S2 into a matrix form; generalize to obtain the echo signal of a surface target composed of multiple pixels;

[0010] S4: Perform range and azimuth matching filtering on the echo signal at the receiving end: perform range matching filtering on the echo using the baseband signal to obtain the total normalized delay, and use the normalized distance to obtain the matched filtering result in discrete form; fix the range parameters, introduce the matrix representation of the receiving sequence of different receiving antennas, and use the weighted vector of the receiving antenna to perform azimuth matching filtering;

[0011] S5: After azimuth matched filtering, a two-dimensional observation data matrix is ​​obtained. The observation data matrix consists of a scattering coefficient matrix and a complex Gaussian noise matrix of the detection area.

[0012] S6: According to the probability density function of the scattering coefficient matrix and the complex Gaussian noise matrix, the differential entropy of the matched observation data and the conditional differential entropy of the observation data with a given scattering coefficient are obtained;

[0013] S7: The scattering information of the surface target is obtained according to the mutual information definition; the greater the amount of scattering information, the better the imaging effect.

[0014] Furthermore, the method for establishing the mathematical model of the surface target in step S1 is:

[0015] The entire detection area is regarded as a surface target, and the detection area is sampled. The sampling points are called pixel points based on the optical concept. The detection area is a two-dimensional sector surface with range and azimuth directions. Through sampling, the detection area is decomposed into U pixel points in the range direction and V pixel points in the azimuth direction. Polar coordinates are used to establish a mathematical model of the surface target, and the number of array antennas is M. (u, v) is used to represent the pixel coordinates, u represents the range direction, v represents the azimuth direction, u∈[1,U], v∈[1,V]; the pixel position is determined by the distance r between the target and the reference origin p and the angle θ between the target direction and the coordinate normal; let R be the distance from the closest point of the sector detection area to the reference origin, and θ be the angle from the closest point to the normal; the reciprocal of the baseband signal bandwidth △r=1 / B is used as the sampling interval in the range direction, and △β is used as the sampling interval in the azimuth direction. θ =2π / M as the sampling interval to ensure no interference between sampling points; distance r p , spatial frequency △β θ The value range of the angle θ is:

[0016] r p ∈{R+(u-1)Δr|u=1,2,…,U}

[0017] β θ ∈{β Θ +(v-1)△β θ |v=1,2,…,V}

[0018] θ∈{arcsin[2dsinΘ / λ+2(v-1) / M]|v=1,2,…,V}.

[0019] Furthermore, the implementation process of step S2 is as follows:

[0020] The polar coordinate system is used to establish a MIMO radar single pixel point detection system, with the first antenna as the origin and the (u,v)th pixel point position as (r p,u,v ,θ u,v ); the distance between the (u,v)th pixel and the qth antenna is:

[0021]

[0022] Where d is the distance between antennas;

[0023] Approximate the distance between the (u,v)th pixel and the qth antenna to obtain the corresponding one-way delay of the qth antenna for transmission or reception:

[0024]

[0025] Among them, c represents the propagation speed of electromagnetic waves;

[0026] The expression of the echo signal of the (u,v)th pixel received by the qth antenna is:

[0027]

[0028] Where m is the serial number of the transmitting antenna, q is the serial number of the receiving antenna, and α is the amplitude of the target complex scattering coefficient. is the initial phase, f c is the carrier frequency, ψ m (t) represents the baseband signal transmitted by the mth antenna, τ(r p,u,v ,θ u,v ,m,q) represents the round-trip time delay, w q (t) represents noise with a mean of 0 and a bandwidth of B / 2;

[0029] After down-conversion to baseband, the echo signal of the (u,v)th pixel received by the qth antenna is:

[0030]

[0031] Furthermore, the implementation process of step S3 is as follows:

[0032] The radar transmits orthogonal signal delay vector:

[0033]

[0034] The sending direction vector is:

[0035] a(θ u,v )=[1,exp(jπsinθ u,v ),…,exp(jπ(M-1)sinθ u,v )] T

[0036] Write the echo signal of a certain antenna in matrix form:

[0037]

[0038] The echo signal of a surface target composed of multiple pixels is specifically:

[0039]

[0040] Furthermore, the distance matched filtering implementation process in step S4 is as follows:

[0041] After matching the echo with the baseband signal:

[0042]

[0043] Where:

[0044]

[0045] make:

[0046]

[0047]

[0048] When this item is a diagonal element, i=g, let:

[0049]

[0050] but:

[0051]

[0052] Where, B = △fL ZC ;

[0053] When this term is a non-diagonal element, i≠g:

[0054]

[0055] so:

[0056]

[0057] The result of distance matching filtering is:

[0058]

[0059] Where W q (τ)=∫D H (t,τ)w q (t)dt;

[0060] The matching results are sampled at the Nyquist sampling rate B, the delay is normalized to τ = Bτ, and the distance is normalized to r u,v =2Br p,u,v / c, the discrete distance matching result is:

[0061]

[0062] According to the orthogonal characteristics of complex sinusoidal signals, let of The result of distance matching filtering is:

[0063]

[0064] Furthermore, the azimuth matched filtering implementation process in step S4 is as follows:

[0065] Introduce the matrix representation of the received sequence of different receiving antennas:

[0066]

[0067] In the formula, b(θ v )=[1,exp(jπsinθ v ),…,exp(jπ(M-1)sinθ v )] T ;

[0068] After azimuth matching filtering using the receiving antenna's weighted vector:

[0069]

[0070] Where:

[0071] because:

[0072]

[0073] Let β θ =β θv of The result of azimuth matched filtering is:

[0074]

[0075] Furthermore, the two-dimensional observation data matrix in step S5 is:

[0076] Y'=M 2 S'+W'

[0077] In the formula: Y'=[Y1,…,Y V ], component Y v =[y(1,v),y(2,v),…,y(U,v)] T represents the U pixels in the vth column of the surface target; S' is the scattering coefficient matrix of the detection area; W' is the complex Gaussian noise matrix;

[0078] The observed data vector after vectorization is:

[0079] Y=M 2 S+W

[0080] Where: Y = vec (Y') = [Y1 T ,…,Y V T ] T ;S=vec(S'); W=vec(W').

[0081] Furthermore, the implementation process of step S6 is as follows:

[0082] The scattering coefficient matrix S' obeys the matrix variable complex Gaussian distribution, and the probability density function of S' is:

[0083]

[0084] Where: Σ and Ω are covariance matrices; the probability density function of S after vectorization is:

[0085]

[0086] In the formula, represents the Kronecker product of two matrices; the complex Gaussian noise matrix W' is a complex Gaussian random process matrix, each element of which is an independent one-dimensional complex Gaussian random variable, and the probability density function of W' is:

[0087]

[0088] Where N0 is the variance of each complex Gaussian random variable; the differential entropy of the matched observation data is:

[0089] h(Y)=log[(πe) UV |R Y |]

[0090] Where:

[0091] R Y =E[YY H ]

[0092] =M 4 E[SS H ]+E[WW H ]

[0093] =M 4 Ψ+N0I UV

[0094] The conditional differential entropy of the observed data for a given scattering coefficient is:

[0095] h(Y|S)=h(W)=log[(πe) UV |N0I UV ].

[0096] Furthermore, the surface target scattering information in step S7 is:

[0097]

[0098] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are as follows: the existing MIMO radar imaging evaluation performance indicator resolution is intended to characterize the radar's ability to resolve close-range objects, while the present invention calculates scattering information to provide a specific calculation and measurement standard for the amount of information contained in the image presented by the MIMO radar; the law of information change reflects the imaging effect of the radar system and provides guidance for system designers. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] Figure 1 is a flow chart of the present invention;

[0100] Figure 2 It is a schematic diagram of the mathematical model of the surface target in the present invention;

[0101] Figure 3 Schematic diagram of the polar coordinate system of the MIMO radar in the present invention;

[0102] Figure 4 This is the simulation result diagram of MIMO radar imaging scattering information. DETAILED DESCRIPTION

[0103] The present invention will be further described below in conjunction with the accompanying drawings.

[0104] The present invention provides a MIMO radar imaging evaluation method based on scattering information, which regards MIMO radar imaging as a communication process, the resulting image as an echo signal, and defines the scattering information of the MIMO radar as the mutual information between the matched observation data and the scattering characteristics. This is because the information about the target in the matched observation data can be considered as the statistical uncertainty or entropy reduction about the target state. The total scattering information contained in an image is the sum of the scattering information contained in all the pixels constituting the image. The two-dimensional observation data matrix of the MIMO radar is derived by performing matched filtering twice in the range and azimuth directions at the receiving end. The probability distribution function is used to derive the scattering information value of the MIMO radar imaging; the law of information change reflects the imaging effect of the radar system. Figure 1 As shown, the specific steps include:

[0105] Step 1: Take the entire detection area as the radar detection object, and establish a mathematical model of the surface target with two dimensions, namely, range and azimuth, by sampling the detection area.

[0106] The entire detection area is considered as a surface target. Considering that the detection area is continuous in the actual scene, the detection area is sampled, and the sampling points are called pixels based on the optical concept. The detection area is a two-dimensional fan-shaped surface with range and azimuth. Through sampling, the detection area can be decomposed into U pixels in the range and V pixels in the azimuth.

[0107] like Figure 2As shown in the figure, the mathematical model of the surface target is established using polar coordinates, and the number of array antennas is M. The pixel coordinates are represented by (u, v), where u represents the range direction and v represents the azimuth direction, u∈[1,U], v∈[1,V]. The pixel position is determined by the distance r between the target and the reference origin. p The angle θ between the target direction and the coordinate normal is composed of. Let R be the distance from the closest point of the sector detection area to the reference origin, and θ be the angle from the closest point to the normal. The reciprocal of the baseband signal bandwidth △r=1 / B is used as the sampling interval in the range direction, and △β is used as the sampling interval in the azimuth direction. θ =2π / M as the sampling interval to ensure no interference between sampling points. p , spatial frequency △β θ The value range of the angle θ is:

[0108] r p ∈{R+(u-1)Δr|u=1,2,…,U}

[0109] β θ ∈{β Θ +(v-1)△β θ |v=1,2,…,V}

[0110] θ∈{arcsin[2dsinΘ / λ+2(v-1) / M]|v=1,2,…,V}.

[0111] Step 2: Use polar coordinate system to establish MIMO radar single pixel point detection system model, such as Figure 3 As shown, due to the large number of antennas Figure 3 Through the one-way delay, the echo signal of a certain antenna is obtained.

[0112] Taking the first antenna as the origin, the position of the (u,v)th pixel is (r p,u,v ,θ u,v ). It is assumed that the pixel is in the far field, the transmitted signal is a narrowband signal, and each antenna is considered to be able to transmit and receive signals independently.

[0113] The distance between the (u,v)th pixel and the qth antenna is:

[0114]

[0115] Wherein, d is the distance between antennas, d=λ / 2, and λ is the wavelength of the transmitted signal.

[0116] In the far field assumption, d / r p.u.v <<1, approximate the distance between the (u,v)th pixel and the qth antenna, and obtain the corresponding one-way delay of the qth antenna transmitting or receiving:

[0117]

[0118] Among them, c represents the propagation speed of electromagnetic waves.

[0119] Each antenna transmits a signal, which is reflected after reaching the far-field target and superimposed at the receiving antenna; the expression of the echo signal of the (u, v)th pixel point received by the qth antenna is:

[0120]

[0121] Where: m represents the serial number of the transmitting antenna, q represents the serial number of the receiving antenna, α is the amplitude of the target complex scattering coefficient, is the initial phase, f c is the carrier frequency, ψ m (t) represents the baseband signal transmitted by the mth antenna, τ(r p,u,v ,θ u,v ,m,q) represents the round-trip time delay, w q (t) represents white noise with mean 0 and bandwidth B / 2.

[0122] After down-conversion to baseband, the expression of the echo signal of the (u, v)th pixel received by the qth antenna is:

[0123]

[0124] The transmission signal of the MIMO radar system is an orthogonal signal composed of the OFDM signal and the Zadoff-Chu sequence. The time domain expression of the transmission signal of the mth antenna is:

[0125]

[0126] Step 3: Define the delay vector of the radar transmitting orthogonal signal, write the sum of the echo signals in step 2 into a matrix form; generalize to obtain the echo signal of a surface target composed of multiple pixels.

[0127] The radar transmits orthogonal signal delay vector:

[0128]

[0129] The sending direction vector is:

[0130] a(θ u,v )=[1,exp(jπsinθ u,v ),…,exp(jπ(M-1)sinθ u,v )] T

[0131] Write the sum of the echoes received by a certain antenna from multiple transmitted signals in matrix form:

[0132]

[0133] Extended to a surface target composed of multiple pixels, the echo signal received by the qth antenna is:

[0134]

[0135] Step 4: Perform range and azimuth matched filtering on the echo signal at the receiving end: perform range matched filtering on the echo using the baseband signal to calculate the total normalized delay, and use the normalized distance to obtain the matched filtering result in discrete form; fix the range parameters, introduce the matrix representation of the receiving sequence of different receiving antennas, and use the weighted vector of the receiving antenna to perform azimuth matched filtering.

[0136] The process of distance matching filtering is as follows:

[0137] After matching the echo with the baseband signal:

[0138]

[0139] Where:

[0140]

[0141] make:

[0142]

[0143]

[0144] When this item is a diagonal element, i=g, let:

[0145]

[0146] but:

[0147]

[0148] Where: B = △fL ZC .

[0149] When this term is a non-diagonal element, i≠g:

[0150]

[0151] so:

[0152]

[0153] The result of distance matching filtering is:

[0154]

[0155] Where: W q (τ)=∫D H (t,τ)w q (t)dt.

[0156] The matching result is sampled at Nyquist sampling rate B, and the delay is normalized Distance normalization r u,v =2Br p,u,v / c, get the distance matching result in discrete form:

[0157]

[0158] because:

[0159]

[0160] Let △fk=F, then:

[0161]

[0162] According to the orthogonal characteristics of complex sinusoidal signals:

[0163]

[0164] make of The result of distance matching filtering is:

[0165]

[0166] After completing the above steps, the distance direction of the echo signal of the surface target is fixed, and the matched filtering in the sending and receiving directions can be performed on the specific distance unit respectively. The matrix representation of the receiving sequence of different receiving antennas is introduced:

[0167]

[0168] Where: b(θ v )=[1,exp(jπsinθ v ),…,exp(jπ(M-1)sinθ v )] T .

[0169] After azimuth matching filtering:

[0170]

[0171] Where:

[0172] because:

[0173]

[0174] make of The result of azimuth matched filtering is:

[0175]

[0176] Step 5: After azimuth matched filtering, a two-dimensional observation data matrix is ​​obtained. The observation data matrix consists of the scattering coefficient matrix and the complex Gaussian noise matrix of the detection area.

[0177] The two-dimensional observation data matrix is:

[0178] Y'=M 2 S'+W'

[0179] In the formula: Y'=[Y1,…,Y V ], component Y v =[y(1,v),y(2,v),…,y(U,v)] T represents the U pixels in the vth column of the surface target; S' is the scattering coefficient matrix of the detection area; W' is the complex Gaussian noise matrix.

[0180] The observed data vector after vectorization is:

[0181] Y=M 2 S+W

[0182] Where: Y = vec (Y') = [Y1 T ,…,Y V T ] T ;S=vec(S'); W=vec(W').

[0183] Step 6: According to the probability density function of the scattering coefficient matrix and the complex Gaussian noise matrix, the differential entropy of the matched observation data and the conditional differential entropy of the observation data with a given scattering coefficient are obtained.

[0184] The scattering coefficient matrix S' obeys the matrix variable complex Gaussian distribution, and the probability density function of S' is:

[0185]

[0186] Where: Σ and Ω are covariance matrices; the probability density function of S after vectorization is:

[0187]

[0188] In the formula, represents the Kronecker product of two matrices; the complex Gaussian noise matrix W' is a complex Gaussian random process matrix, each element of which is an independent one-dimensional complex Gaussian random variable, and the probability density function of W' is:

[0189]

[0190] Where N0 is the variance of each complex Gaussian random variable; the differential entropy of the matched observation data is:

[0191] h(Y)=log[(πe) UV |R Y |]

[0192] Where:

[0193] R Y =E[YY H ]

[0194] =M 4 E[SS H ]+E[WW H ]

[0195] =M 4 Ψ+N0I UV

[0196] The conditional differential entropy of the observed data for a given scattering coefficient is:

[0197] h(Y|S)=h(W)=log[(πe) UV |N0I UV |].

[0198] Step 7: Obtain the surface target scattering information according to the mutual information definition; the greater the amount of scattering information, the better the imaging effect. The surface target scattering information is:

[0199] I(Y;S)=h(Y)-h(Y|S).

[0200] =log(N0 -UV |M 4 Ψ+N0I UV |)

[0201] In order to verify the effectiveness of the method of the present invention, a simulation test was carried out on the method of the present invention. The specific simulation results are as follows: Figure 4 shown. Figure 4 Simulation results of MIMO radar detecting scattering information of a surface target with 4 pixels in the distance direction and 4 pixels in the azimuth direction under different signal-to-noise ratio conditions. It can be seen that with the improvement of signal-to-noise ratio, the scattering information increases, indicating a more accurate imaging effect.

Claims

1. A MIMO radar imaging evaluation method based on scattering information, characterized in that: The following steps are involved: S1: The entire detection area is taken as the radar detection object, and a mathematical model of the surface target with two dimensions, range and azimuth, is established by sampling the detection area; S2: Establish a single pixel detection system for MIMO radar and obtain the echo signal of a certain antenna through one-way delay; S3: Define the delay vector of the radar transmitting orthogonal signal, write the echo signal in S2 into a matrix form; generalize to obtain the echo signal of a surface target composed of multiple pixels; S4: Perform range and azimuth matching filtering on the echo signal at the receiving end: perform range matching filtering on the echo using the baseband signal to obtain the total normalized delay, and use the normalized distance to obtain the matched filtering result in discrete form; fix the range parameters, introduce the matrix representation of the receiving sequence of different receiving antennas, and use the weighted vector of the receiving antenna to perform azimuth matching filtering; S5: After azimuth matched filtering, a two-dimensional observation data matrix is ​​obtained. The observation data matrix consists of a scattering coefficient matrix and a complex Gaussian noise matrix of the detection area. S6: According to the probability density function of the scattering coefficient matrix and the complex Gaussian noise matrix, the differential entropy of the matched observation data and the conditional differential entropy of the observation data with a given scattering coefficient are obtained; S7: Obtain the surface target scattering information according to the mutual information definition; The greater the amount of scattered information, the better the imaging effect; The method for establishing the mathematical model of the surface target in step S1 is: The entire detection area is regarded as a surface target, and the detection area is sampled. The sampling points are called pixel points based on the optical concept. The detection area is a two-dimensional sector surface with range and azimuth directions. Through sampling, the detection area is decomposed into U pixel points in the range direction and V pixel points in the azimuth direction. Polar coordinates are used to establish a mathematical model of the surface target, and the number of array antennas is M. (u, v) is used to represent the pixel coordinates, u represents the range direction, v represents the azimuth direction, u∈[1,U], v∈[1,V]; the pixel position is determined by the distance r between the target and the reference origin p and the angle θ between the target direction and the coordinate normal; let R be the distance from the closest point of the sector detection area to the reference origin, and θ be the angle from the closest point to the normal; the reciprocal of the baseband signal bandwidth Δr=1 / B is used as the sampling interval in the range direction, and Δβ is used as the sampling interval in the azimuth direction. θ =2π / M as the sampling interval to ensure no interference between sampling points; distance r p , spatial frequency Δβ θ The range of the angle θ is: r p ∈{R+(u-1)Δr|u=1,2,...,U} b θ ∈{β Θ +(v-1)Δβ θ |v=1,2,...,V}| θ∈{arcsin[2dsinΘ / λ+2(v-1) / M]|v=1,2,...,V}; The implementation process of step S2 is as follows: The polar coordinate system is used to establish a MIMO radar single pixel detection system, with the first antenna as the origin and the (u,v)th pixel position as (r p,u,v ,θ u,v ); the distance between the (u,v)th pixel and the qth antenna is: Where d is the distance between antennas; Approximate the distance between the (u,v)th pixel and the qth antenna to obtain the corresponding one-way delay of the qth antenna for transmission or reception: Where c represents the propagation speed of electromagnetic waves; The expression of the echo signal of the (u,v)th pixel received by the qth antenna is: Where m is the serial number of the transmitting antenna, q is the serial number of the receiving antenna, and α is the amplitude of the target complex scattering coefficient. is the initial phase, f c is the carrier frequency, ψ m (t) represents the baseband signal transmitted by the mth antenna, τ(r p,u,v ,θ u,v ,m,q) represents the round-trip time delay, w q (t) represents noise with a mean of 0 and a bandwidth of B / 2; After down-conversion to baseband, the echo signal of the (u,v)th pixel received by the qth antenna is: The implementation process of step S3 is as follows: The radar transmits orthogonal signal delay vector: The sending direction vector is: a(θ u,v )=[1,exp(jπsinθ u,v ),…,exp(jπ(M-1)sinθ u,v )] T Write the echo signal of a certain antenna in matrix form: The echo signal of a surface target composed of multiple pixels is specifically: The process of implementing the distance matched filtering in step S4 is as follows: After matching the echo with the baseband signal: Where: make: When this item is a diagonal element, i = g, let: but: Where, B = ΔfL ZC ; When this term is a non-diagonal element, i≠g: so: The result of distance matching filtering is: where, W q (τ) = ∫ D H (t, τ) w q (t) dt; The matching result is sampled at Nyquist sampling rate B, and the delay is normalized Distance normalization r u,v =2Br p,u,v / c, the discrete distance matching result is: According to the orthogonal characteristics of complex sinusoidal signals, let of The result of distance matched filtering is: The azimuth matched filtering implementation process described in step S4 is as follows: Introduce the matrix representation of the received sequence of different receiving antennas: where b(θ v ) = [1, exp(jπsinθ v ),..., exp(jπ(M - 1)sinθ v )] T ; After azimuth matching filtering using the receiving antenna's weighted vector: Where: because: make of The result of azimuth matched filtering is: The two-dimensional observation data matrix in step S5 is: Y'=M 2 S'+W' In the formula: Y'=[Y1,...,Y V ], component Y v =[y(1,v),y(2,v),…,y(U,v)] T represents the U pixels in the vth column of the surface target; S' is the scattering coefficient matrix of the detection area; W' is the complex Gaussian noise matrix; The observed data vector after vectorization is: Y=M 2 S+W Where: S = vec(S'); W = vec(W'); The implementation process of step S6 is as follows: The scattering coefficient matrix S' obeys the matrix variable complex Gaussian distribution, and the probability density function of S' is: Where: ∑ and Ω are covariance matrices; the probability density function of S after vectorization is: In the formula, represents the Kronecker product of two matrices; the complex Gaussian noise matrix W' is a complex Gaussian random process matrix, each element of which is an independent one-dimensional complex Gaussian random variable, and the probability density function of W' is: Where N0 is the variance of each complex Gaussian random variable; the differential entropy of the matched observation data is: h(Y)=log[(πe) UV |R Y |] Where: R Y =E[YY H ] =M 4 E[SS H ]+E[WW H ] =M 4 Ψ+N0I UV The conditional differential entropy of the observed data for a given scattering coefficient is: h(Y|S)=h(W)=log[(πe) UV |N0I UV |]; The surface target scattering information in step S7 is:

Images