Azimuth super-resolution method based on beam space transformation

Abstract

The invention relates to the field of active phased array radar array signal processing, in particular to an azimuth super-resolution technology based on beam space transformation. The method comprises the following steps: step 1, establishing an array response matrix; step 2, wave beam space conversion: converting the received signal matrix into a small-dimension wave beam space; and step 3, carrying out azimuth super-resolution estimation on the signal after the beam space transformation by using a deterministic maximum likelihood algorithm, and the like. According to the method, the bandwidth of data transmission is greatly reduced, implementation of a system communication system is facilitated, and meanwhile the calculation complexity is reduced.

Description

Technical Field

[0001] The invention relates to the field of active phased array radar array signal processing, and in particular to an azimuth super-resolution technology based on beam space transformation. Background Art

[0002] A basic task of radar is to detect targets and provide measurement information such as the target's azimuth, distance, and altitude. Measurement accuracy is an important indicator of radar performance. Azimuth measurement information is obtained by scanning the direction (main lobe) of the antenna beam's maximum gain, and the azimuth resolution is one half-power beam width. However, when multiple targets are within the same beam width, the beam scan cannot distinguish these signals. In order to achieve the purpose of distinguishing targets with similar azimuths, the antenna aperture can only be increased to reduce the beam width. However, in actual application environments, increasing the antenna aperture is unrealistic.

[0003] Azimuth super-resolution technology is to distinguish multiple targets with an azimuth spacing less than one beam width without changing the antenna aperture. The echo data received by the array at a certain moment is actually the spatial sampling of the signal. Filtering the spatial signal is to enhance the signal in the direction of interest or suppress the signal in other directions, obtain the spatial spectrum, and extract the spatial information of the signal. The resolution of the super-resolution algorithm is less than one beam width, and it can distinguish multiple targets within the same beam width, realizing the transition from low resolution to high resolution.

[0004] Commonly used array super-resolution algorithms mainly include subspace eigendecomposition algorithms, maximum likelihood algorithms, and sparse reconstruction algorithms. These algorithms all require obtaining the echo of each array element and performing relevant processing. Currently, phased array radars have many array elements and data rates as high as tens of gigahertz, making data transmission difficult, computational complexity high, and engineering implementation difficult. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides an azimuth super-resolution method based on beam space transformation. The present invention first receives array element echo signals, then performs beam space transformation on the array element echo signals to reduce the echo data dimension, then uses multidimensional maximum likelihood estimation to estimate the target angle, obtains multiple angle estimation values, and finally distinguishes the number of targets through threshold discrimination. The present invention reduces the amount of data transmission, is relatively simple in calculation, and is easy to implement in engineering.

[0006] The technical solution of the present invention is: an azimuth super-resolution method based on beam space transformation, characterized in that it comprises the following steps:

[0007] Step 1: Establish the array response matrix a(θ k );

[0008] Step 2: beam space transformation, converting the received signal matrix into a beam space of small dimension;

[0009] Step 3: Use the deterministic maximum likelihood algorithm to perform azimuth super-resolution estimation on the signal after beam space transformation.

[0010] The beneficial effects of the present invention are: when the resolution probabilities are not much different, the bandwidth of data transmission is greatly reduced, the system communication system is easy to implement, and the calculation complexity is reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is an azimuth super-resolution processing flow based on beam space transformation.

[0012] Figure 2 is the antenna pattern of beam space transformation.

[0013] Figure 3 This is a conventional maximum likelihood azimuth super-resolution simulation image.

[0014] Figure 4 This is a simulation image of azimuth super-resolution based on beam space transformation.

[0015] Glossary:

[0016] DOA: Direction of Arrival.

[0017] ML: Maximum Likelihood Estimation Algorithm. Specific implementation methods

[0019] The present invention is further described below in conjunction with the accompanying drawings.

[0020] The present invention provides an azimuth super-resolution method of beam space transformation. Through beam space transformation, the data rate can be reduced while ensuring the resolution probability, thereby reducing the computational complexity of the super-resolution method and facilitating engineering implementation.

[0021] like Figure 1 As shown, the azimuth super-resolution method based on beam space transformation of the present invention first receives array element echo signals, then performs beam space transformation on the array element echo signals to reduce the dimension of the echo data, then uses multidimensional maximum likelihood to estimate the target angle to obtain multiple angle estimation values, and finally uses threshold discrimination to distinguish the number of targets.

[0022] like Figure 2 As shown, the directional diagram of the beam space transformation used in the present invention assumes that the number of array elements N=18, the beam synthesis parameter is B=6, the starting beam number is b=-3, and the data is reduced from 18 to 6 after the beam space transformation.

[0023] like Figure 3As shown, assuming that the antenna array consists of 18 equidistant linear elements, that is, N = 18, the wavelength λ is 0.23m, and the element spacing d is half a wavelength, the half-power beam width is calculated according to the following formula, that is, the angular resolution of the conventional beamforming algorithm is

[0024]

[0025] The calculated half-power beamwidth is 5.6°.

[0026] Assuming that the angles of the two dual targets are 0° and 2.8° respectively (the angle difference between the two targets is equal to half of the half-power beamwidth), in the same beam, with noise and without array channel amplitude and phase errors, the conventional maximum likelihood estimation algorithm is used to resolve the angles of the two targets to be -0.4° and 2.8°.

[0027] like Figure 4 As shown, for Figure 3 Based on the simulation environment and target assumptions, the azimuth super-resolution algorithm based on beam space transformation is used to estimate the angles of the two targets to be -0.3° and 3.1°.

[0028] The present invention provides an azimuth super-resolution method for beam space transformation, comprising the following steps:

[0029] Step 1: Create array response matrix

[0030] Assume that there are N identical omnidirectional receiving array elements forming a uniformly distributed linear array, and there are K far-field targets at angles θ1, θ2, …, θ K The incident light is incident on the linear array, and the incident light source and the antenna array are located in the same plane. t At time , the echo signal received by the receiving antenna array can be expressed as

[0031] x(t)=As(t)+n(t)

[0032] in, is the complex envelope of K targets, {·} T represents the transpose operation, represents Gaussian white noise, is the response matrix of the array. Any column vector a(θ k )(k=1,2,…,K) is the incident angle θ in space k The steering vector is

[0033]

[0034] Among them, λ is the wavelength of the incident signal source, and d is the distance between two adjacent array elements, which is generally half a wavelength.

[0035] Step 2: Beam space transformation: convert the received signal matrix into a small-dimensional beam space

[0036] Beam space transformation refers to first transforming the spatial array elements into one or more beams, and then using the synthesized beam data to estimate DOA. The core of beam space transformation is to transform the original N-dimensional received signal matrix into a B (B < N)-dimensional transformation space, and then use B The dimensional beam space replaces the original array element space for subsequent processing, thereby achieving the purpose of matrix dimensionality reduction.

[0037] If the observation azimuth angle range of the linear array is -90°≤θ≤90°, let u=sinθ, -1≤u≤1, and the steering vector

[0038]

[0039] Since the period of u is 2, the following N×N beamforming matrix can be defined:

[0040]

[0041] Each column represents the main lobe direction of the beam There are N beamformers with n=0,1,…,N-1. The interval between the main lobes of each adjacent beamformer is

[0042] The required normalized weight matrix is ​​formed by selecting B adjacent beamformers in the above formula

[0043]

[0044] Where b is the starting beam of beam synthesis.

[0045] T is the beam space transformation matrix, then the output after beam space transformation is

[0046] y(t)=T H x(t)

[0047] Y=T H X

[0048] The output changes from a vector of size N×1 or N×M to a vector of size B×1 or B×M. The covariance matrix corresponding to the echo data of a single snapshot is becomes

[0049]

[0050] The beamforming matrix is ​​an orthogonal matrix beamformer composed of conjugate centrosymmetric weight vectors and generates beams with common out-of-band nulls. The conjugate centrosymmetry of the weight vectors allows the real part of the beamspace sample covariance matrix to be processed in the eigenanalysis stage, thereby reducing the computational complexity.

[0051] Step 3: Use the deterministic maximum likelihood algorithm to perform azimuth super-resolution estimation on the signal after beam space transformation

[0052] Step 3.1: Deterministic Maximum Likelihood Algorithm

[0053] Assuming that the received array antenna echo data at a certain moment is x(t), then the M-time echo data can be expressed as

[0054]

[0055] The instantaneous covariance matrix of the array is

[0056]

[0057] in,{·} H Represents the conjugate transpose operation.

[0058] The conditional joint probability density function of the unknown parameters θ of the M received data echo samples is:

[0059]

[0060] where σ 2 is the variance of the probability density function.

[0061] Take the logarithm of

[0062]

[0063] First, estimate σ 2 , for σ 2 Find the partial derivative and set it equal to 0, and we get

[0064]

[0065] Among them, P Α =A(θ)[A H (θ)A(θ)] -1 A H (θ) is the projection matrix of matrix A(θ), For P Α An orthogonal matrix, I is the unit matrix, that is, the projection matrix of the noise subspace, and tr{·} represents the trace operation.

[0066] Substitute the estimated result into the original likelihood function and ignore the constant term to obtain

[0067]

[0068] Then fix θ and get the maximum likelihood estimate of s(t):

[0069]

[0070] Will Substitute into the likelihood function and solve for θ:

[0071]

[0072] Then, the maximum likelihood estimate of θ is

[0073]

[0074] Generally speaking, when there are multiple targets, the ML algorithm involves multi-dimensional optimization problems, which require a lot of computation. The alternating projection method can be used to solve multi-dimensional nonlinear function optimization problems. Mathematically, this is multi-dimensional optimization, and physically, it is to search the multi-dimensional signal subspace to fit the array data so that the projection error is minimized.

[0075] Step 3.2: Azimuth super-resolution based on beam space transformation

[0076] The output of beam space transformation is

[0077] y(t)=T H x(t)

[0078] The corresponding covariance matrix is

[0079]

[0080] Then, the maximum likelihood estimation of θ after beam space transformation is

[0081]

[0082] Among them, P B =B(θ)[B H (θ)B(θ)] -1 B H (θ), B(θ) = T H A(θ) is the array echo beam transformation space.

[0083] Table 1 Comparison between array element estimation and beam transformation estimation

[0084]

[0085] For the array element number N=18, the number of beams formed after beam space transformation is B=6, the array element echo data rate is 5M, the data bit width is 64bit, and the repetition period is 3ms. The resolution probability, data bandwidth and computational complexity of the array element space angle estimation and the beam space transformation angle estimation are compared, as shown in Table 1.

Claims

1. An azimuth super-resolution method based on beam space transformation, characterized in that: The following steps are involved: Step 1: Establish the array response matrix a(θ k ); Step 2: beam space transformation, converting the received signal matrix into a beam space of small dimension; The observation azimuth angle range of the linear array is -90°≤θ≤90°, let u=sinθ, -1≤u≤1, and the steering vector Define an N×N beamforming matrix as follows Each column represents the main lobe direction of the beam There are N beamformers in total, and the interval between the adjacent main lobes is Select adjacent B beamformers to form the required normalized weight matrix Where b is the starting beam of beam synthesis; T is the beam space transformation matrix, then the output after beam space transformation is y(t)=T H x(t) Y=T H X The output is changed from a vector of size N×1 or N×M to a vector of size B×1 or B×M, and the covariance matrix corresponding to the echo data of a single snapshot is obtained. Step 3: Use the deterministic maximum likelihood algorithm to perform azimuth super-resolution estimation on the signal after beam space transformation Step 3.1: Deterministic Maximum Likelihood Algorithm The received echo data of the array antenna at a certain moment is x(t), and the M-time echo data can be expressed as The instantaneous covariance matrix of the array is in,{·} H represents the conjugate transpose operation; M The conditional joint probability density function of the unknown parameters θ of the received data echo samples is: where σ 2 is the variance of the probability density function; Take the logarithm of Estimate σ 2 , for σ 2 Find the partial derivative and set it equal to 0, and we get Among them, P Α =A(θ)[A H (θ)A(θ)] -1 A H (θ) is the projection matrix of matrix A(θ), For P A An orthogonal matrix, I is the identity matrix, and tr{·} represents the trace operation; Substitute the estimated result into the original likelihood function and ignore the constant term to obtain Then fix θ and get the maximum likelihood estimate of s(t): Will Substitute into the likelihood function and solve for θ: The maximum likelihood estimate of θ is ； Step 3.2: Azimuth super-resolution based on beam space transformation The output of beam space transformation is y(t)=T H x(t) The corresponding covariance matrix is The maximum likelihood estimation of θ after beam space transformation is: Among them, P B =B(θ)[B H (θ)B(θ)] -1 B H (θ), B(θ) = T H A(θ) is the array echo beam transformation space.

2. The azimuth super-resolution method based on beam space transformation according to claim 1, characterized in that: In step 1, the array response matrix is: Array Response Matrix A Any column vector a(θ k )(k=1,2,…,K) is the incident angle θ in space k The steering vector is Among them, λ is the wavelength of the incident signal source, d is the distance between two adjacent array elements, which is generally half a wavelength, K is the number of complex envelopes of the target, and N is the distributed linear array.

3. The azimuth super-resolution method based on beam space transformation according to claim 1, characterized in that: In step 2, the covariance matrix corresponding to the echo data of a single snapshot is given by becomes

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