阅读说明：本技术 基于非圆信号的单基地展开互质阵列mimo雷达doa估计方法 (Single-basis expansion co-prime array MIMO radar DOA estimation method based on non-circular signals ) 是由 周围 王强 唐俊 张维 潘英杰 于 2020-03-29 设计创作，主要内容包括：本发明涉及雷达技术领域,尤其涉及基于非圆信号的单基地展开互质阵列MIMO雷达DOA估计方法,对接收阵元匹配滤波后的数据进行采样,得到等价虚拟阵列的接收数据,随后进行共轭处理并组合为新的扩展接收数据,进行空间协方差矩阵和特征值分解,根据噪声子空间与导向矢量的正交性构造空间谱的计算表达式,谱峰搜索K个谱峰的位置即为K个来波的波达方向估计。本发明的方法将展开互质阵列作为MIMO雷达的发射阵列和接收阵列,使得收发阵列的阵列空间大大扩展,并同时将非圆信号作为MIMO雷达的发射阵列的发射信号,结合非圆信号的非圆特性、MIMO雷达优异的空间分辨率和参数识别性、展开互质阵列扩展的阵列孔径的三重优点,极大提高了DOA估计性能。(The invention relates to the technical field of radars, in particular to a non-circular signal-based single-base expanded co-prime array MIMO radar DOA estimation method, which comprises the steps of sampling data after matching and filtering of receiving array elements to obtain receiving data of an equivalent virtual array, then carrying out conjugation processing and combining the data into new expanded receiving data, carrying out spatial covariance matrix and eigenvalue decomposition, constructing a calculation expression of a spatial spectrum according to the orthogonality of a noise subspace and a guide vector, and searching the positions of K spectral peaks by the spectral peaks, namely estimating the arrival directions of K incoming waves. The method of the invention takes the expanded co-prime array as the transmitting array and the receiving array of the MIMO radar, greatly expands the array space of the transmitting and receiving array, simultaneously takes the non-circular signal as the transmitting signal of the transmitting array of the MIMO radar, combines the non-circular characteristic of the non-circular signal, the excellent spatial resolution and parameter identification of the MIMO radar and the triple advantages of the expanded array aperture of the expanded co-prime array, and greatly improves the DOA estimation performance.)

1. A DOA estimation method of a monostatic expansion co-prime array MIMO radar based on a non-circular signal is characterized by comprising the following steps:

s1, sampling the data subjected to matching filtering of the receiving array elements for L times to obtain receiving data X (t) of an equivalent virtual array;

s2, obtaining the conjugate X of the received data X (t)^*(t), further mixing X (t) with X^*(t) combining into new extended received data y (t);

s3, carrying out spatial covariance matrix on the new extended received data Y (t)(ii) an estimate of (d);

s4, a spatial covariance matrix is pairedCarry out eigenvalueSolving and obtaining a noise subspace;

s5, constructing a calculation expression of a space spectrum according to the orthogonality of the noise subspace and the guide vector, and searching a spectrum peak according to the calculation expression of the space spectrum, wherein the positions of the K spectrum peaks are the direction of arrival estimation of the K incoming waves.

2. The method for estimating the DOA of the non-circular signal based monostatic unfolding coprime array MIMO radar as claimed in claim 1, wherein the monostatic unfolding coprime array MIMO radar comprises a transmitting array and a receiving array, the transmitting array and the receiving array respectively comprise a sub-array 1 and a sub-array 2 of two sparse uniform linear arrays, the sub-array 1 and the sub-array 2 are completely unfolded and arranged in opposite directions, and the last array element of the sub-array 1 is coincident with the first array element of the sub-array 2.

3. The method of claim 2, wherein the number of elements of sub-array 1 and sub-array 2 is M, N, and M, N are mutually prime, M < N, the pitch of elements of sub-array 1 is N λ/2, the pitch of elements of sub-array 2 is M λ/2, λ represents the wavelength of the electromagnetic signal incident on the spread mutually prime array, and the number of elements of the transmitting array and the receiving array is M + N-1.

4. The non-circular signal based single-radix spread mutual-prime array MIMO radar DOA estimation method according to claim 3, wherein the received data X (t) is as follows:

X(t)＝AS(t)+N(t)

wherein S (t) is an echo signal vector, A represents a virtual array manifold of a monostatic expansion co-prime array MIMO radar, N (t) is a mean value of 0 and a variance σ²An additive white gaussian noise vector.

5. The non-circular signal based single-radix spread mutual-prime array MIMO radar DOA estimation method of claim 4, wherein the spatial covariance matrix isThe following were used:

where Σ denotes a summation operation and H denotes a conjugate transpose operation.

6. The method of claim 5, wherein the spatial covariance matrix is obtained by eigenvalue decomposition

Wherein E_sIs R_YYThe eigenvectors corresponding to the K principal eigenvalues of (E), i.e. the signal subspace_nIs 2(M + N-1)²The eigenvectors corresponding to the K other eigenvalues, i.e. the noise subspace, U_sAnd U_nRespectively K main eigenvalues and 2(M + N-1)²-a diagonal matrix of K other eigenvalues.

7. The non-circular signal based single-radix unfolding mutual-prime array MIMO radar DOA estimation method according to claim 6, wherein the calculation expression of the spatial spectrum is as follows

In the formula (I), the compound is shown in the specification,

Technical Field

The invention relates to the technical field of radars, in particular to a single-basis expansion co-prime array MIMO radar DOA estimation method based on non-circular signals.

Background

In recent years, the idea of Multiple Input Multiple Output (MIMO) technology in the communication field has been introduced into the radar field, and the proposed MIMO radar system has attracted much attention. The MIMO radar fully utilizes signal diversity and space domain diversity gain to obtain higher degree of freedom compared with the traditional radar, and the target detection capability, the parameter estimation capability and the like of the MIMO radar are widely recognized. Due to the many advantages Of MIMO radar, research on MIMO radar is rapidly developing, wherein the problem Of Direction Of Arrival (DOA) estimation Of MIMO radar is a major research topic.

Most of current researches on the estimation of the DOA of the MIMO radar are based on a uniform linear array, and the rotation invariance (ESPRIT) or a multi-signal classification mode is utilized to obtain the performance (spatial resolution, anti-noise performance and the like) which is more excellent than that of the traditional system radar. However, the MIMO radar is generally half-wavelength in the array element spacing between the transmitting array and the receiving array, which limits the array aperture, and thus the performance is limited to a certain extent. The co-prime array is an inhomogeneous linear array, has larger array aperture compared with the homogeneous linear array, and has higher lateral precision and resolution because the co-prime array space spectrum estimation algorithm utilizes the co-prime characteristic of the number of sub-array elements to identify the target source. However, in the existing methods, the co-prime array is treated as two sparse uniform arrays respectively, so that the following problems exist: firstly, the degree of freedom is limited by the number of sub-array elements, and is reduced by at least half compared with a uniform array; the second is that further operations are required to eliminate the ambiguity problem. The expanded co-prime array is different from the traditional co-prime array in that two sub-arrays are expanded and arranged in opposite directions, the aperture of the array is further expanded, all array elements are used for receiving data to construct a spatial covariance matrix, then the MUSIC algorithm is used for obtaining DOA estimation, and the co-prime of the number of the array elements inhibits the phase ambiguity problem.

The DOA estimation method based on the conventional phased array radar often uses a circular signal to construct a received data matrix, and does not consider the existence of a non-circular signal, however, in practical application, the non-circular signals such as BPSK, AM, and MASK are more and more widely used, so that the DOA estimation method by fully using the characteristics of the non-circular signals is an important subject of the spatial spectrum estimation theory. For DOA estimation based on MIMO radar, a general method is to transplant a traditional method, for example, a subspace MUSIC method is applied to a two-dimensional MUSIC method, a dimension reduction MUSIC method and the like of the MIMO radar, but the method is often large in calculated amount and is not suitable for a method adopting non-circular signal direction finding, when a coherent source exists, the performance is rapidly deteriorated, the DOA estimation performance is low or the DOA estimation is difficult to realize. Therefore, how to perform coherent source DOA estimation based on the single-base MIMO radar by using the characteristics of the non-circular signal is an urgent technical problem to be solved.

Disclosure of Invention

In view of this, the present invention provides a method for estimating DOA of a single-basis unfolding co-prime array MIMO radar based on non-circular signals, in which an unfolded co-prime array is used as a transmitting array and a receiving array of the MIMO radar, so that the array space of the transmitting and receiving array is greatly expanded, and simultaneously, the non-circular signals are used as the transmitting signals of the transmitting array of the MIMO radar, and the DOA estimation performance is greatly improved by combining the non-circular characteristics of the non-circular signals, the excellent spatial resolution and parameter identification of the MIMO radar, and the triple advantages of the array aperture of the unfolded co-prime array.

The invention solves the technical problems by the following technical means:

a DOA estimation method of a monostatic expansion co-prime array MIMO radar based on a non-circular signal comprises the following steps:

s1, sampling the data subjected to matching filtering of the receiving array elements for L times to obtain receiving data X (t) of an equivalent virtual array;

s2, obtaining the conjugate X of the received data X (t)^*(t), further mixing X (t) with X^*(t) combining into new extended received data y (t);

s3, carrying out spatial covariance matrix on the new extended received data Y (t)(ii) an estimate of (d);

s4, a spatial covariance matrix is pairedCarrying out eigenvalue decomposition and obtaining a noise subspace;

s5, constructing a calculation expression of a space spectrum according to the orthogonality of the noise subspace and the guide vector, and searching a spectrum peak according to the calculation expression of the space spectrum, wherein the positions of the K spectrum peaks are the direction of arrival estimation of the K incoming waves.

Further, the monostatic expansion co-prime array MIMO radar comprises a transmitting array and a receiving array, wherein the transmitting array and the receiving array respectively comprise a sub-array 1 and a sub-array 2 of two sparse uniform linear arrays, the sub-array 1 and the sub-array 2 are completely expanded and arranged in opposite directions, and the last array element of the sub-array 1 is coincident with the first array element of the sub-array 2.

Further, in the monostatic unfolding co-prime array MIMO radar, the number of the array elements of the sub-array 1 and the sub-array 2 is respectively M, N and M, N co-prime, M is less than N, the array element interval of the sub-array 1 is N lambda/2, the array element interval of the sub-array 2 is M lambda/2, lambda represents the wavelength of an electromagnetic signal incident to the unfolding co-prime array, and the array element numbers of the transmitting array and the receiving array are both M + N-1.

Further, the received data x (t) is as follows:

X(t)＝AS(t)+N(t)

wherein S (t) is an echo signal vector, A represents a virtual array manifold of a monostatic expansion co-prime array MIMO radar, N (t) is a mean value of 0 and a variance σ²An additive white gaussian noise vector.

Further, the spatial covariance matrixThe following were used:

where Σ denotes a summation operation and H denotes a conjugate transpose operation.

Further, the space covariance matrix is obtained by performing eigenvalue decomposition

Wherein E_sIs R_YYThe eigenvectors corresponding to the K principal eigenvalues of (E), i.e. the signal subspace_nIs 2(M + N-1)²The eigenvectors corresponding to the K other eigenvalues, i.e. the noise subspace, U_sAnd U_nRespectively K main eigenvalues and 2(M + N-1)²-a diagonal matrix of K other eigenvalues.

Further, the calculation expression of the spatial spectrum is as follows

In the formula (I), the compound is shown in the specification,

compared with the prior art, the invention has the following advantages:

(1) the expanded co-prime array is combined with the MIMO radar, and the excellent DOA estimation performance is realized by utilizing the large array aperture of the expanded co-prime array and the excellent spatial resolution, the freedom degree, the parameter identifiability and other performances of the MIMO radar and combining with the classical MUSIC algorithm.

(2) The DOA estimation method is different from the traditional co-prime array DOA estimation algorithm that the received data of two sub-arrays are respectively processed, so that the degree of freedom is reduced by at least half, the whole receiving array is taken as a whole, and the received data of all receiving array elements are used for DOA estimation.

(3) The non-circular signals are used as the transmitting signals of the transmitting array of the expanded co-prime array MIMO radar, and then the receiving signals and the conjugate of the receiving signals are combined into new expanded receiving signals, so that the dimensionality of the original receiving signals is multiplied, the non-circular characteristic of the non-circular signals is fully utilized, the performance can be further improved under the excellent DOA estimation performance of the expanded co-prime array MIMO radar, and the degree of freedom is theoretically doubled.

Drawings

Fig. 1 is a diagram of the geometry of an extended co-prime MIMO radar array according to the present invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Firstly, establishing a system mathematical model

The method comprises the following specific steps of forming an expanded co-prime array MIMO radar by using 2M +2N-1 antenna array elements, wherein M and N represent two co-prime integers, receiving an echo signal of a transmitting array transmitting signal reflected by K targets by a receiving array of the MIMO radar, and constructing the expanded co-prime array MIMO radar:

the single-base expanded co-prime array MIMO radar in the embodiment of the invention comprises a transmitting array and a receiving array, the geometrical structures of the transmitting array and the receiving array are shown in figure 1, the transmitting array and the receiving array respectively comprise a sub-array 1 and a sub-array 2 of two sparse uniform linear arrays, the sub-array 1 and the sub-array 2 are completely expanded and arranged in opposite directions, and the last array element of the sub-array 1 is overlapped with the first array element of the sub-array 2. The number of the array elements of the subarray 1 and the subarray 2 is M, N respectively, M, N are relatively prime, and M < N is set without loss of generality. The array element spacing of the subarray 1 is N lambda/2, the array element spacing of the subarray 2 is M lambda/2, wherein lambda represents the wavelength of an electromagnetic signal incident to the expanded co-prime array, and the array element numbers of the transmitting array and the receiving array are both M + N-1.

Then, the array element positions of the transmitting array and the receiving array can be expressed as

P_t＝P_r＝{Mnd₀|0≤n≤(N-1)}∪{M(N-1)d₀+Nmd₀|0≤m≤(M-1)} (1)

Wherein d is₀Is a half wavelength, and thus the aperture of the spread co-prime array is M (N-1) d₀+N(M-1)d₀Compared with uniform array aperture Nd₀Conventional coprime array aperture max (M (N-1) d)₀，N(M-1)d₀) It can be seen that the aperture of the expanded co-prime array is greatly improved.

Each transmitting array element simultaneously transmits a same-frequency orthogonal periodic phase coding signal, and the transmitting signals meet the conditional formula (2)

Wherein s is_i、s_jThe signals of the ith and jth transmit array elements, respectively, L is the number of phase codes per repetition period, and ∑ represents the summation operation.

Acquiring the guide vectors of a transmitting subarray and a receiving subarray:

assume that there are K far-field targets that are uncorrelated with each other and satisfy K<(M+N-1)²The echo arrival angles of the targets are respectively theta₁,θ₂…θ_KTherefore, the steering vectors of the transmitting array and the receiving array with respect to the k-th target can be expressed by equations (3) and (4), respectively

Wherein, a_t1(θ_k)、a_t2(θ_k) Respectively, the guide vectors of the transmitting array sub-array 1 and the sub-array 2, a_r1(θ_k),a_r2(θ_k) Then the steering vectors for sub-array 1 and sub-array 2 are received, K is 1 and 2 … K respectively. The guide vector expressions of the transmitting subarray and the receiving subarray are respectively

Thus obtaining the array manifold A of the transmitting array and the receiving array_t、A_rAs follows

A_t＝[a_t(θ₁)a_t(θ₂)…a_t(θ_K)](7)

A_r＝[a_r(θ₁)a_r(θ₂)…a_r(θ_K)](8)

Further obtaining the virtual array manifold of the single-basis expansion co-prime array MIMO radar

Wherein

Represents the Khatri-Rao product,representing the Kronecker product. Thus, the received data of the receiving array element after matched filtering can be obtained

X(t)＝AS(t)+N(t) (11)

Where S (t) is the echo signal vector

β_kRadar cross section coefficient (RCS), f of the k point target_dkDoppler frequency, f, of the k point target_sThe pulse repetition frequency of the transmit waveform. N (t) is a mean of 0 and a variance of σ²An additive white gaussian noise vector.

Single-basis expansion co-prime array MIMO radar DOA estimation method based on non-circular signals

Taking conjugate of matched and filtered received signal X (t) to obtain X^*(t), further mixing X (t) with X^*(t) combining to obtain an extended received signal Y (t)

Computing a spatial covariance matrix R for the spread received signal Y (t)_YY

R_YY＝E[Y(t)Y^H(t)](15)

R in practical engineering_YYCan be estimated from L finite snapshots.

For the spatial covariance matrix R_YYPerforming eigenvalue decomposition

Wherein E_sIs R_YYThe eigenvectors corresponding to the K principal eigenvalues of (E), i.e. the signal subspace_nIs 2(M + N-1)²The eigenvectors corresponding to the K other eigenvalues, i.e. the noise subspace, U_sAnd U_nRespectively K main eigenvalues and 2(M + N-1)²-a diagonal matrix of K other eigenvalues. According to the orthogonality of the noise subspace and the guide vector, a calculation expression of a space spectrum can be constructed

The positions corresponding to the K spectral peaks are the estimated DOA, wherein

Although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims. The techniques, shapes, and configurations not described in detail in the present invention are all known techniques.