Underdetermined MUSIC direction finding method based on spatial shift invariance

Abstract

The present application belongs to the technical field of signal processing, and particularly relates to an under fast-sampling MUSIC direction-finding method based on spatial translation invariance. The method of the present application utilizes the spatial translation invariance characteristic of a uniform linear array, proposes a calculation method of space-time cross-correlation function, and then based on the Hermitian-Toeplitz characteristic of a signal ideal covariance matrix, uses the space-time cross-correlation function to construct a pseudo-covariance matrix, further constructs a MUSIC spatial spectrum, and extracts a wave direction. Compared with the traditional MUSIC algorithm, the present application can still maintain high-precision angle estimation ability under the condition that the number of fast-sampling is limited, and does not greatly increase the calculation amount; compared with the spatial smoothing MUSIC algorithm, the present application does not need to divide sub-arrays, fully utilizes the full-array aperture, and avoids resolution loss.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of signal processing, and particularly relates to an under fast-sampling MUSIC direction finding method based on spatial translation invariance. BACKGROUND

[0002] Spatial spectrum estimation is an important research direction in array signal processing, and has extremely wide application prospects in many fields such as radar, communication, sonar and the like. It focuses on the ability of a processing system composed of a spatial multi-sensor array to accurately estimate various parameters of a spatial signal of interest, and the main purpose is to estimate the spatial domain parameters or source position of the signal. Multiple signal classification (MUSIC) algorithm is an important cornerstone of spatial spectrum estimation theory. It introduces the concept of vector space into spatial spectrum estimation, and realizes super-resolution estimation of the signal source direction according to the orthogonal characteristics of the signal subspace and the noise subspace. The signal subspace is composed of the eigenvectors corresponding to the larger eigenvalues (corresponding to the signal power) of the observation covariance matrix of the array received data; and the noise subspace is composed of the eigenvectors corresponding to the smaller eigenvalues (corresponding to the noise variance) of the observation covariance matrix.

[0003] In actual processing, the data received by the array is a limited number of samples (also called fast-sampling or fast-capture) in a limited time period. In this period of time, it is assumed that the direction of arrival does not change, the fading of each signal is independently distributed, and the noise is white noise independent of the signal. Since the MUSIC algorithm relies on the observation covariance matrix of the array received data, the key of this step is the accumulation of the number of fast-sampling, that is, a sufficient number of signal samples need to be collected to make the observation covariance matrix more accurate. Therefore, in the scene with high real-time requirement, especially when the number of fast-sampling is less than the number of signals (i.e. under fast-sampling), the covariance matrix is under-rank, which leads to the failure of correct separation of the signal space and the noise space, and greatly reduces the estimation performance. Although the algorithm based on spatial smoothing can supplement the rank of the observation covariance matrix, the effective aperture of the array is lost.

[0004] The commercialization and development of the fifth generation mobile communication system have emerged new scenarios such as smart factories, unmanned aerial vehicle networks and vehicle-to-everything networks, which have both communication and sensing requirements, so that the integrated sensing and communication (ISAC) technology has been continuously concerned by the industry. Among them, how to meet the growing real-time sensing requirements is an important application challenge that these new scenarios generally face in-depth development; in addition, due to the limitation of the total amount of communication and sensing resources, how to guarantee the communication and sensing performance to the greatest extent with low sensing overhead is also one of the key problems. Therefore, the array direction finding technology in the under-snapshot scenario is a key problem to be solved for the in-depth development of the ISAC system. SUMMARY

[0005] The algorithm uses the spatial shift-invariance characteristic of the uniform linear array, proposes a method for calculating the space-time cross-correlation function, and then constructs a pseudo-covariance matrix based on the Hermitian-Toeplitz characteristic of the ideal signal covariance matrix, and further constructs a MUSIC spatial spectrum to extract the direction of the wave. Compared with the traditional MUSIC algorithm, the application can still maintain high-precision angle estimation ability under the condition of limited snapshots, and does not greatly increase the computational amount; compared with the spatial smoothing MUSIC algorithm, the application does not need to divide the subarray, fully utilizes the full array aperture, and avoids the loss of resolution.

[0006] In order to better illustrate the present application, the terms and system structure used in the technical scheme of the present application are introduced first.

[0007] AoA: Angle of Arrival, angle of arrival;

[0008] AWGN: Additive White Gaussian Noise, additive white Gaussian noise;

[0009] MUSIC: Multiple Signal Classification, multiple signal classification;

[0010] RMSE: Root Mean Square Error, root mean square error;

[0011] SNR: Signal-to-Noise Ratio, signal-to-noise ratio;

[0012] ULA: Uniform Linear Array, uniform linear array.

[0013] Figure 1 The system schematic diagram involved in the present application is shown:

[0014] The system includes a receiving end Rx equipped with N-antenna ULA, and L independent sending ends Tx, and assumes that the devices are in a far-field line-of-sight environment. Consider that the azimuth angle of the lth Tx (l ∈ {1, 2,..., L}) to Rx is The corresponding (after fading) signal in the qth snapshot (q ∈ {1, 2,..., Q}) is x l Q is the total number of snapshots, and the received signal of the Rx can be expressed as:

[0015]

[0016] wherein, represents the antenna array response, and for a horizontal ULA with an element interval of half a wavelength, can be specifically expressed as:

[0017]

[0018] In addition, represents the AWGN, wherein N0 represents the noise power.

[0019] The technical scheme adopted by the present application is:

[0020] S1, the space-time cross-correlation of the received signal is calculated, and is defined as

[0021]

[0022] S2, the Hermitian-Toeplitz reconstruction is performed on , and the pseudo-covariance matrix is obtained, and is specifically:

[0023]

[0024] S3, the eigenvalue decomposition is performed on the pseudo-covariance matrix, and the MUSIC spatial spectrum of the angle of arrival is calculated, and is specifically:

[0025] S31, the eigenvalue decomposition is performed on , that is,

[0026]

[0027] wherein is a diagonal matrix, and the diagonal elements are the eigenvalues of arranged in descending order; the eigenmatrix is composed of the corresponding characteristic vectors;

[0028] S32, the noise space is divided, and is specifically: the first L columns of the eigenmatrix U are deleted to obtain U N ;

[0029] S33, calculating the MUSIC spatial spectrum:

[0030]

[0031] S4, extracting the spatial spectrum The angle corresponding to the first L highest peaks of the spatial spectrum is taken as the AoA estimation result.

[0032] The beneficial effects of the present application are:

[0033] The present application proposes an under-snapshot MUSIC direction finding algorithm based on spatial shift invariance, which defines a new space-time cross-correlation calculation method, and reconstructs the pseudo-covariance matrix by space-time cross-correlation according to the Hermitian-Toeplitz characteristics of the ideal signal covariance matrix. Since the rank of the reconstructed pseudo-covariance matrix is independent of the snapshot number, the proposed algorithm effectively solves the problem of failure of the traditional MUSIC algorithm in the scene of insufficient observation snapshots. At the same time, the algorithm makes full use of the array aperture, significantly reduces the noise level, and at the same time maintains the similar calculation complexity as the traditional MUSIC. The above characteristics enable the proposed algorithm to maintain high precision and high stability in complex and variable signal environments, providing a solution for angle estimation scenarios with high real-time requirements. Simulation results show that the algorithm can significantly improve the spatial spectrum peak-to-average ratio under the condition of under-snapshot, and has higher estimation accuracy and stability. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 : the system schematic diagram involved in the present application;

[0035] Figure 2 : comparison of spatial spectrum of the scheme proposed in the present application and the traditional algorithm;

[0036] Figure 3 : RMSE-SNR curve of the scheme proposed in the present application and the traditional algorithm; DETAILED DESCRIPTION

[0037] The technical solutions of the present application have been described in detail in the summary section, and the practicality of the present application will be illustrated below in combination with the drawings and simulation examples.

[0038] In Figure 2 and Figure 3 Simulation examples, unless otherwise specified, SNR=10dB, Q=1, N R =16 and the number of multipath L=5 are used for system configuration, the receiving array is a uniform linear array with half-wavelength element spacing, the AoA configuration of each path is 30°, 70°, 90°, 120° and 150°, and the angle resolution is taken as 0.1°.

[0039] Figure 2The spatial spectrum comparison of the scheme (labeled as STE) of the application, the traditional algorithm (labeled as CONV) and the spatial smoothing algorithm (labeled as SS) is given, and the size of the subarray of the spatial smoothing algorithm is set to 14. It can be obviously observed that the spatial spectrum of the scheme of the application has a steeper peak value at the position corresponding to AoA; the traditional algorithm cannot present a peak value at the corresponding AoA position; and the spatial smoothing algorithm has an obvious peak at the position corresponding to AoA, but the noise platform is higher. This feature shows that the scheme of the application overcomes the problem that the traditional scheme cannot be applied to the single fast-snapshot angle estimation scene, and has a stronger noise tolerance ability compared with the spatial smoothing algorithm.

[0040] Figure 3 The RMSE-SNR curves of the scheme (labeled as STE) of the application, the traditional algorithm (labeled as CONV) and the spatial smoothing algorithm (labeled as SS) are given, and the parameter settings are consistent with Figure 2 It can be seen from the figure that the traditional MUSIC algorithm is almost invalid, the spatial smoothing algorithm can improve the direction finding precision, but is far less than the scheme of the application.

[0041] In summary, the under-snapshot MUSIC direction finding algorithm based on spatial translation invariance provided by the application has higher estimation precision. Compared with the traditional MUSIC algorithm, it not only can stably run under the condition of under-snapshot number, but also shows higher stability and noise resistance, thereby providing strong support for practical application.

Claims

1. A spatial translation invariant based under fast time MUSIC direction finding method, defining a direction finding system comprising a receiving end Rx equipped with a ULA of N antennas, L independent transmitting ends Tx, the azimuth angle of the lth Tx to Rx is l∈{1,2,…,L}, the corresponding faded signal in the qth fast time is x l , q∈{1,2,…,Q}, Q is the total number of fast times, the received signal of Rx is represented as: wherein represents the antenna array response, represents the AWGN, where N0represents the noise power and I is the identity matrix; The method is characterized in that the direction-finding method comprises the following steps: S1, calculating the space-time cross-correlation of the received signal: S2, to Hermitian-Toeplitz reconstruction is performed to obtain the pseudo-covariance matrix: S3, performing eigenvalue decomposition on the pseudo-covariance matrix to calculate the MUSIC space spectrum of the angle of arrival, specifically: S31, to perform eigenvalue decomposition, i.e. wherein is a diagonal matrix whose diagonal elements are the eigenvalues of the matrix are arranged in descending order; the eigenvectors S32, dividing the noise space, specifically: deleting the first L columns of the feature matrix U to obtain U N ; S33, calculating the MUSIC space spectrum: wherein represents the array response; S4, extracting spatial spectrum the angles corresponding to the L highest peaks of the spatial spectrum as the estimation result.

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