Under-snapshot MUSIC direction finding method based on spatial translation invariance

Abstract

The invention belongs to the technical field of signal processing, and particularly relates to an under-snapshot MUSIC direction finding method based on spatial translation invariance. According to the method, a space translation invariant characteristic of a uniform linear array is utilized, a calculation method of a space-time cross-correlation function is provided, a pseudo-covariance matrix is constructed by using the space-time cross-correlation function based on a Hermitian-Toeplitz characteristic of a signal ideal covariance matrix, a MUSIC spatial spectrum is constructed, and a wave direction is extracted. Compared with a traditional MUSIC algorithm, the method still can maintain the high-precision angle estimation capability under the condition that the number of snapshots is limited, and does not greatly improve the calculation amount. Compared with a spatial smoothing MUSIC algorithm, the method does not need to divide sub-arrays, fully utilizes the full array aperture, and avoids the loss of resolution.

Description

Technical Field

[0001] The invention belongs to the technical field of signal processing, and in particular relates to an under-snapshot MUSIC direction finding method based on spatial translation invariance. Background Art

[0002] Spatial spectrum estimation is an important research direction in array signal processing. It has extremely broad application prospects in many fields such as radar, communication, and sonar. It focuses on studying the ability of the processing system composed of spatial multi-sensor arrays to accurately estimate multiple parameters of the spatial signal of interest. The main purpose is to estimate the spatial parameters of the signal or the source position. The 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 direction of the signal source based on 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) in the observation covariance matrix of the array received data; the noise subspace is composed of the eigenvectors corresponding to the smaller eigenvalues ​​(corresponding to the noise variance) in the covariance matrix.

[0003] In actual processing, the data received by the array is a limited number of samples (also called snapshots or snap shots) within a limited time period. During this period, it is assumed that the direction of the incoming wave does not change, the fading of each signal is independently distributed, and the noise is white noise that is unrelated to the signal. Since the MUSIC algorithm relies on the observation covariance matrix of the array received data, the key to this step is the accumulation of snapshots, that is, it is necessary to collect enough signal samples to make the observation covariance matrix more accurate. Therefore, in scenarios with high real-time requirements, especially when the number of snapshots is less than the number of signals (i.e., under-snapshots), the covariance matrix has a lack of rank problem, resulting in the inability to correctly separate the signal space from the noise space, greatly reducing the estimation performance. Although the algorithm based on spatial smoothing can supplement the rank of the observation covariance matrix, it loses the effective aperture of the array.

[0004] The commercialization and development of the fifth-generation mobile communication system has brought about new scenarios with both communication and perception requirements, such as smart factories, drone networks, and vehicle networks, which have attracted continuous attention from the industry for integrated sensing and communication (ISAC) technology. Among them, an important application challenge is how to meet the growing demand for real-time perception, which is a common problem faced by the in-depth development of these new scenarios; in addition, due to the limitation of the total amount of communication and perception resources, how to maximize the communication and perception performance with a low perception overhead is also one of the key issues. Therefore, array direction finding technology in the scenario of insufficient snapshot is a key issue that needs to be solved in the in-depth development of the ISAC system. Summary of the invention

[0005] The algorithm uses the spatial translation invariance of the uniform linear array, proposes a calculation method for the space-time cross-correlation function, and then constructs a pseudo-covariance matrix based on the Hermitian-Toeplitz characteristic of the ideal covariance matrix of the signal using the space-time cross-correlation function, and then constructs the MUSIC spatial spectrum to extract the outgoing wave direction. Compared with the traditional MUSIC algorithm, the present invention can still maintain high-precision angle estimation capability when the number of snapshots is limited, and does not significantly increase the amount of calculation; compared with the spatial smoothing MUSIC algorithm, the present invention does not need to split the subarray, fully utilizes the full array aperture, and avoids resolution loss.

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

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

[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 Shown is a schematic diagram of the system involved in the present invention:

[0014] The system consists of a receiver Rx equipped with N antennas ULA and L independent transmitters Tx, and it is assumed that these devices are in a far-field line-of-sight environment. Consider the azimuth angle from the lth Tx (l∈{1,2,…,L}) to Rx is The corresponding (faded) signal in the qth snapshot (q∈{1,2,…,Q}) is x l , Q is the total number of snapshots, then the received signal of Rx can be expressed as:

[0015]

[0016] in, It represents the antenna array response. For a horizontal ULA with an array element spacing of half a wavelength, it can be specifically expressed as:

[0017]

[0018] also, represents AWGN, where N0 represents the noise power.

[0019] The technical solution adopted by the present invention is:

[0020] S1. Obtain the space-time cross-correlation of the received signal, defined as

[0021]

[0022] S2, yes Perform Hermitian-Toeplitz reconstruction to obtain the pseudo covariance matrix, which is:

[0023]

[0024] S3. Perform eigenvalue decomposition on the pseudo-covariance matrix and calculate the MUSIC spatial spectrum of the arrival angle, specifically:

[0025] S31, yes Perform eigenvalue decomposition, that is

[0026]

[0027] in is a diagonal matrix with diagonal elements The eigenvalues ​​of are arranged in descending order; the characteristic matrix It is composed of corresponding characteristic vectors;

[0028] S32, divide the noise space, specifically: delete the first L columns of the feature matrix U to obtain U N ;

[0029] S33. Calculate the MUSIC spatial spectrum:

[0030]

[0031] S4. Extracting spatial spectrum The angles corresponding to the first L highest peaks are taken as the AoA estimation results.

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

[0033] The present invention proposes an under-snapshot MUSIC direction-finding algorithm based on spatial translation invariance. The algorithm defines a new space-time cross-correlation calculation method. According to the Hermitian-Toeplitz characteristics of the ideal covariance matrix of the signal, the pseudo-covariance matrix is ​​reconstructed using space-time cross-correlation. Since the rank of the reconstructed pseudo-covariance matrix is ​​independent of the number of snapshots, the proposed algorithm effectively solves the problem of failure of the traditional MUSIC algorithm in scenarios with insufficient observation snapshots. At the same time, the algorithm makes full use of the array aperture and significantly reduces the noise level, while maintaining a computational complexity similar to that of traditional MUSIC. The above characteristics enable the proposed algorithm to maintain high accuracy and high stability in complex and changeable 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 under-snapshot conditions, showing higher estimation accuracy and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 : Schematic diagram of the system involved in the present invention;

[0035] Figure 2 : Comparison of the spatial spectrum between the proposed scheme and the traditional algorithm;

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

[0037] The technical solution of the present invention has been described in detail in the content of the invention. The practicability of the present invention is explained below with reference to the accompanying drawings and simulation examples.

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

[0039] Figure 2The spatial spectrum comparison of the proposed solution (marked as STE), the traditional algorithm (marked as CONV), and the spatial smoothing algorithm (marked as SS) is given, and the subarray size of the spatial smoothing algorithm is set to 14. It can be clearly observed that the spatial spectrum of the proposed solution has a steeper peak at the position corresponding to AoA; the traditional algorithm cannot present a peak at the corresponding AoA position; although the spatial smoothing algorithm has an obvious peak at the position corresponding to AoA, the noise platform is higher. This feature shows that the proposed solution overcomes the problem that the traditional solution is not applicable to the single snapshot angle estimation scenario, and has a stronger noise tolerance than the spatial smoothing algorithm.

[0040] Figure 3 The RMSE-SNR curves of the proposed solution (labeled as STE), the traditional algorithm (labeled as CONV), and the spatial smoothing algorithm (labeled as SS) are given. Figure 2 As can be seen from the figure, the traditional MUSIC algorithm is almost ineffective, and the spatial smoothing algorithm can improve the direction finding accuracy but is far inferior to the solution proposed by the present invention.

[0041] In summary, the under-snapshot MUSIC direction finding algorithm based on spatial translation invariance proposed in the present invention has higher estimation accuracy. Compared with the traditional MUSIC algorithm, it can not only operate stably under under-snapshot conditions, but also show higher stability and noise resistance, providing strong support for practical applications.

Claims

1. A sub-snapshot MUSIC direction finding method based on spatial translation invariance, defining a direction finding system comprising a receiver Rx equipped with N antennas ULA, L independent transmitters Tx, and the azimuth from l Tx to Rx is l∈{1,2,…,L}, the corresponding signal after fading in the qth snapshot is x l , q∈{1,2,…,Q}, Q is the total number of snapshots, and the received signal of Rx is expressed as: in, represents the antenna array response, represents AWGN, where N0 represents the noise power and I is the unit matrix; Characterized in that the direction finding method comprises: S1. Obtain space-time cross-correlation of the received signal: S2, yes Perform Hermitian-Toeplitz reconstruction to obtain the pseudo covariance matrix: S3. Perform eigenvalue decomposition on the pseudo-covariance matrix and calculate the MUSIC spatial spectrum of the arrival angle, specifically: S31, yes Perform eigenvalue decomposition, that is in is a diagonal matrix with diagonal elements The eigenvalues ​​of are arranged in descending order; the characteristic matrix It is composed of corresponding characteristic vectors; S32, divide the noise space, specifically: delete the first L columns of the feature matrix U to obtain U N ; S33. Calculate the MUSIC spatial spectrum: in represents the array response; S4. Extracting spatial spectrum The angles corresponding to the first L highest peaks are taken as the estimation results.

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