Under-shot 2D-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 a kind of under fast 2D-MUSIC direction finding method based on spatial translation invariance.The method of the present application utilizes the spatial translation invariance characteristics of uniform linear array or uniform planar array, proposes the calculation method of forward and backward space-time cross-correlation function, and then based on the Hermitian-block Toeplitz characteristics of signal ideal covariance matrix, constructs pseudo covariance matrix using space-time cross-correlation function, and further constructs MUSIC spatial spectrum to extract the direction of arrival.Compared with the traditional 2D-MUSIC algorithm, the present application can still maintain high-precision angle estimation ability under the condition of limited fast shots, and does not significantly increase the computational load;Compared with the spatial smoothing MUSIC algorithm, the present application does not need to divide subarray, fully utilizes the full array aperture, and avoids the loss of resolution.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of signal processing, and particularly relates to a 2D-MUSIC direction finding method based on spatial shift invariance. BACKGROUND

[0002] The commercialization and development of the fifth generation mobile communication system have given rise to a series of new scenarios that have both communication and sensing needs, such as unmanned aerial vehicle networks and vehicle-to-everything networks. Therefore, integrated sensing and communication (ISAC) technology is now attracting much attention in the industry. In an ISAC network, a key application challenge is how to meet the growing demand for real-time sensing. For example, unmanned aerial vehicle networks have high dynamicity and flexibility and have wide application prospects in the fields of logistics, environmental monitoring, and emergency communication. However, the dynamic adjustment of the network and the stability of the communication link highly depend on accurate real-time positioning technology to ensure the effectiveness and reliability of the network. In addition, due to the limitation of the total amount of communication and sensing resources, the ISAC network cannot allocate too many resources for sensing purposes. Therefore, how to achieve the sensing and communication indicators of the ISAC network with low sensing overhead is also one of the key problems.

[0003] However, traditional positioning algorithms often require a large amount of resource overhead to accurately estimate the time delay, angle, and other information of the signal. In the field of signal processing technology, a classic array direction finding algorithm is multiple signal classification (MUSIC), which introduces the concept of vector space into spatial spectrum estimation and uses the orthogonal characteristics of signals and noise to achieve super-resolution estimation of incoming signals. For direction finding problems in three-dimensional space, the two-dimensional multiple signal classification (2D-MUSIC) algorithm is an evolution of the MUSIC algorithm and is used to estimate the elevation angle and azimuth angle. In fact, the 2D-MUSIC algorithm can also be used to process the bistatic radar positioning problem in a two-dimensional plane. The estimated channel matrix is pulled into a column vector, and the equivalent array response has a similar structure to the array response in three-dimensional space. However, since the MUSIC algorithm relies on the observation covariance matrix of the array received data or the estimated covariance matrix of the channel, a sufficient number of signal samples need to be collected to make the covariance matrix relatively accurate. Otherwise, the rank of the matrix will be deficient, resulting in a large estimation error and limiting its practicality. SUMMARY

[0004] This method utilizes the spatial translation-invariance properties of uniform linear or planar arrays to propose a method for calculating the forward and backward space-time cross-correlation function. Based on the Hermitian-block Toeplitz properties of the ideal signal covariance matrix, this space-time cross-correlation function is used to construct a pseudo-covariance matrix, thereby constructing a MUSIC spatial spectrum and extracting the outgoing wave direction. Compared to traditional 2D-MUSIC algorithms, this method maintains high-precision angle estimation capabilities even with a limited number of snapshots, without significantly increasing computational complexity. Compared to spatially smoothed MUSIC algorithms, this method eliminates the need for sub-array segmentation, fully utilizing the full array aperture and avoiding resolution loss.

[0005] 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.

[0006] AoA:Angle of Arrival, arrival angle;

[0007] AoD: Angle of Departure, leaving 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] UPA: Uniform Planar Array, uniform planar array;

[0014] 2D-MUSIC: Two-Dimensional Multiple Signal Classification, two-dimensional multiple signal classification;

[0015] Figure 1 and Figure 2 Shown is a schematic diagram of the system involved in the present invention:

[0016] Figure 1The figure shows a direction finding system in three-dimensional space, including a receiving end Rx equipped with MxN antennas, placed on the yOz plane, and L independent single-antenna transmitting ends Tx, and it is assumed that these devices are in a far-field line-of-sight environment. It is considered that the azimuth angle of the lth Tx (l ∈ {1, 2,..., L}) to Rx is The elevation angle is θ l , and the corresponding (after fading) signal in the qth snapshot (q ∈ {1, 2,..., Q}) is x l , and Q is the total number of snapshots, then the received signal of Rx can be expressed as:

[0017]

[0018] wherein represents the antenna array response, and for a UPA with an element interval of half a wavelength, it can be specifically expressed as:

[0019]

[0020] wherein

[0021]

[0022] and

[0023]

[0024] In addition, represents AWGN, wherein N0 represents the noise power. The received signal is stacked in order into an NxM matrix, so that y q = vec(Y q ), so that

[0025]

[0026] Figure 2 The figure shows a bistatic radar positioning system in a two-dimensional plane, including a transmitting end Tx and a receiving end Rx, which are respectively equipped with M and N antennas, and it is assumed that the array elements are placed horizontally with an element interval of half a wavelength. It is assumed that the devices are in a far-field multipath condition, and follow the Salen-Valenzula channel model: it is considered that there are L independent multipaths from Tx to Rx, and the AoD of the lth (l ∈ {1, 2,..., L}) multipath is The AoA is θ l ∈ [0°, 180°), and the attenuation in the qth (q ∈ {1, 2,..., Q}) snapshot is β ql , and Q is the total number of snapshots. It is considered that the transmitted pilot is the unit matrix I, so the received signal in the qth snapshot can be expressed as:

[0027]

[0028] where a R (θ l )、 are the array responses of the receiving and transmitting ends respectively, which are specifically represented as:

[0029]

[0030] and

[0031]

[0032] In addition, is AWGN, and each element is independently and identically distributed as N0 represents the noise power. It can be seen that the bistatic radar positioning model in the two-dimensional plane has a similar structure to the direction finding model in the three-dimensional space.

[0033] The technical scheme adopted by the present application is:

[0034] S1, calculating the forward space-time cross-correlation of Y q , which is specifically defined as:

[0035]

[0036] S2, calculating the backward space-time cross-correlation of Y q , which is specifically defined as:

[0037]

[0038] S3, performing Hermitian-block Toeplitz reconstruction on and to obtain a pseudo-SCM, which is specifically:

[0039]

[0040] where

[0041]

[0042] S4, performing eigenvalue decomposition on to calculate the MUSIC spatial spectrum of the receiving-transmitting angle, which is specifically:

[0043] S41, performing eigenvalue decomposition on , that is,

[0044]

[0045] where is a diagonal matrix, and the diagonal elements are arranged in descending order of the eigenvalues of ; the eigenmatrix consisting of corresponding characteristic vectors;

[0046] S42, dividing the noise space, specifically: deleting the first L columns of the feature matrix U, to obtain U N ;

[0047] S43, calculating the MUSIC spatial spectrum: if it is a direction finding problem in a three-dimensional space, the MUSIC spatial spectrum is defined as:

[0048]

[0049] If it is a bistatic radar positioning problem in a two-dimensional plane, the MUSIC spatial spectrum is defined as:

[0050]

[0051] S5, extracting the spatial spectrum The angle pair corresponding to the first L highest peaks of the spatial spectrum is taken as the estimation result.

[0052] The beneficial effects of the present application are:

[0053] The present application proposes a fast 2D-MUSIC direction finding method based on spatial translation invariance, and defines a forward / backward space-time cross-correlation calculation method, reconstructs a pseudo-covariance matrix by space-time cross-correlation according to the Hermitian-block Toeplitz characteristic of the ideal signal covariance matrix. Since the rank of the reconstructed pseudo-covariance matrix is independent of the number of fast shots, the proposed algorithm effectively solves the problem of failure of the traditional 2D-MUSIC algorithm in the under-fast-shot scene. In addition, this method makes full use of the array aperture, significantly reduces the noise level, and at the same time maintains a similar calculation complexity to the traditional 2D-MUSIC. The above characteristics enable the proposed method to maintain high-precision direction estimation ability in complex and variable signal environments, providing strong technical support for application scenarios with strict real-time requirements. Simulation results show that this method can significantly improve the spatial spectrum peak-to-average ratio under low SNR and under-fast-shot conditions, and has higher estimation accuracy and stability. BRIEF DESCRIPTION OF DRAWINGS

[0054] Figure 1 : The three-dimensional space direction finding system involved in the present application is shown in the schematic diagram;

[0055] Figure 2 : The two-dimensional plane bistatic radar positioning system involved in the present application is shown in the schematic diagram;

[0056] Figure 3 : The spatial spectrum of the traditional 2D-MUSIC algorithm is shown in the schematic diagram;

[0057] Figure 4: spatial spectrum of the spatial smoothing 2D-MUSIC algorithm;

[0058] Figure 5 : spatial spectrum of the scheme proposed in the present application; DETAILED DESCRIPTION

[0059] In the summary section, the technical scheme of the present application has been described in detail, and the practicality of the present application will be illustrated in combination with the accompanying drawings and simulation examples.

[0060] In Figures 3-5 In the simulation example, unless otherwise specified, the system configuration is SNR=0dB, Q=1, M=N=16, and multipath number L=5, the transceiver is a uniform linear array with half-wavelength antenna spacing, the pilot matrix is Angle vs. The configurations are (-60°, -60°), (-20°, 60°), (0, 0), (30°, -30°), and (60°, 10°), and each path fading is independently and identically distributed in The angle resolution is taken as 1°, and SNR is defined as 1 / N0.

[0061] Figure 3 The spatial spectrum of the traditional 2D-MUSIC algorithm is given. It can be obviously observed that although the traditional 2D-MUSIC produces peaks at the expected angle coordinates, the peak-to-average ratio of these peaks is small, indicating that the estimation accuracy is very limited and the noise resistance is weak.

[0062] Figure 4 The spatial spectrum of the spatial smoothing 2D-MUSIC algorithm is given, and the subarray size is set to 14x14. It can be seen that spatial smoothing can greatly improve the peak-to-average ratio, thus greatly improving the estimation accuracy and noise resistance.

[0063] Figure 5 The spatial spectrum of the scheme proposed in the present application is given. It can be observed that the scheme proposed in the present application further improves the peak-to-average ratio and improves the sharpness of the peak. This means that the scheme proposed in the present application has higher estimation accuracy, resolution, and noise resistance. The improvement in performance is mainly due to the fact that the algorithm does not need to divide the subarray and can utilize the full array aperture.

[0064] It can be seen that the under-sampling 2D-MUSIC direction finding algorithm based on spatial shift invariance proposed in the present application has high estimation accuracy. Compared with the spatial smoothing algorithm, it exhibits higher estimation accuracy, resolution, and noise resistance, providing strong support for practical applications.

Claims

1. A spatial translation invariant based under fast fading 2D-MUSIC direction finding method for direction finding system in three dimensional space, define the direction finding system includes a receiving end Rx with M x N antennas, L independent single antenna transmitting ends Tx, in three dimensional coordinate system, Rx is placed on yOz plane, where O is the origin, the azimuth angle of the lth Tx to Rx is the elevation angle is θ l , l ∈ {1, 2, …, L}, the corresponding faded signal in the qth fast fading is x l , q ∈ {1, 2, …, Q}, Q is the total number of fast fading, the received signal of Rx is: wherein q denotes the q-th snapshot, denotes the antenna array response, denotes the AWGN, where N0represents the noise power and I is the identity matrix; The method is characterized in that the direction finding method comprises: S1, y q stacked in order into an N x M matrix Y q such that y q = vec(Y q ); S2, calculating Y q the forward-backward space-time cross-correlation function of S2, in particular: S21, compute Y q Forward space-time cross-correlation of S22, calculate Y q backward space-time cross-correlation of S3, to and performing Hermitian-block Toeplitz reconstruction to obtain a pseudo-covariance matrix, specifically: Wherein S4, to Eigenvalue decomposition is performed to calculate the MUSIC spatial spectrum of the receiving and transmitting angle, specifically: S41、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 characteristic matrix is composed of the corresponding characteristic vectors. S42, dividing the noise space, specifically: deleting the first L columns of the feature matrix U to obtain U N ; S43, calculating the MUSIC spatial spectrum: wherein with a z (θ) denotes the array response along the y-axis and along the z-axis, respectively; S5, extracting spatial spectrum The angles corresponding to the first L highest peaks of the spatial spectrum are taken as the estimation result.

2. A spatial shift-invariance based underfast-time 2D-MUSIC direction finding method for bistatic radar positioning system in two-dimensional plane, defining the system comprising a transmitting end Tx with M antennas and a receiving end Rx with N antennas, there are L independent multipaths from Tx to Rx, the AoD of the lth multipath is AoA is θ l ∈ [0°, 180°), the attenuation in the qth fast-time is β ql , l ∈ {1, 2,..., L}, q ∈ {1, 2,..., Q}, Q is the total number of fast-time; characterized in that The direction finding method comprises: The sending end: S1, in the qth fast shot, transmitting an M-order unit matrix pilot; The receiving end: S2, with represents the received signal within the q-th snapshot: where a R (θ l ), are the array responses of the receiver and transmitter, respectively, is the AWGN, each element is independent and identically distributed N0 represents the noise power; the forward and backward space-time correlation functions are calculated as follows: S21, compute Y q the forward-backward space-time cross-correlation of X, defined as: S22, compute Y q the backward space-time cross-correlation of the Y, defined as: S3, to and performing Hermitian-block Toeplitz reconstruction to obtain a pseudo-covariance matrix, specifically: Wherein S4, to Eigenvalue decomposition is performed to calculate the MUSIC spatial spectrum of the receiving and transmitting angle, specifically: S41、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 S42, dividing the noise space, specifically: deleting the first L columns of the feature matrix U to obtain U N ; S43, calculating the MUSIC spatial spectrum: wherein with a R (Θ) represent the array responses of Tx and Rx, respectively; S5, extracting spatial spectrum The angles corresponding to the first L highest peaks of the spatial spectrum are taken as the estimation result.

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