Under-snapshot 2D-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 2D-MUSIC direction finding method based on spatial translation invariance. According to the method, the space translation invariant characteristic of a uniform linear array or a uniform planar array is utilized, a calculation method of a forward and backward space-time cross-correlation function is provided, a pseudo covariance matrix is constructed by using the space-time cross-correlation function based on the Hermitian-block Toeplitz characteristic of a signal ideal covariance matrix, then a MUSIC spatial spectrum is constructed, and the wave direction is extracted. Compared with a traditional 2D-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 2D-MUSIC direction finding method based on spatial translation invariance. Background Art

[0002] The commercialization and development of the fifth generation mobile communication system has spawned a series of new scenarios with both communication and perception requirements, such as drone networks and vehicle networks. Therefore, integrated sensing and communication (ISAC) technology has attracted much attention in the industry. In ISAC networks, a key application challenge is how to meet the growing demand for real-time perception. For example, drone networks have high dynamics and flexibility, and have broad application prospects in logistics, environmental monitoring, emergency communications and other fields. However, the dynamic adjustment of the network and the stability of the communication link are highly dependent 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 perception resources, it is impossible for ISAC networks to allocate more resources to achieve perception purposes. Therefore, how to achieve the perception and communication indicators of ISAC networks with lower perception overhead is also one of the key issues.

[0003] However, traditional positioning algorithms often require a lot of resource overhead to accurately estimate the signal's time delay, angle and other information. 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 signal and noise to achieve super-resolution estimation of incoming signals. For the direction finding problem 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 pitch angle and azimuth angle. In fact, the 2D-MUSIC algorithm can also be used to deal with the bistatic radar positioning problem on a two-dimensional plane, pulling the estimated channel matrix into a column vector, and the equivalent array response has a structure similar to the array response in three-dimensional space. However, since the MUSIC algorithm relies on the observed covariance matrix of the array receiving data or the estimated covariance matrix of the channel, it is necessary to collect enough signal samples to make the covariance matrix more accurate, otherwise it will cause a loss of matrix rank and produce a large estimation error, thereby limiting its practicality. Summary of the invention

[0004] The method of the present invention utilizes the spatial translation invariance characteristics of a uniform linear array or a uniform planar array, proposes a method for calculating the forward and backward space-time cross-correlation function, and then constructs a pseudo covariance matrix based on the Hermitian-block Toeplitz characteristics of the ideal covariance matrix of the signal using the space-time cross-correlation function, thereby constructing a MUSIC spatial spectrum and extracting the outgoing wave direction. Compared with the traditional 2D-MUSIC algorithm, the present invention can still maintain high-precision angle estimation capabilities 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 segment the subarray, fully utilizes the full array aperture, and avoids 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 receiver Rx equipped with M×N antennas, placed on the yOz plane, and L independent single-antenna 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 pitch angle is θ l , 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:

[0017]

[0018] in, Represents the antenna array response. For a UPA with an array element spacing of half a wavelength, it can be specifically expressed as:

[0019]

[0020] in

[0021]

[0022] and

[0023]

[0024] also, represents AWGN, where N0 represents the noise power. The received signals are stacked sequentially into an N×M matrix so that y q =vec(Y q ), so we have

[0025]

[0026] Figure 2 The figure shows a bistatic radar positioning system on a two-dimensional plane, including a transmitter Tx and a receiver Rx, which are equipped with M and N antennas respectively, both of which are assumed to be horizontally placed ULAs with an array element spacing of half a wavelength. Assuming that the device is in a far-field multipath condition, following the Salen-Valenzula channel model: Considering that there are L independent multipaths from Tx to Rx, the AoD of the lth (l∈{1,2,...,L}) multipath is AoA is θ l ∈[0°,180°), the decay in the qth (q∈{1,2,…,Q}) snapshot is β ql , Q is the total number of snapshots. Considering the transmitted pilot as the unit matrix I, 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 end and the transmitting end, respectively, which are specifically expressed as:

[0029]

[0030] and

[0031]

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

[0033] The technical solution adopted by the present invention is:

[0034] S1. Calculate Y q The forward space-time cross-correlation of is specifically defined as:

[0035]

[0036] S2. Calculate Y q The backward space-time cross-correlation of is specifically defined as:

[0037]

[0038] S3, yes and Perform Hermitian-block Toeplitz reconstruction to obtain the pseudo-SCM, which is:

[0039]

[0040] in

[0041]

[0042] S4, yes Perform eigenvalue decomposition and calculate the MUSIC spatial spectrum of the transmitting and receiving angles, specifically:

[0043] S41, yes Perform eigenvalue decomposition, that is

[0044]

[0045] 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;

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

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

[0048]

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

[0050]

[0051] S5. Extracting spatial spectrum The angle pairs corresponding to the first L highest peaks are taken as the estimation results.

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

[0053] The present invention proposes a method for direction finding based on spatial translation invariance for under-snapshot 2D-MUSIC. The present invention defines a forward / backward space-time cross-correlation calculation method. According to the Hermitian-block 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 2D-MUSIC algorithm in under-snapshot scenarios. In addition, the method makes full use of the array aperture and significantly reduces the noise level, while maintaining a computational complexity similar to that of the traditional 2D-MUSIC. The above characteristics enable the proposed method to maintain high-precision direction estimation capabilities in complex and changeable signal environments, providing strong technical support for application scenarios with strict real-time requirements. Simulation results show that the method can significantly improve the spatial spectrum peak-to-average ratio under low SNR and under-snapshot conditions, showing higher estimation accuracy and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 : Schematic diagram of the three-dimensional space direction finding system involved in the present invention;

[0055] Figure 2 : Schematic diagram of a two-dimensional bistatic radar positioning system according to the present invention;

[0056] Figure 3 :Schematic diagram of the spatial spectrum of the traditional 2D-MUSIC algorithm;

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

[0058] Figure 5 : Schematic diagram of the spatial spectrum of the solution proposed in the present invention; DETAILED DESCRIPTION

[0059] 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.

[0060] exist Figure 3-5 In the simulation examples, unless otherwise specified, the system configurations of SNR = 0 dB, Q = 1, M = N = 16, and multipath number L = 5 are used. Both the transmitting and receiving ends are uniform linear arrays with half-wavelength antenna spacing, and the pilot matrix Angle The configurations are (-60°, -60°), (-20°, 60°), (0, 0), (30°, -30°) and (60°, 10°). The fading of each path is independent and identically distributed. The angular resolution is taken as 1° and the SNR is defined as 1 / N0.

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

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

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

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

Claims

1. A sub-snapshot 2D-MUSIC direction finding method based on spatial translation invariance is used for a direction finding system in three-dimensional space. The direction finding system is defined as a receiving end Rx with M×N antennas and L independent single-antenna transmitting ends Tx. In the three-dimensional coordinate system, Rx is placed on the yOz plane, where O is the origin and the azimuth angle from the lth Tx to Rx is The pitch angle is θ l , 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: in, q represents the qth snapshot, represents the antenna array response, represents AWGN, where N0 represents the noise power and I is the identity matrix; Characterized in that the direction finding method comprises: S1, y q Stack them sequentially into an N×M matrix Y q Make y q =vec(Y q ); S2. Calculate Y q The forward and backward space-time cross-correlation function is as follows: S21. Calculate Y q Forward space-time cross-correlation of: S22. Calculate Y q Backward space-time cross-correlation of: S3, yes and Perform Hermitian-block Toeplitz reconstruction to obtain the pseudo covariance matrix, which is: in S4. Yes Perform eigenvalue decomposition and calculate the MUSIC spatial spectrum of the transmitting and receiving angles, specifically: S41, 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; S42, divide the noise space, specifically: delete the first L columns of the feature matrix U to obtain U N ; S43. Calculate the MUSIC spatial spectrum: in with a z (θ) represents the array response along the y-axis and along the z-axis respectively; S5. Extracting spatial spectrum The angle pairs corresponding to the first L highest peaks are taken as the estimation results.

2. A sub-snapshot 2D-MUSIC direction finding method based on spatial translation invariance is used for a bistatic radar positioning system on a two-dimensional plane. The system is defined as a transmitter Tx with M antennas and a receiver 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 decay in the qth snapshot is β ql , l∈{1,2,...,L}, q∈{1,2,…,Q}, Q is the total number of snapshots; It is characterized in that The direction finding method comprises: Sending side: S1, in the qth snapshot, transmit the M-order unit array pilot; Receiver: S2, use Represents the received signal in the qth snapshot: where a R (θ l ), are the array responses at the receiving and transmitting ends, respectively, is AWGN, and each element is independent and identically distributed in N0 represents the noise power; its forward and backward space-time cross-correlation function is calculated as follows: S21. Calculate Y q The forward and backward space-time cross-correlation of is specifically defined as: S22. Calculate Y q The backward space-time cross-correlation of is specifically defined as: S3, yes and Perform Hermitian-block Toeplitz reconstruction to obtain the pseudo covariance matrix, which is: in S4. Yes Perform eigenvalue decomposition and calculate the MUSIC spatial spectrum of the transmitting and receiving angles, specifically: S41, 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; S42, divide the noise space, specifically: delete the first L columns of the feature matrix U to obtain U N ; S43. Calculate the MUSIC spatial spectrum: in with a R (θ) represents the array responses of Tx and Rx respectively; S5. Extracting spatial spectrum The angle pairs corresponding to the first L highest peaks are taken as the estimation results.

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