An Improved Multiple-Toeplitz Matrices Reconstruction Algorithm for DOA Estimation of Coherent Signals

Abstract

The Toeplitz matrix reconstruction algorithms exploit the row vector of an array output covariance matrix to reconstruct Toeplitz matrix, which provide the directionof-arrival (DOA) estimation of coherent signals. However, the Toeplitz matrix reconstruction method based on any row vector of the array output covariance matrix suffers from signal correlation, it results in poor robustness. The methods based on multi-row vectors suffer serious performance degradation when in the low signal-to-noise ratio (SNR) owing to the noise energy is the square of the input noise energy. To solve the above problems, we propose an improved method that exploits all rows of the time-space correlation matrix to reconstruct the Toeplitz matrix, namely TS-MTOEP. This method firstly uses the coherence of the narrowband signal and the uncorrelated noise at different snapshots to construct the time-space correlation matrix, it effectively eliminates the influence of noise. Then, the Toeplitz matrix is reconstructed via all rows of the time-space correlation matrix, which effectively improves the energy of the signal, and further results in the improvement of the SNR. Finally, the DOAs can be obtained by combining it with the subspace-based methods. The theoretical analysis and simulation results indicate that compared with the existing Toeplitz and spatial smoothing methods, the proposed method in this paper provides good performance on estimation and resolution in cases with low input signal-to-noise due to time-space correlation matrix processing. Furthermore, in cases where the DOAs between the coherent sources are closely spaced and the snapshot number is low, our proposed method significantly improves the performance of the DOA estimation. We also provide the code to realize the reproducibility of the proposed method.

Improved multiple-Toeplitz matrices reconstruction method using quadratic spatial smoothing for coherent signals DOA estimation

“…Furthermore, similar to the spatial smoothing, because of the increased spatial smoothing number, the MTOPE method will achieve better DOA estimation performance when compared to the FB-PTMR method. However, the estimation accuracy of the reconstructed matrix for the FB-PTMR and MTOEP methods may become poor under a low SNR, which further results in degradation of the DOA estimation performance (Qi, 2022; Qi and Li, 2021; Qi and Liu, 2021, 2022).…”

“…To improve the estimation performance, we consider facilitating ( 23) by the forward/ backward spatial smoothing as follows (Qi, 2022;Qi and Li, 2021) Improved quadratic spatial smoothing method…”

“…However, these methods suffer serious performance degradation in the case of coherent signals owing to the rank loss of the source covariance matrix. Thus, the rank restoration for the source covariance matrix is the key to the decoherence methods (Qi, 2022; Qi and Li, 2021; Qi and Liu, 2021).…”

Underwater wideband coherent signals DOA estimation using sparse representation and deconvolution

“…It is noticeable that, T( f j ) is a Hermitian matrix that matches T H ( f j )T( f j ) = I. To construct the focusing matrix, we can rewrite (14) as follows:…”

“…can be classified into two categories: subspace-based [9,10], and beamforming-based [11]. Representative subspace-based algorithms, such as MUSIC [9] and ESPRIT [10], can be combined with various decoherence techniques [12][13][14][15] to obtain high-resolution DOA estimation. However, it is necessary to know the number of coherent sources and the covariance matrix of the signals.…”