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

The Toeplitz matrix reconstruction algorithms exploit the row vector of an array output covariance matrix to reconstruct Toeplitz matrix, which provide the direction-of-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.