Sparse frame DOA estimations via a rank-one correlation model for low SNR and limited snapshots

Abstract

As a typical problem of sparse frame representations or compressed sensing with frames, direction of arrival (DOA) estimations, via sparse recovery methodologies such as nonlinear optimizations or various greedy algorithms, suffer seriously under severe noisy measurement without proper treatment. In this article, a crucial and effective correlation operation is outlined to mitigate the severe noise effect from the sparse representation point of view. A fast and super resolution method for DOA estimations is therefore established under very low signal-to-noise ratio, and by a sparse recovery technique of null space tuning in the context of compressed sensing and sparse representations. Improvement to the technique using the thresholding difference and alternating grid refinements are also outlined to estimate the source/target numbers dynamically and to improve the precision. Another characteristic is that only a very small number of snapshots are needed in comparison with other techniques. Simulation results demonstrate apparent advantages of the proposed technique over known approaches. The proposed method has the effectiveness at simultaneous high resolution, robustness to noise, and source number estimations. The algorithm is also computationally efficient, which is critical for large array systems and/or mission critical real-time applications.

Sparse representation based direction‐of‐arrival estimation in nonuniform noise via tail minimisation

“…To alleviate this problem, � Bvecð c � R s Þ can be seen as an initial rough estimate. A † is refined by exploiting the DOAs of incident signals determined via (15). � Bvecð c � R s Þ is then further updated in the next iteration.…”

A novel wideband DOA estimation method based on a fast sparse frame

“…When the number of sensors is small, the accuracy of DOA algorithms based on NHF will decrease. In [14], when using NHF algorithm to narrowband DOA estimation, only one signal is measured at a time, then the received signals are projected onto the null space of the signal that has been measured. Although problems can be avoided in this way, the projection operation of each angle will undoubtedly increase the computational complexity.…”

Single Snapshot DOA Estimation by Minimizing the Fraction Function in Sparse Recovery

“…Theorem 1. For the measurement matrix A(Ω) ∈ C M×n defined in (10), if θ * ⊆ Θ, K < ((M + 1)/2) and there is no noise during the measurement; then, the real solution Θ * of DOA estimation can be recovered by l 0 -minimization (14), i.e.,…”

“…As one of the most important methods designed for single snapshot DOA estimation, sparse recovery has its own advantage for single snapshot case [14][15][16][17]. By dividing the angle range into grid points, the number of source is much less than that of grid points.…”