Direction of Arrival Estimation by Matching Pursuit Algorithm With Subspace Information

Abstract

Traditional orthogonal matching pursuit (OMP) algorithms for direction of arrival (DOA) estimation suffer from poor angular resolution and noise suppression. In this paper, we analyze the reason why the OMP algorithm has difficulties in resolving closely separated DOAs and conclude that it lies in the rules of support detection. Moreover, we propose a solution to this problem via developing the connection between the sparse reconstruction class algorithm and the subspace algorithm from the structure of the redundant dictionary. Based on the framework of the matching pursuit (MP) algorithm, the effective information of the signal and noise subspaces is integrated, and a noise subspace reprojection orthogonal matching pursuit (NSRomp) algorithm for DOA estimation is proposed. By adopting signal subspaces to reconstruct the original signal, the proposed NSRomp can reduce both the influence of noise on the selection of the support set and the computing time. By implementing the minimum norm method to optimize the noise subspace into a vector, which corrects the selection rules of the support set during each iteration, the angular resolution of the proposed algorithm is improved. From the simulation results, when the signal to noise ratio (SNR) is lower than or near 0, the angular resolution can be improved by > 15 • using OMP algorithms to by < 5 • using the proposed NSRomp algorithm.

Joint Model-Order and Robust DoA Estimation for Underwater Sensor Arrays

“…On the other hand, when the two DoAs are located away from the array boresight, i.e., −58 • and −53 • in this scenario, all the standard and proposed algorithms failed to distinguish the two signal sources as shown in Figure 9. Hence, the results obtained are consistent with theory and show that the angular resolution of standard and proposed OMP and SOMP algorithms is the Rayleigh limit proportional to the array aperture N × d [34].…”

“…The comparative recovery performance of the aforementioned algorithms is analyzed in terms of the RMSE of DoA estimates defined as [34,62,63]…”

“…In many underwater deployment scenarios, sensor array systems have to face different problems such as gain and phase uncertainties [ 26 ], non-uniform noise [ 27 ], faulty sensors in the array [ 28 , 29 , 30 ], unknown source order [ 31 , 32 ], resolution of closely spaced sources [ 33 , 34 ], off-grid DoAs [ 35 , 36 ], availability of limited snapshots [ 20 , 23 ], and low SNR [ 37 , 38 ].…”

“…Furthermore, for two sources closely spaced in the angular domain, the desired mutually coherent condition of CS-based methods is violated in greedy algorithms such as the OMP and as a result the beamformer shows a single peak instead of distinguishing between the coherent sources. Several works have discussed different variants of the classical OMP, e.g., regularized OMP (ROMP), to improve its DoA estimation accuracy under these conditions [ 33 , 34 ]. Another popular greedy method is the simultaneous OMP (SOMP) algorithm for DoA estimation using multiple snapshots [ 19 , 22 ].…”

Compressed Sensing of Traction Motor Bearing Vibration Signals based on Discrete Fourier Transform and Generalized Orthogonal Matching Pursuit Algorithm

“…Convex relaxation algorithms transform the nonconvex problem computational problem into a convex problem computational problem with a paradigm-based compression-aware framework, such as iterative hard thresholding (IHT), gradient projection (GP) algorithm, and basis pursuit (BP) algorithm [13]. The main greedy algorithms currently used for the signal reconstruction part of the CS framework are subspace matching pursuit (SMP) [14], orthogonal matching pursuit (OMP), regularized orthogonal matching pursuit (ROMP), matching pursuit (MP), compressed sampling matching pursuit (CSMP) [15], sparse adaptive matching pursuit [16], sparse segmented orthogonal matching pursuit (StOMP), and generalized orthogonal matching pursuit (gOMP) [17], etc.…”