Low-Complexity Direction-of-Arrival Estimation With Orthogonal Matching Pursuit for Large-Scale Lens Antenna Array

This paper explores two novel compressed sensing (CS) strategies for estimating the directions of incoming signals in a coherent environment using a lens antenna array (LAA). Compared to the subspace-based algorithm family, CS techniques, such as the conventional orthogonal matching pursuit (OMP), can effectively address the direction-of-arrival (DoA) estimation without prior knowledge about the number of signals at low complexity. However, they are sensitive to noise and can be adversely affected by multipath distortion. To overcome these limitations, we leverage the energy-concentrating property of an LAA and introduce the signal covariance matrix-based OMP (SCM-OMP) method. This method enhances the accuracy of angular estimation, even in regions with low signal-to-noise ratio (SNR). Furthermore, by analyzing the definition of mutual coherence (MC), we demonstrate that the SCM-OMP scheme achieves improved performance with a large number of antennas. We then propose the multiple sub-covariance matrices-based OMP (MSCM-OMP) to reduce computational complexity. We also analyze the exact recovery conditions of the studied OMP algorithms and utilize the noise reduction property to show that our proposed SCM-OMP and MSCM-OMP algorithms have better successful recovery probabilities than the OMP scheme. Moreover, we combine the Rife method with two proposed CS-based algorithms to overcome the off-grid effect. Simulation results confirm that the SCM- and MSCM-OMP schemes outperform other high-resolution DoA estimation methods in both on-grid and off-grid scenarios. Furthermore, the MSCM-OMP method can achieve a detection accuracy of higher than 60%, even in a low-SNR regime, i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rm {SNR}=-10$ </tex-math></inline-formula> dB.