A-OMP: An Adaptive OMP Algorithm for Underwater Acoustic OFDM Channel Estimation

A fundamentally difficult problem to apply the orthogonal matching pursuit (OMP) to estimate the underwater acoustic (UWA) orthogonal frequency division multiplexing (OFDM) channel is designing a proper iteration termination condition. However, existing OMP-based algorithms that design termination conditions based on the physical sparsity suffer the limited estimation accuracy in high-level noise cases and the difficult balance between the accuracy and computational costs in low-level noise cases. We find that it is the recovery sparsity, a quantity related to but possibly significantly different from the physical sparsity, that should be utilized to devise termination conditions. Based on this observation, we first exploit the recovery sparsity to derive a closed-form expression for the termination condition to improve the estimation accuracy in high-level noise cases. Then, to balance the estimation accuracy and computational costs in low-level noise cases, we design another termination condition based on the residual vector and the observation vector. By embedding these two conditions into the OMP structure, we propose an innovative channel estimation algorithm for UWA-OFDM communication systems, referred to as the adaptive OMP (A-OMP). Simulation results show that, compared with the OMP, the A-OMP can achieve comparable or even higher estimation accuracy with smaller computational costs in all considered noise cases. Specially, the A-OMP can increase the estimation accuracy by 71.31% with only 13.48% CPU running time in high-level noise cases.