Sparse channel estimation for wavelet-based underwater acoustic communications

In this paper, concerning underwater acoustic (UWA) communications, we propose a wavelet filter bank system as the extension of orthogonal frequency-division multiplexing system. We exploit the convolutional structure of a UWA channel and formulate the pilot-assisted channel estimation as a sparse recovery problem. Then, we investigate the restricted isometry property of the measurement matrix via eigenvalue analysis and Gershgorin circle theorem. The sparse recovery problem is proven to satisfy the restricted isometry property. Moreover, we also propose a low-complexity complex-field homotopy algorithm for sparse channel estimation, regarding the fact that the channel taps of each path are usually complex valued in practice. Simulation results show that the wavelet filter bank system achieves more accurate UWA channel estimation performance than orthogonal frequency-division multiplexing system under the same conditions of bandwidth, duration, data rate and channel profile. The proposed complex homotopy algorithm outperforms orthogonal matching pursuit (OMP) and stagewise OMP in both systems, whereas its computational complexity is similar to OMP. Copyright (c) 2012 John Wiley & Sons, Ltd.