Iterative Sparse Channel Estimation and Spatial Correlation Learning for Multichannel Acoustic OFDM Systems

This article addresses the problem of coherent detection of acoustic orthogonal frequency division multiplexing (OFDM) signals using a sparse channel estimation method based on a physical model of multipath propagation. Unlike the conventional sample-spaced and subsample-spaced methods, such as least squares and orthogonal matching pursuit (OMP), which target the taps of an equivalent discrete-delay channel response, the path identification (PI) method targets the physical propagation paths in a continuous-delay domain, and focuses on explicit estimation of delays and complex amplitudes of the channel paths in an iterative fashion. When multiple receive elements are available, two situations are possible: one in which the array elements see uncorrelated channel responses, and another in which the channel responses are correlated. In the first case, channel estimation must be accomplished element-by-element. This is done simply by applying the PI algorithm to each element individually. In the second case, correlation between the elements can be exploited. In doing so, our goal is to reduce the signal processing complexity without compromising the performance. Toward this goal, an adaptive precombining method is proposed. Without requiring any a priori knowledge about the spatial distribution of received signals, the method exploits spatial coherence between receive channels by linearly combining them into fewer output channels so as to reduce the number of subsequent channel estimators. The algorithm learns the spatial coherence pattern recursively over the carriers, thus effectively achieving broadband beamforming. The reduced-complexity precombining method relies on differential encoding that keeps the receiver complexity at a minimum and requires a very low pilot overhead. Using synthetic data as well as 210 experimental signals transmitted over a 3–7-km shallow-water channel in the 10.5–15.5-kHz acoustic band during a 3.5-h experiment, we study the system performance in terms of data detection mean-squared error (MSE), symbol error rate, and bit error rate (BER), and show that the PI algorithm achieves excellent MSE performance while its complexity is considerably lower than that of the OMP algorithm. We also demonstrate that the receiver equipped with the proposed reduced-complexity precombining scheme requires three times fewer channel estimators while achieving the same MSE and BER performance as the full-complexity receiver.