Error Rate Improvement in Underwater MIMO Communications Using Sparse Partial Response Equalization

Shallow-water horizontal underwater acoustic (UWA) channels are characterized by a time-varying multipath structure with a long delay spread. This causes significant signal distortion in phase coherent transmissions by introducing intersymbol interference (ISI), which can span several hundreds of symbols. The multipath structure is usually very sparse. This paper proposes an adaptive sparse partial response equalizer (SPRE) well matched with the channel characteristics to mitigate the ISI efficiently, and communicate reliably. Unlike the conventional equalizers that try to eliminate the ISI completely, the proposed structure performs equalization in two steps. In the first step, the channel is equalized to a judiciously chosen target impulse response (TIR), thereby leaving controlled residual ISI at the output of the SPRE. In the second step, the residual ISI is further mitigated by a near-optimal, graph-based, low-complexity symbol detection algorithm known as belief propagation (BP). We demonstrate that due to the sparse nature of the long ISI channel, and the well-matched adaptive TIR, this two-step equalization process is particularly useful. The idea here can be compared to what is done in the magnetic recording literature [i.e., partial response maximum-likelihood (ML) equalization] to avoid excessive noise enhancement, with the difference that the TIR needs to be designed adaptively using training symbols and that in the second step, instead of using a ML detector, a BP algorithm is used. The proposed SPRE algorithm is designed for a general multiple-input-multiple-output (MIMO) system and it provides soft outputs for the transmitted bits as a by-product of the BP-type equalization algorithm. Hence, it can be efficiently employed in coded systems (e.g., turbo or low-density-parity-check-coded, interleaved systems) with an iterative decoding/equalization scheme, providing significant improvements in achievable error rates. Finally, we note that the proposed SPRE scheme also incorporates a phase locked loop (PLL) structure so as to track the Doppler shift introduced by the channel. To evaluate the effectiveness of the proposed equalizer, we compare it with several decision feedback equalizers (DFEs) proposed by Stojanovic (J. Ocean. Eng. vol. 19, no. 1, pp. 100-111, Jan. 1994), Roy (Proc. MTS/IEEE TECHNO-OCEAN Conf., vol. 1, pp. 26-33, Nov. 2004), and Roy (J. Ocean. Eng., vol. 32, no. 3, pp. 663-688, Jul. 2004) both through simulations and experimental results. The results demonstrate that the SPRE receiver outperforms the decision-feedback-based receivers when the channel has long, yet sparse (possibly, nonminimum phase) structure, by reducing the frame error rates (FERs), improving the post-equalization signal-to-noise ratio (SNR), and decreasing the required number of turbo iterations (reduced latency).