Sparse channel estimation and equalization for underwater filtered multitone

In this work we review Filtered Multitone modulation (FMT) for underwater communications. This multicarrier modulation splits the transmission across several sub-bands with high spectral containment, and may be thought of as a hybrid between the widely popular single-carrier and OFDM schemes. As in OFDM the receiver architecture is conceptually based on a bank of filters, but in our envisaged scenarios the number of sub-carriers is relatively low, resulting in non-flat channel distortion across sub-bands that requires equalization at the receiver. This work addresses the design of (time-domain) channel-estimation-based equalizers for FMT receivers, specifically focusing on how the sparsity of many underwater channels can be taken into account to improve the demodulation performance by providing higher-quality channel estimates. To this end, we consider several methods for computing sparse channel estimates independently at each sub-band and evaluate their impact. We then take advantage of the filterbank structure and propose a fusion procedure that takes raw (non-sparse) subcarrier channel estimates and produces a high-quality, sparse, global channel estimate that may be filtered and fed back to the equalizers. Best results are obtained with a sparsification method based on time-recursive approximate L0-norm minimization. We illustrate the performance of FMT numerically using both simulated and real data and compare it to single-carrier modulation, highlighting its flexibility and ease of parameterization.