Channel Estimation and Data Detection in DS-Spread Channels: A Unified Framework, Novel Algorithms, and Waveform Comparison

We present a unified receiver processing framework for communication over delay-scale (DS)-spread channels, as encountered in underwater acoustic (UWA) communications. In particular, we develop novel channel estimation (CE) and data detection algorithms for different modulation waveforms: OFDM, OTFS, OCDM, and ODSS, through a common input–output relation. We then conduct a fair and comprehensive comparative study of these waveforms under similar receiver complexities.

We first develop a novel iterative variational Bayesian (VB) off-grid CE technique to estimate the delay and scale parameters of the channel paths, using two approaches: a first-order approximation scheme (FVB) and a second-order approximation scheme (SVB). We then propose a low-complexity variational soft symbol detection (VSSD) algorithm that outputs soft symbols and log-likelihood ratios, which is used for data detection across different waveforms. Next, we improve the performance of CE and data detection further using an iterative CE and data detection (ICED) scheme, which utilizes the detected data symbols as virtual pilots.

Our numerical results reveal the efficacy of the proposed algorithms for CE and data detection. In terms of the relative performance of different waveforms, in uncoded communications, (a) with a low-complexity subcarrier-by-subcarrier equalizer, ODSS offers the best performance, followed by OCDM and OTFS, while OFDM performs the worst, and (b) with a VSSD algorithm, OTFS, OCDM, and ODSS perform similarly, and they outperform OFDM. With coded communications, interestingly, all waveforms offer nearly the same BER when a VSSD receiver is employed. Hence, we conclude that when the receiver complexity is constrained, waveform choice matters, especially under harsh channel conditions, whereas with more sophisticated receiver algorithms, these differences disappear.