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

## TL;DR

This paper introduces a unified framework for channel estimation and data detection in DS-spread channels, develops novel algorithms for underwater acoustic communications, and compares multiple waveforms under realistic conditions.

## Contribution

It presents a comprehensive framework, new variational Bayesian algorithms for channel estimation, and a detailed comparison of waveforms in DS-spread channels.

## Key findings

- ODSS outperforms other waveforms with low-complexity equalizer
- VSSD algorithm equalizes performance among waveforms in coded scenarios
- Waveform differences diminish with advanced detection algorithms

## Abstract

We present a unified receiver processing framework for communication over delay-scale (DS)-spread channels that arise in underwater acoustic (UWA) communications that addresses both channel estimation (CE) and data detection for different modulation waveforms, namely OFDM, OTFS, OCDM, and ODSS, through a common input--output relation. Using this framework, we conduct a fair and comprehensive comparative study of these waveforms under DS-spread UWA channels and similar receiver complexities. We also develop a novel iterative variational Bayesian (VB) off-grid CE algorithm to estimate the delay and scale parameters of the channel paths, via two approaches: a first-order approximation scheme (FVB) and a second-order approximation scheme (SVB). We propose a low-complexity variational soft symbol detection (VSSD) algorithm that outputs soft symbols and log-likelihood ratios for the data bits, and a data-aided iterative CE and data detection (ICED) scheme that utilizes detected data symbols as \emph{virtual} pilots to further improve the CE and data detection accuracy. Our numerical results reveal the efficacy of the proposed algorithms for CE and data detection. In terms of 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 the VSSD algorithm, OTFS, OCDM, and ODSS perform similarly, and they outperform OFDM. With coded communications, interestingly, all waveforms offer nearly the same BER when the 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.