Iterative Detection for Orthogonal Time Frequency Space Modulation Using Approximate Message Passing with Unitary Transformation

The orthogonal time frequency space (OTFS) modulation has emerged as a promising modulation scheme for high mobility wireless communications. To harvest the time and frequency diversity promised by OTFS, some promising detectors, especially message passing based ones, have been developed by taking advantage of the sparsity of the channel in the delay-Doppler domain. However, when the number of channel paths is relatively large or fractional Doppler shift has to be considered, the complexity of existing detectors is a concern, and the message passing based detectors may suffer from performance loss due to the short loops involved in message passing. In this work, we investigate the design of OTFS detectors based on the approximate message passing (AMP) algorithm. In particular, AMP with unitary transformation (UTAMP) based detectors are developed, which enjoy the structure of the channel matrix and allow efficient implementation, e.g., by exploiting the property of block circulant matrix with circulant block (BCCB), the complexity of the UTAMP-based detector per symbol is in the order of the logarithm of OTFS block length. In addition, the estimation of noise variance is incorporated into the UTAMP-based detectors (while existing detectors assume perfect noise variance). Thanks to the robustness of UTAMP relative to AMP, the UTAMP-based detectors are able to deliver much better performance, and outperform state-of-the-art detectors significantly. The investigations are also extended to iterative joint detection and decoding in a coded OTFS system, where the OTFS detectors are integrated into a powerful turbo receiver, leading to a considerable performance gain.