Transceiver Design and Analysis for Indexed Time Reversal in 6G Systems

6G waveforms are essential for enabling next-generation wireless communication systems, providing enhanced spectral efficiency, low latency, and support for massive connectivity. However, managing complex propagation environments in 6G networks remains a challenging problem, particularly in low-complexity systems. In this context, time reversal (TR) has emerged as an efficient technique that focuses energy spatio-temporally, rendering it a useful tool for inter-symbol interference (ISI) mitigation in energy-constrained devices. Despite its advantages, conventional TR is subject to limitations in data rates due to high symbol back-off rates. To address these challenges, we introduce a novel indexed time reversal (ITR) scheme that leverages channel state information (CSI)-based shaping filters. Each of these shaping filters results in a unique signal interaction with the wireless propagation environment, enabling the indices of the shaping filters to carry distinct information bits without increasing symbol overhead. We further propose a two-stage detection scheme to reduce decoding complexity. The proposed detector not only improves data throughput but also preserves low-complexity ISI mitigation. Additionally, we develop a mathematical framework for the proposed ITR system from which we derive a closed-form approximation for the overall bit error rate (BER) performance. Corresponding simulation results show that the ITR scheme significantly outperforms conventional TR, and the number of indexed data bits can be substantially increased in rich multi-path environments.