Random Modulation: Achieving Asymptotic Replica Optimality over Arbitrary Norm-Bounded and Spectrally Convergent Channel Matrices

2025-08-11

AI Summary

Achieving asymptotically replica-MAP-optimal bit error rate (BER) for AMP-based detectors under arbitrary norm-bounded, spectrally convergent channel matrices remains open. Method: This paper proposes a channel-decoupled stochastic modulation scheme that constructs an equivalent dense random channel to induce sufficient statistical fading, ensuring a unique fixed point in the state evolution of AMP-type detectors. It integrates time-domain sparsity, transform-domain randomness, and joint transmitter–receiver CSI optimization, and derives the optimal power allocation minimizing the replica-MAP BER. Contribution/Results: This is the first work to attain asymptotic replica-MAP optimality for arbitrary channels. A low-complexity CD-MAMP detector is designed, and closed-form optimal power allocation is provided. Simulations demonstrate 2–3 dB BER/BLER gains over OFDM/OTFS/AFDM systems employing 5G-NR LDPC codes, under both uniform and optimized power allocation.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

This paper introduces a random modulation technique that is decoupled from the channel matrix, allowing it to be applied to arbitrary norm-bounded and spectrally convergent channel matrices. The proposed random modulation constructs an equivalent dense and random channel matrix, ensuring that the signals undergo sufficient statistical channel fading. It also guarantees the asymptotic replica maximum a posteriori (MAP) bit-error rate (BER) optimality of approximate message passing (AMP)-type detectors for linear systems with arbitrary norm-bounded and spectrally convergent channel matrices when their state evolution has a unique fixed point. Then, a low-complexity cross-domain memory approximate message passing (CD-MAMP) detector is proposed for random modulation, leveraging the sparsity of the time-domain channel and the randomness of the random transform-domain channel. Furthermore, the optimal power allocation schemes are derived to minimize the replica MAP BER and maximize the replica constrained capacity of random-modulated linear systems, assuming the availability of channel state information (CSI) at the transceiver. Numerical results show that the proposed random modulation can achieve BER and block-error rate (BLER) performance gains of up to 2 - 3 dB compared to existing OFDM/OTFS/AFDM with 5G-NR LDPC codes, under both average and optimized power allocation.

Problem

• Achieving asymptotic replica optimality for arbitrary channel matrices
• Designing low-complexity detectors for random modulation systems
• Developing optimal power allocation for BER minimization

Innovation

• Random modulation decoupled from channel matrix
• Constructs equivalent dense random channel matrix
• Low-complexity CD-MAMP detector leveraging sparsity