Interleaved Block-Sparse Transform

TL;DR

This paper introduces a low-complexity interleaved block-sparse transform and an associated estimator to improve hardware efficiency in compressed sensing and multicarrier systems while maintaining high performance.

Contribution

It proposes a novel interleaved block-sparse transform and an IBS-CD-MAMP estimator that reduce hardware complexity without sacrificing estimation accuracy.

Findings

Reduced implementation scale and complexity in systems

Maintained high estimation performance

Effective in compressed sensing and interleave frequency division multiplexing

Abstract

Low-complexity Bayes-optimal memory approximate message passing (MAMP) is an efficient signal estimation algorithm in compressed sensing and multicarrier modulation. However, achieving replica Bayes optimality with MAMP necessitates a large-scale right-unitarily invariant transformation, which is prohibitive in practical systems due to its high computational complexity and hardware costs. To solve this difficulty, this letter proposes a low-complexity interleaved block-sparse (IBS) transform, which consists of interleaved multiple low-dimensional transform matrices, aimed at reducing the hardware implementation scale while mitigating performance loss. Furthermore, an IBS cross-domain memory approximate message passing (IBS-CD-MAMP) estimator is developed, comprising a memory linear estimator in the IBS transform domain and a non-linear estimator in the source domain. Numerical results show that the IBS-CD-MAMP offers a reduced implementation scale and lower complexity with excellent performance in IBS-based compressed sensing and interleave frequency division multiplexing systems.