Asymptotically Optimal Estimation Algorithm for the Sparse Signal with Arbitrary Distributions

TL;DR

This paper introduces an asymptotically optimal and robust sparse signal estimation algorithm suitable for wireless systems, demonstrating near-MMSE performance and faster convergence than existing methods.

Contribution

The paper presents a new sparse signal estimation algorithm that is asymptotically optimal, robust to distribution variations, and converges faster than existing algorithms.

Findings

Approaches the MMSE bound at extreme SNRs.

Converges faster than TSR-DFT and AMP algorithms.

Validated by numerical simulations.

Abstract

In this paper, we propose a sparse signal estimation algorithm that is suitable for many wireless communication systems, especially for the future millimeter wave and underwater communication systems. This algorithm is not only asymptotically optimal, but also robust to the distribution of non-zero entries of the sparse signal. Then, we derive its upper bound and lower bound, and show that the Mean Square Error (MSE) of the proposed algorithm can approach the Minimum Mean Square Error (MMSE) bound when the Signal Noise Ratio (SNR) goes to infinite or zero. Numerical simulations verify our theoretical analysis and also show that the proposed algorithm converges faster than existing algorithms, e.g., TSR-DFT, AMP, etc.