Compressed Sensing Channel Estimation for OFDM with non-Gaussian Multipath Gains

TL;DR

This paper investigates how non-Gaussian multipath amplitude distributions affect compressed sensing channel estimation in OFDM, revealing that channels with higher fourth moments require fewer dominant MPCs for accurate estimation.

Contribution

It introduces a new analytical framework linking MPC amplitude distribution's fourth moment to the number of MPCs needed for effective compressed sensing channel estimation.

Findings

Channels with high fourth moment MPCs need fewer dominant components for accurate estimation.

Orthogonal Matching Pursuit performs nearly as well as Basis Pursuit De-Noising for high fourth moment channels.

Simulation results validate the analytical relationship between MPC distribution and CS estimation performance.

Abstract

This paper analyzes the impact of non-Gaussian multipath component (MPC) amplitude distributions on the performance of Compressed Sensing (CS) channel estimators for OFDM systems. The number of dominant MPCs that any CS algorithm needs to estimate in order to accurately represent the channel is characterized. This number relates to a Compressibility Index (CI) of the channel that depends on the fourth moment of the MPC amplitude distribution. A connection between the Mean Squared Error (MSE) of any CS estimation algorithm and the MPC amplitude distribution fourth moment is revealed that shows a smaller number of MPCs is needed to well-estimate channels when these components have large fourth moment amplitude gains. The analytical results are validated via simulations for channels with lognormal MPCs such as the NYU mmWave channel model. These simulations show that when the MPC amplitude distribution has a high fourth moment, the well known CS algorithm of Orthogonal Matching Pursuit performs almost identically to the Basis Pursuit De-Noising algorithm with a much lower computational cost.