Bias Compensation in Iterative Soft-Feedback Algorithms with Application to (Discrete) Compressed Sensing

TL;DR

This paper introduces principles for unbiased estimation in iterative soft-feedback algorithms, demonstrating a 1.2 dB performance gain in compressed sensing applications through proper unbiasing techniques.

Contribution

It presents a novel approach to unbiased estimation in soft feedback algorithms, applicable to iterative compressed sensing reconstruction.

Findings

Unbiasing principles can be applied to soft feedback algorithms.

Proper unbiasing yields a 1.2 dB improvement in compressed sensing.

Numerical results validate the effectiveness of the proposed method.

Abstract

In all applications in digital communications, it is crucial for an estimator to be unbiased. Although so-called soft feedback is widely employed in many different fields of engineering, typically the biased estimate is used. In this paper, we contrast the fundamental unbiasing principles, which can be directly applied whenever soft feedback is required. To this end, the problem is treated from a signal-based perspective, as well as from the approach of estimating the signal based on an estimate of the noise. Numerical results show that when employed in iterative reconstruction algorithms for Compressed Sensing, a gain of 1.2 dB due to proper unbiasing is possible.