A Convex Relaxation Approach to Higher-Order Statistical Approaches to Signal Recovery

TL;DR

This paper introduces a convex relaxation method for higher-order statistical signal recovery, improving convergence and effectiveness in blind and semi-blind scenarios for SISO and MIMO systems.

Contribution

It develops a convex optimization framework for higher-order statistical methods, overcoming local convergence issues of previous gradient-based algorithms.

Findings

Effective for short packet data transmission

Suitable for blind equalization and source separation

Works with minimal pilot symbols

Abstract

In this work, we investigate an efficient numerical approach for solving higher order statistical methods for blind and semi-blind signal recovery from non-ideal channels. We develop numerical algorithms based on convex optimization relaxation for minimization of higher order statistical cost functions. The new formulation through convex relaxation overcomes the local convergence problem of existing gradient descent based algorithms and applies to several well-known cost functions for effective blind signal recovery including blind equalization and blind source separation in both single-input-single-output (SISO) and multi-input-multi-output (MIMO) systems. We also propose a fourth order pilot based cost function that benefits from this approach. The simulation results demonstrate that our approach is suitable for short-length packet data transmission using only a few pilot symbols.