Optimal and Suboptimal Finger Selection Algorithms for MMSE Rake Receivers in Impulse Radio Ultra-Wideband Systems

TL;DR

This paper introduces convex relaxation-based algorithms for finger selection in MMSE Rake receivers in impulse radio ultra-wideband systems, balancing near-optimal performance with computational feasibility.

Contribution

It formulates the finger selection as a non-convex integer programming problem and proposes convex relaxation techniques to find practical suboptimal solutions.

Findings

Algorithms achieve performance close to optimal schemes

Convex relaxation simplifies complex optimization problems

Proposed methods outperform conventional finger selection algorithms

Abstract

Convex relaxations of the optimal finger selection algorithm are proposed for a minimum mean square error (MMSE) Rake receiver in an impulse radio ultra-wideband system. First, the optimal finger selection problem is formulated as an integer programming problem with a non-convex objective function. Then, the objective function is approximated by a convex function and the integer programming problem is solved by means of constraint relaxation techniques. The proposed algorithms are suboptimal due to the approximate objective function and the constraint relaxation steps. However, they can be used in conjunction with the conventional finger selection algorithm, which is suboptimal on its own since it ignores the correlation between multipath components, to obtain performances reasonably close to that of the optimal scheme that cannot be implemented in practice due to its complexity. The proposed algorithms leverage convexity of the optimization problem formulations, which is the watershed between `easy' and `difficult' optimization problems.