A Cramer-Rao Bound for Semi-Blind Channel Estimation in Redundant Block Transmission Systems

TL;DR

This paper derives a Cramer-Rao bound for semi-blind channel estimation in redundant block transmission systems, providing a fundamental performance limit useful for system design and analysis.

Contribution

It introduces a general CRB applicable to systems with full-rank linear redundant precoders, including OFDM, and simplifies CRB derivation for complex parameters.

Findings

CRB applicable to OFDM and similar systems

Simplified CRB forms for complex parameters

Provides a lower bound for unbiased semi-blind estimators

Abstract

A Cramer-Rao bound (CRB) for semi-blind channel estimators in redundant block transmission systems is derived. The derived CRB is valid for any system adopting a full-rank linear redundant precoder, including the popular cyclic-prefixed orthogonal frequency-division multiplexing system. Simple forms of CRBs for multiple complex parameters, either unconstrained or constrained by a holomorphic function, are also derived, which facilitate the CRB derivation of the problem of interest. The derived CRB is a lower bound on the variance of any unbiased semi-blind channel estimator, and can serve as a tractable performance metric for system design.