Cramer-Rao Bound for Blind Channel Estimators in Redundant Block Transmission Systems

TL;DR

This paper derives the Cramer-Rao bound for blind channel estimation in redundant block transmission systems, providing a benchmark for estimator performance and highlighting potential for improvement.

Contribution

It introduces a general CRB for blind channel estimators applicable to various redundant precoders, including ZP and CP, and compares it with existing methods.

Findings

CRB derived for blind channel estimation in ZP and CP systems

Existing estimators do not reach the CRB, indicating room for improvement

Numerical results validate the theoretical bounds

Abstract

In this paper, we derive the Cramer-Rao bound (CRB) for blind channel estimation in redundant block transmission systems, a lower bound for the mean squared error of any blind channel estimators. The derived CRB is valid for any full-rank linear redundant precoder, including both zero-padded (ZP) and cyclic-prefixed (CP) precoders. A simple form of CRBs for multiple complex parameters is also derived and presented which facilitates the CRB derivation of the problem of interest. A comparison is made between the derived CRBs and performances of existing subspace-based blind channel estimators for both CP and ZP systems. Numerical results show that there is still some room for performance improvement of blind channel estimators.