On the Design of Channel Estimators for given Signal Estimators and Detectors

TL;DR

This paper investigates the optimality of common channel estimators like MVU and MMSE for digital receivers, analyzing their performance in terms of error probability and MSE, and proposes improvements based on specific metrics.

Contribution

It examines the limitations of traditional estimators and proposes new designs tailored to specific performance metrics in a simplified SISO flat fading channel model.

Findings

Traditional estimators may not be optimal for all performance metrics.

Proposed estimators improve performance in terms of error probability and MSE.

Design dependencies of estimators on target metrics are highlighted.

Abstract

The fundamental task of a digital receiver is to decide the transmitted symbols in the best possible way, i.e., with respect to an appropriately defined performance metric. Examples of usual performance metrics are the probability of error and the Mean Square Error (MSE) of a symbol estimator. In a coherent receiver, the symbol decisions are made based on the use of a channel estimate. This paper focuses on examining the optimality of usual estimators such as the minimum variance unbiased (MVU) and the minimum mean square error (MMSE) estimators for these metrics and on proposing better estimators whenever it is necessary. For illustration purposes, this study is performed on a toy channel model, namely a single input single output (SISO) flat fading channel with additive white Gaussian noise (AWGN). In this way, this paper highlights the design dependencies of channel estimators on target performance metrics.