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The fundamental task of a digital receiver is to decide the transmittedsymbols in the best possible way, i.e., with respect to an appropriatelydefined performance metric. Examples of usual performance metrics are theprobability of error and the Mean Square Error (MSE) of a symbol estimator. Ina coherent receiver, the symbol decisions are made based on the use of achannel estimate. This paper focuses on examining the optimality of usualestimators such as the minimum variance unbiased (MVU) and the minimum meansquare error (MMSE) estimators for these metrics and on proposing betterestimators whenever it is necessary. For illustration purposes, this study isperformed 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 targetperformance metrics.

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