Reciprocal Mean-Square Error and Signal-to-Noise Ratio as Distinct Performance Measures in Below-Threshold Communication

In above-threshold communication situations, the estimation bias and hence the modulation suppression are practically negligible; so that the output signal-to-noise ratio (SNR) is numerically very close to the reciprocal of the normalized mean-square error (MSE). The two last performance measures are, however, conceptually distinct as well as numerically widely different below threshold. Whereas in estimation and control problems the latter is of primary interest, much effort having been invested in its calculation and bounding, the former is very often more meaningful when transmitting sampled continuous data. This paper purports to review the relations between the previously mentioned quantities in time-discrete communications; to conjecture a functional dependence of bias and MSE on the value of the transmitted parameter, that simplifies these relations; to present some results of a Monte-Carlo simulation that tests these conjectures and provides performance curves for the maximum a posteriori probability, the (minimum-MSE-optimal) conditional mean and other derived estimators; and finally to speculate about the relative merits of these averaging type estimators as compared with the discriminator types in a frequency-position-modulation system, from the point of view of the aural character of the output noise below threshold.