An Adaptive Receiver Implementation for the Gaussian Scatter Channel

To implement the minimum probability of error receiver for
M
-ary frequency-shift-keyed (FSK) communications over a Gaussian scatter channel, a minimum mean-squared error estimate of the scattered channel output signal must be constructed. It has been difficult to construct the optimum receiver since the correlation function of the scattered signal must be measured, and the impulse response of the estimation filter must then be found by solving a difficult integral equation. Stochastic approximation methods are used to develop an on-line algorithm for generating a self-optimizing filter. This filter is then used in the minimum probability of error receiver to estimate the sample function at the output of an ultrasonic model of a needles scatter channel. Experiments have been performed which indicate that the proposed adaptive receiver structure can be of practical utility because of its ease of implementation and speed of operation.