Experiments in Adaptive Estimation of Unknown Binary Waveforms

A special-purpose adaptive machine is described which carries out estimation in real time of an unknown binary waveform which is perturbed with additive Gaussian noise. Unknown waveforms of over 103 samples in duration can be recovered. The unknown waveforms are of unknown epoch and can reappear at either random or periodic time intervals. The observed signal is received at moderate or low signal-to-noise ratios so that a single observation of the received data (even if one knew the precise signal arrival time) is not sufficient to provide a good estimate of the signal waveshape. Experimental results are described which show transient behavior waveform estimate. The transient behavior is expressed as the number of errors in the current estimate of the signal plotted vs. time. In a noisy environment, each ``learning' transient is a random time function. These learning transients are shown for several different signal-to-noise ratios and indicate the threshold noise levels for various types of initial states of the machine memory.