Blind deconvolution of a dynamic noisy channel using model-based signal processing techniques

It is common in acoustics and communications to measure a signal that has been degraded by propagation through an unknown channel prior to measurement. While only the degraded measured signal may be available for processing, the actual data of interest may be the original signal or perhaps the filtering properties of the channel itself. In these situations, it may be desirable to reverse the filtering process through the application of an inverse filter to recover the original signal. In a situation where neither the input signal properties nor the channel properties are deterministically known, this problem is known as blind deconvolution (BDC).; Typically, BDC algorithms assume that the system is noiseless, the propagation channel is static, and the source signal is stationary. While maintaining the source signal stationarity assumption, these existing methods are extended to apply to cases in which the former two assumptions may not hold. This is done using a model-based approach to incorporate a priori information about the system dynamics.; The well-known Extended Kalman filter (EKF) and the more recently developed Unscented Kalman filter (UKF) are modified for application to blind processing techniques. They are then formulated for use with the widely accepted Natural Gradient BDC algorithm given a model of the inverse channel dynamics. One such simple channel model is presented allowing for an indirect arrival following the direct path arrival at a time-varying delay. Simulation results using the modified EKF and UKF BDC formulations with this model suggest that they are capable of tracking the dynamic channel using only noisy measurements of the degraded signal given a reasonable initialization. The result in the example cases considered is an improvement in the mean square error (MSE) of the recovered signal by roughly 15 dB over the standard NG BDC algorithm for a dynamic channel described by this model.