NONLINEAR DIGITAL SIGNAL PROCESSING TECHNIQUES FOR ROBUST DETECTION AND MMSE PREDICTION
Abstract
The problem of nonlinear MMSE prediction is considered by using an augmented Hibert Space approach. Random variables that are powers of the samples of the random process are summed and thus the predictor becomes a linear functional on this space. The orthogonality principle is then applied to determine the coefficients of the functional. Also considered is an iterative approach to designing predictors that are characterized as zero memory nonlinearities (ZNL) followed by linear filters. In each case, comparisons of performance are made to the optimum linear predictors and are shown to dramatically decrease the mean squared prediction error. Also considered are classes of random processes that exhibit the above predictors as their optimum predictors. We also compute the optimum predictor associated with memoryless invertible transformations of these random processes. In this way, all that needs to be done is to compute the coefficients by knowing or estimating various moments and crossmoments of the random processes involved. We then present a method for the robust detection of a constant signal in noise. The detector is designed by optimizing a ZNL which is found to be characterized by a Fredholm Integral equation with a Pincherle-Goursat (P-G) kernel. The robustness characteristics are demonstrated by computing the asymptotic relative efficiency (ARE) over the generalized Cauchy distribution. Also presented is the robust characteristics of a detector utilizing a median filter. The efficacy of the median filter detector is computed using Central Limit Theorem results for m-dependent noise. The robustness is demonstrated again by computing the ARE over the generalized Cauchy distribution.
Degree
Ph.D.
Subject Area
Electrical engineering
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