Estimation and Blind Deconvolution of AR Systems with Nonstationary Binary Inputs

Abstract

The problem of parameter estimation and blind deconvolution of AR systems with independent nonstationary binary inputs is considered. The estimation procedure consists of applying an MA filter (equalizer) to the observed data and adjusting the parameters of the filter so as to minimize a criterion that measures the binariness of its output. The output sequence itself serves as an estimate of the unobservable binary input of the AR system. Without assuming stationarity of the inputs, it is shown that the proposed method produces a consistent estimator of the AR system, not only in the sense of converging to the true parameter as the sample size increases, but also attaining the true parameter of the AR system for sufficiently large sample size. For noisy data, the estimation criterion is modified based upon an asymptotic analysis of the effect of the noise. It is shown that the modified criterion is also consistent (in the usual sense) and its variability depends upon the filtered noise. Some simulation results are also presented to demonstrate the performance of the proposed method for parameter estimation as well as for blind deconvolution.