Estimation - Correlation, Modeling and Identification in Adaptive Array Processors

Abstract This paper studies the system modeling and identification issues that arise in implementation of maximum likelihood detectors and adaptive array processors of signals that have propagated over randomly time-varying propagation and scattering channels. A multidimensional estimator correlator processor is used to combine the ideas of system modeling and identification with detection theory and adaptive array processing. Part of the estimator structure can be obtained from received data by the usual adaptive array processing techniques (estimation and inversion of noise covariance matrices), but the channel output estimator requires prior knowledge of the signal part of the channel output covariance matrix. This requires modeling and identification of deterministic and stochastic propagation and scattering operators. A number of convenient matrix representations for these operators have been developed. Identification of stochastic operators is based on the vector Karhunen-Loeve expansion. It is shown that in the special case of wide-sense stationary stochastic processes and periodic signal vector, orthonormal basis and eigenvalues for channel modeling and identification can be determined by discrete Fourier transform and singular value decomposition.