Multichannel detection using the discrete-time model-based innovations approach

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical Engineering and Computer Science


Donald D. Weiner

Second Advisor

P. K. Varshney


Signal processing

Subject Categories

Electrical and Computer Engineering


This dissertation makes several contributions in the general area of multichannel detection and estimation. First, model-based likelihood ratios are developed for the multichannel binary detection problem using error vector processes assuming wide-sense stationarity of the baseband Gaussian processes. These error residuals are obtained through prediction error filtering operations via estimation of the process parameters. An important feature of the model-based methods is their ability to utilize modern parameter estimators in the signal processing. Furthermore, a more general likelihood ratio is also developed applicable for Gaussian processes with unconstrained quadrature components where the assumptions associated with stationarity on the associated bandpass processes are relaxed.

Second, a synthesis procedure is developed to generate time domain multichannel autoregressive (AR) random processes allowing for the control of their temporal and cross-channel correlation. The synthesized processes provide an input to the likelihood ratio implementations analyzed in this dissertation to obtain detection results as a function of channel signal-to-noise and process correlation parameters. The synthesis method is then generalized to produce the more general class of Gaussian processes with non-stationary bandpass processes noted above.

Third, the likelihood ratio developed for the non-stationary bandpass processes utilized a more powerful estimator than previously noted. This estimator is capable of whitening not only the complex observation processes, but also their quadrature components. Furthermore, coefficients for the more general linear estimator are obtained using the same form as algorithms proposed for wide-sense jointly stationary complex baseband processes but extended to the quadrature form. Thus, the resulting likelihood ratios apply to the more general class of Gaussian processes with unconstrained quadrature components.

Finally, analytic expressions are developed for the error variance of time-averaged correlation function estimators for discrete, complex baseband processes. A unique aspect of this development is the determination of the functional dependence of these expressions not only in terms of data window sizes, but also the process correlation characteristics. This analysis is of particular significance since detection performance limits result due to the errors associated with the time-averaged estimates using finite data windows.


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