Signal Design for Efficient Detection in Randomly Dispersive Media,
STANFORD RESEARCH INST MENLO PARK CALIF ELECTRONICS AND RADIO SCIENCES DIV
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The optimum structure of a signal to be transmitted over a randomly time-varying and frequency-selective medium is investigated. A model is developed that treats the medium as a randomly time-varying linear filter. By viewing the filters transfer function as a homogeneous random field on the time-frequency plane, a second-order theory results that relates various second-order measures of the time and frequency structures of input and output processes. A Neyman-Pearson detector is assumed, and a signal-design strategy, based on the asymptotic behavior of the false-dismissal probability when the detector is presented with a sequence of observations of the medium output, is developed. This approach leads to the strategy of maximizing the Kullback-Leibler information number. It is shown that this criterion minimizes the false-dismissal probability for any reasonable false-alarm probability when the medium satisfies Prices low-energy coherence condition.