Exact Performance of General Second-Order Processors for Gaussian Inputs
NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT
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The characteristic functions of general second-order processors with nonstationary nonzero mean Gaussian inputs is derived in closed form. Three classes of processors are considered in the first, the decision variable is the sum of K independent terms, each of second-order form involving two statistically dependent Gaussian random variables the second class of processor is a narrowband cross-correlator of arbitrary Gaussian processes, with accumulation of K independent low pass filter output samples in the third class, the decision variable is a general quadratic-plus-linear form of M random variables, all statistically dependent on each other. Specializations to various forms of weighted energy detectors and correlators are made. Also, the characteristics function for the first class of processor subject to fading is evaluated. Programs for evaluating the cumulative and exceedance distribution functions of all three classes of processors are given and have been used to plot representative examples of performance. A comparison with a simulation result corroborates the analysis and program of the first class of processor.
- Electrical and Electronic Equipment
- Statistics and Probability
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