David Middleton; Arthur D. Spaulding
Abstract: In this second part of an ongoing study, the general problem of optimum and suboptimum detection of threshold (i.e. weak) signals in highly nongaussian interference environments is further, developed from earlier work ([la],[lb];). Both signal processing algorithms and performance measures are obtained canonically, and specifically when the electromagnetic interference environment (EMI) is either Class A or Class B noise. Two types of results are derived: (1), canonical analytic threshold algorithms and performance measures, chiefly error probabilities and probabilities of detection; and (2), various typical numerical results which illustrate the quantitative character of performance. Suboptimum systems are also treated, among them simple cross– and auto–correlators (which are optimum in gaussian interference), and clipper–correlators which employ hard limiters (and are consequently optimum in "Laplace noise"). The various modes of reception considered explicitly here include:(i), coherent and incoherent reception; (ii), "composite" or mixed reception (when there is a nonvanishing coherent component in the received signal; (iii), "on–off" and binary, signals, as well as varieties of fading and doppler spread.
Both local optimality (LO) and asymptotic optimality (AO) are demonstrated, along with the critical influence of the proper bias in the optimum algorithms, which maintain their LO and AO character as sample size is increased, without having to add additional terms in the original threshold expansion (and thus produce insurmountable system complexity for the very large samples required for effective detection of weak signals). It is shown that for AO, as well as LO, two conditions may be needed to establish the largest magnitude of the minimum detectable input signal which can be permitted and still maintain the optimal character of the algorithm. In addition to the more general Bayes risk and probabilistic measures of performance, Asymptotic Relative Efficiencies (ARE1s) are also included and their limitations discussed. A number of numerical examples which illustrate the determination of performance and performance comparisons are provided, with an extensive set of Appendices containing many of the analytic details developed and presented here for future use, as well.
Keywords: non-Gaussian noise; threshold signal detection; optimum threshold detection algorithms; performance measures; electromagnetic interference environments (EMI); suboptimum detectors; locally optimum and asymptotically optimum algorithms; Class A, B noise; correlation detectors; clipper-correlators; error probabilities; minimum detectable signals; processing gain; bias; EMI scenarios; composite threshold detection algorithms; on-off binary signal detection; performance comparison; non-Gaussian interference
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