Nonparametric Hard Limiting and Sign Detection of Narrow-Band Deterministic and Random Signals

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Hard limiting or sign detection schemes for low-pass known and random signals in additive noise are popular as very simple signal detectors maintaining constant values for their false-alarm probabilities under the rather weak assumption that the sampled noise observations have zero median values. For nonparametric detection of narrow-band signals the natural extension of the zero medians assumption is the zero marginal medians assumption on the in-phase and quadrature noise components. Nonparametric detectors operating under this assumption are developed here for narrow-baud signals; these can be taken to be the logical counterparts of the low-pass sign correlator and polarity coincidence correlator detectors of low-pass theory. The concept of conditional testing, which has been applied previously to obtain efficient multilevel versions of low-pass sign detection schemes, is shown to enter quite naturally in the definition of narrow-band counterparts of the sign correlator and the polarity coincidence correlator detectors. It is also shown that under the diagonal symmetry extension of the low-pass univariate symmetry condition on the noise probability density function, multilevel extensions of these conditional test narrow-hand detectors may also be defined as counterparts of the multilevel conditional test schemes for low-pass signals.