Noncoherent NAR power estimators for adaptive detection

Quadratic noise-alone-reference (NAR) power estimators in the form of finite impulse response filters operating on square-law demodulated samples are analyzed. A generalized NAR estimator is obtained by constraining the standard estimator to be nonnegative and unbiased to a symmetrically observed signal. A quasi-NAR estimator is derived to be nonnegative, to be unbiased in the absence of a signal, and to minimize both the variance due to noise alone and the bias due to a symmetrically observed signal. This estimator depends on the signal´s normalized envelope but not on the amplitude. The derived estimators are used in determining the structures of two noncoherent adaptive signal detectors in an unknown level additive noise. For independent noise samples, the first detector reduces to a uniform integrator with a cell-averaging constant-false-alarm-rate circuit, and the second reduces to a filter matched to the squared signal envelope but with quasi-NAR automatic gain control, which can regulate faster noise power fluctuations