A detection system is considered that analyzes the spectrum of the time-series output from a sensing element. The spectral data consist of a matrix of estimates of the energy in many small time-frequency cells. A decision procedure is formulated that is based on the multiple use of a two-sample statistic operating on the columns of the matrix. If the input noise is Gaussian with unknown power, the asymptotically optimum statistictis a ratio of two sample means. Since in certain applications the Gaussian input assumption may be unreliable, nonparametrie techniques based on the Mann-WhitneyUand SavageTstatistics are studied. Asymptotic relative efficiency (ARE) is computed for general positive spectral noise data and a scale alternative. This alternative is appropriate since it includes, for SNR\rightarrow 0, a Gaussian input with either a sinusoidal or Gaussian target. For a Gaussian inputARE_{U/t} \geq \frac{3}{4}andARE_{T/t} \geq0.816. Non-Gaussian examples indicate thatUandTcan be much better thant. It is shown that, subject to a reasonable restriction on the noise cumulative distribution function (cdf),ARE_{U/t} \geq \frac{27}{64}. The results obtained here for noncoherent detection, though not quite as strong, are analogous to the known bounds on ARE for linear coherent detection (a translation alternative).

A new general approach to the formulation of a non-parametric detector using dependent samples is introduced and applied to a space-diversity system employing dc signaling. A comparison based on a form of asymptotic relative efficiency is made between the new detector and a Mann-Whitney detector. Under certain conditions the new procedure demonstrates an improvement in transmission efficiency.

The proposed detector uses three vector samples to decide which one of two distinct stationary or quasi-stationary stochastic processes is present at its input. A reference sample is obtained from each of the two processes during an initial learning interval, and the third sample is taken on the decision interval. It is assumed that independent samples can be obtained from the stochastic processes. A weighted linear combination of two2-sample Mann-Whitney statistics defined on the three vector samples is used at the detector. An upper bound on the asymptotic or large-sample error probability is obtained, which indicates that, unlike the2-sample detector, the new detector is insensitive to the {\em a priori} signal probability and operates well in an unspecified environment. Comparisons are made between the proposed model and the standard2-sample model at both small and large values of signal-to-noise ratio. An extension to intermediate values of signal-to-noise ratio is obtained by considering two examples, dc signal in additive noise and Lehmann's nonparametric class of alternatives. Owing mainly to an invariant optimum threshold setting, the proposed procedure results in a significantly better performance over a wide range of signal-to-noise ratio.