Nonparametric detection using spectral data
Melvin N. Woinsky · IEEE Transactions on Information Theory · 1972
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).