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Nonparametric detection using spectral data

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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 statistic t is a ratio of two sample means. Since in certain applications the Gaussian input assumption may be unreliable, nonparametrie techniques based on the Mann-Whitney U and Savage T statistics 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 input ARE_{U/t} \geq frac{3}{4} and ARE_{T/t} \geq 0.816. Non-Gaussian examples indicate that U and T can be much better than t . 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).

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Information Theory, IEEE Transactions on  (Volume:18 ,  Issue: 1 )