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Nonparametric detection using spectral data

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1 Author(s)

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 SNRrightarrow 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).

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