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Structural characterization of locally optimum detectors in terms of locally optimum estimators and correlators

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1 Author(s)

Explicit formulas for locally (SNRrightarrow 0)optimum (MMSE) signal estimators (smoother, filter, and predictor) for discrete-time observations of a random signal in additive random noise are derived and used to characterize the locally optimum (likelihood ratio) signal detector for on-off signaling. The characterizations are canonical (distribution-free) detector structures involving estimator-correlators. These structural characterizations provide new interpretations of known detectors for various special cases. If the one-step signal predictor is recursive and the noise is white (possibly non-Gaussian or nonstationary), there is a canonical structure that admits recursive computation. The primary motivation for these structural characterizations is to render the estimator-correlator design philosophy applicable for the purpose of simplifying implementations and enhancing adaptability. Unlike the known esfimator-correlator structural characterizations for continuous-time globally optimum detectors, the new characterizations apply for non-Gaussian as well as Gaussian noise, and the estimators are explicit rather than implicit.

Published in:

Information Theory, IEEE Transactions on  (Volume:28 ,  Issue: 6 )

Date of Publication:

Nov 1982

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