Estimation of a quadrature cross- correlation detector by analog, polarity-coincidence, and relay methods (Corresp.)

Abstract

The variance of the output of a cross-correlation detector, which is called a quadrature cross-correlation detector, is estimated. In this type of detector two zero-mean Gaussian quadrature processes <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\alpha(t)</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\beta(t)</tex> of a complex process <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(\alpha(t) -j \beta(t))</tex> are cross correlated. This cross-correlation function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_{A} (\tau)</tex> is estimated when neither of the two processes is distorted (the analog method), when both processes are distorted by a signum function before being cross correlated (the polarity coincidence method), and when one of the two processes is distorted by either a signum function or by a "comparator logic" function (the relay method). These quadrature cross-correlation detectors then are compared on the basis of output signal-to-noise ratio (s/n) and the clipping and relay losses are computed for two test quadrature processes of an Edgeworth-expansion-approximated power spectrum. Since <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_{A} (0)</tex> is zero, the four corresponding differential estimators, such as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(R_{A} (\tau) - R_{A} (0))</tex> are also estimated and are compared on the basis of s/n. For these differential estimators, the clipping and relay losses are computed for the two test processes. In all cases the exact expressions for the s/n are derived as a function of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\tau</tex> . Some applications of these correlation detectors are outlined. The mathematical techniques employed here are thought to have potential usefulness for related problems in statistical communication theory and signal processing.