Signal-to-noise ratio requirements for detection of multiple pulses subject to partially correlated fading with chi-squared statistics of various degrees of freedom

Abstract : The transmitted signal in a fading medium is composed of several pulses separated in time so as to achieve diversity and thereby combat deep fades and loss of signal. Receiver processing consists of matched filtering of each of the pulses, followed by summation of the squared envelopes of all the filter outputs. In addition to additive Gaussian background noise, the signal is subject to slow medium fading which has a chi-squared first-order distribution and which may be correlated from pulse to pulse to an arbitrary degree. The false alarm and detection probabilities of this system are derived in various series expansions which are amenable to efficient computer evaluation. Programs are presented and exercised for various combinations of signal-to-noise ratio, number of pulses, degree of correlated fading, and (noninteger) number of degrees of freedom of the chi-squared fading. Required input signal-to-noise ratios for several false alarm and detection probabilities are computed and plotted for cases of the fading normalized correlation coefficient ranging from 0 to 1; results for a nonfading medium are superposed for easy comparison. As special cases of the above formulation, we have independent Rayleigh amplitude fading, as well as completely dependent Rayleigh amplitude fading.