Envelope and Phase Statistics for Non-Gaussian Noise and Resulting Error Probabilities for Digital Communications Systems,
PLESSEY ELECTRONIC SYSTEMS RESEARCH LTD ROKE MANOR (ENGLAND)
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It is becoming increasingly realised that the electromagnetic environment through which signalling is to be performed should be given serious attention from the point of view of its statistical characteristics when systems of communication, command, or control, are planned. When data from a particular scenario is processed to produce a distribution of instantaneous noise amplitudes it is often observed that the statistics are non-Gaussian, with a slow fall-off in the distribution tail. The problem addressed here is how such noise affects the envelope and the phase of narrow-band transmissions operating in such scenarios, leading on to performance predictions for the standard digital modulation techniques. In the paper statistical properties of the envelope and phase are first derived in a general manner. A new formula is given, for example, for the probability that a noise envelope sample exceeds a sample of the envelope of Signal Noise. This is the basic statistic needed for assessing incoherently detected situations such as Or-ing or FSK. In order to apply the results to specific noise types three kinds of non-Gaussian noise are studied which have intrinsic interest. These are a Cauchy noise, b Quartic noise, and c A mixture of Gaussian Impulsive noise.