Mathematical expressions for error probabilities of coherent amplitude - and phase-shift keyed digital communication systems in the presence of additive narrow-band noise are developed. A digital computer program is developed which evaluates these error probabilities if the noise envelope has a distribution of the form developed by Petr Beckmann in 1964 (Ref 3:723-736). Beckmann postulated noise as the sum of overlapping impulses of energy whose envelopes are of exponential form. Typical error probabilities as a function of signal-to-noise ratio and number of levels in the system are plotted.
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