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An improved ChebyÂ¿shev approximative analytical expression for the probability distribution of the normalised envelope of atmospheric noise (a.n.) in narrowband receiver is presented. A new probabilistic interpretation of the derived expression is given, and the error probabilities for the m-c.p.s.k. receiver with finite-width decision threshold and an ideal f.s.k. receiver are calculated. The expressions obtained are explicit and they represent the weighted sum of the error probabilities due to Gaussian noises of different noise powers.