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A moments-based method is used for calculating the error probability of partially coherent phase shift keying (PSK) wireless diversity systems. The probability of error is formulated in terms of the Beaulieu series for the cumulative distribution function (cdf) of a sum of random variables. Since the characteristic function (CF) needed in the series derivation might not be known explicitly in some practical cases, the use of a moments-based method is proposed to determine it. The advantages of the method include both avoiding the use of numerical integration methods and yielding simple expressions, since the moments for many distributions encountered in communications analyses are easily available in closed-forms. Upper bounds on the systematic errors occuring in the computation via combining the Beaulieu series with the proposed method are derived.