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In this paper, we perform the analysis of average symbol error probability (SEP) for a diversity system over generalized Rician fading channels with correlated branches. This class of fading subsumes generalized Rayleigh fading, Nakagami-q (Hoyt) fading, generalized gamma fading, Nakagami fading, Rician fading, and Rayleigh fading as special cases, which are among the most popular fading models considered in the published literature. We derive a series expression of the average SEP for a general class of M-ary modulation schemes (including MPSK, MQAM, BFSK, and MSK) with maximal-ratio combining (MRC). The series expression is in canonical form as a weighted sum of elementary closed-form expressions, which are the closed-form expressions for the average SEP of a single-branch system in Nakagami fading environments.