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The exact symbol and bit error probabilities of linearly modulated signals in frequency non-selective Rician fading channels with Lth diversity branches are derived, where coherent detection with maximum ratio combining (MRC) is used at the receiver. For performance evaluation, the multiplicative distortion is combined with the additive Gaussian noise and form an additive noise is formed. This method allows computing the exact symbol and bit error probabilities of M-ary phase shift keying (M-PSK), M-ary quadrature amplitude modulation (M-QAM), M-ary amplitude modulation (M-AM) and M-ary amplitude modulation phase modulation (M-AMPM) for any arbitrary bit mappings. The results contain several versions of one simple integral. The error probabilities are also obtained for Rayleigh channel, which is a special case of Rice channel. Further, the results for Nakagami-m channel with the integer parameter are found. The results quite match with the previous ones while having simple forms. Also, for some unsolved cases, the exact error probabilities are presented. Simulations are carried out to verify the analytical evaluations.