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The fluctuating two-ray (FTR) fading model provides a much better fit than other fading models for small-scale fading measurements in millimeter wave communications. In this paper, using a mixture of gamma distributions, new exact analytical expressions for the probability density and cumulative distribution functions of the FTR distribution with arbitrary fading parameters are presented. Moreover, the performance of digital communication systems over the FTR fading channel is evaluated in terms of the channel capacity and the bit error rate. The interaction between channel fading parameters and system performance is further investigated. Our newly derived results extend and complement previous knowledge of the FTR fading model.