Signal Fading due to multipath propagation severely impairs the performance of high-speed mobile communication systems. Effective diversity scheme for fading channel is STTD (Space Time Transmitter Diversity) method. This scheme is very simple and using 2 transmit antennas and 1 receive antenna provides a diversity order of two[1],[2]. In this paper, we derive the new probability density function of the envelope of the received signal over correlated Rayleigh fading channel. Using the new pdf of the envelope we analyze the performance of noncoherent M-ary FSK, DPSK and ASKSTTD (Space Time Transmitter Diversity) a system on correlated Rayleigh fading channel.