In this thesis, we simulate GSM burst mode 0.3GMSK signal with Matlab program, implement the modulator and study the coherent demodulation algorithm in fixed point DSP chip. We use the training sequence in every burst to aid the timing synchronization and phase recovery. Also simulate the receiver performance of timing synchronization and Viterbi equalizer. In order to recovery the timing in fading channel, we use the feedforward demodulation. Finally, In order to implement the modulation and coherent demodulation algorithm in TMS320C6X, we simulate the 16-bit fixed-point format arithmetic in Matlab program and study the feasibility of implementation.