Mathematical analysis of 4-ary MSK signal spectrum based on Markov chain Process Strategy

A Markov chain is applied to build a complete model to analyze the modulation process of 4-ary MSK signals and to derive the analytic expressions of the spectrum when the modulation index h=1/2. In the derivation process, the autocorrelation function is derived first, and the spectral expressions are obtained from the autocorrelation function by Fourier transform. The accuracy of the expressions is then confirmed by numerical simulation of the MSK signal using MATLAB. Finally the specific bandwidth power output graphs, which objectively and clearly express the spectrum roll-off rate. The results show that the 4-ary MSK has better spectral efficiency and characteristics than the binary system, which is more conducive to improving the communication rate and utilizing the limited bandwidth. For the next step to improve the spectrum structure, System BER, optimize the spectrum characteristics of the preliminary work made.