According to the analysis of meteor burst communication (MBC) mechanism, a model of signal processing based on the structure of data frame is suggested for adaptive modulation and coding (AMC) of MBC system in this paper. There are two distinct modes of operation for signal processing: acquisition and tracking. The acquisition mode is a training period to initialize the channel estimation by frame header. The tracking mode is jointly to equalize payload data and to trace channel, where the principle of per-survivor processing (PSP) for maximum likelihood sequence detection (MLSD) is performed. A suboptimal method called D-PSP is adopted to save the computational time and memory size, which agrees with the slow-fading characteristic of meteor channel and makes the MLSD possible for adaptive modulation and coding of MBC system. Computer simulation results are included to support our development.