Cycle slip analysis of the M-th power NDA feedforward carrier synchronizer for M-PSK using narrowband postfiltering

The M-th power nondecision-aided (NDA) feedforward (FF) carrier synchronizer proposed by Viterbi and Viterbi (1983), operating on an M-PSK modulated signal, provides rapid preambleless phase synchronization; therefore it is very suitable for burst-type transmission systems (e.g. TDMA satellite communication systems). For short bursts, only one phase estimate per burst is needed and cycle slips cannot occur. For long bursts, multiple phase estimates per burst are made to enable the synchronizer to track phase variations through the burst. Additional postprocessing of these NDA FF phase estimates is then needed to eliminate equivocation. Unfortunately, the postprocessing also makes cycle slipping possible because it introduces feedback. The cycle slipping behaviour of the NDA FF carrier synchronizer using narrowband postfiltering is analysed using Fokker-Planck techniques. The authors describe the operation of the NDA FF synchronizer and present the postprocessing structure. An approximate expression for the mean time between slips is derived and evaluated. The results are verified by computer simulations and discussed