Coarse and Fine Timing Sychronisation for Partial Response CPM in a Frequency Hopped Tactical Network

A two-stage symbol timing estimation algorithm is proposed for partial response continuous phase modulation (PR-CPM) in a frequency hopped network, where interleavers span several hop durations. The algorithm consists of an initial one-shot coarse estimation of the timing error, followed by an iterative non-coherent fine timing algorithm based on the maximum likelihood approach. Simulation results illustrate the convergence behaviour of both coarse and fine timing schemes and demonstrate the expected losses in bit error rate performance for a variety of modulation indices, memory lengths and alphabet sizes, as a function of the symbol timing error. It is shown that, to achieve a low complexity solution to reliable communications, in the presence of timing errors, then a binary alphabet is desirable for PR-CPM. Furthermore, for small modulation memory lengths and relatively large index values, an iterative receiver is robust to residual timing errors after only a coarse timing estimate.