Backtracking sequential detection of continuous phase modulated signals

A new sequential detection algorithm is introduced. The technique is suitable when the memory of the source induces a large trellis. This is typical when bandwidth efficient digital modulation systems are used. When the channel is power and bandwidth limited an efficient modulation scheme is needed. Continuous phase modulated signals can represent a solution but they involve an increase in the receiver complexity; and this factor becomes a severe limitation when a coded modulation is required. As a direct consequence, CPM schemes with both power and bandwidth efficient utilization, and a good overall performance in terms of error probability are expected to be much more expensive than traditional methods. The big problem of handling the increased memory in the use of complex coded/modulation schemes are caused first of all by the presence of the Viterbi detector in the receiver. Sequential decoding is a valid alternative, and particularly the backtracking algorithm. Purely breadth first sequential decoding algorithms such as M-algorithm and Stack algorithm are in fact simple to analyze and present inherent parallelism but are, as pointed out by Anderson (1992), less efficient in terms of average number of paths searched with respect to the backtracking algorithm. The aim of the paper is twofold. First, we propose a technique which is a modified version of a Fano-like (1963) algorithm in which the forward operations ore performed by means of a breadth first algorithm. Second, an important application of the algorithm in the coherent detection of continuous phase modulation is described