Tail-biting in optimal CPM detectors

The maximum a posteriori (MAP) detection of a continuous phase modulation (CPM) signal deploys the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm that utilises the trellis structure of the CPM signal. For optimal results the start as well as the end state must be known to the MAP detector. While the start state is usually the zero state by convention, the end of the trellis must be terminated properly to yield a defined end state. This leads to an overhead, which size is dependent on the particular CPM parameters. To overcome the decrease of spectral efficiency, a tail-biting technique is presented and compared to termination and truncation in a fair comparison regarding spectral efficiency.