On the minimum Euclidean distance for a class of signal space codes

The minimum Euclidean distance for a class of constant envelope phase modulation codes is studied. Bandwidth and power efficient signals with continuous phase are considered. The information carrying phase varies piecewise linearly and the slopes are cyclically changed for successive symbol time intervals, yielding the so-called multi- signals. It has previously been shown that this class of signals contains bandwidth and power efficient signals when coherent maximum likelihood sequence detection is used. Bounds on the achievable Euclidean distance for signals in the above class are given. Upper bounds are calculated as well as minimum distance results for specific multilevel multi- signals. It is concluded that quaternary and octal muiti- schemes considerably outperform the binary schemes. Furthermore in the important small modulation index region, codes gain the maximum 3 dB. Larger gains are not available by increasing the number of values.