Minimum Euclidean distance for continuous phase modulation with time-limited phase shaping pulses

Recently, CPM signals employ information sequence with time-limited phase shaping pulse (CPM-TL) have been shown to achieve power and bandwidth efficient transmission. It is well known that minimum Euclidean distance could be used to estimate the error performance of CPM for moderate and large signal to noise ratio. In this paper, we further investigate the minimum Euclidean distance of CPM-TL with more time-limited phase shaping pulses (PSP) and compared with conventional CPM with time-unlimited PSP (CPM-TU). CPM-TL scheme has the advantages that any real number modulation index (h) could be applied and the resultant trellis structure of CPM guarantees the maximum constraint length allowed by the number of states in the MLSD receiver. Previous work showed that conventional CPM schemes with h > 1 could not achieve larger Euclidean distance with bandwidth expansion. However, we found that CPM-TL scheme could obtain significantly larger Euclidean distance for h > 1. Good CPM-TL schemes outperform previous work are given for the same complexity and similar bandwidth with up to 5 dB coding gain over MSK. Also, CPM-TU schemes have weak modulation indexes for all the PSP and modulation levels yet numerical results show that CPM-TL schemes with odd constraint length have no weak modulation index in many cases.