Low complexity receiver for continuous phase modulation using 3RC-TL phase shaping pulses

In our previous work, we presented an alternative continuous phase modulation (CPM) scheme using time-limited phase shaping pulses (PSP), named as the CPM-TL. It could achieve large coding gains over conventional CPM using time-unlimited PSP (CPM-TU) in many cases. Also, we found a useful class of binary CPM-TL schemes that employed time-limited raised cosine (RC) PSP, with pulse width equal to 3, denoted as 3RC-TL of CPM scheme. It has large coding gains over the Minimum Shift Keying (MSK) and Gaussian MSK (GMSK) that are two of most popular modulators among the family of CPM-UT scheme. The MSK and GMSK modulators of CPM-TU scheme are known to have lower complexity in receiver design and excellent power-bandwidth performance. Basically, the optimal receiver of the 3RC-TL CPM scheme requires more complexity than the MSK or GMSK (using suboptimum receiver). In this paper, we deal with the reduce-complexity problem in receiver design for the 3RC-TL of CPM-TL scheme. To do so, we decompose the CPM-TL signal into a set of pulse-amplitude modulated (PAM) waveforms, using Euler´s formula, which is different from the one suggested by Laurent in 1986. We show that the complexity of PAM-based 3RC-TL receiver can be simplified, and to be implemented with the Viterbi algorithm (VA) that contains two-PAM waveforms and two states. Similarly, we also compare with the GMSK (BT=0.25) using the PAM-based receiver, that required only one PAM waveform and two states, or two PAM waveforms and four states. We found that 3 RC-TL of CPM scheme has 2.5~3.45 dB coding gains over the GMSK with simplified PAM-based receiver.