On convolutionally encoded partial response CPM

Convolutionally encoded partial response CPM is studied for an AWGN channel constrained by a narrow spectrum mask which puts hard requirements on both the width of the spectral main lobe and the size of the spectral side lobes. A family of uncoded partial response CPM schemes of different complexity based on the GMSK phase pulse are obtained. The schemes with best minimum Euclidean distance are compared with convolutionally encoded schemes meeting the same spectrum and information bit rate requirements. It is found that for 4-ary CPM there is a coding gain, but the best scheme is an 8-ary uncoded scheme and in most cases there is a coding loss, at least for the studied low memory order convolutional codes.