A communications receiver receives a received continuous phase modulation (CPM) signal having an original modulation index of h and includes a filter, a continuous phase reconstructor using phase unwrapping, and a modulation index scaler for generating a reconstructed CPM signal having a scaled modulation index H from the received CPM signal having a small modulation index h, with the scaled modulation index H preferably being greater than the original modulation index h, so that, the transmitted CPM signal occupies a narrow bandwidth, yet, during reception, the reconstructed CPM signal with the high modulation index H can be reliably data demodulated for improved performance with reduced demodulation complexity.