A quadrature-multiplexed continuous phase modulation (QM-CPM) signal is made up of the real parts of two underlying CPM signals whose information content can be recovered from just their real parts. The real parts of two such signals are I/Q multiplexed and transmitted onto a single channel to approximately double the bits/Hz of the underlying CPM signals, while maintaining the same or similar minimum distance. A class of QM-CPFSK (QM-continuous phase frequency shift keyed) signals are presented that use binary signaling but more phase states, and M2-ary QM-CPFSK signals are derived from constant envelope M-ary CPFSK signals. M2-ary multi-amplitude CPFSK signaling schemes are constructed that maintain the same distance as known multi-amplitude CPFSK schemes, but more than double the bandwidth efficiency in bits/Hz. In addition to these CPFSK based embodiments, embodiments are provided that more generally use CPM, non-continuous phase modulated signals, and even trellis-based PAM based signals.