Multiplexing precoding scheme for STC-CPM with parametric phase discriminator IWM receiver

A constant envelope continuous phase modulation (CPM) class of Multi-Channel (MC) modulations for multi-antenna transmitters is considered. Each receive antenna receives a superposition of CPM waveforms. The useful signal at the receiver spans a curved space - the information waveform manifold (IWM). Particularly it has the form of a cylinder on a cylinder for 2-component CPM signals. At the receiver, we use a nonlinear preprocessor consisting of a nonlinear projector on the IWM, optional processing on the curved space, and a decoding isomorphism. A particular form of the preprocessor, the 2-component IWM phase discriminator, is analyzed. We show that the discriminator can separate individual instantaneous phases of the component CPM modulations and therefore has multiplexing capabilities with respect to the individual transmitted components. Two parallel channels are created without the need for a time domain processing since the procedure fully relies on the curved space properties of the IWM, and thus can be combined with arbitrary outer space-time coding of MC-CPM. An information theoretic analysis of the multiplexing properties based on the mutual information regions is presented. The discriminator solution has a two-fold ambiguity. We show that the discriminator provides good separation of component phases conditioned on a perfect ambiguity resolution. We propose a transmit spatial-differential precoding scheme that allows the ambiguity resolution.