Spatially irregular space-waveform coded CPFSK with full rank optimized waveforms

A nonlinear modulation, the constant envelope CPM class being of particular interest, has multi-dimensional signal waveforms. We introduce a spatial code for multi-antenna CPFSK system using a different waveform (constellation) space on each antenna. The 2-dimensional space-waveform codeword spans an antenna (spatial) and constellation (waveform) domains. We optimize the waveforms for rank and determinant criterion. The resulting space-waveform code exhibits a full rank without any need of temporal domain encoding. Numerical results are presented for a selected set of CPFSK class of signals and 2-antenna transmitter. In this particular case, the procedure leads to an elegant implementation by Spatially Mirrored Tilted Phase CPFSK. The presented scheme is well suited for the concatenation with outer scalar temporal domain code.