The Generalized Linear Decomposition of Multilevel CPM Signals

Multilevel continuous phase modulated (CPM) signals feature a perfectly constant envelope, attractive spectral properties and excellent power efficiency. However, their non-linear nature makes them less tractable and their processing more complex. Fortunately, a linear decomposition exists, allowing to apply linear signal processing techniques. This decomposition was originally developed for binary CPM schemes only, and is not suited for schemes with an integer modulation index. It was extended to multilevel CPM schemes, by decomposing the multilevel input sequence in a product of binary subsequences, and applying the binary decomposition to these subsequences. When one or more of these subsequences has an integer modulation index though, this technique fails. We present a general solution, and prove how many pulses are needed to represent the CPM signal in this particular case. The decomposition of the quaternary 3RC system with h = 1/2 is given as an example. A receiver based on this solution is presented.