On higher-order representations of Polyphase-Coded FM radar waveforms

It has recently been shown that arbitrary polyphase codes can be implemented as FM waveforms through a radar-specific version of the Continuous Phase Modulation (CPM) framework. These waveforms, denoted as Polyphase-Coded FM (PCFM) can be viewed as a first-order hold representation of the phase function (where traditional codes represent a zero-order hold). Here we examine higher-order representations as a means to achieve further variety over the space of possible waveform functions one may optimize. Specifically, the relationships between the first, second, and third-order representations are considered, along with the optimization of the coding for each.