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The recently developed polyphase-coded FM implementation for physical radar waveforms is generalized to higher-order representations to facilitate greater design freedom (with MATLAB scripts provided in the appendix). Being FM, waveforms realized with these implementations have the benefit of being readily amenable to a high-power radar transmitter while possessing parameterized structures that are advantageous for optimization. Here various attributes of these implementations are examined. Specifically, it is shown that higher-order representations can, in special cases, be made equivalent, and through these relationships appropriate signal structure attributes can be inferred. Higher-order coding guidelines are also derived based on the need to ensure spectral containment. Example waveforms are optimized for each particular implementation to highlight their individual properties, towards the ultimate goal of establishing new ways to realize waveform-diverse emission structures that are physically realizable.
Tan et al. (2019) studied this question.