Viable/Inviable Polynomial-Phase Modulations for "Stretch Processing"

For pulse compression, "stretch processing" offers a low sampling rate, computationally simple alternative to the conventional matched-filter-based approach for radar/sonar receivers to pulse-compress the linear frequency modulated (a.k.a. "chirp," "linear chirp," or "sweep signal") radar returns. A question remains in the open literature whether this "stretch processing" method could be applied to other constant-modulus polynomial-phase modulations. A concise mathematical proof is presented to show the answer as "no"; the linear frequency modulation (LFM) is the only constant-modulus polynomial-phase-based pulse compression suitable for "stretch processing".