New Piecewise Linear Polyphase Sequences Based on a Spectral Domain Synthesis

A new class of piecewise linear polyphase codes of perfect square length, named PAT codes, is introduced. PAT codes derive from an innovative design procedure and present excellent performance in terms of both merit factor and peak to side-peak ratio with respect to previously proposed sequences such as Frank, P1, P2, and Px codes. In particular, for odd lengths, the merit factor of PAT codes is larger than that of all other polyphase sequences under analysis, and the peak to side-peak ratio is as large as that of the best of these sequences (namely the Frank and P1 codes). For even lengths, the merit factor and the peak to side-peak ratio performance of PAT codes coincide with those of Px and P2 codes, which are the best polyphase sequences under analysis. PAT code synthesis is based on a rigorous analytical method in the code spectral domain and leads to a simple recursive formula for the generation of sequences of arbitrary length.