Some Constructions of Almost-Perfect, Odd-Perfect and Perfect Polyphase and Almost-Polyphase Sequences

Abstract

In the paper, some new almost-perfect (AP), odd-perfect (OP) and perfect polyphase and almost-polyphase sequences derived from the Frank and Milewski sequences are presented. The considered almost-polyphase sequences are polyphase sequences with some zero elements. In particular, we constructed AP 2^t + 1- and 2^t + 2-phase sequences of length 2·4^t and 4^t + 1, OP 2^t + 1- and 2^t + 2-phase sequences of length 4^t and 2·4^t, OP 2^t + 1- and 2^t + 2 - phase sequences of length 4^t(p ^m + 1), $(p^m-1)\equiv 0 \pmod {2\cdot 4^t}$ with 4^t zeroes and length 2·4^t(p ^m + 1), $(p^m-1) \equiv 0 \pmod {4^{t+1}}$ with 2·4^t zeroes, and perfect 2^t + 1- and 2^t + 2 - phase sequences of length 4^t + 1(p ^m + 1) with 4^t + 1 zeroes and 2·4^t + 1(p ^m + 1) with 2·4^t + 1 zeroes. It is shown that the phase alphabet size of the obtained OP and perfect almost-polyphase sequences is much smaller in comparison with the known OP and perfect polyphase sequences of the same length and the alphabet size of some new OP polyphase sequences is minimum.