On Binary Sequence Pairs with Two-Level Periodic Autocorrelation Function

Abstract

Binary sequence pairs as a class of mismatched filtering of binary sequences can be applied in radar, sonar, and spread spectrum communication system. Binary sequence pairs with two-level periodic autocorrelation function (BSPT) are considered as the extension of usual binary sequences with two-level periodic autocorrelation function. Each of BSPT consists of two binary sequences of which all out-phase periodic crosscorrelation functions, also called periodic autocorrelation functions of sequence pairs, are the same constant. BSPT have an equivalent relationship with difference set pairs (DSP), a new concept of combinatorial mathematics, which means that difference set pairs can be used to research BSPT as a kind of important tool. Based on the equivalent relationship between BSPT and DSP, several families of BSPT including perfect binary sequence pairs are constructed by recursively constructing DSP on the integer ring. The discrete Fourier transform spectrum property of BSPT reveals a necessary condition of BSPT. By interleaving perfect binary sequence pairs and Hadamard matrix, a new family of binary sequence pairs with zero correlation zone used in quasi-synchronous code multiple division address is constructed, which is close to the upper theoretical bound with sequence length increasing.