Topic：Constructions of Gaussian Integer Sequences with Ideal Periodic Autocorrelation Functions

Date&Time：2016/03/04 (五) 14:20

Speaker： 李志鵬 教授(中山大學通訊所)

Location：清華大學台達館 R216

Abstract：
A Gaussian integer is a complex number whose real and imaginary parts are both integers. Meanwhile, a sequence is defined as perfect if and only if the out-of-phase value of the periodic autocorrelation function is equal to zero. This talk presents two approaches for constructing Perfect Gaussian Integer Sequences (PGISs). In the first approach, PGISs are constructed by linearly combining base sequences or their cyclic shift equivalents with arbitrary nonzero complex coefficients of equal magnitudes, where the nonzero elements of these base sequences belong to the set {±1, ±j}. In particular, the construction of sparse PGISs (SPGISs) is also presented, in which most of the sequence elements are zero. It is interesting to note that the periodic cross-correlation functions of both PGISs and SPGISs have the same mathematical expression as the investigated sequences. In the second approach, PGISs are constructed using cyclotomic classes and finite field theory. The presentation is commenced by constructing PGISs of arbitrary odd prime period. The presentation is then extended to the construction of PGISs of arbitrary composite length.