Gaussian Integer Sequences with Ideal Periodic Autocorrelation Functions

A Gaussian integer is a complex number whose real and imaginary parts are both integers. In addition, a sequence is defined to be perfect if and only if the out-of-phase value of the periodic autocorrelation function (PACF) equals zero. This paper commences by presenting a novel class of perfect sequences. The investigated perfect sequences are generated by two groups of base sequences with four base sequences in each group. The nonzero elements of these base sequences belong to the set {±1,±j}. A perfect sequence can be obtained by linearly combining these base sequences or their cyclic shift equivalents with arbitrary nonzero complex coefficients of equal magnitude. In particular, if the complex coefficients are Gaussian integers, the resulting perfect sequences are Gaussian integer sequences and are termed as the Gaussian integer perfect sequences (GIPSs).