Correlation properties of sequences from the 2-D array structure of Sidelnikov sequences of different lengths and their union

摘要

In this paper, we show that the cross-correlation of two properly chosen column sequences from the array structure of two different Sidelnikov sequences of periods qe-1 and qf - 1, where e ≠ f, is bounded by (e+f-1)√q+1. From this result, we construct new sequence families by combining sequence families from the array structure of Sidelnikov sequences of period q2 - 1, q3 - 1,..., qd - 1 for some d with 2 ≤ d ≤ 1/2(√q - 2/√q + 1). The maximum non-trivial complex correlation of any two pair of sequences in the constructed sequence family is upper-bounded by (2d - 1)√q + 1: thus, the combining process does not affect the maximum non-trivial complex correlation.