Generalized cross-correlation properties of Chu sequences

In this paper, detailed cross-correlation properties for Chu sequences are investigated. All possible values of the cross-correlation function of Chu sequences are derived for any given sequence length and lag, and the maximum magnitude distribution function $\rho -{N}(x)$, which is defined as the number of all Chu sequence pairs with length-$N$ whose maximum magnitude of the cross-correlation function is ${\sqrt {Nx}}$, is obtained. Also, good lower and upper bounds on the maximum number of available Chu sequences and a construction algorithm for the corresponding partial Chu sequence set are proposed when the maximum magnitude of the cross-correlation among the sequences is constrained. Numerical examples show that the proposed bounds are quite tight and the proposed construction algorithm is near-optimal up to fairly large value of $N$.