Generalized Cross-Correlation Properties of Chu Sequences
Jae Won Kang, Younghoon Whang, Byung Hoon Ko, Kwang Soon Kim · IEEE Transactions on Information Theory · 2011
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$N$.