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 ρN(x), which is defined as the number of all Chu sequence pairs with length-N whose maximum magnitude of the cross-correlation function is √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.

[1]  Robert L. Frank,et al.  Polyphase codes with good nonperiodic correlation properties , 1963, IEEE Trans. Inf. Theory.

[2]  Liru Lu,et al.  Extended orthogonal polyphase codes for multicarrier CDMA system , 2004, IEEE Communications Letters.

[3]  Pingzhi Fan,et al.  Generalised Sarwate bounds on periodic autocorrelations and cross-correlations of binary sequences , 2002 .

[4]  Changho Suh,et al.  Preamble design for channel estimation in MIMO-OFDM systems , 2003, GLOBECOM '03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489).

[5]  Naoki Suehiro,et al.  Modulatable orthogonal sequences and their application to SSMA systems , 1988, IEEE Trans. Inf. Theory.

[6]  Robert L. Frank,et al.  Phase shift pulse codes with good periodic correlation properties (Corresp.) , 1962, IRE Trans. Inf. Theory.

[7]  M.B. Pursley,et al.  Crosscorrelation properties of pseudorandom and related sequences , 1980, Proceedings of the IEEE.

[8]  T. Kasami.  WEIGHT DISTRIBUTION FORMULA FOR SOME CLASS OF CYCLIC CODES , 1966 .

[9]  R. C. Heimiller,et al.  Phase shift pulse codes with good periodic correlation properties , 1961, IRE Trans. Inf. Theory.

[10]  Dilip V. Sarwate,et al.  Bounds on crosscorrelation and autocorrelation of sequences (Corresp.) , 1979, IEEE Transactions on Information Theory.

[11]  R. Frank,et al.  Comments on 'Polyphase codes with good periodic correlation properties' by Chu, David C , 1973, IEEE Trans. Inf. Theory.

[12]  Pingzhi Fan,et al.  SEQUENCE DESIGN FOR COMMUNICATIONS APPLICATIONS , 1996 .

[13]  Ji-Woong Choi,et al.  Low-Complexity Mean-Delay Estimation for OFDM Systems , 2009, IEEE Transactions on Vehicular Technology.

[14]  J. Massey,et al.  Welch’s Bound and Sequence Sets for Code-Division Multiple-Access Systems , 1993 .

[15]  Branislav M. Popovic,et al.  Generalized chirp-like polyphase sequences with optimum correlation properties , 1992, IEEE Trans. Inf. Theory.

[16]  Seokho Yoon,et al.  A new polyphase sequence with perfect even and good odd cross-correlation functions for DS/CDMA systems , 2002, IEEE Trans. Veh. Technol..

[17]  Grzegorz Zwara,et al.  The Divisibility of Integers and Integer Relatively Primes 1 , 1990 .

[18]  P. Vijay Kumar,et al.  4-phase Sequences with Near-optimum Correlation Properties , 1992, IEEE Trans. Inf. Theory.

[19]  A.M.D. Turkmani,et al.  Performance evaluation of maximal-length, Gold and Kasami codes as spreading sequences in CDMA systems , 1993, Proceedings of 2nd IEEE International Conference on Universal Personal Communications.

[20]  Kwang Soon Kim,et al.  Optimal Pilot Sequence Design for Multi-Cell MIMO-OFDM Systems , 2011, IEEE Transactions on Wireless Communications.

[21]  Shayne Waldron,et al.  Generalized Welch bound equality sequences are tight fram , 2003, IEEE Trans. Inf. Theory.

[22]  Robert Gold,et al.  Maximal recursive sequences with 3-valued recursive cross-correlation functions (Corresp.) , 1968, IEEE Trans. Inf. Theory.

[23]  Lloyd R. Welch,et al.  Lower bounds on the maximum cross correlation of signals (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[24]  Pingzhi Fan,et al.  Modified Chu sequences with smaller alphabet size , 2004 .

[25]  Underwood Dudley.  Elementary Number Theory , 1978 .

[26]  David C. Chu,et al.  Polyphase codes with good periodic correlation properties (Corresp.) , 1972, IEEE Trans. Inf. Theory.