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4-phase sequences with near-optimum correlation properties

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3 Author(s)
S. Boztas ; Dept. of Electr. & Comput. Syst. Eng.. Monash Univ., Vic., Australia ; R. Hammons ; P. Y. Kumar

Two families of four-phase sequences are constructed using irreducible polynomials over Z4. Family A has period L =2r-1. size L+2. and maximum nontrivial correlation magnitude Cmax⩽1+√(L+1), where r is a positive integer. Family B has period L=2(2r-1). size (L+2)/4. and Cmax for complex-valued sequences. Of particular interest, family A has the same size and period as the family of binary Gold sequences. but its maximum nontrivial correlation is smaller by a factor of √2. Since the Gold family for r odd is optimal with respect to the Welch bound restricted to binary sequences, family A is thus superior to the best possible binary design of the same family size. Unlike the Gold design, families A and B are asymptotically optimal whether r is odd or even. Both families are suitable for achieving code-division multiple-access and are easily, implemented using shift registers. The exact distribution of correlation values is given for both families

Published in:

IEEE Transactions on Information Theory  (Volume:38 ,  Issue: 3 )