A construction for binary sequence sets with low peak-to-average power ratio

Abstract

Complementary sequences (CS) have peak-to-average power ratio (PAR) /spl les/ 2 under the one-dimensional continuous discrete Fourier transform (DFT/sub 1//sup /spl infin//). Davis and Jedwab (see IEEE Trans. Inform. Theory, vol.45, no.7, p.2397-2417, 1999) constructed binary CS (DJ set) for lengths 2/sup n/ described by s = 2/sup -n/2/ (-1)/sup p(x)/, p(x) = /spl Sigma//sub j=0//sup L-2/x/sub /spl pi/(j)/x/sub /spl pi/(j+1)/+c/sub j/x/sub j/+k, c/sub j/, k /spl isin/ Z/sub 2/. Hamming distance, D, between sequences in this set satisfies D /spl ges/ 2/sup n-2/. However the rate of the DJ set vanishes for n /spl rarr/ /spl infin/, and higher rates are possible for PAR /spl les/ O(n) and D large. We present such a construction which generalises the DJ set. These codesets have PAR /spl les/ 2/sup t/ under all linear unimodular unitary transforms (LUUTs), including all one and multi-dimensional continuous DFTs, and D /spl ges/ 2/sup n-d/ where d is the maximum algebraic degree of the chosen subset of the complete set.