New Mutually Orthogonal Complementary Sets With Non-Power-of-Two Lengths

Abstract

Mutually orthogonal complementary sets (MOCSs) have found a number of practical applications in wireless communications and radar owing to their perfect aperiodic auto-correlation and cross-correlation properties. Recently, toward the challenge of designing MOCSs with non-power-of-two lengths, direct constructions were presented by Wu et al. using generalized Boolean functions (GBFs). In this letter, a new construction of MOCSs is proposed based on GBFs, which leads to MOCSs with flock size 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k+1</sup> and length 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> + 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sup> , whose set size is 1/2 of the flock size, where integers 0 ≤ t <; k ≤ m. In addition, the constructed MOCSs can yield column sequence peak-to-mean envelope power ratio (PMEPR) of at most 2.