A complementary construction using mutually unbiased bases

Abstract

We propose a construction for complementary sets of arrays that exploits a set of mutually-unbiased bases (a MUB). In particular we present, in detail, the construction for complementary pairs that is seeded by a MUB of dimension 2, where we enumerate the arrays and the corresponding set of complementary sequences obtained from the arrays by projection. We also sketch an algorithm to uniquely generate these sequences. The pairwise squared inner-product of members of the sequence set is shown to be 1 2 $\frac {1}{2}$ . Moreover, a subset of the set can be viewed as a codebook that asymptotically achieves 3 2 $\sqrt {\frac {3}{2}}$ times the Welch bound.