Mutually Unbiased Sets of Orthogonal Vectors: Bound and Constructions

With the development of MIMO communication technology, the sequences for channel estimation assigned to the same user are required to be orthogonal, while the magnitude of the inner product of sequences assigned to different users is expected to be as small as possible. Suppose that there are K users and each user has M mutually orthogonal normalized sequences of length L. In this paper, a lower bound of the maximum magnitude of the inner product between sequences assigned to the different users is given. It is also proved that the magnitude of the inner product between any pair of sequences for different users is equal, when the lower bound is met. Such sequence sets meeting the lower bound are referred to as mutually unbiased sets of orthogonal vectors (MUSOVs), and two infinite class of MUSOVs is constructed by combinatorial methods.