Codebook Design for Noncoherent MIMO Communications Via Reflection Matrices

This paper studies the codebook design problem for noncoherent multiple input multiple output (MIMO) communications. Each codeword in the codebook is considered to be a point in a Grassmann manifold. In this paper, the codebook design is formulated as an inverse eigenvalue problem. A new algorithm using reflection matrices is proposed to obtain the optimal codebook for noncoherent block fading channels where the channel state information (CSI) is unknown at both the receiver and transmitter. The key contribution of this paper is that our algorithm is able to construct an optimal codebook via a sequence of reflection matrices.