Incorporating Stiefel Geometry in Codebook Design and Selection for Improved Base Station Cooperation

Base station cooperation is expected to enhance spectrum efficiency of future cellular system. Performance heavily depends on the channel state information available at the transmitter. In practical systems, channel information are acquire through a limited feedback channel. Typically, quantization of the channel at the receiver side is done with a fixed pre-designed codebook. In this paper, we consider the codebook design and codeword selection problem when a product codebook is employed, reusing a point-to-point codebook. Point-to-point codebooks are often designed as Grassmannian packings. To improve the performance of the codebook for base station cooperation without impairing the performance for single cell transmission, we propose a novel joint Grassmann-Stiefel codebook design. In addition, we propose a method for independently selecting the per-cell codewords by using a distance on the Stiefel manifold.