Vector quantization techniques for multiple-antenna channel information feedback

This paper presents vector quantization (VQ) techniques in the context of multiple-antenna systems with finite-rate feedback. For MISO systems, we introduce a new design criterion and develop the corresponding iterative design algorithm for quantization of the beamforming vector. For complexity-limited systems, tree-structured VQ is also examined and compared with the full-search VQ method. The method is extended to MIMO channels by employing a parameterization method that exploits the orthonormality in the spatial information matrix and using the MISO approach in a sequential manner. The parameterization method can also be used to develop an effective low-complexity scheme to deal with quantization of time-varying channels. Also briefly discussed is a matrix quantization method for feeding back the beamforming matrix in MIMO spatial multiplexing systems.