Review and Performance Comparison of Finite-rate Feedback Strategies: Vector Quantization, Systematic Unitary Construction and Grassmannian Packing

Channel knowledge at the transmitter can greatly improve the error probability of multi-input multi-output wireless communication system. Though receivers can obtain accurate channel estimates through training with pilot signals, transmitters can have only limited amount of the channel knowledge due to the limited rate of the feedback channel. One simple solution is the receiver quantizes the channel estimate and transfers it back to the transmitter. To reduce the feedback bits, better methods of beamforming codebook design based on Grassmannian packing and systematic unitary design were developed. In this report, we review these methods and compare the performance of each methods. Surprisingly the vector quantization outperformed others in simulation.