Trellis Coded Line Packing: Large Dimensional Beamforming Vector Quantization and Feedback Transmission

In this paper we study the beamforming vector quantization and feedback transmission problem for a cooperative transmission environment. Feedback is the primary means of providing the transmitter with channel state information (CSI) in a frequency division duplex (FDD) system. The conventional codebook approach uses a common codebook at the transmitter and at the receiver, while the feedback takes the form of the index of the codebook. This approach has a complexity that scales exponentially with the number of transmit antennas M, making the approach less favorable when M is large. We propose to use trellis-based quantization to reduce the complexity to grow linearly in M. A codebook design criteria is derived for the trellis-based quantizer. We also present three enhancements to the base scheme, each giving 0.2-0.8 dB gain. These enhancements address issues relevant to feedback error, trellis termination, and unequal path-loss from different transmission points. Performance results are shown in numerical simulations.