A vector quantization based approach for equal gain transmission

In this work, we consider quantization of the beamforming vector for finite rate feedback-based communication in flat-fading multi input single output (MISO) systems with a per-antenna power constraint. Using the capacity loss with respect to perfect channel feedback as performance metric, we derive a new criterion, the mean-square weighted inner product (MSwIP) criterion, for designing the quantized beamforming vectors. We develop an iterative algorithm (based on the Lloyd algorithm) to generate the beamforming vector codebook that locally optimizes the design criterion. For the case of i.i.d. flat fading channels, we analyze the performance of the proposed algorithm in terms of capacity loss and the outage probability. We show that the capacity loss (in terms of bits) of a MISO system with quantized beamforming under a per-antenna power constraint is roughly half that obtained under a total power constraint. Simulation results verify the accuracy of the analytical expressions