Joint power control and beamforming codebook design for MISO channels under the outage criterion

This paper investigates the joint design of power control and beamforming codebooks for limited-feedback multiple-input single-output (MISO) wireless systems. The problem is formulated as the minimization of the outage probability subject to the transmit power constraint and cardinality constraints on the beamforming and power codebooks. We show that the two codebooks need to be designed jointly in this setup, and provide a numerical method for the joint optimization. For independent and identically distributed (i.i.d.) Rayleigh channel, we also propose a low-complexity approach of fixing a uniform beamforming codebook and optimizing the power codebook for that particular beamformer, and show that it performs very close to the optimum. Further, this paper investigates the optimal tradeoffs between beamforming and power codebook sizes. We show that as the outage probability decreases, optimal joint design should use more feedback bits for power control and fewer feedback bits for beamforming. The jointly optimized beamforming and power control modules combine the power gain of beamforming and diversity gain of power control, which enable it to approach the performance of the system with perfect channel state information as the feedback link capacity increases—something that is not possible with either beamforming or power control alone.