Construction of phase tracking codebooks based on the Lloyd-Max vector quantization

In this paper, we propose a codebook construction method for multiple-input multiple-output (MIMO) beamforming systems operating under the per-antenna power constraint (PAPC). Under the PAPC which limits the individual power of each transmit antenna, it is known that only phase steering information is required to form the optimal beamforming vector at the transmitter. For systems with non-reciprocal uplink and downlink channels, the optimal phase steering information should be chosen at the receiver based on the estimated channel state information, and fed back to the transmitter through rate-limited feedback links. To efficiently encode the phase steering information in the feedback messages, phase steering codebooks have been previously proposed in the literature. In order to exploit the temporal correlation property of the wireless fading channels, we propose to use the phase tracking information between adjacent feedback slots as feedback messages, and provide the construction algorithm for the phase tracking codebook. The objective function for the phase steering codebook is reformulated as a new objective function for the phase tracking codebook to apply the generalized Lloyd-Max vector quantization (VQ) algorithm. The performance of the two codebooks is evaluated and the effectiveness of the proposed codebook is demonstrated by Monte-Carlo simulations.