A Scalable Limited Feedback Design for Network MIMO using Per-Cell Product Codebook

Abstract: In network MIMO systems, channel state information is required at the transmitter side to multiplex users in the spatial domain. Since perfect channel knowledge is difficult to obtain in practice, \emph{limited feedback} is a widely accepted solution. The {\em dynamic number of cooperating BSs} and {\em heterogeneous path loss effects} of network MIMO systems pose new challenges on limited feedback design. In this paper, we propose a scalable limited feedback design for network MIMO systems with multiple base stations, multiple users and multiple data streams for each user. We propose a {\em limited feedback framework using per-cell product codebooks}, along with a {\em low-complexity feedback indices selection algorithm}. We show that the proposed per-cell product codebook limited feedback design can asymptotically achieve the same performance as the joint-cell codebook approach. We also derive an asymptotic \emph{per-user throughput loss} due to limited feedback with per-cell product codebooks. Based on that, we show that when the number of per-user feedback-bits $B_{k}$ is $\mathcal{O}\big( Nn_{T}n_{R}\log_{2}(\rho g_{k}^{sum})\big)$, the system operates in the \emph{noise-limited} regime in which the per-user throughput is $\mathcal{O} \left( n_{R} \log_{2} \big( \frac{n_{R}\rho g_{k}^{sum}}{Nn_{T}} \big) \right)$. On the other hand, when the number of per-user feedback-bits $B_{k}$ does not scale with the \emph{system SNR} $\rho$, the system operates in the \emph{interference-limited} regime where the per-user throughput is $\mathcal{O}\left( \frac{n_{R}B_{k}}{(Nn_{T})^{2}} \right)$. Numerical results show that the proposed design is very flexible to accommodate dynamic number of cooperating BSs and achieves much better performance compared with other baselines (such as the Givens rotation approach).