On the Scaling Behavior of the Average Rate Performance of Large-Scale Distributed MIMO Systems

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To support the massive data traffic in the near future, the distributed antenna system has become a promising candidate for the next-generation cellular system. Due to the lack of a closed-form expression, how the average rate performance scales with a large number of distributed base-station (BS) antennas is not well understood. This paper focuses on the average rate performance of the downlink channel of a large-scale distributed antenna system. By assuming that the number of BS antennas at each cluster $N_c$ and the number of user antennas $N_c$ go to infinity with $N/N_c\rightarrow \eta$ , asymptotic lower-bounds of the average per-antenna capacities with and without channel state information at the transmitter side (CSIT) in the single-user case are characterized as an explicit function of the ratio $\eta$ and the number of BS antenna clusters $L$ . Simulation results verify that the average per-antenna capacities with and without CSIT logarithmically increase with $L$ in the orders of $\Theta (\frac{\alpha }{2}\log _2 L)$ and $\Theta ((\frac{\alpha }{2}-1)\log _2 L)$ , respectively, where $\alpha >\text{2}$ is the path-loss factor. The analysis is further extended to the multiuser case with $K$ uniformly distributed users. By assuming that $N,N_c\rightarrow \infty$ with $N/N_c\rightarrow \eta$ , an asymptotic lower-bound of the average per-antenna rate with block diagonalization (BD) is derived. Simulation results verify that the average per-antenna rate scales in the order of $\Theta(\log _2 \frac{\lfloor L-\eta (K-1)\rfloor ^{\alpha /2}}{K})$ if the ratio $\eta$ is fixed. The effect of the cluster size on the average rate performance is further analyzed. Simulation results verify that for a given number of BS antennas, the average per-antenna capacities with and without CSIT in the single-user case and the average per-antenna rate with BD in the multiuser case increase monotonically as the number of BS antennas at each cluster decreases, which indicates that a fully distributed BS antenna layout can achieve the highest average rate performance.