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

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 <inline-formula><tex-math notation="LaTeX">$N_c$</tex-math> </inline-formula> and the number of user antennas <inline-formula><tex-math notation="LaTeX">$N_c$</tex-math> </inline-formula> go to infinity with <inline-formula><tex-math notation="LaTeX">$N/N_c\rightarrow \eta$</tex-math> </inline-formula>, 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 <inline-formula><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> and the number of BS antenna clusters <inline-formula><tex-math notation="LaTeX">$L$</tex-math></inline-formula>. Simulation results verify that the average per-antenna capacities with and without CSIT logarithmically increase with <inline-formula> <tex-math notation="LaTeX">$L$</tex-math></inline-formula> in the orders of <inline-formula><tex-math notation="LaTeX"> $\Theta (\frac{\alpha }{2}\log _2 L)$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX"> $\Theta ((\frac{\alpha }{2}-1)\log _2 L)$</tex-math></inline-formula>, respectively, where <inline-formula> <tex-math notation="LaTeX">$\alpha >\text{2}$</tex-math></inline-formula> is the path-loss factor. The analysis is further extended to the multiuser case with <inline-formula><tex-math notation="LaTeX">$K$</tex-math></inline-formula> uniformly distributed users. By assuming that <inline-formula><tex-math notation="LaTeX">$N,N_c\rightarrow \infty$ </tex-math></inline-formula> with <inline-formula><tex-math notation="LaTeX">$N/N_c\rightarrow \eta$</tex-math> </inline-formula>, 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 <inline-formula> <tex-math notation="LaTeX">$\Theta(\log _2 \frac{\lfloor L-\eta (K-1)\rfloor ^{\alpha /2}}{K})$</tex-math> </inline-formula> if the ratio <inline-formula><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> 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.