This paper presents some exact results on the sum-rate of multi-user multiple-input multiple-output (MU-MIMO) systems subject to multi-cell pilot contamination under correlated Rayleigh fading. With multi-cell multi-user channel estimator, we give the lower bound of the sum-rate. We derive the moment generating function (MGF) of the sum-rate and then obtain the closed-form approximations of the mean and variance of the sum-rate. Then, with Gaussian approximation, we study the outage performance of the sum-rate. Furthermore, considering the number of antennas at base station becomes infinite, we investigate the asymptotic performance of the sum-rate. Theoretical results show that compared to MU-MIMO system with perfect channel estimation and no pilot contamination, the variance of the sum-rate of the considered system decreases very quickly as the number of antennas increases.Massive multiple-input multiple-output (MIMO) antenna technology has emerged as an effective technique for significantly improving the capacity of wireless cellular systems, since the pioneering works in [1][2][3]. When base station (BS) is equipped with large-scale antenna array, large number of users can be served in the same time-frequency resource. From the theoretical point of view, when BS has perfect channel state information (CSI) of its own users, the sum-rate of multi-user MIMO (MU-MIMO) system can be arbitrary large as the number of antennas at BS becomes infinite. However, a bottleneck of massive MIMO is the acquisition of CSI. Usually, the pilot number is linear increasing with the number of users, even for time-division duplex system. Due to the limitation of the pilot resource, multi-cell multi-user orthogonal pilot design is not practical in massive MIMO system. Thus, pilot contamination due to pilot reuse in adjacent cells becomes a new character of massive . Some recent work [7,8] proposes efficient schemes to reduce the effect of inter-cell interference caused by pilot contamination in massive MIMO systems. In this paper, we focus on the analysis of the capacity performance for MIMO systems subject to pilot contamination.
Differences and Motivation (Regarding the Related Work)The capacity performance for MU-MIMO with the pilot contamination has been studied under the independently and identically distributed (i.i.d.) Rayleigh fading channels [9]. However, for practical systems, when the number of antennas is very large, the channels are not i.i.d. usually. In [10][11][12], the