Abstract
This paper aims to derive expressions of the downlink ergodic user rates in a multi-cell large-scale multi-user multiple-input single-output (MISO) system under the assumption that each base station (BS) employs maximum ratio transmission (MRT) precoding and that single-antenna users in each cell are divided into groups, where channels of users in the same group share common covariance matrices and follow the double scattering channel model. Moreover, both channel estimation errors and pilot contamination effects caused by re-use of pilot sequences in neighboring cells are taken into consideration in this work. The analysis is carried out using statistical tools under the exact and asymptotic regimes in which the number of antennas at BS N , the number of users in each cell K , and the number of scatterers S grow large at the same pace. Furthermore, the obtained exact expressions and deterministic approximations of the ergodic rates are expressed in simplified closed-forms under the special case of multi-keyhole channels to yield useful insights. They reveal that signal-to-noise plus interference ratio (SINR) without user grouping in a multi-keyhole channel is similar to that under standard Rayleigh channel in the asymptotic regime. However, under user grouping, we show that the massive multiple-input multiple-output (MIMO) gains promised by deploying large-scale antenna arrays in multi-cell settings are limited by the number of scatterers even if the number of antennas grows large. Simulation results illustrate the close match provided by the asymptotic analysis for moderate system dimensions and confirm the insights drawn from the theoretical findings.