Asymptotic Analysis of MRT over Double Scattering Channels with MMSE Estimation

This paper studies the ergodic rate performance of maximum ratio transmission (MRT) precoding in the downlink of a multi-user multiple-input single-output (MISO) system, where the channel between the base station (BS) and each user is modeled using the double scattering model. We utilize the minimum-mean-square-error (MMSE) channel estimate for this model, which is used in the design of the MRT precoding. Within this setting, we are interested in deriving tight approximations of the ergodic rate under the assumption that the number of BS antennas $\left ({N}\right)$ , the number of users $\left ({K}\right)$ and that of scatterers $\left ({S}\right)$ grow large with the same pace. These approximations are expressed in simplified closed-form expressions for the special case of multi-keyhole channels. They reveal that unlike the standard Rayleigh channel in which the SINR grows as $\mathcal {O}\left ({\frac {N}{K}}\right)$ , the SINR associated with a multi-keyhole channel scales as $\mathcal {O}\left ({\frac {S}{K}}\right)$. This particularly shows that the reaped gains of the large-scale MIMO over double scattering channels do not linearly increase with the number of antennas and are limited by the number of scatterers. We further provide simulation results that confirm the close match provided by the asymptotic analysis for moderate system dimensions and provide some useful insights into the interplay between $N$ , $K$ and $S$.