# Capacity Bounds for Dense Massive MIMO in a Line-of-Sight Propagation Environment
## 1 Introduction
Additionally, in wireless and cellular communications, the probability that the devices have LoS to the BS is highly probable in many scenarios [19]. Among the approaches and opportunities cited here, the Internet of Things (IoT) for drones, sensors, automated processes, etc. [20] pose several unsolved research challenges. For example, in the near future, swarms of drones, sensors, and actuators will be omnipresent adding up to billions of devices [21; 22; 23]. In this ultra-dense scenario, these devices will be always moving around the cell at different speeds and positions with a dominant LoS link to the BS. The sum-capacity achieved by a BS serving a massive number of drones, which have a dominant LoS link to the BS and are constantly moving around the cell, is still an open issue. As shown in [1], the huge gains in performance offered by the massive MIMO technology are only obtained when the spatial signature of the devices are mutually orthogonal. Differently from independent and identically distributed (i.i.d.) flat Rayleigh fading channels, in LoS scenarios, the spatial signatures are only determined by the position of the devices within the cell. This way, the power of the device-interference will continuously change as the devices randomly move around the cell. Therefore, there will be several independent realizations of the device-interference power within a short interval. Consequently, the devices experience several different realizations of the device-interference power during the transmission of a single codeword. For that reason, in this work we are interested in analyzing the achieved ergodic sum-capacity by averaging the instantaneous sum-capacity over all possible locations of the devices. Therefore, in this work, we assume a dominant (i.e., pure with no multi-path) LoS environment in a massive MIMO scenario with favorable propagation serving a massive number of devices constantly moving within the cell. With this aspect in mind, the objective of this investigation is to find capacity limits concerning the number of devices, number of base station antennas, and signal-to-noise ratio (SNR). More specifically, given the aforementioned assumptions, the contributions of this work are as follows. * Derive an analytical expression for the ergodic channel sum-capacity. * Show that the transmit power of each device can be made inversely proportional to the number of BS antennas. * Find analytical expressions for the upper- and lower-bound ergodic channel sum-capacities. * Present expressions for the ergodic channel sum-capacity in low- and high-SNR regimes. * Demonstrate that a Gamma probability density function (PDF) can also approximate the PDF of the summation of the channel's singular values (also known as total power gain of the channel matrix) as the number of devices increases. * Demonstrate that the Gamma PDF can approximate the PDF of the instantaneous channel sum-capacity in low- and high-SNR regimes. * Demonstrate that the approximated PDF of the instantaneous channel sum-capacity can be used to calculate the outage probability in low- and high-SNR regimes. * We extend the distance from favorable propagation measure defined in [1] for the ergodic sum-capacity case assumed in this work. The remaining of this paper is organized as follows: Section 2 discusses some related works. Section 3 presents the system model adopted in this work, while Section 4 discusses aspects of favorable propagation in the current investigated conditions. Section 5 reviews the concept of favorable propagation. Section 6 presents the results with parameters from reference systems. Finally, we close our discussion in Section 7 summarizing our conclusions.