Abstract

The use of large-scale antenna arrays grants considerable benefits in energy and spectral efficiency to wireless systems due to spatial resolution and array gain techniques. By assuming a dominant line-of-sight environment in a massive multiple-input multiple-output scenario, we derive analytical expressions for the sum-capacity. Then, we show that convenient simplifications on the sum-capacity expressions are possible when working at low and high signal-to-noise ratio regimes. Furthermore, in the case of low and high signal-to-noise ratio regimes, it is demonstrated that the Gamma probability density function can approximate the probability density function of the instantaneous channel sum-capacity as the number of served devices and base station antennas grows, respectively. A second important demonstration presented in this work is that a Gamma probability density function can also be used to approximate the probability density function of the summation of the channel’s singular values as the number of devices increases. Finally, it is important to highlight that the presented framework is useful for a massive number of Internet of Things devices as we show that the transmit power of each device can be made inversely proportional to the number of base station antennas.

Highlights

  • During the past years, we have been witnessing massive multiple-input multiple-output (MIMO)becoming an efficient and indispensable sub-6 GHz physical-layer technology for wireless and mobile networks

  • We show that the sum-capacity for low- and high-signal-to-noise ratio (SNR) regimes can be accurately described by the derived approximated closed-form equations

  • We investigated ways to find capacity limits concerning the number of users, number of base stations (BS) antennas, and SNR

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Summary

Introduction

We have been witnessing massive multiple-input multiple-output (MIMO). As the wavelengths of mmWave bands are extremely short, it becomes possible to add a huge number of antenna elements to a small area, which helps in achieving the high multiplexing gains offered by the massive MIMO technology at both the BS and devices [10]. 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).

Related Work
System Model
Channel Sum-Capacity in LoS and Favorable Propagation Conditions
B H H H HB
Approximated Distribution of the Total Power Gain
Low-SNR Regime
High-SNR Regime
Outage Probability
Average Distance from Favorable Propagation
Simulation Results and Discussion
Conclusions
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