# Analysis and Evaluation of Performance Gains and Tradeoffs for Massive MIMO Systems
## 1 Introduction
On another side, the work of our paper considers the downlink massive system and the system performance gains are discussed and their mathematical expressions are derived for multi-cell massive MIMO system under the effect of non-orthogonal pilot sequences on them, then we study the main important tradeoffs among these gains under the effects of pilot contamination. The effect of channel state information delay on system performance was studied by [14]. This delay impacts on diversity gain in term of outage probability and bit error rate, otherwise the present work will discuss the impact of channel estimation error on spatial diversity gain in term of outage probability and it will show how massive MIMO can improve this gain through increasing the number of antennas. Authors in [15] were the first to discuss the tradeoff between diversity gain and multiplexing gain in MIMO system. They also showed that how these gains cannot be enhanced at the same time, but they proved that it can achieve an optimal multiplexing and diversity tradeoff rather than achieving maximum multiplexing gain or diversity gain separately, but their research work had been done for perfect CSI. Authors of [16] discussed the tradeoff between the energy efficiency and spectral efficiency under no CSI state and perfect CSI state for a single user and multi-user massive MIMO system, then they found the optimal energy efficiency points at low and high spectral efficiency region. As a contrast to previous works, the authors of [17] used a Rician fading for modeling the channel between the terminals and the base station in analyzing the uplink performance of multi-cell massive MIMO system. This work found that system performance can be enhanced via increasing the proportion of line-of-sight (LOS) component, especially when increasing both the number of antennas (M) and the number of Rician K-factor for each terminal so that the pilot contamination can be eliminated completely. While our work uses Rayleigh fading for modeling the channel between the terminals and the base station in analyzing the system performance gains of multi-cell massive MIMO system at the downlink side under the effect of non-orthogonal pilot sequences. Consequently, we will show through our simulation results that the system performance gains can be improved via increasing the number of antennas with fixed number of users otherwise the system performance gains will be degraded as the number of terminals increases due to the interference from terminals in other cells. The work of [18] involves proposing a new method for diminishing the effect of non-orthogonal pilot sequence on multi-cell massive MIMO downlink system to improve the achievable sum rate which degrades due to inter-cell interference from other cells based on beamforming training scheme at the user side. The quality of channel state information is affected by high user mobility as discussedin [19] in multi-cell massive MIMO system at downlink side because the coherence time of the channel will shrink with a high user speed and as a result, the system performance will degrade (i.e., the multiplexing gain is limited by high mobility users), however the performance in other cells will not affect. In our work, we discuss the effect of interference among cells on channel state information and show how the system performance gain (i.e., energy efficiency, spectral efficiency and outage probability) in a cell and other neighboring cells will degrade due to imperfect CSI. On the other side, few researchers studied the tradeoffs among the performance gains (antenna gain, diversity gain and multiplexing gain).