# Analysis and Evaluation of Performance Gains and Tradeoffs for Massive MIMO Systems
## 5 Simulation Results  
Consider a multi-cell massive MIMO system each with a hexagonal shape sharing the same frequency band in order to study the effect of non-orthogonal pilot sequences on system performance. We assume that the operation frequency is 2 GHz band, the transmission bandwidth = 20 MHz, the channel coherence bandwidth is \(B_{coh}\) = 180 KHz and the channel coherence time is 10 ms with coherence block length is \(T_{coh}\) = 1800 symbols note that these simulation parameters are inspired from previous works [4,14] under the 3 GPP channel model for the propagation environment [42]. Assuming the number of cells \(L=7\) and each cell has interference from 6 neighbor cells, proposing the cells are near to each other. Each cell has one base station and \(K\) users uniformly distributed. The distance from the base station to the vertex is 250 m and the minimum distance between the user and the base station is 35 m. If it is assumed that all direct gains \(\beta_{\ell\ell}\) are equal to 1 and all cross gains \(\beta_{j\ell}\) are equal to 0.11, the interference factor is being \(\beta\in\) [0,1]. The large scale fading factor \(\beta\) is modeled according to the following expression  
\[\beta_{k}=\frac{z_{k}}{\left(d_{k}/d_{h}\right)^{\phi}}, \tag{82}\]  
where \(d_{k}\) is the space between the transceiver and \(k\)th user, \(d_{h}\) is the minimum space between \(k\)th user and BS. \(\phi\) is the path loss and it is equal to 3.8, \(z_{k}\) is the shadow fading with zero means and variance \(\sigma_{\text{shadow}}\) = 8 dB. It is assumed here that transmit power = 10 dB, number of served users (\(K\)) = 10 and number of antennas (\(M\)) = 300. All simulations in this work are performed using Matlab software. In Figure 5, array gain is plotted with different values of base station antennas (\(M\)). With massive MIMO system as the numbers of antenna increases without boundaries, the efficiency of transmit power will increase which it means the received power will also increase. High array gain is possible relying on how much the transceiver \"base station\" knows about the channel state. Figure 5 is plotted for the array gain under two considerations, perfect and imperfect channel state information in multi-cell system. Array gain is high with massive MIMO system as the number of antennas increases, i.e., \"the transmission SNR rises with M\". The reduction in the curve is due to the fact that MRT is better at low SNR. With imperfect estimation, array gain deteriorates due to interfering of non-orthogonal pilot sequences from users in other cells which it makes pollution in channel estimation, hence the system performance is degraded. In Figure 6, the spatial multiplexing gain is drawn with the number of antennas (\(M\)) under perfect and imperfect channel estimation with multi-cell system. At favorable propagation conditions such as expressions (19) and (20) with i.i.d propagation channel matrix, the multiplexing gain rises with increasing the number of base station antennas. Consequently, the number of served terminals also increases (i.e., more degree of freedom provided). With perfect CSI, as the number of transceiver's antennas rises, the degree of freedom offered per users increases, which means more users are served through the same time and frequency, hence the system can achieve the sum rate of massive MIMO when \(M>>\) K \"high multiplexing gain\". Practically, multiplexing gain impacts with the interfering pilot sequences in multi-cell system, hence low signal to noise ratio faced by two practical considerations, firstly, the terminals that are at the edge of a cell (terminals near the cell edge will suffer pollution in their received signal from neighboring cells due to reuse of non-orthogonal pilot signals in multi-cell system).