# Evaluation of Multi-Beam Massive MIMO Considering MAC Layer Using IEEE802.11 ac and FDD-LTE
## 4 Computer Simulation
### Fdd-Ite  
We evaluated the proposed method under FDD-LTE (Release 15) [6].We assumed a bandwidth of 20 [MHz] per UT and 100 resource blocks (RBs). Table 5 shows the relationship between the MCS index and the transmission rate in LTE when there is one antenna. The transport block size (TBS) is based on [6], and the transmission rate is calculated based on the efficiency per bandwidth. The TBS corresponds to an actual data component divided into RBs and transmitted, while user data indicate the resource size for a given control signal. As in the IEEE802.11 ac simulation, we compared the values of \(R\) and \(R^{\prime}\) produced by the respective approaches and evaluated the results in terms of the corresponding transmission rates. The throughput in LTE, which is denoted here by \(T\), can be calculated as follows: [6; 33]. \[ \begin{array}{llll}T&=TBS\times N_{\text{str}}\\ &\coloneqq N_{\text{subc}}\times N_{\text{slot}}\times N_{\text{sym}}\times M \times N_{\text{str}}\times CR\ \left[\text{bps}\right],\end{array} \]  
where \(N_{\text{subc}}\) is the number of sub-carriers, \(N_{\text{slot}}\) is the number of slots per second, \(N_{\text{sym}}\) is the number of symbols per slot, \(N_{\text{str}}\) is the number of streams, and CR is the coding rate. We apply Equation (3) to consider control signals because Equation (3) cannot express the number of control signals that can be eliminated under multi-beam massive MIMO. \[T=TBS\times\frac{Userdata^{\prime}}{Userdata}\times N_{\text{subf}}\times N_{ \text{str}}\ \left[\text{bps}\right], \tag{3}\]  
where \(N_{\text{subf}}\) is the number of sub-frames per second. The value of \(Userdata^{\prime}\) is obtained by increasing or decreasing the number of control signals from secured \(Userdata\), which is defined in [6]. For example, when \(I_{\text{{MCS}}}=27\) in Table 1, \(Userdata\) is obtained as 120,000 [bits]. This corresponds to a \(Userdata^{\prime}\) of 128,000 [bits] in the multi-beam massive MIMO, which is obtained by removing the control signal from \(Userdata\). As there is no complete definition of a control signal in the case of 64 elements, we assumed that one antenna port would be added to handle the additional control signal required each time the number of antennas was doubled. Therefore, \(Userdata^{\prime}\) was 83,200 [bits] for 64 antennas under the full-digital configuration. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(I_{\text{MCS}}\) & **Modulation** & **TBS** & **User Data** & **Coding Rate** & \(R^{\prime}\) **[bits/symbol]** & **Transmission Rate [Mbps]** \\ \hline
0 & QPSK & 2792 & 30000 & 0.094 & 0.188 & 7.22 \\
1 & QPSK & 4548 & 30000 & 0.154 & 0.308 & 9.61 \\
2 & QPSK & 7224 & 30000 & 0.242 & 0.484 & 21.7 \\  & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\
27 & 256 QAM & 84760 & 120000 & 0.707 & 5.656 & 127.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Relationship between MCS index and transmission rate under frequency division duplex (FDD)-LTE (100 RBs, 20 MHz). Figure 7: Characteristics of transmission rate and throughput under IEEE802.11 ac. Figure 8 shows the relationship between the transmission rate and throughput based on Equation (3). We used this figure to evaluate throughput based on overhead for each configuration. Figure 9 shows the CDF characteristics of the transmission rate and throughput under FDD-LTE. The modulation scheme for each characteristic is determined in the same manner as that used in the evaluation under IEEE802.11 ac. The transmission rate follows the same trend as that under IEEE802.11 ac. However, unlike IEEE 802.11 ac, a high transmission rate can be achieved even with a low modulation order. This suggests that the performance of the hybrid BF approaches that of multi-beam massive MIMO. An evaluation of throughput based on Figure 8 reveals that it increases linearly with transmission rate under all configurations. Given that multi-beam massive MIMO has the lowest number of control signals of all configurations, it achieves the highest throughput at a given transmission rate.