# Evaluation of Multi-Beam Massive MIMO Considering MAC Layer Using IEEE802.11 ac and FDD-LTE
## 4 Computer Simulation
### IEEE802.11 ac  
We evaluated the indicator shown in Table 2 and the downlink effectiveness of multi-beam massive MIMO transmission based on the IEEE802.11 ac procedures [5; 30]. The simulation conditions and model were the same as those used in Section 4. Equation (2) was used as an index of evaluation based on the BER calculated on the UTs. \[R=\left\{ \begin{array}{cc}M\left(1-\text{BER}\right)&\left(\text{BER}\leq 1 0^{-2}\right)\\ 0&\left(\text{otherwise}\right)\end{array} \right. [\text{bit/symbol}], \tag{2}\]  
where \(M\) denotes the number of bits per symbol and \(R\) denotes the number of bits per symbol obtained independently of the coding rate. The assessment was divided into parts, i.e., the evaluation of the PHY layer without considering the overhead arising from the control signal and the evaluation of the MAC layer considering overhead. Table 3 shows the relationship between the MCS index and the transmission rate under the IEEE802.11 ac 20-[MHz] operation [5]. The values of \(R^{\prime}\) are obtained by multiplying the modulation order by the coding rate, and they are equivalent to \(R\), which is the number of bits per symbol. Accordingly, it was assumed that an MCS index that satisfies \(R\geq R^{\prime}\) could be applied to the \(R\) obtained on the UTs. Based on this, we could evaluate the transmission rate corresponding to the MCS index. In the MAC layer, throughput is calculated according to the downlink MU-MIMO procedure shown in Figure 6[5]. As seen in the figure, the BS first transmits request signals to all UTs to obtain channel information. Once the BS has obtained channel feedback from each UT data transmission signal, data reception processing is performed for all UTs. Throughput is obtained by dividing the data size of frame aggregation, which was set as 63,000 bytes in this evaluation, by the time required by the processes. As multi-beam massive MIMO does not require procedures such as CSI estimation or feedback, we assumed that no time other than that necessary for data transmission was required. \begin{table}
\begin{tabular}{c c} \hline \hline
**Modulation Scheme** & **Conditions** \\ \hline None & \(\rho<0.4\) \\
16-QAM & \(\rho\geq 0.4\) and \(P<20\) [dB] \\
32-QAM & \(\rho\geq 0.4\) and \(20\leq P<24\) [dB] \\
64-QAM & \(\rho\geq 0.4\) and \(24\leq P<28\) [dB] \\
128-QAM & \(\rho\geq 0.4\) and \(P\geq 28\) [dB] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Adaptive modulation scheme for eight user terminals (UTs). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(I_{MCS}\) & **Modulation** & **Coding Rate** & \(R^{\prime}\) **[bits/symbol]** & **Transmission Rate [Mbps]** \\ \hline
0 & BPSK & 1/2 & 0.5 & 7.2 \\
1 & QPSK & 1/2 & 1.0 & 14.4 \\ \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) \\
9 & 256 QAM & 3/4 & 6.0 & 86.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Relationship between MCS index and transmission rate under IEEE802.11 ac at 20 MHz. We evaluated the performance of a typical hybrid BF massive MIMO and compared it with those of the sub-array and full-digital BF configurations discussed in Section 2. Table 4 shows the precoding and decoding methods used under each configuration in the downlink. For the hybrid BF, we assumed that maximum ratio combining (MRC) was performed in the analog component using a phase shifter [31]. In the digital component, the minimum mean square error (MMSE) weight calculated in the uplink was used as a precoder [31]. Eight sub-arrays (\(N_{K}=8\)) and eight sub-array elements (\(N_{L}=8\)) were utilized, resulting in 64 elements. In the full-digital BF, transmission precoding was performed using a block diagonalization (BD) method with 64 elements [32]. Figure 7 shows the cumulative distribution function (CDF) characteristics of transmission rate and throughput. The adaptive modulation results show the characteristics obtained for each trial when the highest modulation order is selected in the modulation scheme in which the BER is \(10^{-2}\) or less.