## 5 Throughput Performance Using IEEE802.11 ac Signals  
To verify the efficacy of the IBF method with the proposed calibration technique, we conducted simulations using the IEEE802.11 ac signal format. In this section, the performance is verified when considering the amplitude and phase errors shown in Figures 6 and 7. The main simulation parameters are listed in Table 2. These simulations assumed path loss under the International Telecommunication Union (ITU) Radiocommunication Sector (ITU-R) model [31] and independent and identically distributed (i.i.d.) Rayleigh fading. The block diagonalization (BD) algorithm was employed for MU-MIMO transmission [8]. \begin{table}
\begin{tabular}{c c} \hline \hline \(\mathbf{N_{T}}\) & \(\mathbf{4,8,16}\) \\ \hline \(N_{R}\) & 1 \\ \(N_{U}\) & 4 \\ Frequency (\(f_{c}\)) & 5200 MHz \\ Bandwidth & 40 MHz \\ Transmit distance (\(d\)) & 1–50 m \\ Path loss (\(L\)) & \(31\log_{10}(d)+20\log_{10}(t_{c})-28\) \\ Transmit power & 19 dBm \\ Antenna gain & 2 dBi \\ Null Data Packet Announcement & 60 \(\upmu\)s \\ (NDPA) & \\ Null Data Packet (NDP) & 100 \(\upmu\)s \\ NDP (for IBF (Implicit beamforming)) & 40 \(\upmu\)s \\ Beamforming report (BR) & 1400 \(\upmu\)s (max) \\ Beamforming report polling (BA) & 52 \(\upmu\)s \\ Beamforming (Acknowledgement)ACK (BA) & 64 \(\upmu\)s \\ Beamforming ACK request (BAR) & 56 \(\upmu\)s \\ Frame aggregation & 5000–40,000 byte \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation conditions. Figure 11: \(C\) vs. difference in directions of arrival (DoA) between desired and interference signals (\(\theta_{d}=0^{\circ}\)). Table 3 illustrates the relationship between the transmission rate (TR) and SNR for IEEE802.11 ac (40 MHz mode) [28]. Rmin is the minimum received power in Table 3.  
As the eigenvalues given by the BD (\(\tilde{\lambda}_{BD}(i)\)) determine the modulation scheme, the modulation schemes were selected on the basis of \(\tilde{\lambda}_{BD}(i)/(N_{T}\sigma^{2})\) for each trial, where \(\sigma^{2}\) is the noise power. The SNR values listed in Table 3 were obtained when the bit error rate (BER) was less than \(10^{-7}\). The TRs were averaged using the results for each trial. Figure 12 shows the average TR with respect to the transmit distance \(d\) between the BS and UT. We note that the calibration error was not considered here, and \(N_{T}\) was set to 4, 8, or 16. A four-user MU-MIMO was assumed, with one antenna at the UT (\(N_{R}\)). As can be seen from Figure 12, the TR and the service area were both increased by the transmit diversity effect when a larger number of antennas were located at the BS. For example, when \(N_{T}\) was increased from 4 to 8 or 16 with \(d=15\) m, the TR increased by a factor of 2 or 2.5, respectively. Moreover, although the service area was only 35 m when \(N_{T}=4\), this increased to more than 50 m when \(N_{T}=8\) or 16. Figure 13 shows the average TR versus the transmit distance with and without calibration. We note that the overhead from control signals such as the CSI feedback (BR in Table 2) was not considered and that \(N_{T}\) was 16. The calibration errors were taken from the phase-error results shown in Figure 6. In Figure 13, we can observe that the TR without calibration was less than that with calibration and less than that without calibration errors when \(d\) was 6 m. Moreover, when \(d\) was 15 rather than 6 m, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Modulation** & **Rate** & **Rmin** & **TR (Mbps)** & **SNR (dB)** \\ \hline BPSK & \(1/2\) & \(-79\) & 15 & 6 \\ QPSK & \(1/2\) & \(-76\) & 30 & 9 \\ QPSK & \(3/4\) & \(-74\) & 45 & 11 \\
16-QAM & \(1/2\) & \(-71\) & 60 & 14 \\
16-QAM & \(3/4\) & \(-67\) & 90 & 18 \\
64-QAM & \(2/3\) & \(-63\) & 120 & 22 \\
64-QAM & \(3/4\) & \(-62\) & 135 & 23 \\
64-QAM & \(5/6\) & \(-61\) & 150 & 24 \\
256-QAM & \(3/4\) & \(-56\) & 180 & 29 \\
256-QAM & \(5/6\) & \(-54\) & 200 & 31 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Relationship between modulation scheme and transmission rate (TR; 40 MHz mode).