## 3 Proposed Configuration and Beamforming Method Eliminating CSI in the Downlink
### Effectiveness of Proposed Configuration and Method Through Computer Simulations  
The effectiveness of the proposed configuration and method is verified using QAM signals (4 QAM to 1024 QAM) on the downlink, considering a Rayleigh fading environment. By comparing the transmission signals and the demodulated received signals, the BER is derived. The modulation scheme with maximum bit rate is selected when the BER is less than \(10^{-3}\)[25]. If the BER is greater than \(10^{-3}\), we assume that the bit rate is zero. In this way, we derive the bit rate considering the angular difference between the receiving UTs. Table 1 shows the simulation conditions. Because it is assumed that the channel reciprocity between the transmission and reception is guaranteed in 5G system where time division duplex (TDD) operation with the high data rate is used [10], this simulation is performed in a static environment between the transmission and reception to verify the basic performance of the proposed system. As the future work, we should evaluate the performance when considering the Doppler shift. In order to evaluate pure interference rejection by the proposed method, the SNR is set to be 30 dB. In the simulation, we focus on evaluating the ideal performance at the UTs by securing a sufficient number of symbols and iterations so that the weight of the CMA converges ideally even when using QAM signals. In order to evaluate the performance using beam control alone, Figure 4 shows the cumulative density function (CDF) versus signal-to-interference-plus-noise power ratio (SINR), when the difference in the AoA between two UTs is set to be 10, 30, 60, or 120 degrees. The SINR is improved according to the increase in the AoA between two users. This result shows that the UTs can be separated by analog beam patterns at the BS. However, as can be seen in Figure 3, user separation is not perfect because the interference signals are still received by the sidelobes of the beams facing the other UTs. Figure 5 shows the CDF versus SINR when the residual interference of Figure 4 is cancelled by using CMA at the UTs. In the case of relatively close AoAs between two UTs, such as 10 degrees, the SINR is greatly improved by applying CMA. Moreover, the SINR is improved even if the AoAs between two UTs are relatively large, such as 120 degrees. However, in CMA, because the signals of maximum power among the received signals are regarded as the desired signals, erroneous signals may be extracted if the received powers of the interference signals are higher than that of the desired signals. Figure 3: An example of analog beam patterns selected on the uplink channel. Therefore, the SINR drops extremely by applying CMA when the SINR is less than 0 dB. This problem occurs when the beams selected for different users are close. It can be improved by implementing beam selection that does not select close beams in the uplink. Next, we increase the number of beams used for transmission in order to improve the performance. The power of the desired signals increases when using the adjacent beam along with the selected beams of the uplink channel, if considering the angular spread. Therefore, it is possible to improve the transmission rate in an environment with low SNR. When a large number of beams are used, Doppler effects which are caused by the movement of the UTs are also mitigated, because total beam \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of Transmission antennas & 64 \\ Number of receive user terminals (UTs) & 2 \\ Angular difference between receive UTs & 0\(\sim\)120 degrees \\ Number of receive antennas at each UT & 2 \\ Number of beams & 1\(\sim\)3 \\ Symbol length & 10000 symbols \\ Least-square constant modulus algorithm (LS-CMA) smoothing size & 500 symbols \\ Number of pilot signals & 5 symbols \\ Number of trials & 1000 times \\ Average signal to noise power ratio (SNR) & 30 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation conditions.