# Hybrid Beamforming for Reduction of Inter-Beam Interference in Millimeter-Wave Cellular Systems
## 3 Simulation  
In this section, we evaluate the performance of the proposed hybrid beamforming technique for the reduction of IBI in mm-wave cellular systems. To do this, we perform computer simulations in a simple scenario shown in Figure 2. Here, we assume that four \(MS\)s are served by each \(BS\) in a three-cellenvironment. The \(BS\) and \(MS\) employ \(8\times 8\) and \(4\times 4\) UPAs, respectively. We also assumed that \(MS\)s are located randomly in a cell, and that a single LoS path is present between the \(BS\) and \(MS\). The azimuth and elevation angles of AoD at the \(BS\) follow uniform distributions of (\(0\), \(\pi\)) and (\(0\), \(\pi/2\)), respectively. The path gain and the transmission power of \(BS\) are all normalized to \(1\). More sophisticated simulation can be performed with an accurate mm-wave channel model under realistic assumption [28]. In the first numerical simulation, we compared the averaged achievable rates per user for different hybrid beamforming techniques. In Figure 3, the legend \"analog-only beamforming\" refers to the case where only the \(RF\) precoders are used. In this case, beams are formed in the direction of \(MS\)s to maximize the desired signal power. However, its averaged achievable rate per user is the lowest because, in this case, we did not consider IBI. We can achieve the highest averaged achievable rate when we used the beamformer with \"Single-cell, Single-user\". In this case, the best performance is achieved because there is no IBI from the serving cell or neighboring cells. The averaged achievable rates of the proposed hybrid beamforming techniques lie between \"Analog-only Beamforming\" and \"single-cell, single-user.\" The Type-1 precoder has the lowest achievable rates among the proposed techniques, and its achievable rate does not increase linearly as SNR increases because the interference from neighboring \(BS\)s is not removed. Note that the Type-1 precoder removes IBI in the serving cell, and does not consider IBI from neighboring cells. The achievable rates of Type-2, Type-3, and Type-4 precoders increase linearly as SNR increases, because the IBI from neighboring cells as well as the serving cell is reduced. The achievable rate is higher in the order of Type-2, Type-3, and Type-4 precoders (i.e., the highest is Type-2). Figure 4 compares the BER performance of different hybrid beamforming techniques in the same environment as in Figure 3. By comparing these two figures, we can see that the BER performance in Figure 4 is consistent with the averaged achievable rates in Figure 3. This is because the achievable rate per user increases as the interference decreases, resulting in a decreased BER. The \"analog-only beamforming\" case shows the worst performance (error floor) because IBI is not considered. In addition, the \"Single-cell, Single-user\" case shows the best performance because there is no IBI. The Type-1 precoder shows the lowest performance (error floor) of the proposed techniques because it cannot reduce the IBI from neighboring cells. The BER performance is better in the order of Type-2, Type-3, and Type-4 precoders (i.e., the best is Type-2). The reason for which the BER curves show noticeable performance gaps compared with the achievable rates is that the BER curve reflects the worst case more significantly. For the BER simulation, we randomly selected the values of AoAs  
Figure 3: Achievable rates of proposed hybrid beamforming techniques. and AoDs between _BSs_ and _MSs_. In the process of averaging the error rates, the lowest error rate usually dominates the averaged BER performance. Type-1, Type-2, and Type-4 precoders require at least _U RF_ chains to serve _U MSs_ simultaneously in the serving cell. However, the number of _RF_ chains in Type-3 precoder needs to be equal to or greater than the number of total _MSs_ in neighboring cells to remove IBI. In the cellular system with 12 _MSs_ in 3 neighboring cells, 12 _RF_ chains are required for each _BS_ to remove IBI.