# Cell Selection Technique for Millimeter-Wave Cellular Systems with Hybrid Beamforming
## 3 Proposed Cell Selection Technique
### Channel Estimation and Cell Selection
Here, \(G_{TX}=G_{TX}^{\phi}=180\) and \(G_{TX}^{\theta}=1\). The fine grid point is increased with 1 degree of resolution in azimuth angle. For UPA, the elevation angle is fixed to \(\pi/4\) for convenience. Before applying the proposed technique to the mm-wave cellular system, the properties of the proposed CBSS, discussed in Section 3, are verified. In Figure 4, the correlation property of the CBSS is shown when STO is not present. Here, the reference CID and BID are set to 0 (\(r^{2}=54\)) and 7, respectively. The parameter \(L\) is set to 1. From Figure 4, it can be seen that the intra-beam correlation in the same cell (CID = 0) is zero except in the case of the same BID (BID = 7), as given by Equation (9). The normalized inter-cell correlation with the CID equal to 1 (\(r^{2}=59\)) is equal to 0.03 (\(1/\sqrt{N_{z}}\)) for all values of BID, as given by Equation (10). Figure 5 shows the correlation property of the CBSS in the time domain when STO exists. The reference CID and BID are set to 0 (\(r^{2}=54\)) and 0, respectively. It can be seen that when the STO is zero, correlation values are zero except for the lag \(l=0\). When the values of STO are 1 and 2, the peak shifts by one and two lags, respectively. So, the shift increases proportionally to the STO value. If the parameter \(L\) is set to 1, there may be an error in BID detection. Therefore, the parameter \(L  
Figure 6 shows the achievable channel capacity when the conventional and proposed techniques are used. In the conventional technique, the serving cell is selected by measuring SNRs for all candidate cells with Tx/Rx beam sweeping, and choosing the cell with the highest SNR. Cell 1 is selected as the serving cell in the conventional technique because cell 1 has a stronger LoS path than cell 0. However, in the proposed technique (LoS + NLoS(1), LoS + NLoS(2), LoS + NLoS(4)), cell 0 will be selected as the serving cell. That is because more multipath channels are considered for cell selection in the proposed technique as the number of RF chains \((N_{RF})\) increases. When \(N_{RF}\) is set to {2, 3, 5}, an additional gain of {0.64, 1.8, 3.23} and {1.24, 3.64, 6.6} bps/Hz at an SNR of 9 dB can be achieved for ULA and UPA, respectively. In the proposed technique, the serving cell is selected using Equations (25) and (26). Figure 7 shows the achievable channel capacity when the proposed technique is used with varying \(k\)-factor and different antenna configurations. Figure 7a shows the results for ULA with 16 \(\times\) 8 and 32 \(\times\) 16 antenna configurations and Figure 7b shows the results for UPA with 64 \(\times\) 16 and 16 \(\times\) 8 antenna configurations. Here, the channel capacity is measured at SNR 9 dB when \(k\)-factor varies from 2 to 20 with a step size of 2. As can be seen in Figure 7, spectral efficiencies for all cases (LOS, LOS + NLoS(1), LOS + NLoS(2), LOS + NLoS(4)) converge towards LOS case, irrespective of ULA/UPA. That is because LOS path becomes stronger than other NLOS paths as  
Figure 5: Correlation property of CBSS when STO exists. Figure 6: Achievable channel capacity when the conventional and proposed techniques are used. \(k\)-factor increases. The spectral efficiency increases as \(k\)-factor decreases, because NLOS components become more significant. When the \(k\)-factor is equal to 6 dB, the ULA configuration with 32 \(\times\) 16 obtains 2.0-2.5 bps/Hz gain in spectral efficiency over the ULA with 16 \(\times\) 8, while the UPA configuration with 64 \(\times\) 16 obtains 4.0-5.5 bps/Hz gain over the UPA with 16 \(\times\) 8. Figure 8 shows the bit error rate (BER) performance of the mm-wave system in the data transmission stage after a serving cell is selected by two different techniques. Here, QPSK is used for modulation. For reference, the analytic curve for a Rician fading channel with a \(k\)-factor equal to 6 dB is inserted.