# Efficient Preamble Design Technique for Millimeter-Wave Cellular Systems with Beamforming
## 4 Simulation
Figure 6 shows the bit error rate (BER) performance of an \(8\times 8\) mmWave system in Figure 2. The BER is measured during the data transmission period after completing the cell and beam search period. A quadrature phase shift keying (QPSK) signal is used for the input and the channel impulse response is assumed to be known. In this figure, analytic curves for AWGN and Rician channel (k-factor = 10 dB) with an \(8\times 8\) beamforming are included for comparison. From this figure, it can be seen that the BER performance of the beamforming system (one-cell) is better than the analytic (Rician) curve because the channel can be approximated as an AWGN when beamforming is performed in the direction of an LoS path. The performance is slightly worse than the AWGN case because a small power transmitted through the non-LOS path of the Rician channel will not be received in the MS. The previous and proposed (Type-1 and Type-2) techniques exhibit the same performance because the success probability of the CBID detection is one in the range of SNR, \(>\)\(-\)30 dB, as shown Figure 5. In a one-cell environment, the BER performance of the proposed (or previous) technique with an \(8\times 8\) beamforming is similar to the AWGN case. In a two-cell environment, the BER performance is  
Figure 5: Success probability of the CBID detection in one-cell and two-cell environments: (**a**) \(8\times 8\); (**b**) \(8\times 1\); (**c**) \(8\times 1\). degraded by approximately 4 dB compared to the one-cell case because of the interference from the adjacent BS. Table 3 shows the number of complex multiplications required for CBID detection at the MS for each Rx beam direction. From this table, it can be seen that the numbers of complex multiplications required for the Type-1 and Type-2 preambles are reduced to 1.9% and 0.6%, respectively, compared to the previous technique, when \(N_{C}\) is 1020. A significant reduction in the computational complexity can be achieved using the Type-2 preamble. Figure 7 shows the number of complex multiplications required for the CBID detection when \(N_{C}\) varies. When \(N_{C}\) is 1020, the number of multiplications required for the Type-1 and Type-2 preambles are 1,175,040 and 396,288, respectively. When \(N_{C}\) is 24, the number of multiplications required for the previous technique is 1,470,240 that is larger than that for the proposed technique (Type-1 and Type-2), when \(N_{C}\) is equal to 1020. Therefore, the proposed technique (Type-1 and Type-2) can provide an increase in the number of CIDs by a factor of 43, compared to the previous technique, when the same number of complex multiplications is used for the CBID detection. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **The Number of Complex Multiplications** & **Example** \\ \hline Previous technique & \(N_{C}N_{B}\overline{L}(\chi_{max}+1)\) & 62,485,200 \\ \hline Proposed technique & \(N_{r}(N/2)\times\log_{2}(N/2)\) & Type-1 (\(N_{r}=255\)) & 1,175,040 \\  & Type-2 (\(N_{r}=86\)) & 396,288 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Number of complex multiplications required for the CBID detection. Figure 6: BER performance in one-cell and two-cell environments.