# Efficient Preamble Design Technique for Millimeter-Wave Cellular Systems with Beamforming
## 4 Simulation
The root index pairs corresponding to the CIDs  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Parameters for Preamble Generation**} \\ \hline \((\widetilde{L},\,L_{P})\) & & (509,3) \\ \((N_{C},\,N_{g},\,N_{o},\,N_{B},\,N_{M})\) & & (1020,255,4,12,12) \\  & Type-1 & Type-2 \\ \(N_{r}\) & 255 & 86 \\ \(b\) & 0–11 \\ \(\{Q_{0}^{\rm{o}},O_{1}^{\rm{o}}\}\) & \{0,256\},[36,292],[72,328],[108,36] \\ \((N,\,N_{CP})\) & (1024,256) \\ \hline \hline \multicolumn{3}{c}{**Parameters for Beamforming**} \\ \hline The number of antenna elements at BS and MS & 8 \\ Antenna spacing & \(\lambda/2\) \\ Steering factor of \(m\)-th antenna at ULA & \(e^{j\pi\cos(\phi)\sin(\theta)m}\), \(m=0\)–7 \\ Set of predefined angles (degree) at ULA & \(\phi=\{-55,\,-45,\,-35,\,-25,\,-15,\,-5,\,5,\,15\,25,\,35,\,45,\,55\}\), \\ (\(\phi=\) azimuth angle, \(\theta=\) elevation angle) & \(\theta=0\) (fixed) \\ Steering factor of \(m\)-th antenna at UCA & \(e^{j\pi\sin(\theta)\sin(\phi-2\pi m/8)m}\), \(m=0\)–7 \\ Set of predefined angles (degree) at UCA & \(\phi=\{0,30,\,60,\,90,\,120,\,150,\,180,\,-150,\,-120,\,-90,\,-60\), \\ (\(\phi=\) azimuth angle, \(\theta=\) elevation angle) & \(-30\}\), \(\theta=0\) (fixed) \\ AOD (Line-of-sight) &
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(618, 622, 954, 962) are ([69, 70], [70, 71], [68, 70], [70, 72]), whereas the root index pair corresponding to the CID (278) is [70,70]. A high correlation occurs at these four CIDs with BID = 6 because the same root index, 70, is used. Figure 5 shows the success probability of the CBID detection in one-cell and two-cell environments. CBID detection using the preambles simultaneously transmitted from the BS(s), is performed at the MS using Equations (12)-(14). The success of the CBID detection refers to the case where the CID and BID detected at the MS match the ones used in the BS for the beam transmission. Simulations are performed for three different cases (\(1\times 1,8\times 1,8\times 8\)), where the first and second terms denote the number of antenna elements in the BS and MS, respectively. When the number of antenna elements is equal to one, an omnidirectional antenna is used. From this figure, it can be seen that an array gain of 9 dB is obtained when the number of antenna elements increases from one to eight. The success probability of the CBID detection decreases in a two-cell environment compared to a one-cell environment because of the interference transmitted from the adjacent BS. It can be seen from this figure that the proposed techniques (both Type-1 and Type-2) are robust to the STO and achieve almost the same performance as the previous technique. The reason that the proposed technique, Type-2, does not suffer from a performance degradation is that the parameters that can avoid the condition in Property 3 and ambiguities in the (GID, SID, BID) detection are selected at the cell planning stage. In the simulation, the CIDs of BS1 and BS2 are selected as 278 and 378. The root index pairs corresponding to the CIDs are [70, 70] and [9, 10], respectively, where no common root index is used. The performance degradation caused by the intercell interference (high correlation) in the Type-2 preamble can be avoided by selecting appropriate root index pairs at the cell planning stage. Note that the computational complexity required for the CBID detection in the Type-2 preamble is reduced to 33.3%, compared to the Type-1 preamble because \(N_{r}\) in the Type-2 preamble is 1/3 that of the Type-1 preamble. Figure 4: Correlation properties of the proposed preamble depending on the value of \(N_{r}\): (**a**) Type-1; (**b**) Type-2.