# Efficient Preamble Design Technique for Millimeter-Wave Cellular Systems with Beamforming
## 3 Efficient CBID Detection Technique for mmWave Cellular Systems  
In this section, an efficient detection technique that can reduce the computational complexity of the CBID search using the preamble sequence described in the previous section is proposed for mmWave cellular systems. Figure 2 shows an example of an mmWave cellular system with two BSs and one MS. It is assumed that the switched beamforming technique with a set of predefined angles is used at both the BS and the MS. It is also assumed that the BS has multiple antenna arrays, whereas the MS has only one antenna array. That is, multiple beams are transmitted simultaneously from the BS, while a single switched beam is used at the MS. The sidelobes of each beam are omitted in this figure for simplicity. Details on the parameters for the preamble generation, beamforming, and the CBID information will be described in Section 4. Figure 3 shows the preamble structures used in the proposed technique. Figure 3 shows only the preamble segment, ignoring the data transmission segment in the frame structure. In this figure, \(N_{B}\) and \(N_{M}\), denote the number of Tx beams (BIDs) and Rx beams, respectively. The variables for the set of BIDs and Rx beam indices are defined as \(b\in\{0\), 1, \(\cdots\), \(N_{B}-1\}\) and \(i\in\{0\), 1, \(\cdots\), \(N_{M}-1\}\), respectively. In Figure 3, '\(SP\)' represents a synchronization preamble from which the symbol timing offset (STO) and carrier frequency offset (CFO) are estimated. The beam ID associated with the cell ID is acquired from the '\(BP\)' (BID preamble). In this paper, we assume that the synchronization procedure has been completed with the \(SP\) using the same approach as in an LTE system with synchronization signals or in a Mobile WiMAX with preambles [12; 15]. In this paper, we will focus only on the design of the \(BP\). As shown in Figure 3, \(N_{B}\) beams are simultaneously transmitted from the BS and the Rx beams are swept over in this period. \(N_{B}\) beams are transmitted repeatedly, \(N_{M}\) times, until one round of the Rx beam sweep is completed. The Rx beam switching takes place for every 2\({}^{\text{nd}}\) symbol such that the MS can receive a pair of preambles (\(SP\) and \(BP\)) for each beam. Note that the processing time for the beam training when the CDM-based scheme is used is \(N_{B}\) times smaller than in the case of the TDM-based scheme. Figure 2: Example of an mmWave cellular system. If the CDM-based technique is used for multiple beam transmission in cellular communication systems, the BID as well as the corresponding CID needs to be transmitted in the preamble because the BID needs to be detected in a multicell environment. Therefore, the information (both the CID and the BID) assigned to the beam should be transmitted in the \(BP\). A hierarchical preamble design concept is used to carry the BID information as well as the CID information in the \(BP\). The information on the CID (\(c\)) and BID (\(b\)) are mapped to the root indices (\(r_{0}\), \(r_{1}\)) and the cyclic shifts (\(d_{0}\), \(d_{1}\)) given in Equation (1) as follows:  
\[Z_{s}^{c,b}\left(m\right)=Z_{s}^{g}\left(m+d_{s}^{c,b}\right)=Z_{s}^{g}\left(m \right)P_{s}^{v,b}\left(m\right)S_{s}^{c,b} \tag{6}\]  
where \(Z_{s}^{g}\left(m\right)=e^{-j\pi r_{s}^{g}\left(m\right)\left(m+1\right)/L}\), \(S_{s}^{c,b}=e^{-j\pi d_{s}^{c,b}\left(d_{s}^{c,b}+1\right)/L}\)  
\[P_{s}^{v,b}\left(m\right)=e^{-j\pi 2Z_{s}^{g}d_{s}^{c,b}m/L}=e^{-j\pi 2\widehat{ d}_{s}^{v,b}m/L},\widehat{d}_{s}^{v,b}=bL_{p}+O_{s}^{v}\]  
\[c\in\left\{0,1,\cdots,N_{c}-1\right\},\,c=N_{v}g+v,\,N_{g}=\left[N_{c}/N_{v} \right]\]  
\[g\in\left\{0,1,\cdots,N_{g}-1\right\},v\in\left\{0,1,\cdots,N_{v}-1\right\}\]  
Here, \(g\) and \(v\) denote the group ID (GID) and sequence ID (SID), respectively. The CID (\(c\)) is expressed by a combination of \(g\) and \(v\). \(N_{C}\), \(N_{g}\), and \(N_{v}\) denote the number of CIDs, GIDs, and SIDs, respectively. \(L_{p}\) denotes the scaling factor for a phase change.