# Hybrid Beamforming for Reduction of Inter-Beam Interference in Millimeter-Wave Cellular Systems
## 2 Hybrid Beamforming Techniques for a Multicell Multiuser Environment
### Channel Estimation  
So far, we assumed that the channel information required for the precoder design is known perfectly. However, the channels between the \(MS\) and neighboring \(BSs\), as well as the channel between the \(MS\) and the serving \(BS\), should be estimated beforehand for the design of the proposed precoder. The processing time required for channel estimation in the proposed approach increases proportionally to the product of the number of neighboring cells and the number of Tx beams. In order to reduce the processing time significantly, we apply the cell and beam reference signal (CBRS) technique to the effective network channel estimation for the design of the proposed precoder [18]. Here, we assume that the \(RF\) precoder in the \(BS\) and the \(RF\) combiner in the \(MS\) are successfully obtained after completion of the first stage in the analog domain. In the CBRS technique, multiple beams are transmitted simultaneously from neighboring \(BSs\) (including the serving cell) to reduce the processing time for channel estimation. In order to estimate all channels between the \(MS\) and neighboring \(BSs\) with multiple beams, CBRSs are simultaneously transmitted from multiple beams of neighboring \(BSs\). The CBRS carries a cell ID (CID) as well as a beam ID (BID). If the CBRS carries only BID information, it will be impossible to determine which cell had transmitted the BID. Therefore, a large number of different sequences (CID \(\times\) BID) need to be generated. In the proposed CBRS technique, the BID is designed in conjunction with CID because the BID must be detected in a multicell environment. The hierarchical structure of CBRS gives the advantage of enabling the reuse of the same BIDs in neighboring cells, enabling us to generate a large set of sequences. The CBRS technique can be viewed as a combination of a Chu sequence and a polyphase sequence. In the CBRS technique, a sequence is generated by mapping the CID to the root index of the Chu sequence, and the BID to the index of the polyphase sequence. The Chu sequence is selected as a base sequence because it is widely used in the design of synchronization signals and the random access preamble in Long Term Evolution (LTE) systems owing to its good correlation property [27]. A combination of a Chu sequence and a polyphase sequence is selected for CBRS because these signals can be transmitted simultaneously with minimal IBI in a multicell environment. The CBRS is defined by the product of a prime-length Chu sequence and a polyphase sequence in the frequency domain as follows:  
\[ \begin{array}{l}S_{c,i}(k)=Z_{c}(k)P_{i}(k)\\ Z_{c}(k)=e^{\frac{i\pi ik(k+1)}{N}},\ P_{i}(k)=e^{\frac{-\beta mik}{N}},\ k=0,1, \ldots,N-1\end{array}  \tag{33}\]  
where \(Z_{c}(k)\) and \(P_{i}(k)\) denote a prime-length Chu sequence and polyphase sequence, respectively. In addition, \(c\in\mathbf{N_{C}}\), \(i\in\mathbf{N_{I}}\), \(\mathbf{N_{C}}=\{1,\,2,\,\ldots,\,N_{C}-1\}\), and \(\mathbf{N_{I}}=\{0,\,1,\,\ldots,\,N_{I}-1\}\) denote the root index of the Chu sequence, index of polyphase sequence, set of CIDs, and set of BIDs, respectively. \(N_{C}\), \(N_{I}\), and \(N\) denote the number of available CIDs, BIDs, and sequence length, respectively. \(L\) is a parameter used to avoid the incorrect detection of the cell ID when there is a symbol timing offset (STO). The beams are generated by the \(RF\) precoder at the \(BS\), which is obtained after completion of the first stage. The signal received at the \(MS\) after CBRS transmission is given by  
\[y_{u_{i,m}}=\left(\mathbf{w}_{RF}^{u_{i,m}}\right)^{*}\left\{\sum_{l=1}^{B} \left(\mathbf{H}_{u_{i,m}}^{b_{l}}\mathbf{F}_{RF}^{b_{l}}\mathbf{s}^{b_{l}} \right)+\mathbf{n}_{u_{i,m}}\right\} \tag{34}\]  
Note that only the \(RF\) precoder is used at the \(BS\). The baseband precoder will be designed in the second stage using the information of the estimated channels. Here, \(\mathbf{s}^{b_{l}}\) denotes the CBRSs that are transmitted from the \(BS\)\(b_{l}\).