# Cell Selection Technique for Millimeter-Wave Cellular Systems with Hybrid Beamforming
## Preliminaries
### System Model  
Consider a mm-wave cellular system in which a transmitter with \(N_{TX}\) antennas transmitting \(N_{S}\) data streams to a receiver with \(N_{RX}\) antennas. It is assumed that, in the data transmission stage, hybrid beamforming is used at the BS, and analog beamforming with a set of predefined angles is used at the MS. The BS is equipped with \(N_{RF}\) transmit chains to enable \(N_{S}\) data streams transmission, such that \(N_{S}\leq N_{RF}\leq N_{TX}\)[12; 21]. This architecture enables the transmitter to apply an \(N_{RF}\times N_{S}\) baseband precoder by using \(N_{RF}\) transmit chains, followed by an \(N_{TX}\times N_{RF}\) RF precoder using analog circuitry. In the proposed technique, it is assumed that all Tx beams are simultaneously transmitted from all candidate BSs, and Rx beams are swept over in this period, to reduce the processing time required for channel estimation. All Tx beams are transmitted repeatedly until one round of Rx beam sweep is completed. In the proposed technique, CBSSs are mapped to the corresponding Tx beams, simultaneously transmitted from candidate BSs. Because the BID needs to be detected in a multicell environment with multiple beams, the CBSS is designed such that the BID is mapped on a synchronization sequence in association with its CID. Both the BID and CID are transmitted on a single CBSS to facilitate joint detection of the BID and CID. This hierarchical structure enables the MS to identify the CID of the beam from the received CBSS. In a mm-wave cellular system based on orthogonal frequency division multiplexing (OFDM), the signals received by the \(i\)-th Rx beam at the MS in the initialization stage can be expressed in the frequency domain as follows:  
\[Y_{i}(k)=\sum_{c=0}^{N_{C}-1}\sum_{b=0}^{N_{B}-1}\mathbf{q}_{i}{}^{\prime} \mathbf{H}^{c}(k)\mathbf{p}^{c,b}X^{c,b}(k)+\mathbf{q}_{i}{}^{\prime}\mathbf{W }(k) \tag{1}\]  
where \(\mathbf{q}_{i}\in\mathbb{C}^{N_{RX}\times 1}\) and \(\mathbf{p}^{c,b}\in\mathbb{C}^{N_{TX}\times 1}\) denote an analog combiner for the \(i\)-th Rx beam at the MS, and an analog precoder for the \(b\)-th beam in the \(c\)-th cell, respectively. Here, \(N_{I}\), \(N_{B}\), and \(N_{C}\) denote the number of Rx beams at the MS, the number of Tx beams at the BS, and the number of candidate cells, respectively. \(\mathbf{H}^{c}(k)\) is an \(N_{RX}\times N_{TX}\) matrix at subcarrier \(k\) that represents the mm-wave channel between the \(N_{B}\) beams of the \(c\)-th cell and the \(N_{I}\) Rx beams of the MS. \(X^{c,b}(k)\) and \(\mathbf{W}(k)\) denote the  
Figure 1: Example of a mm-wave cellular system with two BSs. CBSS transmitted from the \(b\)-th beam of the \(c\)-th cell and additive white Gaussian noise (AWGN), respectively. If a total number of Tx beams at the BS is \(N_{B}\) and the number of available RF transmit chains is \(N_{RF}(\leq N_{B})\), then only \(N_{RF}\) beams can be simultaneously transmitted, and \(N_{I}\) Rx beams are swept over in this period. The same procedure needs to be repeated \(N_{B}/N_{RF}\) times by switching the set of \(N_{RF}\) beams until all the Tx beams are transmitted. For example, if the values of \(N_{B}\), \(N_{RF}\), and \(N_{I}\) are 16, 1, and 8, respectively, then only one beam will be transmitted until one round of Rx beam sweep is completed. This procedure will be repeated 16 times. If the value of \(N_{RF}\) is 8, then 8 beams will be simultaneously transmitted until one round of Rx beam sweep is completed. This procedure will be repeated only 2 times. Thus, the processing time required for channel estimation increases as the number of RF transmit chains decreases. In this paper, it is assumed that the number of RF transmit chains is the same as the number of Tx beams for notational convenience. In Equation (1), the matrix \(\mathbf{H}^{c}(k)\) represents the channel at subcarrier \(k\), which is derived from the delay-\(\tau\) channel matrix \(\mathbf{H}^{c}(\tau)\).