# Hybrid Beamforming for Reduction of Inter-Beam Interference in Millimeter-Wave Cellular Systems
## 2 Hybrid Beamforming Techniques for a Multicell Multiuser Environment
\begin{array}{c}1,\cdots,e^{i\frac{2 \pi}{d}\left(\varepsilon\cos(\phi_{MS}^{u_{u},m},b_{n})\right)}\sin(\theta_{ MS}^{u_{u},m},b_{n})+q\sin(\phi_{BS}^{u_{u},m},b_{n})\sin(\theta_{MS}^{u_{u},m},b_{n}) ),\cdots\\,e^{i\frac{2\pi}{d}\left(\left(E-1\right)\cos(\phi_{MS}^{u_{u},m},b_{n}) \right)}\sin(\theta_{MS}^{u_{u},m},b_{n})+\left(Q-1\right)\sin(\theta_{MS}^{u_ {u},m},b_{n})\sin(\theta_{MS}^{u_{u},m},b_{n}))\\ \end{array} \right]^{T} \tag{4}\]  
\[\mathbf{a}_{MS}\left(\phi_{MS}^{u_{u},m},b_{MS}^{u_{u},m},\theta_{MS}^{u_{u},m },b_{n}\right)=\frac{1}{\sqrt{N_{MS}}}\left[ \begin{array}{c}1,\cdots,e^{i \frac{2\pi}{d}\left(\varepsilon\cos(\phi_{MS}^{u_{u},m},b_{n})\right)}\sin( \theta_{MS}^{u_{u},m},b_{n})+q\sin(\phi_{MS}^{u_{u},m},b_{n})\sin(\theta_{MS}^{ u_{u},m},b_{n})\\,e^{i\frac{2\pi}{d}\left(\left(E-1\right)\cos(\phi_{MS}^{u_{u},m},b_{n}) \right)}\sin(\theta_{MS}^{u_{u},m},b_{n})+\left(Q-1\right)\sin(\theta_{MS}^{u_ {u},m},b_{n})\sin(\theta_{MS}^{u_{u},m},b_{n}))\\ \end{array} \right]^{T} \tag{5}\]  
where \(\phi_{BS}^{u_{u},m},b_{n},\rho\) and \(\theta_{BS}^{u_{u},m},b_{n},\rho\) denote the azimuth and elevation angles of departure (AoD), and \(\phi_{MS}^{u_{u},m},\rho\) and \(\theta_{MS}^{u_{u},m},\rho\) denote azimuth and elevation angles of arrival (AoA), respectively. \(N_{MS}\) denotes the number of antenna arrays at the \(MS\). In addition, \(d\) is the distance between antenna elements, and \(e\left(0,\ \cdots,\ E-1\right)\) and \(q\ (0,\ \cdots,\ Q-1)\) are indices of the two axes formed in the antenna array plane. In a multiuser communication system, multiple antennas allow the \(BS\) to transmit multiple data streams to a number of \(MS\)s simultaneously. In the case of conventional low-frequency communication systems, many different precoding techniques such as channel inversion, block diagonalization, dirty paper coding (DPC), and Tomlinson-Harashima precoding (THP) have been used to reduce the co-channel interference in multiuser systems under the assumption that full channel information is available at the \(BS\)[19]. However, in mm-wave systems, it is difficult to obtain full channel information at the \(BS\) because mm-wave systems with a large number of antennas require large training and feedback overhead. In [20; 21; 22; 23], a two-stage hybrid precoding algorithm for multiuser mm-wave systems is proposed to reduce the computational complexity using the sparse nature of mm-wave channels. In the first stage, Tx-Rx beamforming is performed in the analog (_RF_) domain to maximize the desired signal power, ignoring the IBI among \(MS\)s. In the second stage, the digital precoder is designed to minimize IBI among \(MS\)s. The computational complexity and feedback overhead can be significantly reduced by dividing the calculation of the precoder into two stages. However, in a multicell multiuser environment, the \(MS\) may receive IBI not only from a serving \(BS\) but also from neighboring \(BS\)s, because the beams formed toward \(MS\)s in the serving cell may generate significant interference to \(MS\)s in neighboring cells, especially for \(MS\)s at the cell boundary. In this paper, we propose digital precoding techniques that can reduce IBI in mm-wave cellular systems with a hybrid beamformer, considering interference signals not only from the serving cell but also from neighboring cells. In the proposed technique, we also use the two-stage approach to reduce computational complexity and feedback overhead. We made the following three assumptions in the design of the proposed digital precoder. First, the first stage of Tx-Rx beamforming has been successfully performed in the analog (_RF_) domain, ignoring the IBI among \(MS\)s. Thus, in this paper, we focus on the design of a digital precoder (second stage) that can reduce IBI from neighboring cells as well as the serving cell. Second, there is no information loss in the feedback channel in which the effective channel values estimated by \(MS\)s are transmitted.