# A Novel Multi-User Codebook Design for 5G in 3D-MIMO Heterogeneous Networks
## 3 System Model  
The traditional base station is equipped with a ULA array. As shown in Figure 1, multiple beams for a terminal cannot be implemented in the vertical plane, so that the base station can form three beams in the horizontal dimension to align users with different angles from the base station, but in the horizontal dimension. Users with the same angle as the base station, such as User Equipment 2 and 3 (UE2 and UE3), whose beams interfere with each other. The 3D-MIMO technology provides vertical plane beamforming. As shown in Figure 2, UE2 and UE3 can be distinguished in the vertical dimension to form the beams that are aligned with them to serve them, thereby controlling the interference of adjacent cells and improving the spectrum efficiency [19]. Figure 1: Conventional antenna beamforming. This paper adopts the space division multiple access (SDMA) heterogeneous network system model composed of the microbase station and macro base station and multiuser. The distribution of micro base station follows the isomorphous Poisson Point Process (PPP) \(\Phi(\lambda)\), with a density of \(\lambda\). Each micro base station is equipped with an \(N_{t}\) root antenna and the transmission power is \(P\); the distribution of macro base station follows the isomorphism PPP \(\Phi(\lambda_{M})\), where the density is \(\lambda_{M}\), each macro base station is equipped with \(N_{M}\) antennas and the transmission power is \(nP\). Each base station serves \(K\) users, \(K\leq N_{t}\) and \(N_{S}\leq N_{M}\), and it is assumed that the user obeys the independent stable point process and is randomly distributed in a circle whose radius is \(d_{\text{max}}\) centered on the serving base station. For the fading model, it is assumed that all point-point channels obey the unitary mean of independent, identically distributed Rayleigh block fading, and the received power varies with distance \(d\) by \(d^{-\alpha}\), where \(\alpha\) is the path loss index and \(\alpha>2\). The channel vectors from the micro base station \(T_{0}\), the \(m\)th macro base station, and the \(i\)th macro base station to the user \(U_{0}^{(k)}\) are represented as \(\mathbf{h}_{0k}\in\mathbb{C}^{N_{S}\times 1}\), \(\mathbf{h}_{mk}\in\mathbb{C}^{N_{M}\times 1}\), \(\mathbf{h}_{ik}\in\mathbb{C}^{N_{S}\times 1}\), respectively, which are all composed of independent complex Gaussian random variables with zero mean unit variance. The normalized transmitted signal vectors of the micro base station \(T_{0}\), the \(m\)th macro base station, and the \(i\)th micro base station are respectively represented as \(x_{0}\in\mathbb{C}^{N_{S}\times 1}\), \(\mathbf{x}_{m}\in\mathbb{C}^{N_{M}\times 1}\), \(\mathbf{x}_{i}\in\mathbb{C}^{N_{S}\times 1}\), and the transmitted signal vector \(\mathbf{x}\) is a linear function \(\mathbf{x}=\sum_{\mathbf{k}=\mathbf{k}}^{\mathbf{K}}\mathbf{W}_{k}S_{k}\), where \(S_{k}\) is the data symbol of the \(k\)th user, \(\mathbf{W}_{k}\) is the unit norm beamforming vector for the \(k\)th user. Because the transmission power of the micro base station is low, the macro cell users far away from the micro base station can only obtain a small gain even if the macro base station and the micro base station cooperatively transmit data under the coordinated multipoint (CoMP) mechanism [20]. Therefore, this article only analyzes downlink information transmission for users in the micro base station. Assuming that the serving base station of each user is the closest base station to it, the micro base station serving the \(k\)th specific user \(U_{0}^{(k)}\) is represented as \(T_{0}\). Assuming that it is located at the origin, the distance between \(U_{0}^{(k)}\) and \(T_{0}\) is \(d_{k}\).