## 3 System Model
### Resource Blocks and Structure  
Fifth Generation NR is highly dependent on Orthogonal Frequency-Division Multiplexing (OFDM) and can also coexist with LTE on the same frequency band. The 5G NR frame has a time length of 10 ms consisting of 10 subframes, each having a time length of 1 ms. In an OFDM network, 5G NR can enable transmission to begin at any OFDM symbol and will continue on several symbols that are required for the communication, and the data transmitted in the downlink (DL) are split into RBs. The amount of radio resources in a subframe of 1 ms in a specific sub-carrier spacing of a carrier can be perceived as a resource grid composed of subcarriers in frequency and OFDM symbol in time. Hence, each resource element in the resource grid occupies a subcarrier in frequency and another in OFDM symbol in time, which is often regarded as the Transmission Time Interval (TTI). A sub-frame is also regarded as the frequency blocks at a given TTI. In a 5G NR frame structure, each sub-frame comprises \(2^{\eta}\) time slots to handle a broad variety of applications for which it was created for and of course the large spectrum availability. Each TTI contains 14 OFDM symbols or resource elements (12 resource elements in the event of when extended cyclic prefix is used). Consequently, symbol duration is equal to \((14\times 2^{\eta})^{-1}\) ms or \((12\times 2^{\eta})^{-1}\) ms if extended cyclic prefix is used [12]. Therefore, the number of symbols constituting each subframe greatly depends on \(\eta\). This means a larger value of \(\eta\) will lead to more sub-carrier spacing. The RB spacing and period ensure that there is feedback on the quality of the channel and also ensures that the DL scheduler optimizes the utilization of the channel. RBs are the scheduling units in a 5G NR system and are devoted to a particular UE. The RB scheduler ensures that RBs are allocated to connections between the cells and the UEs while maximizing the bearer's utilization [34]. The antenna system of the cell comprises the an array of \(Y_{a}\) elements consisting of \(Y_{b}\) static beam. For simplicity of our system model, we employ 14 sub-carriers in a single resource block, assuming that they all possess the same characteristics. * The parameter \(n\) is considered to be the number of user equipment, the number of antennas involved in the beamforming is considered to be \(Y_{a}\), while the number of sub-channels is taken as \(u\). * \(g_{n,k}=\left[g_{1}^{n,k}\ \dots\ g_{Y_{a}}^{n,k}\right]^{T}\in\mathbb{C}^{Y_{a} \times 1}\) is considered to be the gain vector. * While \(z_{n,k}=\left[g_{1}^{n,k}\ \dots\ g_{Y_{a}}^{n,k}\right]^{T}\in\mathbb{C}^{Y_{a} \times 1}\) is considered to be the steering vector. * \(w_{n,k}\in\mathbb{C}\) is considered to be the information signal and \(P_{n,k}=A\left[\left|w_{n,k}\right|^{2}\right]\) to be the transmission power. * \(l_{n,k}\in\mathbb{C}\) is considered as the additive noise under the assumption that the noise is white additive Gaussian noise (AWGN) with a variance of \(N_{0}\). * With the assumption that the channel coefficients for the different UEs are independent, the received signal by a specific UE \(n\) on a particular subcarrier \(k\), \(r_{n,k}\in\mathbb{C}\), is given by: \[r_{n,k}=g_{n,k}^{G}z_{n,k}w_{n,k}+\sum_{m\
eq n}g_{n,k}^{G}z_{m,k}w_{m,k}+l_{n,k}\] (3) The signal-to-interference and noise ratio (SINR) of the UE is given by: \[SINR_{n,k}=\frac{\left|g_{n,k}^{G}z_{n,k}\right|^{2}P_{n}}{\sum_{m\
eq n}\left| g_{n,k}^{G}z_{m,k}\right|^{2}P_{m}+N_{0}}\] (4) While the achievable bit rate \(R_{n,k}\) is expressed by the following equation \[R_{n,k}=log_{2}(1+SINR_{n,k})\] (5) Attenuation matrixes permit the sending of one or multiple signals to one or multiple outputs, while changing the power level of each of the signals. The attenuation matrix \(\left\{A_{n}\right\}_{n=1}^{N}\in R^{K\times Y_{a}}\) is, however, computed as \[A_{n}=