# Secure Beamforming in 5G-Based Cognitive Radio Network
## 3 System Model
### Proposed Technique in Cascaded Transmission of MIMO-NOMA Network  
The cascaded transmission of this approach is used in MIMO-NOMA-based CRN for the secure communication in the multi-cell framework. The intruders will make an attempt to secretly listen to the channel information. The BS does not want the intruders to prevent the data using receiving beamformers. The proposed technique is applied at the BS for the determination of an information leakage within the same and the adjacent cells. The received signal of the PU and the SU in the \(l^{th}\) cluster of a cell A is expressed as [24]  
\[R_{su}^{l_{A}}=G_{su}^{l_{A}}\sum_{m=1}^{L}v^{m,A}+w_{su}^{l_{A}} \tag{2}\]  
\[R_{pu}^{l_{A}}=G_{pu}^{l_{A}}\sum_{m=1}^{L}v^{m,A}+l_{pu}^{l_{A}}\sum_{m=1}^{L}v ^{m,\ B}+w_{pu}^{l_{A}} \tag{3}\]  
Let \(v^{l_{A}}\) be the \(M\times 1\) superposition signal vector for the \(l^{th}\) cluster of the cell A. Note that \(v^{l_{A}}\)\(\in\)\(\mathbb{C}^{M\times 1}\) is the transmitting pr oposed vector and \(w_{pu}^{l_{A}}\), \(w_{su}^{l_{A}}\) is the AWGN process. It will be present in the receiver side of the PU and SU of the \(l^{th}\) cluster in the cell A. Assume \(l\in L\overset{\text{\tiny{def}}}{=}\{1,2,\ldots,L\}\). The secrecy Rate of a PU and a SU is derived as  
\[S_{su}^{l_{A}}\overset{\text{\tiny{def}}}{=}\left[\log_{2}\!\left(1+\psi\! \left|S_{su}^{l_{A}}v^{l_{A}}\right|^{2}\right)-\max_{m,m\
eq l}\log_{2}\! \left(1+\psi\!\left|C_{su}^{m,A}v^{m,A}\right|^{2}\right)\right]^{+} \tag{4}\]  
\[S_{pu}^{l_{A}}\overset{\text{\tiny{def}}}{=}\left[\log_{2}\!\left(1+\psi\! \left|G_{pu}^{l_{A}}v^{l_{A}}\right|^{2}\right)-Y_{1}-Y_{2}\right]^{+} \tag{5}\]  
Figure 4: A two-cell network of multiple-input-multiple-output0 non-orthogonal multiple access (MIMO-NOMA)-based cognitive radio network (CRN). where \(\psi\) is the signal to noise ratio (SNR) transmission at the BS. The idea of [e]\({}^{+}\) is defined as max(0,e). \(\mathrm{Y_{1}}\stackrel{{\mbox{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{ \tiny{\tiny{\tiny{\tiny{\tiny{\tiny{{\tiny{{\tiny{{{\tiny{{{{}}}}}}}}}}}}}}}}}{\rm{max }}\max_{\mathrm{m,m\
eq l}}\log_{2}\!\left(1+\psi\big{|}G_{\mathrm{pu}}^{\mathrm{ m,A}}\mathrm{v}^{\mathrm{m,A}}\big{|}^{2}\right)\) and \(\mathrm{Y_{2}}\stackrel{{\mbox{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{ \tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{ }}}}}}}}}}}}}}}}{\rm{max }}\max_{\mathrm{m}}\log_{2}\!\left(1+\psi\big{|}\mathrm{l}_{\mathrm{pu}}^{ \mathrm{m,A}}\mathrm{v}^{\mathrm{m,B}}\big{|}^{2}\right)\). In Equations (4) and (5), the second term on the right hand side (RHS) contains the formulation of an information leakage for the \(\mathrm{l}^{\mathrm{th}}\) cluster in the same cell. In Equation (5), the third term on the RHS contains the formulation of an information leakage for the \(\mathrm{l}^{\mathrm{th}}\) cluster in the neighboring cell. The information leakage will be overcome by applying the proposed technique in the BS, by knowing that the BS has a CSI for all the users. The CSI is evaluated at the receiving end and it responds to the BS by a feedback channel. Consider a proposed technique in the BS within the same cell without applying a signal alignment in the interfering channel matrix. A proposed technique is used to secure the data in every cluster within the same cell and in the neighboring cell. A proposed technique of \(\mathrm{v}^{I,A}\) needs to be designed at the BS as a non-trivial solution in Equation (6). A non-trivial solution will exist if \(\mathrm{M}\geq 2\mathrm{N}\) (L\(-\)1). So, there must be a large number of antennas in the BS. The proposed method will serve as \(\lfloor(M+1)/3\rfloor\) in a multi-cell framework. This indicates that the number of antennas in the BS will be larger than the number of clusters. Therefore, this will reduce the overall throughput. This problem will be overcome by an alignment matrix \(Q^{A}\in\mathbb{C}^{\mathrm{M}\mathrm{S}}\).