# Secure Beamforming in 5G-Based Cognitive Radio Network
## 3 System Model
### Proposed Technique in Cascaded Transmission of MIMO-NOMA Network
Assuming \(g_{pu}^{I,A}\stackrel{{\mbox{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{ \tiny\tinytiny\tiny{\tinytiny{\tinytiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\mboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmboxmbox \tiny{  \tiny{  }}}}}}}}}}}{\rm{=}}\)\(G_{pu}^{\mathrm{L,A}}Q^{\mathrm{A}}\) and \(g_{su}^{I,A}\stackrel{{\mbox{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{}}}}}}}}}}}}{\rm{=}}\)\(G_{su}^{\mathrm{L,A}}Q^{\mathrm{A}}\) in Equation (7), Equation (10) is as follows:  
\[\overline{G}\stackrel{{\mbox{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tiny{ \tiny{\tiny{\tiny{\tiny{\tiny{\tiny{\tinytinytiny}}}}}}}}}}}}}{\rm{=}}\left[g_{\mathrm{pu}}^{ \mathrm{1,A}}\;g_{\mathrm{su}}^{\mathrm{1,A}}\;\ldots\;g_{\mathrm{pu}}^{ \mathrm{1-1,A}}\;g_{\mathrm{su}}^{\mathrm{-1,A}}\;g_{\mathrm{pu}}^{\mathrm{1+1,A}} \;g_{\mathrm{su}}^{\mathrm{1+1,A}}\;\ldots\;g_{\mathrm{pu}}^{\mathrm{L,A}}\;g_{ \mathrm{su}}^{\mathrm{L,A}}\right]^{\mathrm{T}} \tag{10}\]Then, the solution is given as  
\[R_{pu}^{l_{A}}=G_{pu}^{l_{A}}\sum_{m=1}^{L}v^{m,A}+l_{pu}^{l_{A}}\sum_{m=1}^{L}v ^{m,\ B}+w_{pu}^{l_{A}} \tag{3}\]0  
The MMSE method, along with the transmitting ZFBF approach, is spanned to obtain a proposed solution in the Equation (11). The regularization term of \(\beta\) contains a stability in the transmit power and a noise variance [24] which is denoted as \(C_{x}\) and \(C_{y}\). Then, the term \(\beta\) for a cell A is expressed as  
\[R_{pu}^{l_{A}}=G_{pu}^{l_{A}}\sum_{m=1}^{L}v^{m,A}+l_{pu}^{l_{A}}\sum_{m=1}^{L}v ^{m,\ B}+w_{pu}^{l_{A}} \tag{3}\]1  
Assume S be the data symbol that contains a \(\mathrm{s_{pu}^{L,A}}\), \(\mathrm{s_{su}^{L,A}}\) for the cluster I of cell A. Let \(C_{x}\) be the transmit power and is expressed as [26],  
\[R_{pu}^{l_{A}}=G_{pu}^{l_{A}}\sum_{m=1}^{L}v^{m,A}+l_{pu}^{l_{A}}\sum_{m=1}^{L}v ^{m,\ B}+w_{pu}^{l_{A}} \tag{3}\]2  
Then, \(\omega\) be the power allocation coefficient that contains a \(\omega_{\mathrm{pu}^{L,A}}^{\mathrm{L,A}}\), \(\omega_{\mathrm{su}^{L,A}}^{\mathrm{L,A}}\) for the PUs and the SUs and is assumed as \(\omega_{\mathrm{pu}^{L}}^{\mathrm{L,A}}+\omega_{\mathrm{su}^{L,A}}^{\mathrm{L }}=1\). Let I be the number of clusters, \(\odot\) be the Hadamard product, and \(\mathrm{I}_{\mathrm{d_{N}M}}\) be the N\(\times\)xM identity matrix. Equation (13) assumes that the signal source from different positions are uncorrelated. Let \(C_{y}\) be the noise covariance matrix, expressed as  
\[R_{pu}^{l_{A}}=G_{pu}^{l_{A}}\sum_{m=1}^{L}v^{m,A}+l_{pu}^{l_{A}}\sum_{m=1}^{L}v ^{m,\ B}+w_{pu}^{l_{A}} \tag{3}\]3  
where \(\sigma_{\mathrm{w}}^{2}\) is a variance of the thermal noise and is assumed as additive white Gaussian noise (AWGN). The MMSE strikes the balance of obtaining a maximum signal amplification and then reducing the interference. This view that the signal processing complexity will help to obtain a good solution. In the proposed method, the re-iteration of a transmit power \(C_{x}\) has taken place in the MMSE iterative solutions [26]. The iteration is declared through a data symbol. \[R_{pu}^{l_{A}}=G_{pu}^{l_{A}}\sum_{m=1}^{L}v^{m,A}+l_{pu}^{l_{A}}\sum_{m=1}^{L}v ^{m,\ B}+w_{pu}^{l_{A}} \tag{3}\]4  
The iteration has been terminated by the NMSE solutions and is expressed as [26]  
\[R_{pu}^{l_{A}}=G_{pu}^{l_{A}}\sum_{m=1}^{L}v^{m,A}+l_{pu}^{l_{A}}\sum_{m=1}^{L}v ^{m,\ B}+w_{pu}^{l_{A}} \tag{3}\]5  
So, instead of the Equation (13), we apply an iterated transmitted power [26] as shown in the above Equation (16) for the better MMSE solutions. Therefore, the proposed technique obtains an enhanced solution compared with the existing method.