# An Overview of Key Technologies in Physical Layer Security
## 4 Challenges and Promising PLS Solutions
### Promising PLS Solutions
#### 4.2.6 PLS in Satellite Communication  
Satellite communication is being more incorporated into current terrestrial wireless communication networks mainly because of its features, which include wide-area coverage and high bandwidth. Some noteworthy applications of satellite communication include, but are not limited to, military operations, TV broadcast, and internet access. However, their broadcast nature and ability to provide wide coverage area make them more vulnerable to eavesdropping. Traditionally, security in satellite communication is implemented in the upper layers of the protocol stack by means of encryption. PLS has been identified as an alternative to augment the current cryptography security measures [21]. We demonstrate a PLS concept in satellite using a system model shown in Figure 22 and derive the optimization problem.  
Figure 21: Power and illumination distribution vs distance.  
Suppose that the satellite transmits the signal \(s_{i}\) intended for the \(i\)th legitimate user with average power \(E[|s_{i}|^{2}]=1\). The transmitted signal has a weighted beamforming vector given by \(\mathbf{w}_{i}\in\mathbb{C}^{N\times 1}\). Therefore, the overall transmitted signal is given by  
\[\mathbf{x}=\sum_{i=1}^{M}\mathbf{w}_{i}s_{i} \tag{40}\]  
The signals received by the \(i\)th legitimate and \(i\)th eavesdropper are given by Equations (41) and (42), respectively.  
\[y_{user-i}=\mathbf{h}_{i}^{H}\mathbf{w}_{i}s_{i}+\sum_{m\
eq i}^{M}\mathbf{h}_ {i}^{H}\mathbf{w}_{m}s_{m}+n_{i} \tag{41}\]  
\[y_{e-i}=\mathbf{g}_{i}^{H}\mathbf{w}_{i}s_{i}+\sum_{m\
eq i}^{M}\mathbf{g}_{i} ^{H}\mathbf{w}_{m}s_{m}+n_{e-i} \tag{42}\]  
where \(\mathbf{h}_{i}\in\mathbb{C}^{N\times 1}\) denotes the channel gain vector between the \(i\)th intended user and the satellite, \(\mathbf{g}_{i}\in\mathbb{C}^{N\times 1}\) denotes the channel gain vector between the \(i\)th eavesdropper and the satellite, and \(n_{i}\) and \(n_{e-i}\) are assumed to be zero-mean AWG noise of the \(i\)th intended user and the \(i\)th eavesdropper, respectively. The achievable secrecy rate of the \(i\)th intended user is given by  
\[R_{s}=\log_{2}\left(1+\frac{|\mathbf{h}_{i}^{H}\mathbf{w}_{i}|^{2}}{\sum_{m \
eq i}^{M}|\mathbf{h}_{i}^{H}\mathbf{w}_{m}|^{2}+\sigma_{i}^{2}}\right)- \log_{2}\left(1+\frac{|\mathbf{g}_{i}^{H}\mathbf{w}_{i}|^{2}}{\sum_{m\
eq i}^ {M}|\mathbf{g}_{i}^{H}\mathbf{w}_{m}|^{2}+\sigma_{e-i}^{2}}\right) \tag{43}\]  
Figure 22: Multi-beam satellite communication network [114].  
The typical optimization problem of interest is to maximize the achievable secrecy rate and can be written mathematically as follows:  
\[\begin{split}\underset{\mathbf{w}_{i}}{\text{min}}& R_{s}\\ \text{s.t.}&\sum_{m=1}^{M}||\mathbf{w}_{i}||^{2}\leq P _{T}\end{split} \tag{44}\]  
where \(P_{T}\) is the maximum transmit power of the satellite. The authors in [115] studied the problem of minimizing the transmit power on a multi-beam satellite while fulfilling the minimum per user secrecy rate. They further proposed an iterative algorithm to jointly optimize the transmission power and the beamforming vector by completely eliminating the co-channel interference and perfectly nulling out the received signal at the eavesdropper. [PERSON] et al. in [116] also used PLS to address the issue of confidentiality in bidirectional satellite communication based on network coding. They designed the optimal beamforming weight vector which maximizes the sum secrecy rate by using semi-definite programming.