# An Overview of Key Technologies in Physical Layer Security
## 3 Secure Multi-Antenna Techniques
### Artificial Noise (AN) Precoding
In the scheme the signal received by [PERSON] and [PERSON] can be shown by  
\[\mathbf{y}_{B}=\mathbf{h}_{B}^{H}\mathbf{w}\mathbf{s}_{a}+\mathbf{g}_{B}^{H} \mathbf{v}\mathbf{s}_{a}+n_{B} \tag{26}\]  
\[\mathbf{y}_{E}=\mathbf{h}_{E}^{H}\mathbf{w}\mathbf{s}_{a}+\mathbf{g}_{E}^{H} \mathbf{v}\mathbf{s}_{a}+n_{E} \tag{27}\]  
Therefore, the secrecy rate is now given by  
\[R=\log_{2}\left(1+\frac{|\mathbf{h}_{B}^{H}\mathbf{w}+\mathbf{g}_{B}^{H} \mathbf{v}|^{2}}{\sigma^{2}}\right)-\log_{2}\left(1+\frac{|\mathbf{h}_{E}^{H} \mathbf{v}+\mathbf{g}_{E}^{H}\mathbf{v}|^{2}}{\sigma^{2}}\right) \tag{28}\]  
The optimization problem in the AN precoding scheme is to find an optimal power allocation method for the artificial noise, which ensures maximum secrecy of the legitimate transmission. A comprehensive summary of several methods proposed in the literature for solving the AN precoding optimization is presented below. The classical AN injection schemes are investigated broadly in the literature, and their application in MIMO systems has been shown as promising to exploit in future wireless networks. In [73], the authors demonstrated an approach capable of guaranteeing secrecy without knowledge of the eavesdropper's CSI. In [73], two schemes were proposed for AN generation in PLS. In the first scheme, they proposed a scheme which was based on MIMO technology, while the second scheme used a single transmitter antenna. For the latter scheme, amplifying relays were used to mimic the effects of multiple antennas. Moreover, in the second scheme the transmitter and the intended receiver both transmit independent AN signals to the helper nodes. The eavesdropper receives differently weighted versions of the AN signals from the transmitter and the receiver. The two transmission schemes proposed in the paper transmit both AN and information-bearing signals together. However, the paper does not necessarily find an optimal power allocation for the transmission of message signals and minimal power allocated to the AN. To tackle the shortfall indicated in [73], researchers [74] proposed an AN-assisted secure MIMO-OFDM system to improve the security of the legitimate transmission and find an optimal power allocation scheme. AN precoding scheme is proposed where [PERSON] divides her power between transmitting a message to [PERSON] and transmitting AN into [PERSON]'s nullspace. Assuming [PERSON] and [PERSON]'s channels are independently faded, [PERSON] will see some of the AN in her range space. The authors determined the minimum power consumption that satisfies the legitimate transmission quality with the largest residual power in generating AN. They use convex optimization solvers to find the optimal solution to this problem. This technique's major strength is that the provided secrecy scales well with SNR, since an increase in SNR at Eve will increase the received AN power along with the message power [23]. AN precoding was also used in [50] to implement security in the physical layer. AN was used as a transmit strategy over [PERSON]'s null space with the intention of improving the secrecy of the [PERSON] channel without affecting its quality. The authors examine three approaches of generating AN. Firstly, the minimum power was used for the information-bearing signal, and the rest of the transmit power was distributed to the AN. Secondly, the power was evenly distributed between the transmit signal and the AN signal in order to maximize ergodic secrecy capacity. Lastly, the AN power was progressively varied in order to understand its effects on the secrecy confidence level. Eve was modeled to use the minimum mean-square error (MMSE) as an optimal receiver structure to maximize the SNR. Eve's capability to compromise the secrecy of the main link was defined as the SNR difference between the intended receiver and the eavesdropper.