# An Overview of Key Technologies in Physical Layer Security
## 3 Secure Multi-Antenna Techniques
### Space-Time Coding (STC)  
In 1998, [PERSON] proposed a space-time block code (STBC) to achieve transmitter diversity [85]. Space-time coding is based on the Alamouti scheme. In the conventional transmit schemes, diversity techniques were applied at the receiver using algorithms such as the MRC. These techniques require knowledge of the channel between the transmitter and the receiver to derive the optimal beamforming weights. However, [PERSON] showed that it is possible to transmit data using multiple antennas and perform separation at the receiver using a single receiving antenna, which gives the same diversity gains. To provide diversity using the Alamouti scheme, the time and space blocks are used to encode the information signal. The Alamouti space-time encoder takes a block of two modulated symbols to create an encoding matrix denoted by  
\[\mathbf{C}=\quad \begin{bmatrix}\mathbf{s}_{1}&-\mathbf{s}_{2}^{*}\\ \mathbf{s}_{2}&-\mathbf{s}_{1}^{*}\end{bmatrix} , \tag{32}\]  
where \(s_{1}\) and \(s_{2}\) are the modulated symbols mapped to two transmit antennas in two transmit time slots [86]. The columns of \(\mathbf{C}\) represent timeslots, and the rows represent different transmit antennas. Studies by [87; 88] showed that STBC may be employed to provide secure communication for space-time systems while lowering the eavesdropper's order of diversity. A technique depicted in Figure 15 to achieve a secure STBC without the need to estimate CSI at the transmitter was proposed in [87]. The proposed technique uses mutual received signal strength indicator measurements to generate a pseudo-random sequence used to secure communication. In this model, at each transmit antenna,  
Figure 14: Secrecy with cooperative jamming. random phase rotations \(\theta_{1}\) and \(\theta_{2}\) are applied to the symbols. Each phase shift is applied for one code duration. For a single codeword, the transmitter encodes source information \(s_{1}\) and \(s_{2}\) as  
\[\mathbf{X}=\quad \begin{bmatrix}\mathbf{s}_{1}e^{j\theta_{1}}&\mathbf{s}_{2}^{*} e^{j\theta_{2}}\\ -\mathbf{s}_{2}e^{j\theta_{1}}&\mathbf{s}_{1}^{*}e^{j\theta_{2}}\end{bmatrix}  \tag{33}\]  
Therefore, [PERSON] receives the signal given by  
\[ \begin{split}\mathbf{z}&=\mathbf{Xh}+\mathbf{n}\\ \mathbf{z}&=\mathbf{H}^{+}(\theta_{1},\theta_{2})\mathbf{s}+ \mathbf{\tilde{n}}\\ \left[\begin{matrix}\mathbf{z}_{1}\\ -\mathbf{z}_{2}^{*}\end{matrix}\right]&=\begin{bmatrix}\mathbf{h}_{1}e^{j \theta_{1}}&\mathbf{h}_{2}^{*}e^{j\theta_{2}}\\ -\mathbf{h}_{2}e^{j\theta_{1}}&\mathbf{h}_{1}^{*}e^{j\theta_{2}}\end{bmatrix} \begin{bmatrix}\mathbf{s}_{1}\\ \mathbf{s}_{2}\end{bmatrix}+\begin{bmatrix}\mathbf{n}_{1}\\ -\mathbf{n}_{2}^{*}\end{bmatrix}\end{split}  \tag{34}\]  
Using the MRC algorithm, the source information can be estimated by  
\[\mathbf{\tilde{s}}=\mathbf{H}^{+}(\theta_{1},\theta_{2})\mathbf{z} \tag{35}\]  
[PERSON]'s received signal is given by \(y\), which can be also be decomposed to \(\mathbf{\hat{y}}\) as  
\[ \begin{split}\mathbf{y}&=\mathbf{Xg}+\mathbf{e}\\ \mathbf{\tilde{y}}&=\mathbf{G}^{+}(\theta_{1},\theta_{2})s+ \mathbf{\tilde{e}}\end{split}  \tag{36}\]  
where \(\mathbf{H}^{+}\) and \(\mathbf{G}^{+}\) are the pseudo-inverse of \(\mathbf{H}\) and \(\mathbf{G}\), respectively. The transmitter manipulates the transmitted symbols by generating and applying the maximum number of phase rotations so that the eavesdropper is completely denied access to the source information. The strength of this technique is that improved security is achieved without the knowledge of the CSI, unlike in the preceding security schemes which assumes that the CSI is available. However, it was shown in [88] that the security of the transmitted signal is compromised if the eavesdropper can obtain one of the space angles and is in close proximity to [PERSON]. To avoid this, the authors proposed a technique that was able to achieve zero diversity for the eavesdropper even under enhanced receive diversity. This was achieved through signal and space rotations.