# Securing Relay Networks with Artificial Noise: An Error Performance-Based Approach +
## 6 Conclusions  
In this paper, we have investigated physical layer secrecy for a two-hop single-antenna relay channel, where one source aims to transmit to one destination assisted by one untrusted relay. In particular, the source adopts a squared \(M\)-square quadrature amplitude modulated (\(M\)-QAM) modulation scheme, which is widely used in current cellular standards. A novel artificial noise (AN) scheme was proposed to achieve physical layer secrecy to protect the \(M\)-QAM signals from the source to the destination. The objective was to design AN symbols generated by the destination node that degrades the error probability performance at the untrusted relay by maximizing its achieved symbol error rate (SER) performance. For the case where perfect instantaneous channel state information (CSI) of the source-to-relay and relay-to-destination links is available at the destination, we have derived exact analytical SER expressions for the relay and studied the optimal design of the AN signal to maximize the corresponding SER. It was shown that the Gaussian distribution, which is frequently used in the context of AN [7; 49; 50], is not optimal in general. The optimal AN for the considered relay channel was found to be QAM or rotated QAM phase selection. Moreover, compared with the Gaussian AN, our optimal AN distribution can yield remarkably higher SER at the relay. For the case where the AN design is based on the long-term CSI of the source-to-relay and relay-to-destination links, we presented the corresponding average SER (ASER) expression at the relay, and the optimal AN distribution to maximize the ASER performance was determined accordingly. Interestingly, it was shown that the phase of the AN does not affect the ASER performance at the relay. Regarding the design of the power distribution of the AN, the obtained power distribution was shown to deliver improved ASER performance compared to various other power distributions, such as the uniform and exponential distributions. Finally, we mention that there are many directions for further extensions of this work. For example, when perfect CSI of the source-to-relay and relay-to-destination links is not available, opportunistic scheduling with low-rate CSI feedback might be applied [51]. Other interesting directions include the AN design for imperfect CSI knowledge as well as for the multiple-antenna relay channel and two-way communication networks.  
**Acknowledgments:** [PERSON], [PERSON], and [PERSON] acknowledge the financial support of the Seventh Framework Programme for Research of the European Commission under grant number: ADEL-619647. This work was partially performed within the LOEWE Priority Program Cocoon ([[http://www.cocoon.tu-darmstadt.de](http://www.cocoon.tu-darmstadt.de)]([http://www.cocoon.tu-darmstadt.de](http://www.cocoon.tu-darmstadt.de))) supported by the LOEWE research initiative of the state of Hesse/Germany.  
**Author Contributions:** [PERSON] and [PERSON] developed the work in discussion with [PERSON] and [PERSON]. [PERSON] wrote the paper with comments from [PERSON] and [PERSON]. All authors have read and approved the final manuscript.  
**Conflicts of Interest:** The authors declare no conflict of interest.