# Securing Relay Networks with Artificial Noise: An Error Performance-Based Approach +
###### Abstract  
We apply the concept of artificial and controlled interference in a two-hop relay network with an untrusted relay, aiming at enhancing the wireless communication secrecy between the source and the destination node. In order to shield the square quadrature amplitude-modulated (QAM) signals transmitted from the source node to the relay, the destination node designs and transmits artificial noise (AN) symbols to jam the relay reception. The objective of our considered AN design is to degrade the error probability performance at the untrusted relay, for different types of channel state information (CSI) at the destination. By considering perfect knowledge of the instantaneous CSI of the source-to-relay and relay-to-destination links, we first present an analytical expression for the symbol error rate (SER) performance at the relay. Based on the assumption of an average power constraint at the destination node, we then derive the optimal phase and power distribution of the AN that maximizes the SER at the relay. Furthermore, we obtain the optimal AN design for the case where only statistical CSI is available at the destination node. For both cases, our study reveals that the Gaussian distribution is generally not optimal to generate AN symbols. The presented AN design takes into account practical parameters for the communication links, such as QAM signaling and maximum likelihood decoding. physical layer secrecy; untrusted relay networks; Rayleigh fading; artificial noise jamming; error maximization; KKT conditions; square quadrature amplitude modulation; symbol error rate 2017 19 384 10.3390/e19080384 10.  
has been extensively studied for various channel models and network setups, such as single-hop wiretap channels [6; 7; 8; 9; 10; 11], multi-user networks [12; 13], and relay networks [14; 15; 16; 17; 18]. In relay networks, secrecy is an important issue even without the presence of external eavesdroppers. Despite the fact that the relay accedes to the request from the source to assist in delivering the message to the destination, it is often desirable to keep the message confidential from the relay [19; 20; 21; 22; 23]. First proposed in [19], the untrusted relay scenario has drawn considerable attention, since it finds diverse and important applications in modern communication systems. For example, in heterogeneous networks, the relay terminal may have a lower secrecy clearance than the source and destination pair [21; 22]. Therefore, the relay can be partly malicious in the sense that it still functions in compliance with the relaying protocol, whilst it leaks secret information. Another application is the multiple-level access control in wireless sensor networks, where sensors have different authorizations and sensitivities depending on their roles (e.g., master and slave sensors) and type of collected data [24; 25; 26; 27]. In such setups, the relaying node might be only allowed to help forwarding messages from one terminal to another, as not all terminals have direct connections to all nodes in the sensor network. For instance, in a secure sensor network at an airport, terminals with low secrecy levels must have restricted data access, whereas a few terminals at a much higher secrecy level are allowed to access all the data [25]. To shield the messages from the untrusted relay and enhance the secrecy of the wireless communication between the source and destination, one popular scheme at the physical layer is to introduce controlled artificial noise (AN) to efficiently jam the signal reception at the relay. This technique has recently been studied from an information-theoretic perspective, such as secrecy rate and secrecy outage probability, see e.g., [28; 29; 30; 31; 32]. However, such metrics are in general valid for ideal communication assumptions of continuous input messages and random encoding schemes with asymptotically large block lengths.