# Securing Relay Networks with Artificial Noise: An Error Performance-Based Approach +
###### Abstract
In order to take discrete modulation alphabets and finite block lengths into consideration, other secrecy performance metrics have also been proposed, such as bit error rate [33; 34]. The observation that in modern wireless communication systems square quadrature amplitude modulation (QAM) is widely used motivates us to address the problem of how to optimally apply AN to enhance the physical layer secrecy in an untrusted relay network. The symbol error rate (SER) of the demodulated signal at the relay is used as a performance metric in this paper. In this work, we consider the communication between a pair of source and destination terminals, where a direct link is absent, and therefore, a half-duplex relay terminal is utilized to assist the communication [35; 36]. To forward the signal from the source to the destination, the relay employs the non-coherent amplify-and-forward (AF) protocol [37], which is considered as the most promising solution for current and future communication systems, since it offers a reasonable tradeoff between the benefits and implementation costs [38]. As a result, these relays have already been incorporated in the Universal Mobile Telecommunications System (UMTS) and Release 8 of Long-Term Evolution (LTE) in the form of repeaters [35]. For the AF protocol, we make the common assumption that the destination has the instantaneous channel state information (CSI) of the relay-to-destination link and the aggregate source-to-relay-to-destination link [39; 40]. Consequently, the destination can obtain the CSI of the relay-to-destination link, which is however not available at the relay. To secure messages against the relay, we propose a novel AN scheme, where the destination designs and broadcasts AN symbols to the relay simultaneously with the transmission of the symbols from the source. It has been shown that a positive secrecy rate can be achievable in this AN-assisted untrusted relay network [41]. For this setup and with the knowledge of instantaneous CSI as assumed in Section 3, we first investigate the problem of how to optimally design the AN to maximize the SER of QAM signals at the relay. Note that the requirement of the instantaneous CSI might be strong in some practical systems. To reduce the requirement, we then investigate the AN design based on statistical CSI in Section 4, i.e., the channel variances. For fading channels, an important performance metric is the average SER (ASER), which quantifies the average decoding error performance over fading channels. Interestingly, for both CSI schemes, our study shows that it is not optimal to generate AN from a Gaussian distribution. For example, based on instantaneous CSI, we note that a QAM or a rotated QAM AN generating method maximizes the SER at the relay. The results in this paper can be used as benchmarks for future analyses of AN-based techniques. The main contributions of this work can be summarized as follows:  
* By assuming that instantaneous CSI is available at the untrusted relay and the destination, upon receiving both of the QAM symbols from the source and the AN from the destination, an exact expression for the SER at the relay when decoding the QAM symbols is first derived. Under an average power constraint, this expression is then utilized to obtain the phase and power distribution of the AN symbols to maximize the SER performance at the relay. * For the case where only statistical CSI is available, we first derive an exact expression for the ASER performance at the relay. Next, the optimal power distribution of the AN symbols that maximizes the ASER performance at the relay is determined. Numerical and simulation results demonstrate that the proposed optimal AN designs guarantee significant error rate performance enhancement compared with conventional AN designs, such as Gaussian distribution. Furthermore, the AN-based scheme studied in this paper is formulated according to the framework of current cellular standards such as LTE/LTE-Advanced of 4G and the next major phase of mobile telecommunications standard 5G [3; 36].