arXiv:1709.00906v3 [cs.IT] 28 Feb 2019 Information Detection and Energy Harvesting Trade-off in Multi-User Secure Communication Ali Kariminezhad, Zohaib Hassan Awan, Hendrik Vogt, and Aydin Sezgin Abstract—The secrecy rate region of wiretap interference channels with a multi-antenna passive eavesdropper is studied under receiver energy harvesting constraints. To stay operational in the network, the legitimate receivers demand energy along- side information, which is fulfilled by power transmission and exploiting a power splitting (PS) receiver. Simultaneous wireless information and power transfer (SWIPT) results in a reduction in the secrecy rates due to the legitimate receivers PS for simul- taneous information detection and energy harvesting. For this setup, lower-bounds for secure communication rate are derived without imposing any limitation at the eavesdropper processing. It turns out that in order to obtain the Pareto boundary of the secrecy rate region, smart tuning of the transmit power and receiver PS coefficient is required. Notice that, granting both, i.e., secrecy in communication as well as enabling energy harvesting, result in shrinkages in the reliable communication rate region, which is captured by this optimal tune. Hence, it is of crucial importance to investigate, which of these two services shrinks the rate region more. Interestingly, we observe that by enabling SWIPT, the convexity of the reliable rate region is preserved. However, granting secrecy for the communication results in a non-convex rate region as the interference power increases. I. I NTRODUCTION Secrecy is one of the main concerns in future communica- tion networks involving a plethora of communicating nodes. This includes wireless sensor networks (WSNs) and Internet of Things (IoTs) [1], [2]. Moreover, due to a steadily increasing number of connected devices, the scarce spectrum needs to be shared among multiple communication pairs. These two factors motivate the study of the wiretap interference channel [3]. In this channel, multiple node pairs exchange data simultaneously over a shared spectrum, which in turn induces interference at the receivers. One way to tackle this problem is to treat the undesired signals at the legitimate receivers as noise — popularly known as treating interference as noise (TIN). Despite, the interference is treated as noise for information detection reasons, it can be treated as a energy source for energy harvesting purposes. This way, securing the desired information assuming TIN, the legitimate users demand a particular amount of energy to stay functional during the communication process [4], [5]. For instance, consider a WSN with limited energy supply at the sensors. By deploying energy harvesting receivers, the energy buffer can be charged wirelessly from energy sources, e.g., solar energy, radio frequency (RF) [6]. One aspect of this work is to investigate the concept of RF signal energy harvesting in the A. Kariminezhad, H. Vogt and A. Sezgin are with the Institute of Digital Communication Systems, Ruhr Universität Bochum (RUB), Germany (emails: {ali.kariminezhad, hendrik.vogt, aydin.sezgin}@rub.de). Zohaib Hassan Awan is with the Institute for Theoretical Information Technology, RWTH Aachen, Germany (email: zohaib.awan@ti.rwth-aachen.de). TX 1 TX K Eve. ID EH RX 1 RX K ID EH Data channel Interference channel Wiretap channel Fig. 1: K-user wiretap interference channel with power splitting structure for simultaneous information detection and energy harvest- ing. context of security. Now, the sensors with scarce energy supply face a trade-off in between information detection (ID) and energy harvesting (EH). Considering a single-antenna receiver, simultaneous ID and EH can be achieved by power splitting (PS). Hence, one part of received signal power undergoes the ID chain while the other part passes through the EH circuitry. Utilizing PS receivers, the required energy constraint is fulfilled by appropriate power transmission. This concept is known as simultaneous wireless information and power transmission (SWIPT) [7]–[9]. For a class of multi-user networks, the authors in [10], [11] establish bounds on secure communication region. The secrecy rate region of the model that we study with EH demands is a function of — i) the transmit power, and ii) the receive PS coefficients. Therefore, to establish the secrecy rate region with EH, it is pivotal to study the joint interaction between transmit power, and, receive PS coefficients at the legitimate pairs. Thus, the optimal design of these parameters captures the trade-off between secure communication rates and harvested energies. A. Contribution In this paper, we investigate the secrecy rate region of the wiretap interference channel with EH legitimate users. Char- acterizing the secrecy capacity of this channel is challenging. Thus, we focus our attention to develop secure rate lower- bounds. For both secure communication and energy harvesting purposes, the transmit power, and receive PS coefficients are optimized jointly in order to capture the trade-off between secure rates and energy demands. This optimization problem is a non-convex problem. Interestingly, this problem turns out to be a signomial program (SP), which in this work is approximated by a geometric program (GP). We propose a