IEEE COMMUNICATIONS LETTERS, VOL. XX, NO. XX, XX 2016 1 Outage Performance of Underlay Multi-hop Cognitive Relay Networks with Energy Harvesting Chi Xu, Meng Zheng, Member, IEEE, Wei Liang, Member, IEEE, Haibin Yu, Member, IEEE and Ying-Chang Liang, Fellow, IEEE Abstract—This letter studies the outage performance of multi- hop cognitive relay networks with energy harvesting in underlay paradigms, wherein the secondary users are powered by a dedi- cated power beacon (PB) and their transmit powers are subject to the harvested energy from PB and the interference constraint from the primary user. We derive the exact outage probability for Rayleigh block fading and prove that the outage probability is monotonically decreasing with respect to the transmit power of PB. Furthermore, we derive the asymptotic outage probability to study the outage saturation phenomenon and propose an iterative algorithm that jointly optimizes the transmit power of PB and the harvest-to-transmit ratio to approximate the minimum outage probability. Simulation results validate the theoretical results. Index Terms—multi-hop, underlay, cognitive relay networks, energy harvesting, outage probability. I. I NTRODUCTION A S energy harvesting can virtually provide perpetual ener- gy supply for energy-constraint networks without manual battery recharging or replacement, energy harvesting cognitive relay networks (EH-CRNs) have recently attracted a great deal of attention. In interweave paradigms, the secondary users (SUs) first harvest energy from ambient energy sources [1] or the RF signals of active primary users (PUs) [2], [3] and then opportunistically access the licensed channels when PUs are detected as inactive. In overlay paradigms, SUs harvest energy from PUs and transmit data for both PUs and SUs provided that there are excellent cooperations between PUs and SUs [4]. In underlay paradigms, SUs harvest energy from PUs [5], [6] or other SUs [7], and transmit as long as the interference to PUs is no larger than a prescribed threshold. More recently, overlay and underlay cognitive wireless powered networks are analyzed and compared in [8]. Moreover, a hybrid interweave and underlay cognitive radio is studied in [9]. Different from the above works, this letter introduces the power beacon (PB) [10] to power SUs for the multi-hop trans- mission in underlay EH-CRNs, since PB can efficiently power SUs with low deployment cost while achieving decoupled si- multaneous wireless information and power transfer (SWIPT) without any backhaul links [11], [12]. Specifically, SUs first harvest energy from the RF signals of a dedicated PB on the common control channel, and then transmit concurrently with Manuscript received December 11, 2015. The associate editor coordinating the review of this letter and approving it for publication was Z. Hadzi-Velkov. This paper is supported by the National Natural Science Foundation of China under Grant 61233007 and 61304263. C. Xu, M. Zheng, W. Liang and H. Yu are with the Key Laboratory of Networked Control Systems, Shenyang Institute of Automation, Chinese A- cademy of Sciences, Shenyang 110016, China (e-mail: {xuchi, zhengmeng 6, weiliang, yhb}@sia.cn). C. Xu is also with University of Chinese Academy of Sciences, Beijing 100049, China. Y.-C. Liang is with the University of Electronic Science and Technology of China, Chengdu 611731, China, and also with the Institute for Infocomm Research, A * STAR, Singapore 138632 (e-mail: liangyc@ieee.org) Digital Object Identifier XX.XXXX/LCOMM.2016.XX.XXXXXX Multi-hop EH-CRN Data transmission links, gDk Energy harvesting links, gEk Interference links, gIk SU1 SU2 SUk SUK SUK+1 PB PU Fig. 1. System model. PU over the same licensed channel using the harvested energy. The transmit powers of SUs are set by jointly considering the harvested energy from PB and the interference constraint from PU, which can maximize the transmit powers under the condition that PU is sufficiently protected. We derive the closed-form outage probability for the underlay multi-hop EH- CRNs and provide insights into the effect of energy conversion efficiency, harvest-to-transmit ratio (HTR), number of hops, transmit power of PB and interference constraint from PU on the outage performance. The main contributions of this letter can be summarized as follows: (i) we derive exact and asymptotic outage proba- bilities for multi-hop EH-CRNs over Rayleigh block fading; (ii) we prove that the outage probability is monotonically decreasing with respect to PB’s transmit power and further investigate the outage saturation phenomenon; (iii) we propose an iterative algorithm to obtain a near-optimal outage proba- bility by jointly optimizing PB’s transmit power and HTR. II. SYSTEM MODEL As shown in Fig. 1, we consider a multi-hop EH-CRN, whose typical application is sensor network, with K + 1 SUs (e.g., sensors) in an underlay paradigm. The PU transmitter is far away from SUs and does not impose any interference on SUs [7], while the PU receiver must be sufficiently protected by controlling the transmit powers of SUs. Each SU is equipped with an energy harvester and operates in half-duplex mode with which SU can only transmit, receive or harvest. All SUs are powered by a dedicated PB and perform multi- hop transmission to lower each hop’s transmit power. With the time division multiple access mechanism, the source SU 1 transmits data to the destination SU K+1 serially via immediate decode-and-forward relays. By time switching [13], the whole communication within a block of time T is divided into two phases, namely, energy harvesting and data transmission. In the energy harvesting phase with duration τ (0 < τ < T ), all SUs harvest energy from the RF signals of PB on the common control channel, wherein the noise energy is neg- ligible compared to the transmit power of PB P t . At the end of this phase, the harvested energy stored in the capacitor of SU k (k = 1, ..., K + 1) is ξ k τ P t d -α Ek g Ek , where 0 ≤ ξ k ≤ 1 is the energy conversion efficiency depending on the design of