AbdElaziz_ICC_17_NOMAWPCN.rar_non orthogonal

<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/62550ee8b744eb386fd87d8e/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62550ee8b744eb386fd87d8e/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Non-Orthogonal Multiple Access Schemes in</div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">Wireless Powered Communication Networks</div><div class="t m0 x3 h3 y3 ff1 fs1 fc0 sc0 ls0 ws0">Mohamed A. Abd-Elmagid</div><div class="t m0 x4 h4 y4 ff2 fs2 fc0 sc0 ls0 ws0">∗</div><div class="t m0 x5 h3 y3 ff1 fs1 fc0 sc0 ls0 ws0">, Alessandro Biason</div><div class="t m0 x6 h4 y4 ff2 fs2 fc0 sc0 ls0 ws0">†</div><div class="t m0 x7 h3 y3 ff1 fs1 fc0 sc0 ls0 ws0">, Tamer ElBatt</div><div class="t m0 x8 h4 y4 ff2 fs2 fc0 sc0 ls1 ws0">∗‡</div><div class="t m0 x9 h3 y3 ff1 fs1 fc0 sc0 ls0 ws0">, Karim G. Seddik</div><div class="t m0 xa h4 y4 ff2 fs2 fc0 sc0 ls0 ws0">§</div><div class="t m0 xb h3 y3 ff1 fs1 fc0 sc0 ls0 ws0">and Michele Zorzi</div><div class="t m0 xc h4 y4 ff2 fs2 fc0 sc0 ls0 ws0">†</div><div class="t m0 xd h4 y5 ff2 fs2 fc0 sc0 ls0 ws0">∗</div><div class="t m0 xe h5 y6 ff1 fs3 fc0 sc0 ls0 ws0">Wireless Intelligent Networks Center (WINC), Nile University, Giza, Egypt</div><div class="t m0 xf h4 y7 ff2 fs2 fc0 sc0 ls0 ws0">†</div><div class="t m0 x10 h5 y8 ff1 fs3 fc0 sc0 ls0 ws0">Department of Information Engineering, University of Padova - via Gradenigo 6b, 35131 Padova, Italy</div><div class="t m0 x11 h4 y9 ff2 fs2 fc0 sc0 ls0 ws0">‡</div><div class="t m0 x12 h5 ya ff1 fs3 fc0 sc0 ls0 ws0">Dept. of EECE, Faculty of Engineering, Cairo University, Giza, Egypt</div><div class="t m0 x13 h4 yb ff2 fs2 fc0 sc0 ls0 ws0">§</div><div class="t m0 x14 h5 yc ff1 fs3 fc0 sc0 ls0 ws0">Electronics and Communications Engineering Department, American University in Cairo, AUC Avenue, New Cairo 11835, Egypt</div><div class="t m0 x15 h5 yd ff1 fs3 fc0 sc0 ls0 ws0">email: m.abdelaziz@nu.edu.eg, biasonal@dei.unipd.it, telbatt@ieee.org, kseddik@aucegypt.edu, zorzi@dei.unipd.it</div><div class="t m0 x16 h6 ye ff3 fs3 fc0 sc0 ls0 ws0">Abstract—We characterize time and power allocations to</div><div class="t m0 x17 h7 yf ff4 fs3 fc0 sc0 ls0 ws0">optimize the sum-throughput of a Wireless Powered Communi-</div><div class="t m0 x17 h7 y10 ff4 fs3 fc0 sc0 ls0 ws0">cation Network (WPCN) with Non-Orthogonal Multiple Access</div><div class="t m0 x17 h7 y11 ff4 fs3 fc0 sc0 ls0 ws0">(NOMA). In our setup, an Energy Rich (ER) source broadcasts</div><div class="t m0 x17 h7 y12 ff4 fs3 fc0 sc0 ls0 ws0">wireless energy to several devices, which use it to simultaneously</div><div class="t m0 x17 h7 y13 ff4 fs3 fc0 sc0 ls0 ws0">transmit data to an Access Point (AP) on the uplink. Differently</div><div class="t m0 x17 h7 y14 ff4 fs3 fc0 sc0 ls0 ws0">from most prior works, in this paper we consider a generic</div><div class="t m0 x17 h7 y15 ff4 fs3 fc0 sc0 ls0 ws0">scenario, in which the ER and AP do not coincide, i.e., two</div><div class="t m0 x17 h7 y16 ff4 fs3 fc0 sc0 ls0 ws0">separate entities. We study two NOMA decoding schemes, namely</div><div class="t m0 x17 h7 y17 ff4 fs3 fc0 sc0 ls0 ws0">Low Complexity Decoding (LCD) and Successive Interference</div><div class="t m0 x17 h7 y18 ff4 fs3 fc0 sc0 ls0 ws0">Cancellation Decoding (SICD). For each scheme, we formulate</div><div class="t m0 x17 h7 y19 ff4 fs3 fc0 sc0 ls0 ws0">a sum-throughput optimization problem over a ﬁnite horizon.</div><div class="t m0 x17 h7 y1a ff4 fs3 fc0 sc0 ls0 ws0">Despite the complexity of the LCD optimization problem, at-</div><div class="t m0 x17 h7 y1b ff4 fs3 fc0 sc0 ls0 ws0">tributed to its non-convexity, we recast it into a series of geometric</div><div class="t m0 x17 h7 y1c ff4 fs3 fc0 sc0 ls0 ws0">programs. On the other hand, we establish the convexity of</div><div class="t m0 x17 h7 y1d ff4 fs3 fc0 sc0 ls0 ws0">the SICD optimization problem and propose an algorithm to</div><div class="t m0 x17 h7 y1e ff4 fs3 fc0 sc0 ls0 ws0">ﬁnd its optimal solution. Our numerical results demonstrate</div><div class="t m0 x17 h7 y1f ff4 fs3 fc0 sc0 ls0 ws0">the importance of using successive interference cancellation in</div><div class="t m0 x17 h7 y20 ff4 fs3 fc0 sc0 ls0 ws0">WPCNs with NOMA, and show how the energy should be</div><div class="t m0 x17 h7 y21 ff4 fs3 fc0 sc0 ls0 ws0">distributed as a function of the system parameters.</div><div class="t m0 x18 h8 y22 ff1 fs4 fc0 sc0 ls2 ws0">I. INTRODUCTION</div><div class="t m0 x16 h8 y23 ff1 fs4 fc0 sc0 ls0 ws0">In the past few years, there has been rapidly growing</div><div class="t m0 x17 h8 y24 ff1 fs4 fc0 sc0 ls0 ws0">interest in developing new strategies and technologies for</div><div class="t m0 x17 h8 y25 ff1 fs4 fc0 sc0 ls0 ws0">prolonging the lifetime of mobile devices. Among a variety</div><div class="t m0 x17 h8 y26 ff1 fs4 fc0 sc0 ls0 ws0">of technologies, Energy Transfer (ET) has recently emerged</div><div class="t m0 x17 h8 y27 ff1 fs4 fc0 sc0 ls0 ws0">as a promising solution. Although ET can be considered as</div><div class="t m0 x17 h8 y28 ff1 fs4 fc0 sc0 ls0 ws0">a new resource for the mobile nodes, it also adds a layer of</div><div class="t m0 x17 h8 y29 ff1 fs4 fc0 sc0 ls0 ws0">complexity to the system design and optimization. The goal of</div><div class="t m0 x17 h8 y2a ff1 fs4 fc0 sc0 ls0 ws0">this paper is to study a particular application of ET, and derive</div><div class="t m0 x17 h8 y2b ff1 fs4 fc0 sc0 ls0 ws0">the optimal strategies to maximize the network throughput.</div><div class="t m0 x16 h8 y2c ff1 fs4 fc0 sc0 ls0 ws0">The concept of energy transfer has been analyzed in different</div><div class="t m0 x17 h8 y2d ff1 fs4 fc0 sc0 ls0 ws0">ﬁelds. For example, in the energy cooperation paradigm [1]–</div><div class="t m0 x17 h8 y2e ff1 fs4 fc0 sc0 ls0 ws0">[3], different devices transfer energy among themselves to</div><div class="t m0 x17 h8 y2f ff1 fs4 fc0 sc0 ls0 ws0">equalize the energy level of the network and improve the over-</div><div class="t m0 x17 h8 y30 ff1 fs4 fc0 sc0 ls0 ws0">all performance. In addition, with the Simultaneous Wireless</div><div class="t m0 x17 h8 y31 ff1 fs4 fc0 sc0 ls0 ws0">Information and Power Transfer (SWIPT) schemes, it became</div><div class="t m0 x17 h8 y32 ff1 fs4 fc0 sc0 ls0 ws0">possible to send a signal carrying both information and energy</div><div class="t m0 x17 h8 y33 ff1 fs4 fc0 sc0 ls0 ws0">simultaneously [4]–[7]. SWIPT was ﬁrst studied from an</div><div class="t m0 x17 h8 y34 ff1 fs4 fc0 sc0 ls0 ws0">information-theoretic perspective in [4], [5]. The fundamental</div><div class="t m0 x17 h8 y35 ff1 fs4 fc0 sc0 ls0 ws0">trade-off between simultaneously transmitting information and</div><div class="t m0 x17 h8 y36 ff1 fs4 fc0 sc0 ls0 ws0">harvesting energy is studied for narrowband noisy channels</div><div class="t m0 x17 h8 y37 ff1 fs4 fc0 sc0 ls0 ws0">in [4] and for frequency-selective channels in [5]. Afterwards,</div><div class="t m0 x17 h8 y38 ff1 fs4 fc0 sc0 ls0 ws0">from a communication-theoretic perspective, [6] character-</div><div class="t m0 x17 h8 y39 ff1 fs4 fc0 sc0 ls0 ws0">ized the fundamental trade-off between transmitting energy</div><div class="t m0 x17 h8 y3a ff1 fs4 fc0 sc0 ls0 ws0">and transmitting information over a point-to-point noisy link.</div><div class="t m0 x19 h8 y3b ff1 fs4 fc0 sc0 ls0 ws0">Since modern energy harvesting circuits are unable to harvest</div><div class="t m0 x19 h8 y3c ff1 fs4 fc0 sc0 ls0 ws0">energy and decode information simultaneously, [7] proposed</div><div class="t m0 x19 h8 y3d ff1 fs4 fc0 sc0 ls0 ws0">two practical receiver designs, namely, time switching and</div><div class="t m0 x19 h8 y3e ff1 fs4 fc0 sc0 ls0 ws0">power splitting. Under the time switching setting, the receiving</div><div class="t m0 x19 h8 y3f ff1 fs4 fc0 sc0 ls0 ws0">antenna periodically switches between energy reception and</div><div class="t m0 x19 h8 y40 ff1 fs4 fc0 sc0 ls0 ws0">information decoding phases. Instead, for the power splitting</div><div class="t m0 x19 h8 y41 ff1 fs4 fc0 sc0 ls0 ws0">scheme, the received signal is split into two streams with</div><div class="t m0 x19 h8 y42 ff1 fs4 fc0 sc0 ls0 ws0">different power levels; one is sent to the energy harvesting</div><div class="t m0 x19 h8 y43 ff1 fs4 fc0 sc0 ls0 ws0">circuitry and the other to the information decoder.</div><div class="t m0 x1a h8 y44 ff1 fs4 fc0 sc0 ls0 ws0">Wireless Powered Communication Networks (WPCNs), a</div><div class="t m0 x19 h8 y45 ff1 fs4 fc0 sc0 ls0 ws0">newly emerging type of wireless networks, has recently at-</div><div class="t m0 x19 h8 y46 ff1 fs4 fc0 sc0 ls0 ws0">tracted considerable attention in the literature [8]–[14]. In</div><div class="t m0 x19 h8 y47 ff1 fs4 fc0 sc0 ls0 ws0">a WPCN, the devices ﬁrst harvest wireless energy from a</div><div class="t m0 x19 h8 y48 ff1 fs4 fc0 sc0 ls0 ws0">dedicated Energy Rich (ER) source, and then use it to uplink</div><div class="t m0 x19 h8 y49 ff1 fs4 fc0 sc0 ls0 ws0">data to the Access Point (AP). [8] assumed that ER and</div><div class="t m0 x19 h8 y4a ff1 fs4 fc0 sc0 ls0 ws0">AP coincide and characterized the optimal time allocations</div><div class="t m0 x19 h8 y4b ff1 fs4 fc0 sc0 ls0 ws0">to achieve the maximum sum-throughput and the max-min</div><div class="t m0 x19 h8 y4c ff1 fs4 fc0 sc0 ls0 ws0">throughput. Although in a large body of the literature the ER</div><div class="t m0 x19 h8 y4d ff1 fs4 fc0 sc0 ls0 ws0">and AP coincide, in this paper we consider them as separate</div><div class="t m0 x19 h8 y4e ff1 fs4 fc0 sc0 ls0 ws0">entities to accommodate a more general setting. [9] exploited</div><div class="t m0 x19 h8 y4f ff1 fs4 fc0 sc0 ls0 ws0">a data-cooperation technique to tackle the doubly near-far</div><div class="t m0 x19 h8 y50 ff1 fs4 fc0 sc0 ls0 ws0">phenomenon that leads to unfair rate allocation among different</div><div class="t m0 x19 h8 y51 ff1 fs4 fc0 sc0 ls0 ws0">users, as observed in [8]. However, this technique is suitable</div><div class="t m0 x19 h8 y52 ff1 fs4 fc0 sc0 ls0 ws0">only for a smaller set of scenarios in which the terminal devices</div><div class="t m0 x19 h8 y53 ff1 fs4 fc0 sc0 ls0 ws0">are closely placed. Moreover, it leads to a higher computational</div><div class="t m0 x19 h8 y54 ff1 fs4 fc0 sc0 ls0 ws0">complexity to derive the scheduling policy. [10] studied a</div><div class="t m0 x19 h8 y55 ff1 fs4 fc0 sc0 ls0 ws0">WPCN with heterogeneous nodes (nodes with and without</div><div class="t m0 x19 h8 y56 ff1 fs4 fc0 sc0 ls0 ws0">RF energy harvesting capabilities) and it was shown how the</div><div class="t m0 x19 h8 y57 ff1 fs4 fc0 sc0 ls0 ws0">presence of non-harvesting nodes can be utilized to enhance the</div><div class="t m0 x19 h8 y58 ff1 fs4 fc0 sc0 ls0 ws0">network performance, compared to pure WPCNs [8]. Unlike</div><div class="t m0 x19 h8 y59 ff1 fs4 fc0 sc0 ls0 ws0">prior slot-oriented optimization frameworks [8]–[10], in which</div><div class="t m0 x19 h8 y5a ff1 fs4 fc0 sc0 ls0 ws0">all the harvested energy is used in the same slot in which it is</div><div class="t m0 x19 h8 y5b ff1 fs4 fc0 sc0 ls0 ws0">harvested, [11] focused on long-term optimization. Although</div><div class="t m0 x19 h8 y5c ff1 fs4 fc0 sc0 ls0 ws0">this incurs high computational overhead, it also signiﬁcantly</div><div class="t m0 x19 h8 y5d ff1 fs4 fc0 sc0 ls0 ws0">improves the throughput of the network while maintaining</div><div class="t m0 x19 h8 y5e ff1 fs4 fc0 sc0 ls4 ws0">fairness. Several papers investigated solutions in contrast to</div><div class="t m0 x19 h8 y5f ff1 fs4 fc0 sc0 ls0 ws0">the limited harvested energy in WPCNs by introducing new</div><div class="t m0 x19 h8 y60 ff1 fs4 fc0 sc0 ls0 ws0">paradigms [12]–[14]. [12] extended the long-term maximiza-</div><div class="t m0 x19 h8 y61 ff1 fs4 fc0 sc0 ls0 ws0">tion of the half-duplex case [11] to the full-duplex scenario,</div><div class="t m0 x19 h8 y62 ff1 fs4 fc0 sc0 ls0 ws0">in which the ER and AP coincide and are able to broadcast</div><div class="t m0 x19 h8 y63 ff1 fs4 fc0 sc0 ls0 ws0">wireless energy signals over the downlink and receive data</div><div class="t m0 x19 h8 y64 ff1 fs4 fc0 sc0 ls0 ws0">signals over the uplink, simultaneously. It was shown that</div><div class="t m0 x19 h8 y65 ff1 fs4 fc0 sc0 ls0 ws0">the throughput region of the full-duplex scenario in notably</div><div class="t m0 x19 h8 y66 ff1 fs4 fc0 sc0 ls0 ws0">larger than that of the half-duplex case [11]. [13] generalized</div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div> </body> </html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62550ee8b744eb386fd87d8e/bg2.jpg"><div class="t m1 x17 h8 y67 ff1 fs4 fc0 sc0 ls0 ws0">conventional TDMA wireless networks (no energy harvesting)</div><div class="t m1 x17 h8 y68 ff1 fs4 fc0 sc0 ls0 ws0">to a new type of wireless networks coined generalized-WPCNs</div><div class="t m1 x17 h8 y69 ff1 fs4 fc0 sc0 ls0 ws0">(g-WPCNs), where nodes are assumed to be equipped with</div><div class="t m1 x17 h8 y6a ff1 fs4 fc0 sc0 ls0 ws0">RF energy harvesting circuitries along with energy supplies. It</div><div class="t m1 x17 h8 y6b ff1 fs4 fc0 sc0 ls0 ws0">was shown that both conventional TDMA wireless networks</div><div class="t m1 x17 h8 y6c ff1 fs4 fc0 sc0 ls0 ws0">and WPCNs with only RF energy harvesting nodes constitute</div><div class="t m1 x17 h8 y6d ff1 fs4 fc0 sc0 ls0 ws0">lower bounds on the performance of g-WPCNs in terms of the</div><div class="t m1 x17 h8 y6e ff1 fs4 fc0 sc0 ls0 ws0">maximum sum-throughput and max-min throughput. Although</div><div class="t m1 x17 h8 y6f ff1 fs4 fc0 sc0 ls0 ws0">most of the literature has focused on orthogonal multiple access</div><div class="t m1 x17 h8 y70 ff1 fs4 fc0 sc0 ls0 ws0">schemes (typically TDMA) for the uplink phase [8]–[13], the</div><div class="t m1 x17 h8 y71 ff1 fs4 fc0 sc0 ls0 ws0">authors in [14] introduced NOMA in WPCNs to enhance</div><div class="t m1 x17 h8 y72 ff1 fs4 fc0 sc0 ls0 ws0">the power-bandwidth efﬁciency. Indeed, it was shown that</div><div class="t m1 x17 h8 y73 ff1 fs4 fc0 sc0 ls0 ws0">NOMA improves the spectral efﬁciency [15] with respect to</div><div class="t m1 x17 h8 y74 ff1 fs4 fc0 sc0 ls0 ws0">orthogonal multiple access schemes. To work properly, NOMA</div><div class="t m1 x17 h8 y75 ff1 fs4 fc0 sc0 ls0 ws0">calls for tuning the transmit power of the devices, so as to</div><div class="t m1 x17 h8 y76 ff1 fs4 fc0 sc0 ls0 ws0">exploit interference cancellation techniques at the receiver side.</div><div class="t m1 x17 h8 y77 ff1 fs4 fc0 sc0 ls0 ws0">However, [14] focused on optimizing the time allocations to</div><div class="t m1 x17 h8 y78 ff1 fs4 fc0 sc0 ls0 ws0">maximize the sum-throughput of the slot-oriented case (all the</div><div class="t m1 x17 h8 y79 ff1 fs4 fc0 sc0 ls0 ws0">harvested energy in a slot is also consumed in the same slot).</div><div class="t m1 x17 h8 y7a ff1 fs4 fc0 sc0 ls0 ws0">This approach, in turn, leads to sub-optimal polices since: 1) it</div><div class="t m1 x17 h8 y7b ff1 fs4 fc0 sc0 ls0 ws0">does not optimize the transmit powers and 2) it does not take</div><div class="t m1 x17 h8 y7c ff1 fs4 fc0 sc0 ls0 ws0">into account the global performance over a larger time horizon.</div><div class="t m1 x17 h8 y7d ff1 fs4 fc0 sc0 ls0 ws0">Therefore, unlike [14], in this paper we jointly optimize time</div><div class="t m1 x17 h8 y7e ff1 fs4 fc0 sc0 ls0 ws0">and power allocations to maximize the sum-throughput over</div><div class="t m1 x17 h9 y7f ff1 fs4 fc0 sc0 ls0 ws0">a ﬁnite horizon of T slots. In our schemes, simultaneous</div><div class="t m1 x17 h8 y80 ff1 fs4 fc0 sc0 ls0 ws0">transmissions can still be successful if the received signal</div><div class="t m1 x17 h8 y81 ff1 fs4 fc0 sc0 ls0 ws0">power is sufﬁciently high, thus no ﬁne synchronization is</div><div class="t m1 x17 h8 y82 ff1 fs4 fc0 sc0 ls0 ws0">required.</div><div class="t m1 x16 h8 y83 ff1 fs4 fc0 sc0 ls0 ws0">Our contributions can be summarized as follows. We pro-</div><div class="t m1 x17 h8 y84 ff1 fs4 fc0 sc0 ls0 ws0">pose Low Complexity Decoding and Successive Interference</div><div class="t m1 x17 h8 y85 ff1 fs4 fc0 sc0 ls0 ws0">Cancellation Decoding, two schemes that aim at optimizing</div><div class="t m1 x17 h8 y86 ff1 fs4 fc0 sc0 ls0 ws0">the sum-throughput of a WPCN with and without interference</div><div class="t m1 x17 h8 y87 ff1 fs4 fc0 sc0 ls0 ws0">cancellation. Since LCD leads to a non-convex problem, we</div><div class="t m1 x17 h8 y88 ff1 fs4 fc0 sc0 ls0 ws0">solve a sub-problem via casting it as a series of geometric</div><div class="t m1 x17 h8 y89 ff1 fs4 fc0 sc0 ls0 ws0">programs. On the contrary, we formally establish the convexity</div><div class="t m1 x17 h8 y8a ff1 fs4 fc0 sc0 ls0 ws0">of the sum throughput maximization problem with SICD and</div><div class="t m1 x17 h8 y8b ff1 fs4 fc0 sc0 ls0 ws0">propose an algorithm to ﬁnd the optimal transmission durations</div><div class="t m1 x17 h8 y8c ff1 fs4 fc0 sc0 ls0 ws0">and powers. Our numerical results show the superiority of the</div><div class="t m1 x17 h8 y8d ff1 fs4 fc0 sc0 ls0 ws0">interference cancellation scheme over the simpler LCD.</div><div class="t m1 x16 h8 y8e ff5 fs4 fc0 sc0 ls0 ws0">Notation and Structure. Subscripts “</div><div class="t m1 x1b ha y8f ff7 fs5 fc0 sc0 ls5 ws0">i,t</div><div class="t m1 x1c h9 y90 ff1 fs4 fc0 sc0 ls0 ws0">” denote the i-th node</div><div class="t m1 x17 h9 y91 ff1 fs4 fc0 sc0 ls0 ws0">in the t-th time slot. Boldface letters are used to indicate all the</div><div class="t m1 x17 h8 y92 ff1 fs4 fc0 sc0 ls0 ws0">elements of a quantity (e.g., E</div><div class="t m1 x1d hb y93 ff9 fs5 fc0 sc0 ls6 ws0">def</div><div class="t m1 x1e h9 y94 ffa fs4 fc0 sc0 ls7 ws0">=[E</div><div class="t m1 x1f hb y95 ff9 fs5 fc0 sc0 ls0 ws0">1,1</div><div class="t m1 x1c h9 y94 ff6 fs4 fc0 sc0 ls8 ws0">,...,E</div><div class="t m1 x20 hb y95 ff9 fs5 fc0 sc0 ls0 ws0">1,t</div><div class="t m1 x21 h9 y94 ff6 fs4 fc0 sc0 ls8 ws0">,...,E</div><div class="t m1 x22 ha y95 ff7 fs5 fc0 sc0 ls9 ws0">K,T</div><div class="t m1 x23 h9 y94 ffa fs4 fc0 sc0 ls0 ws0">]</div><div class="t m1 x17 hc y96 ff1 fs4 fc0 sc0 ls0 ws0">or τ</div><div class="t m1 x24 hb y97 ff9 fs5 fc0 sc0 ls0 ws0">0</div><div class="t m1 x25 hb y98 ff9 fs5 fc0 sc0 ls6 ws0">def</div><div class="t m1 x26 h9 y99 ffa fs4 fc0 sc0 lsa ws0">=[τ</div><div class="t m1 x27 hb y97 ff9 fs5 fc0 sc0 ls0 ws0">0,1</div><div class="t m1 x28 h9 y99 ff6 fs4 fc0 sc0 ls8 ws0">,...,τ</div><div class="t m1 x29 hb y97 ff9 fs5 fc0 sc0 ls0 ws0">0,T</div><div class="t m1 x2a h9 y99 ffa fs4 fc0 sc0 ls0 ws0">]). With “∀i” and “∀t”, we summarize</div><div class="t m1 x17 h9 y9a ff6 fs4 fc0 sc0 ls0 ws0">i =1,...,K and t =1,...,T, respectively.</div><div class="t m1 x16 h8 y9b ff1 fs4 fc0 sc0 ls4 ws0">The paper is organized as follows. Section II presents the</div><div class="t m1 x17 h8 y9c ff1 fs4 fc0 sc0 ls0 ws0">system model. Sections III and IV present the LCD and SICD</div><div class="t m1 x17 h8 y9d ff1 fs4 fc0 sc0 ls0 ws0">schemes, respectively. The numerical results are shown in V.</div><div class="t m1 x17 h8 y9e ff1 fs4 fc0 sc0 ls0 ws0">Finally, Section VI concludes the paper.</div><div class="t m1 x2b h8 y9f ff1 fs4 fc0 sc0 ls2 ws0">II. S</div><div class="t m1 x2c h8 ya0 ff1 fs2 fc0 sc0 lsc ws0">YSTEM MODEL</div><div class="t m1 x16 h8 ya1 ff1 fs4 fc0 sc0 ls0 ws0">We study a WPCN composed of one AP, one ER source</div><div class="t m1 x17 h9 ya2 ff1 fs4 fc0 sc0 ls0 ws0">and K users. The energy rich node is equipped with a stable</div><div class="t m1 x17 h9 ya3 ff1 fs4 fc0 sc0 ls0 ws0">energy supply and transfers wireless energy to the K users</div><div class="t m1 x17 h9 ya4 ff1 fs4 fc0 sc0 ls0 ws0">in the network. User U</div><div class="t m1 x2d ha ya5 ff7 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m1 x2e h9 ya6 ff1 fs4 fc0 sc0 ls0 ws0">, i =1,...,K, receives the energy</div><div class="t m1 x17 h8 ya7 ff1 fs4 fc0 sc0 ls0 ws0">transferred by ER and uses the accumulated energy to send</div><div class="t m1 x17 h8 ya8 ff1 fs4 fc0 sc0 ls0 ws0">uplink data messages to AP. There are no other energy sources</div><div class="t m1 x17 h8 ya9 ff1 fs4 fc0 sc0 ls0 ws0">(neither environmental nor man-made) in the network.</div><div class="t m2 x2f hd yaa ffd fs6 fc1 sc0 ls0 ws0">x axis</div><div class="t m3 x30 he yab ffd fs7 fc1 sc0 ls0 ws0">y axis</div><div class="t m4 x31 hf yac ffe fs8 fc0 sc0 ls0 ws0">1</div><div class="t m4 x32 hf yad ffe fs8 fc0 sc0 ls0 ws0">2</div><div class="t m4 x33 hf yae ffe fs8 fc0 sc0 ls0 ws0">3</div><div class="t m4 x34 hf yaf ffe fs8 fc0 sc0 ls0 ws0">4</div><div class="t m4 x35 hf yb0 ffe fs8 fc0 sc0 ls0 ws0">5</div><div class="t m4 x36 hf yb1 ffe fs8 fc0 sc0 ls0 ws0">6</div><div class="t m4 x37 hf yb2 ffe fs8 fc0 sc0 ls0 ws0">7</div><div class="t m4 x38 hf yb3 ffe fs8 fc0 sc0 ls0 ws0">8</div><div class="t m4 xc hf yb4 ffe fs8 fc0 sc0 ls0 ws0">9</div><div class="t m4 x39 hf yb5 ffe fs8 fc0 sc0 ls0 ws0">10</div><div class="t m4 x3a h10 yb6 ffd fs8 fc0 sc0 ls0 ws0">d</div><div class="t m5 x3b h11 yb7 ffe fs9 fc0 sc0 ls11 ws0">ER−AP</div><div class="t m4 x3c h10 yb8 ffd fs8 fc0 sc0 ls0 ws0">d</div><div class="t m5 x3d h12 yb9 ffd fs9 fc0 sc0 ls0 ws0">U</div><div class="t m4 x3e h13 yba ffe fsa fc0 sc0 ls0 ws0">1</div><div class="t m5 x3f h11 yb9 fff fs9 fc0 sc0 ls0 ws0">−ER</div><div class="t m4 x40 h10 yb8 ffd fs8 fc0 sc0 ls0 ws0">d</div><div class="t m5 x41 h12 yb9 ffd fs9 fc0 sc0 ls0 ws0">U</div><div class="t m4 x42 h13 yba ffe fsa fc0 sc0 ls0 ws0">1</div><div class="t m5 x43 h11 yb9 fff fs9 fc0 sc0 ls0 ws0">−AP</div><div class="t m4 x44 hf ybb ffe fs8 fc0 sc0 ls0 ws0">AP</div><div class="t m4 x44 hf ybc ffe fs8 fc0 sc0 ls13 ws0">ER</div><div class="t m4 x44 hf ybd ffe fs8 fc0 sc0 ls14 ws0">Users</div><div class="t m1 x45 h14 ybe ff1 fs2 fc0 sc0 ls0 ws0">Figure 1: System model.</div><div class="t m1 x1a h8 ybf ff1 fs4 fc0 sc0 ls0 ws0">ER and all users are equipped with a single antenna each,</div><div class="t m1 x19 h8 yc0 ff1 fs4 fc0 sc0 ls0 ws0">operate over the same frequency band and the radios are</div><div class="t m1 x19 h8 yc1 ff1 fs4 fc0 sc0 ls0 ws0">half-duplex. Time is slotted and, without loss of generality,</div><div class="t m1 x19 h8 yc2 ff1 fs4 fc0 sc0 ls0 ws0">we assume the slot duration is normalized to one. Every</div><div class="t m1 x19 h9 yc3 ff1 fs4 fc0 sc0 ls0 ws0">slot t =1,...,T is divided in two phases. In the ﬁrst τ</div><div class="t m1 x46 hb yc4 ff9 fs5 fc0 sc0 ls0 ws0">0,t</div><div class="t m1 x19 h8 yc5 ff1 fs4 fc0 sc0 ls0 ws0">seconds, ER broadcasts wireless energy on the downlink to</div><div class="t m1 x19 h9 yc6 ff1 fs4 fc0 sc0 ls0 ws0">recharge the batteries of the devices. In the remaining 1 − τ</div><div class="t m1 x46 hb yc7 ff9 fs5 fc0 sc0 ls0 ws0">0,t</div><div class="t m1 x19 h8 yc8 ff1 fs4 fc0 sc0 ls0 ws0">seconds, all users transmit data to the AP independently and</div><div class="t m1 x19 h8 yc9 ff1 fs4 fc0 sc0 ls0 ws0">simultaneously.</div><div class="t m1 x1a h8 yca ff1 fs4 fc0 sc0 ls0 ws0">The positions of the users are known a priori, and thus</div><div class="t m1 x19 h8 ycb ff1 fs4 fc0 sc0 ls4 ws0">their average channel gains are pre-estimated and known (in</div><div class="t m1 x19 h8 ycc ff1 fs4 fc0 sc0 ls0 ws0">Section V we will further discuss the channel models). The</div><div class="t m1 x19 h9 ycd ff1 fs4 fc0 sc0 ls16 ws0">downlink channel power gain from ER to U</div><div class="t m1 x3d ha yce ff7 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m1 x3f h8 ycf ff1 fs4 fc0 sc0 ls0 ws0">and the uplink</div><div class="t m1 x19 h9 yd0 ff1 fs4 fc0 sc0 ls17 ws0">channel power gain from U</div><div class="t m1 x47 ha yd1 ff7 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m1 x48 h9 yd2 ff1 fs4 fc0 sc0 ls0 ws0">to AP, during time slot t, are</div><div class="t m1 x19 h9 yd3 ff1 fs4 fc0 sc0 ls0 ws0">denoted by h</div><div class="t m1 x49 ha yd4 ff7 fs5 fc0 sc0 ls5 ws0">i,t</div><div class="t m1 x4a h9 yd5 ff1 fs4 fc0 sc0 ls0 ws0">and g</div><div class="t m1 x4b ha yd4 ff7 fs5 fc0 sc0 ls5 ws0">i,t</div><div class="t m1 x4c h8 yd5 ff1 fs4 fc0 sc0 ls0 ws0">, respectively. Hence, the harvested</div><div class="t m1 x19 h9 yd6 ff1 fs4 fc0 sc0 ls0 ws0">energy by U</div><div class="t m1 x4d ha yd7 ff7 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m1 x49 h8 yd8 ff1 fs4 fc0 sc0 ls0 ws0">in the downlink phase is</div><div class="t m1 x41 h9 yd9 ff6 fs4 fc0 sc0 ls0 ws0">E</div><div class="t m1 x43 ha yda ff7 fs5 fc0 sc0 ls5 ws0">i,t</div><div class="t m1 x4e h9 ydb ffa fs4 fc0 sc0 ls0 ws0">= η</div><div class="t m1 x4f ha yda ff7 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m1 x50 h9 ydb ff6 fs4 fc0 sc0 ls0 ws0">h</div><div class="t m1 x51 ha yda ff7 fs5 fc0 sc0 ls5 ws0">i,t</div><div class="t m1 x52 h9 ydb ff6 fs4 fc0 sc0 ls0 ws0">P</div><div class="t m1 x53 ha yda ff7 fs5 fc0 sc0 ls0 ws0">B</div><div class="t m1 x54 h9 ydb ff6 fs4 fc0 sc0 ls0 ws0">τ</div><div class="t m1 x55 hb yda ff9 fs5 fc0 sc0 ls0 ws0">0,t</div><div class="t m1 xb hb ydc ff9 fs5 fc0 sc0 ls6 ws0">def</div><div class="t m1 x56 h9 ydb ffa fs4 fc0 sc0 ls0 ws0">= γ</div><div class="t m1 x57 ha yda ff7 fs5 fc0 sc0 ls5 ws0">i,t</div><div class="t m1 x32 h9 ydb ff6 fs4 fc0 sc0 ls0 ws0">τ</div><div class="t m1 x58 hb yda ff9 fs5 fc0 sc0 ls0 ws0">0,t</div><div class="t m1 x59 h9 ydb ff6 fs4 fc0 sc0 ls0 ws0">. (1)</div><div class="t m1 x19 h9 ydd ff1 fs4 fc0 sc0 ls0 ws0">where η</div><div class="t m1 x5a ha yde ff7 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m1 x5b h8 ydf ff1 fs4 fc0 sc0 ls0 ws0">denotes the efﬁciency of the energy harvesting</div><div class="t m1 x19 h8 ye0 ff1 fs4 fc0 sc0 ls0 ws0">circuitry,</div><div class="t m1 x5a h15 ye1 ff1 fs5 fc0 sc0 ls0 ws0">1</div><div class="t m1 x5c h9 ye2 ff1 fs4 fc0 sc0 ls0 ws0">and P</div><div class="t m1 x5d ha ye3 ff7 fs5 fc0 sc0 ls0 ws0">B</div><div class="t m1 x5e h8 ye2 ff1 fs4 fc0 sc0 ls0 ws0">is the average transmit power by ER within</div><div class="t m1 x19 h9 ye4 ff6 fs4 fc0 sc0 ls0 ws0">τ</div><div class="t m1 x5f hb ye5 ff9 fs5 fc0 sc0 ls0 ws0">0,t</div><div class="t m1 x60 h8 ye6 ff1 fs4 fc0 sc0 ls0 ws0">.</div><div class="t m1 x61 h8 ye7 ff1 fs4 fc0 sc0 ls2 ws0">III. L</div><div class="t m1 x62 h8 ye8 ff1 fs2 fc0 sc0 ls18 ws0">OW COMPLEXITY DECODING SCHEME</div><div class="t m1 x1a h8 ye9 ff1 fs4 fc0 sc0 ls0 ws0">In this section, we present the Low Complexity Decoding</div><div class="t m1 x19 h8 yea ff1 fs4 fc0 sc0 ls0 ws0">(LCD) scheme, in which the AP uses single-user decoders</div><div class="t m1 x19 h8 yeb ff1 fs4 fc0 sc0 ls0 ws0">to detect the users’ signals without performing interference</div><div class="t m1 x19 h8 yec ff1 fs4 fc0 sc0 ls0 ws0">cancellation. In particular, each user may interfere with all</div><div class="t m1 x19 h8 yed ff1 fs4 fc0 sc0 ls0 ws0">the others. Hence, we can express the average Signal-to-</div><div class="t m1 x19 h9 yee ff1 fs4 fc0 sc0 ls0 ws0">Interference-plus-Noise Ratio (SINR) at the AP for U</div><div class="t m1 x63 ha yef ff7 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m1 x38 h8 yf0 ff1 fs4 fc0 sc0 ls0 ws0">in time</div><div class="t m1 x19 h9 yf1 ff1 fs4 fc0 sc0 ls0 ws0">slot t as</div><div class="t m1 x64 h9 yf2 ff6 fs4 fc0 sc0 ls0 ws0">x</div><div class="t m1 x65 ha yf3 ff7 fs5 fc0 sc0 ls5 ws0">i,t</div><div class="t m1 x41 hb yf4 ff9 fs5 fc0 sc0 ls6 ws0">def</div><div class="t m1 x5d h9 yf5 ffa fs4 fc0 sc0 ls0 ws0">=</div><div class="t m1 x66 h9 yf6 ff6 fs4 fc0 sc0 ls0 ws0">g</div><div class="t m1 x67 ha yf7 ff7 fs5 fc0 sc0 ls5 ws0">i,t</div><div class="t m1 xa h9 yf8 ff6 fs4 fc0 sc0 ls0 ws0">E</div><div class="t m1 xb ha yf7 ff7 fs5 fc0 sc0 ls5 ws0">i,t</div><div class="t m1 x68 h9 yf9 ff6 fs4 fc0 sc0 ls0 ws0">σ</div><div class="t m1 x69 hb yfa ff9 fs5 fc0 sc0 ls0 ws0">2</div><div class="t m1 x6a h9 yf9 ffa fs4 fc0 sc0 ls19 ws0">(1 − τ</div><div class="t m1 x52 hb yfb ff9 fs5 fc0 sc0 ls0 ws0">0,t</div><div class="t m1 x48 h9 yf9 ffa fs4 fc0 sc0 ls1a ws0">)+</div><div class="t m1 x6b h16 yfc ff10 fs4 fc0 sc0 ls0 ws0"></div><div class="t m1 x6c ha yfd ff7 fs5 fc0 sc0 ls0 ws0">K</div><div class="t m1 x6c hb yfe ff7 fs5 fc0 sc0 ls0 ws0">j=1</div><div class="t m1 x6c hb yff ff7 fs5 fc0 sc0 ls0 ws0">j=i</div><div class="t m1 x6d h9 yf9 ff6 fs4 fc0 sc0 ls0 ws0">g</div><div class="t m1 x6e ha yfb ff7 fs5 fc0 sc0 ls1b ws0">j,t</div><div class="t m1 x6f h9 yf9 ff6 fs4 fc0 sc0 ls0 ws0">E</div><div class="t m1 x70 ha yfb ff7 fs5 fc0 sc0 ls1b ws0">j,t</div><div class="t m1 x71 h9 yf5 ff6 fs4 fc0 sc0 ls0 ws0">, (2)</div><div class="t m1 x19 h9 y100 ff1 fs4 fc0 sc0 ls0 ws0">where E</div><div class="t m1 x5a ha y101 ff7 fs5 fc0 sc0 ls5 ws0">i,t</div><div class="t m1 x72 h9 y102 ff1 fs4 fc0 sc0 ls0 ws0">denotes the amount of consumed energy by U</div><div class="t m1 x73 ha y101 ff7 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m1 x74 h8 y102 ff1 fs4 fc0 sc0 ls0 ws0">in</div><div class="t m1 x19 h9 y103 ff1 fs4 fc0 sc0 ls0 ws0">time slot t and σ</div><div class="t m1 x75 hb y104 ff9 fs5 fc0 sc0 ls0 ws0">2</div><div class="t m1 x43 h8 y105 ff1 fs4 fc0 sc0 ls0 ws0">denotes the noise power at the AP. According</div><div class="t m1 x19 h8 y106 ff1 fs4 fc0 sc0 ls0 ws0">to Shannon’s formula, and with the Gaussian approximation for</div><div class="t m1 x19 h9 y107 ff1 fs4 fc0 sc0 ls0 ws0">interference, the achievable throughput of U</div><div class="t m1 x33 ha y108 ff7 fs5 fc0 sc0 ls0 ws0">i</div><div class="t m1 x6f h9 y109 ff1 fs4 fc0 sc0 ls0 ws0">, in time slot t,is</div><div class="t m1 x19 h8 y10a ff1 fs4 fc0 sc0 ls0 ws0">given by</div><div class="t m1 x76 h9 y10b ff6 fs4 fc0 sc0 ls0 ws0">R</div><div class="t m1 x5d ha y10c ff7 fs5 fc0 sc0 ls5 ws0">i,t</div><div class="t m1 x5e hb y10d ff9 fs5 fc0 sc0 ls6 ws0">def</div><div class="t m1 x68 h9 y10e ffa fs4 fc0 sc0 lsb ws0">=(1− τ</div><div class="t m1 x3a hb y10c ff9 fs5 fc0 sc0 ls0 ws0">0,t</div><div class="t m1 x66 h9 y10e ffa fs4 fc0 sc0 ls1d ws0">)log</div><div class="t m1 x77 hb y10f ff9 fs5 fc0 sc0 ls0 ws0">2</div><div class="t m1 x78 h9 y10e ffa fs4 fc0 sc0 ls19 ws0">(1 + x</div><div class="t m1 x58 ha y10c ff7 fs5 fc0 sc0 ls5 ws0">i,t</div><div class="t m1 x3d h9 y10e ffa fs4 fc0 sc0 ls0 ws0">) . (3)</div><div class="t m1 x1a h8 y110 ff1 fs4 fc0 sc0 ls0 ws0">Our objective is to characterize the maximum achievable</div><div class="t m1 x19 h9 y111 ff1 fs4 fc0 sc0 ls0 ws0">sum-throughput over a ﬁnite horizon of T time slots subject to</div><div class="t m1 x19 h8 y112 ff1 fs4 fc0 sc0 ls0 ws0">energy causality constraints and practical decoding constraints.</div><div class="t m1 x19 h9 y113 ff1 fs4 fc0 sc0 ls0 ws0">The energy causality constraints guarantee that, in slot t, only</div><div class="t m1 x79 h17 y114 ff1 fsb fc0 sc0 ls0 ws0">1</div><div class="t m1 x7a h4 y115 ff12 fs2 fc0 sc0 ls0 ws0">η</div><div class="t m1 x7b h18 y116 ff13 fsb fc0 sc0 ls0 ws0">i</div><div class="t m1 x7c h14 y115 ff1 fs2 fc0 sc0 ls0 ws0">depends on the efﬁciency of the harvesting antenna, the impedance</div><div class="t m1 x19 h4 y117 ff1 fs2 fc0 sc0 ls0 ws0">matching circuit and the voltage multipliers. For example, we will use η</div><div class="t m1 x7d h18 y118 ff13 fsb fc0 sc0 ls0 ws0">i</div><div class="t m1 x7e h19 y119 ff14 fs2 fc0 sc0 ls0 ws0">=</div><div class="t m1 x19 h4 y11a ff14 fs2 fc0 sc0 ls0 ws0">0.49 according to the speciﬁcations of the commercial product P2110 [16].</div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>