IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. XX, NO. X, XXXX

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1 This article has een accepted for pulication in a future issue of this journal, ut has not een fully edited. Content may change prior to final pulication. Citation information: DOI 1.119/TWC , IEEE IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. XX, NO. X, XXXX 18 1 Analysis of Dual-Hop Relaying with Energy Harvesting in Nakagami-m Fading Channel Mohammadreza Baaei, Student Memer, IEEE, Ümit Aygölü, Memer, IEEE, and Ertugrul Basar, Senior Memer, IEEE Astract In this paper, the end-to-end it error performance of a dual-hop (DH energy harvesting (EH amplifyand-forward/decode-and-forward (AF/DF system is investigated. In this system, the source communicates with the destination over an intermediate relay when the direct link etween the source and the destination is in deep fade. The channels are assumed to e exposed to Nakagami-m fading and all nodes are equipped with one antenna. The relay uses power splitting ( and time switching ( relaying protocols to harvest energy and uses it to forward the decoded signal or to transmit the amplified version of the received signal to the destination. The it error proailities (BEP of the considered DH-AF and DH-DF systems are analytically derived for oth EH protocols and their performances are comparatively evaluated. Moreover, a system optimization is performed to maximize the performance. For the mode, a list of mixture of modulations is provided for different spectral efficiency values and different time allocation parameters. Our comprehensive results on the performance of AF- and DF-aided DH networks with EH in the relay, provide asic guidelines for the design of future DH-EH systems. Index Terms Energy harvesting, dual-hop network, DF/AF relaying, performance analysis. I. INTRODUCTION ENERGY harvesting (EH from radio frequency (RF signals is a promising approach that has een regarded as an alternative solution to the power efficiency issue [1], []. In EH, nodes can oth harvest energy and process the information concurrently. As a result, the EH node does not need to has an external source of energy since it uses the harvested energy to forward the received signal to a destination. In the literature, practical EH techniques are classified as power splitting ( and time switching ( relaying. In, the EH node divides the incoming signal power in two parts for EH and information processing (IP during the whole transmission interval. In, a certain fraction of the transmission interval is reserved to EH while the reminder fraction to IP. For oth protocols, EH Manuscript received Novemer 8, 17; revised Feruary 1, 18; accepted April 1, 18. Date of pulication XXXXX X, 18; date of current version XXXXX X, 18. This paper was partly presented at the 17 Advances in Wireless and Optical Communications, Riga, Latvia, Novemer 17. This work was supported y the Scientific and Technological Research Council of Turkey (TUBITAK under Grant 114E67. The work of E. Basar was also supported y Turkish Academy of Sciences (TUBA Outstanding Young Scientist Award Programme (GEBIP. The associate editor coordinating the review of this paper and approving it for pulication was Rui Dinis. The authors are with the Department of Electronics and Communication Engineering, Istanul Technical University, Maslak, 34469, Istanul, Turkey, s: (aaei, aygolu, asarer@itu.edu.tr. Color versions of one or more of the figures in this paper are availale online at Digital Oject Identifier 1.119/TWC.18.XXXXXXX node uses the harvested energy to transmit the received signal to its destination. On the other hand, an ideal (unrealistic EH node, which is commonly considered in the literature [] [4], simultaneously harvests energy and processes information with the total received power. A dual-hop decode-and-forward (DH-DF relaying network, where the relay applies and protocols, is considered in [5] and the achievale throughput at the destination is derived from ergodic capacity. In [6], the outage performance of an amplify-and-forward (AF cooperative EH system is derived when the source has the knowledge of channel statistics. Given a total power constraint for the whole system, the parameter is optimized to improve performance compared to. In [3], the outage proaility and ergodic capacity of delaylimited and delay-tolerant transmission schemes are derived for the DH-AF relaying strategy y considering, and ideal EH protocols. Overall sum it error rate ( in a two-way physical layer network coding AF relaying system is derived for two and three transmission intervals in [7] where the relay harvests energy applying. Moreover, the mixture of modulations approach is proposed in [7] to maintain the spectral efficiency at a fixed value when the parameter α varies and the performance is analytically evaluated for fixed spectral efficiency values. An adaptive EH protocol in a half duplex AF transmission system applying and protocols together is considered in [8], where the system throughput is otained y deriving expressions for the outage proaility and ergodic capacity. The results are compared with the conventional and protocols and it is concluded that the adaptive EH protocol provides etter performance in moderate transmission rates where the throughput curves of and cross over each other. In [9], a source communicates with a destination via an EH relay in which the channels are exposed to Nakagami-m fading and all nodes are equipped with multiple antennas. The system throughput is derived for oth and where transmit/receive antenna selection and maximum ratio transmitter/maximum ratio cominer (MRT/MRC are employed for each hop. Achievale rate for the DH-AF relaying system, in which the relay is equipped with multiple antennas, is studied in [1]. The relay uses antenna selection (AS and to decode the information and harvests energy. Moreover, an optimization is jointly effectuated for AS and to improve the system performance. and protocols are considered in [11] to analyze the performance of a DH system with DF relaying. In [11], the relay harvests energy from oth the received signal and the interference signals at the same frequency, which in fact (c 18 IEEE. Personal use is permitted, ut repulication/redistriution requires IEEE permission. See for more information.

2 This article has een accepted for pulication in a future issue of this journal, ut has not een fully edited. Content may change prior to final pulication. Citation information: DOI 1.119/TWC , IEEE IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. XX, NO. X, XXXX 18 increases the relay transmission power. However, this causes a decrease in the relay s received signal-to-noise ratio (SNR. A dynamic power splitting (D receiver operation, which splits the signal power for IP and EH, is proposed in [4]., static and on-off are studied as the special cases of D. Moreover, integrated and separated practical information and EH receivers are presented in [4]. In [1], a wireless powered communication network is proposed for which the source itself is a power-constraint node and harvests energy from the energy transmitters. The relays or destination have constant powers and the source transmits data to the destination with the harvested energy. In [1], two different protocols are proposed and jointly optimized to maximize the throughput for EH. In the first protocol, the relay cooperates only to transfer energy to the source. However, in the second protocol, the relay not only transmits energy to the power-constraint source ut also it forwards the received signal from the source to the destination in order to improve the system performance. An energy harvesting system with spatial modulation is considered in [13] where a receiver architecture is assumed at the receiver. Computational complexity of this system has een analyzed and the optimal factor is determined to maximize the system throughput. Another EH system with SM, in which the source harvests RF energy from an energy transmitter, has een analyzed in [14]. The source is equipped with multiple antennas in which some of them are active during the information transmission, and this enales self-energy recycling at the antennas, which provides more harvested energy at the source node. Two-way relaying (TWR EH systems are studied in [15] [19]. In [15] and [16], and AF are considered. Throughput from the outage proaility and ergodic capacity are derived in the Nakagami-m fading channel in [15]. Moreover, the MRT/MRC technique is applied at the source and destination. In [16], idirectional multiple access roadcast and time division roadcast techniques are proposed. Furthermore, three power transfer policies are investigated at the sources. In [17] and [18], a TW system with architecture is considered. In [17], the energy efficiency optimization prolem under the rate and total power constraints is studied. In [18], a energy accumulation scheme in a TWR system is considered, in which the relay is assumed to e a power-constraint unit and equipped with a rechargeale attery. If the amount of energy at the relay attery reaches a predefined threshold, the relay applies and forwards the signal to the destination. However, if the energy is elow the threshold level, the relay harvests all of the received signal energy in its attery. In [19], the performance of a three-step DF system, in which is used at the relay, is analyzed where idirectional communication of two sources is allowed. EH systems are mostly studied in the literature from the outage performance perspective. To the est of our knowledge, the it error performance of DH-(AF/DF relaying systems with an EH relay in Nakagami-m fading channels as well as comparisons etween various EH protocols have not een studied in the literature yet. In this paper, it error performance of the DH system with S Fig. 1. Considered dual-hop system. h R g d 1 d an EH relay is investigated. For the AF relaying system, the relay harvests energy from the received RF source signal and then using the harvested energy, it forwards the noisy version of the received signal to the destination. For the DF relaying system, the relay decodes and harvests the source signal and then using the harvested energy, transmits the decoded source signal to the destination. For AF/DF relaying strategies,, and ideal EH protocols are considered. Bit error proaility (BEP of the system is analytically derived for the aforementioned EH protocols under AF/DF strategies. Computer simulations are performed for different system parameters and the results are found in perfect match with those analytically otained. The main contriutions of this paper are summarized as follows: analysis of, and ideal operational EH protocols in a DH network with a power constraint relay, which enales wireless energy harvesting and information processing simultaneously, is derived. A unified BEP analysis is presented for the, and ideal protocols. An upper ound on the end-to-end BEP is evaluated for the DH-DF system. End-to-end BEP for the DH-AF system is derived using CDF of the received SNR. Results are given for different system parameters. Moreover, the optimum system parameters minimizing the BEP are determined. performance comparisons etween AF and DF relaying EH systems are provided. To make a fair comparison etween and the other protocols, on an equal spectral efficiency asis, the idea of mixture of modulations given previously in [7] is generalized for different spectral efficiency values. The rest of the paper is organized as follows. In Section II, the considered system model is presented. Section III is destinated to the BEP analysis and in Section IV, theoretical and computer simulation results are presented. Finally, Section V concludes the paper. II. SYSTEM MODEL The considered dual-hop system model is given in Fig. 1 where all nodes are equipped with one antenna. h and g represent the channel fading coefficients etween links S R and R D, respectively. d 1 and d denote the link distances. Both channels are assumed to e exposed to Nakagami-m fading. In the sequel, s and s stand for the transmitted signal from the source and the decoded signal at the relay, respectively. Moreover, it is assumed that E{ s } = E{ s } = 1. n r and n d denote additive white Gaussian noise (AWGN samples at the relay and the destination with distriutions D (c 18 IEEE. Personal use is permitted, ut repulication/redistriution requires IEEE permission. See for more information.

3 This article has een accepted for pulication in a future issue of this journal, ut has not een fully edited. Content may change prior to final pulication. Citation information: DOI 1.119/TWC , IEEE BABAEI et al.: ANALYSIS OF DUAL-HOP RELAYING WITH ENERGY HARVESTING IN NAKAGAMI-M FADING CHANNEL 3 T T T S-R EH: rp s (1-r P s R-D P r S-R S-R R-D EH: Ps Ps Pr S-R EH: P s P s R-D Pr T / T/ a T (1- a T/ (1-a T/ T / T/ (a ( (c Fig.. Time schedule for (a protocol, ( protocol and (c ideal protocol. n r CN (, σr and n d CN (, σd, respectively. Note that since the system performance is analyzed for distances d 1 and d, which are smaller than unity, the path-loss for oth links S R and R D are assumed to e equal to L SR = 1/(1 + d ξ 1 and L RD = 1/(1 + d ξ, respectively, to ensure that the path loss is always smaller than unity for any distance, where ξ is the path-loss coefficient []. P s is the source transmit power, P r is the relay transmit power and P t is the average power consumed y the system during T seconds. Moreover, Gray mapping is applied for all modulation schemes performed at the source and relay transmitters 1. A. DF Relaying 1 DF- EH Protocol: Transmission time schedule for the protocol is given in Fig. (a. As shown in Fig. (a, in protocol, the power of received signal at the relay is divided into EH and IP operations with the energy proportion of ρ/(1 ρ, where ρ is the power harvesting factor. In the first time interval of T/ seconds, the received signal for IP and the harvested energy at the relay are given as and y r = (1 ρp s L SR hs + n r (1 E H = ηρp s L SR h (T/ ( respectively, where < η 1 is the energy conversion coefficient [4]. Considering the total power-constraint P t for the system and the energy constraint P t T = P s T/, we have P s = P t. In the second time interval, the relay forwards the decoded signal s to the destination using the harvested energy E H. The received signal at the destination can e expressed as y d = P r L RD g s + n d (3 where P r = E H /(T/ = ηρp s L SR h. DF- EH Protocol: From the transmission time schedule given in Fig. ( for protocol, in the first and second time intervals of duration αt and (1 αt/ seconds, respectively, the received signal at the relay is given y y r = P s L SR hs + n r (4 1 Notation: erfc(z = (/ π z e t dt is the complementary error function [1, (8.5-4], W p,q( is the Whittaker ( function [1, (9.-4], Γ( is the Gamma function [1, (8.31-1], G m,n p,q ap represents Meijer s q G-Function [1, (9.31] and K v( represents the v th -order modified Bessel function of the second kind [1, (8.43]. where for αt seconds, the harvested amount of energy at the relay is E H = ηp s L SR h αt. Assuming that a total power of P t is consumed in T seconds, the energy constraint for is given as P t T = P s αt + P s (1 αt/. (5 After simplifying, we have P s = P t /(1 + α. In the third time interval of (1 αt/ seconds, the relay forwards the decoded signal to the destination for which the received signal is as given in (3, where P r = E H /(1 αt = η(α/(1 αp s L SR h. 3 DF- EH Protocol: The time schedule for the ideal EH protocol is given in Fig. (c, where during the first time interval of T/ seconds, the relay harvests energy and processes the information from the received source signal with the same total received energy. In the next time interval of T/ seconds, the decoded signal is transmitted from the relay antenna to the destination node using the harvested energy. The received signal at the relay and the destination are given as in (4 and (3, respectively. For this protocol, E H = ηp s L SR h (T/, the relay power is given as P r = E H /T = ηp s L SR h and like, P s = P t. B. AF Relaying In AF relaying strategy. the received signal at the relay is normalized, amplified and then retransmitted from the relay to the destination. Similar to DF relaying, three different EH protocols are analyzed in the following. 1 AF- EH Protocol: Using the received signal y r at the relay given y (1, the received signal at the destination is expressed as y d = (P r L RD /Ngy r + n d (6 where N = P s h (1 ρl SR + σr is a power constraint factor applied at the relay. Sustituting (1 in (6 and after some simplification, we have η h ρ(1 ρp s hgs y d = (1 + d ξ1 (1 + dξ P s h (1 ρ + (1 + d ξ 1 σ r ηps h + ρgn r + n d. (7 1 + d ξ P s h (1 ρ + (1 + d ξ 1 σ r (c 18 IEEE. Personal use is permitted, ut repulication/redistriution requires IEEE permission. See for more information.

4 This article has een accepted for pulication in a future issue of this journal, ut has not een fully edited. Content may change prior to final pulication. Citation information: DOI 1.119/TWC , IEEE 4 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. XX, NO. X, XXXX 18 AF- EH Protocol: The received signal at the destination is given as y d = (P r L RD /Jgy r + n d (8 where J = P s h L SR + σr. Sustituting (4 in (8 and after some simplification, we otain η h αp s hgs y d = (1 α(1 + d ξ1 (1 + dξ P s h + (1 + d ξ 1 σ r ηps h + αgn r + n d. (9 (1 α(1 + d ξ P s h + (1 + d ξ 1 σ r 3 AF- EH Protocol: The received signal at the relay and destination are as given in (4 and (8, respectively. Sustituting (4 in (8, considering P r = E H /T = ηp s L SR h and after some simplification, we have η h P s hgs y d = (1 + d ξ1 (1 + dξ + P s h + (1 + d ξ 1 σ r ηps h gn r (1 + d ξ P s h + (1 + d ξ 1 σ r III. BIT ERROR PROBABILITY ANALYSIS A. BEP for DF Relaying + n d. (1 For the three-node DH relaying system given in Fig. 1, the relay decodes the received signal from the source and transmits the decoded symol s to the destination. The end-to-end BEP can e upper ounded as P DF 1 (1 P S R (1 P R D (11 where P S R and P R D are BEPs of the links S R and R D, respectively, which are calculated for different EH protocols in the following. From the received signals at the relay given in (1 for and in (4 for and ideal protocols, SNR of the link S R can e written as { (1 ρps L SR h /σr, γ sr P s L SR h /σr, (1 and ideal. Using (1 and the exact BEP of the link S R given in [, Chap. 8], P S R can e sustituted in (11. From the received signal at the destination given in (3, SNR of the link R D for all EH protocols can e expressed as γ rd = ΥZ where Z = h g and ηρp s L SR L RD /σd, Υ ηαp s L SR L RD /((1 ασd, (13 ηp s L SR L RD /σd, ideal. From [3, (5-17], PDF of γ rd is given as f γrd (γ = 1 Υ f Z( γ Υ = mh m g Gγɛ 1 K Ω ( Ω h Ω g Υ γ (14 where G = F (m g Ω h /Ω g m h Ω/ (1/Υ ɛ. m h, m g, Ω h, Ω g, ɛ =.5(m h + m g, Ω = m h m g, F and f Z (z are defined in Appendix A. The symol error proaility (SEP of the link R D can e calculated as P R D s = P s (e γ rd f γrd (γdγ (15 where f γrd (γ is calculated in (14 and P s (e γ rd a Q( γ rd = (a/ erfc( γ is the conditional common approximate SEP for coherent modulation []. Here, a and are modulation specific constants. Note that the given conditional SEP is a tight upper ound at high SNR. In order to solve the integral of (15, we express erfc( and K v ( in terms of the Meijer s G-function using [5, ( ] and [6, (14]. Sustituting in (15, the integral can e rewritten as follows Ps R D = Ga π γ ɛ 1 G, 1, ( γ 1, 1 G,, ( H 4 γ Ω/, Ω/ dγ (16 where H = m h m g /Ω h Ω g Υ. Using [1, (9.311] and [6, (1], the closed-form solution for the integral in (16 is otained as ( Ps R D = Ga π ε G 3,3 H,1 ε,.5 ε,1 ε 4,5 4. (17.5Ω,.5Ω,1 ε, ε, BEP for the link R D can e otained using the common approximation [] at high SNR as P R D P R D s /k (18 where k = log M and M is the modulation level. The endto-end BEP can e upper ounded y sustituting P S R and P R D from [, Chap. 8] and (18, in (11, respectively. It is important to note from (17 that the end-to-end BEP of the DF relaying system is dependent on the selected EH protocol through G and H terms, while modulation specific parameters a and also affect the performance. B. BEP for AF Relaying The end-to-end SNR of the received signals in (7, (9 and (1 is given as γ = A h 4 g B h g + C h + D (19 where the constants A, B, C and D are listed in Tale II for different EH protocols. The CDF of γ at high SNR, where D =, is calculated in Appendix B. BEP of the system can e otained using the CDF of SNR given in (3 of Appendix B as [4] P AF a k π e γ γ F γ (γdγ = a k π (I 1 I ( where the constants a and are determined y the modulation order. In (, using [1, (3.381], I 1 is expressed as e γ I 1 = dγ = 1 ( 1 Γ (1 γ For rectangular M-QAM, a = 4(1 1/ M, = 3/(M 1, for non-rectangular M-QAM, a = 4, = 3/(M 1, for M-K, a =, = sin (π/m and for BK, a = 1, = 1 [4] (c 18 IEEE. Personal use is permitted, ut repulication/redistriution requires IEEE permission. See for more information.

5 This article has een accepted for pulication in a future issue of this journal, ut has not een fully edited. Content may change prior to final pulication. Citation information: DOI 1.119/TWC , IEEE BABAEI et al.: ANALYSIS OF DUAL-HOP RELAYING WITH ENERGY HARVESTING IN NAKAGAMI-M FADING CHANNEL 5 TABLE I MIXTURE OF MODULATIONS FOR PROTOCOL (R =.5 AND R = 1 α IP time/t R =.5 R = 1 α IP time/t R =.5 R = 1 1/ 1/ M 1 M 8/15 7/3 (6/7M,(1/7M 3 (5/7M 4,(/7M 5 1/1 11/4 (1/11M 1,(1/11M (9/11M,(/11M 3 11/ 9/4 (7/9M,(/9M 3 (5/9M 4,(4/9M 5 1/7 3/7 (5/6M 1,(1/6M (/3M,(1/3M 3 5/9 /9 (3/4M,(1/4M 3 (1/M 4,(1/M 5 1/6 5/1 (4/5M 1,(1/5M (3/5M,(/5M 3 8/14 3/14 (/3M,(1/3M 3 (1/3M 4,(/3M 5 1/5 /5 (3/4M 1,(1/4M (1/M,(1/M 3 3/4 17/8 (11/17M,(6/17M 3 (5/17M 4,(1/17M 5 1/4 3/8 (/3M 1,(1/3M (1/3M,(/3M 3 3/5 1/5 (1/M,(1/M 3 M 5 4/14 5/14 (3/5M 1,(/5M (1/5M,(4/5M 3 1/16 3/16 (1/3M,(/3M 3 (/3M 5,(1/3M 6 1/3 1/3 (1/M 1,(1/M M 3 /3 1/6 M 3 M 6 3/8 5/16 (/5M 1,(3/5M (4/5M 3,(1/58M 4 14/ 3/ (/3M 3,(1/3M 4 (1/3M 6,(/3M 7 4/1 3/1 (1/3M 1,(/3M (/3M 3,(1/3M 4 5/7 1/7 (1/M 3,(1/M 4 M 7 5/1 7/4 (/7M 1,(5/7M (4/7M 3,(3/7M 4 6/8 1/8 M 4-3/7 /7 (1/4M 1,(3/4M (1/M 3,(1/M 4 7/9 1/9 (1/M 4,(1/M 5-8/18 5/18 (1/5M 1,(4/5M (/5M 3,(3/5M 4 8/1 1/1 M 5-11/4 13/48 (/13M 1,(11/13M (4/13M 3,(9/13M 4 1/1 1/1 M 6-1/ 1/4 M M 4 1/14 1/14 M 7 - TABLE II A, B, C AND D CONSTAN A ηρps (1 ρ B C ηρp s(1 + d ξ 1 σ r (1 ρp s(1 + d ξ 1 (1 + dξ σ d D (1 + d ξ 1 (1 + d ξ σ r σ d A η α 1 α P s B η α 1 α Ps(1 + dξ 1 σ r C P s(1 + d ξ 1 (1 + dξ σ d [1, ( ] we have ( ( 1 + v + u 1 v + u I 3 =.5Θ.5u β 1 Γ Γ ( ( β β exp W.5u,.5v (4 8Θ 4Θ where u = ϖ + 1 and the constants A, B, C and D are given in Tale II. Sustituting (4 in ( and then I 1 and I in (, we finally otain the BEP of the system. As seen from (, the BEP performance of AF relaying system is dependent on the considered EH protocol through only I, which itself contains EH protocol dependent terms T (k, i and I 3. and where ideal D A B C D I = Γ(m g I 3 = (1 + d ξ 1 (1 + d ξ σ rσ d ηp s ηp s(1 + d ξ 1 σ r P s(1 + d ξ 1 (1 + dξ σ d (1 + d ξ 1 (1 + d ξ σ r σ d mh 1 k k= i= T (k, ii 3 ( e γ γ Λ(k, i, γdγ. (3 Here, T (k, i and Λ(k, i, γ are defined in Appendix B. Considering the integral variale γ = δ, Θ = m hb Ω h A +, ϖ = mg i+k 1 mh m, v = m g i, β = gc Ω h Ω ga and using IV. PERFORMANCE EVALUATION This section deals with theoretical and computer simulationaided end-to-end results of the considered DH-(AF/DF systems for different system parameters. Unless otherwise stated, we set the path loss exponent to ξ =.7, energy harvesting efficiency to η = 1 and Ω h = Ω g = E[ h ] = E[ g ] = 1. We consider σ = σr = σd. The source to destination distance is set to unity while the source to relay distance is assumed variant and the three nodes are co-linearly located. Moreover, in all figures, theoretical curves are denoted y straight lines and markers represent computer simulation results. Unlike and ideal relaying for which the transmission time interval is fixed and equals to T/, for the case, information processing time is variant and dependent on the parameter α, where αt and (1 αt, respectively stand for EH and information processing time intervals in Fig. (. As a result, BEP should e calculated only during the time interval of (1 αt in which the information processing time intervals for link S R and R D are equal to (1 αt/. On the other hand, for oth and ideal EH relaying protocols, information processing time interval is equal to T/ for each link (Figs. (a and (c. Consequently, (c 18 IEEE. Personal use is permitted, ut repulication/redistriution requires IEEE permission. See for more information.

6 This article has een accepted for pulication in a future issue of this journal, ut has not een fully edited. Content may change prior to final pulication. Citation information: DOI 1.119/TWC , IEEE 6 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. XX, NO. X, XXXX 18 TABLE III MIXTURE OF MODULATIONS FOR PROTOCOL (R = 1.5 AND R = α IP time/t R = 1.5 R = 1/ 1/ M 3 M 4 1/1 11/4 (8/11M 3,(3/11M 4 (7/11M 4,(4/11M 5 1/7 3/7 (1/M 3,(1/M 4 (1/3M 4,(/3M 5 1/6 5/1 (/5M 3,(3/5M 4 (1/5M 4,(4/5M 5 1/5 /5 (1/4M 3,(3/4M 4 M 5 1/4 3/8 M 4 (/3M 5,(1/3M 6 4/14 5/14 (4/5M 4,(1/5M 5 (/5M 5,(3/5M 6 1/3 1/3 (1/M 4,(1/M 5 M 6 3/8 5/16 (1/5M 4,(4/5M 5 (3/5M 6,(/5M 7 4/1 3/1 M 5 (1/3M 6,(/3M 7 5/1 7/4 (6/7M 5,(1/7M 6 (1/7M 6,(6/7M 7 3/7 /7 (3/4M 5,(1/4M 6 M 7 8/18 5/18 (3/5M 5,(/5M 6-11/4 13/48 (6/13M 5,(7/13M 6-1/ 1/4 M 6-8/15 7/3 (4/7M 6,(3/7M 7-11/ 9/4 (1/3M 6,(/3M 7-5/9 /9 (1/4M 6,(3/4M 7-8/14 3/14 M 7 - TABLE IV MIXTURE OF MODULATIONS FOR PROTOCOL (R =.5 AND R = 3 α IP time/t R =.5 R = 3 1/ 1/ M 5 M 6 1/1 11/4 (6/11M 5,(5/11M 6 (5/11M 6,(6/11M 7 1/7 3/7 (1/6M 5,(5/6M 6 M 7 1/6 5/1 M 6-1/5 /5 (3/4M 6,(1/4M 7-1/4 3/8 (1/3M 6,(/3M 7-4/14 5/14 M 7 - to make a fair comparison etween protocols and the other protocols such as ideal and, on an equal spectral efficiency asis, the idea of mixture of modulations given previously in [7] is generalized for different spectral efficiency values. As a result, Tales I, III and IV are provided for mixture of modulations. From Fig. (, as α increases less, time is allocated for the information processing ((1 αt/ per link. As a result, y increasing the α value, we need to increase the modulation order to maintain the same spectral efficiency, namely, the same total numer of the transmitted its for a fair comparison among three protocols. However, it turns out that not for every value of α an M-(QAM/K modulation scheme is possile (M has to e an integer power of. Therefore, we have considered mixture of two modulations schemes to maintain the same spectral efficiency. In Tales I, III and IV, mixture of modulations are calculated for different rates (its/sec/hz. Furthermore, in these tales, α egins y considering small values and lower modulation orders (more information processing time while higher α values correspond to higher order modulations (less information processing time SNR [db] (a SNR [db] ( Fig. 3. DH system end-to-end performance versus SNR for d 1 = d =.5 and R = 1, (a AF and ( DF. As an example, when α = 1/7, the necessary andwidth is determined y the R D transmission interval of 3T/7 seconds, which is lower than that of S R transmission. In order to maintain the spectral efficiency of R = 1 its/sec/hz, we should transmit 7 its y 3 symols during T seconds, namely, y two 4-QAM symols each transmitting its and one 8-QAM symol transmitting 3 its. The necessary andwidth is ( 3T = 7 T Hz and the spectral efficiency is R = ( (/3 + 3 (1/3 (3/T /(7/T = 1 it/sec/hz 3. Figs. 3(a and 3( depict the of DH-AF and DH- DF systems, respectively, for d 1 = d =.5. In Fig. 3, for each SNR value, the corresponding optimum ρ or α values are numerically calculated as shown in Fig. 4. These optimum values are applied to otain the curves given in Fig. 3 for and protocols. From Figs. 3(a and 3(, provides approximately 3 and 4 db gains in SNR compared to, for the values of 1 and 1 3, respectively, for oth m h = m g = 1 and m h = m g = cases. Furthermore, for m h = m g = 1, DF and AF system performances are nearly equivalent for all protocols, which is consistent with the results given in [7] for the non-eh DH system. However, when m h = m g = for which the impact of AWGN increases, DF provides etter performance than AF ecause of decoding at the relay, which avoids forwarding the noisy version of the signal. It is shown in Fig. 3 that for the case, for oth DF and AF systems, the results are given for SNR values approximately higher than 1 db. We oserve from Fig. 4 that, in protocol, for oth AF and DF relaying, the optimum value of α is equal to 5/7 when the SNR value is elow 9 db and 6 db and, 6 db and 4 db for m h = m g = 1 and m h = m g = cases, respectively. However, for aove these SNR values, 3 Note that in Tales. I, III and IV, M p stands for p -QAM (K constellation (c 18 IEEE. Personal use is permitted, ut repulication/redistriution requires IEEE permission. See for more information.

7 This article has een accepted for pulication in a future issue of this journal, ut has not een fully edited. Content may change prior to final pulication. Citation information: DOI 1.119/TWC , IEEE BABAEI et al.: ANALYSIS OF DUAL-HOP RELAYING WITH ENERGY HARVESTING IN NAKAGAMI-M FADING CHANNEL m h =m g =1 m h =m g = 1 -(M-K -(M-QAM -(4-QAM -(4-QAM SNR [db] (a.7.6 m h =m g =1.5.4 m h =m g = SNR [db] ( or Fig. 4. Optimum ρ and α values in terms of minimum BEP for d 1 = d =.5 and R = 1, (a AF and ( DF. Fig. 5. DH-AF system end-to-end performance versus ρ and α for SNR = 3 db, d 1 = d =.5 and R = 1. the optimum α is equal to 1/3. From Tale I, for R = 1, the corresponding modulation schemes are 18-QAM when α = 5/7 and 8-QAM when α = 1/3. On the other hand, since we have assumed the common approximation of P P s /k, which is valid for the high SNR, at low SNR values where a higher modulation order (18-QAM for α = 5/7 is required (as can e seen from Figs. 4(a and 4(, the computer simulation and theoretical results do not match perfectly with each other. Therefore, the corresponding SNR values for 18- QAM have not een considered in Fig. 3 for oth AF and DF systems. However, the results are given for SNR values for which α = 1/3 and 8-QAM is employed. Finally, for and ideal protocols, the curves in Fig. 3 have een given for SNR values aove db since for these protocols, the same spectral efficiency value (R = 1 is achieved with a lower modulation order (4-QAM. In Figs. 4(a and 4(, the optimum ρ and α values, which minimize the BEP, are depicted with respect to SNR for DH-AF and DH-DF systems, respectively. From these curves we conclude that for protocol, the optimum value of ρ increases from.54 to.7 and from.47 to.73 for AF and DF, respectively, when SNR increases from to 35 db. We oserve that, in protocol, for oth AF and DF, the optimum value of α is equal to 5/7 when the SNR value is elow 9 db and 6 db and, 6 db and 4 db for m h = m g = 1 and m h = m g = cases, respectively. However, for aove these SNR values, the optimum α is equal to 1/3. From Tale I, for R = 1, the corresponding modulation schemes are 18-QAM (K when α = 5/7 and 8-QAM (K when α = 1/3. Note that since the optimization for protocol is performed for specific values of α, the resulting curves are discontinuous for oth AF and DF cases in Fig. 4. Figs. 5 and 6 show the performances of DH-AF and DH-DF systems versus ρ and α, respectively, for the parameters of d 1 = d =.5, SNR = 3 db and R = 1. For comparison purposes, the curves of the ideal protocol are also depicted in these figures for and protocols. For channel parameter values m h = m g = 1, DH-AF and DH-DF systems provide approximately the same performance while for m h = m g =, DH-DF system outperforms DH-AF system. From Figs. 5 and 6, for protocol when R = 1, the optimum α value for oth DH-DF and DH-AF systems is equal to 1/3, which corresponds to 8-QAM (K modulation from Tale I. However, for and ideal protocols, the employed modulation is 4-QAM and independent of ρ. Note that for, curves are not smooth due to the use of different modulation levels for different α values to maintain the spectral efficiency at a fixed value. Moreover, gives etter performance compared to when ρ > 1/3 and ρ >. for the m h = m g = 1 and m h = m g = cases, respectively, for oth AF and DF relaying. Furthermore, theoretical and computer simulation results perfectly match for, and ideal protocols. In Fig. 7, performance is provided with respect to d 1 for, and ideal protocols. For each d 1 value, the optimum α and ρ values are employed in Fig. 7 for oth systems. The results show that d 1 =.5 gives the optimum for oth DH-AF and DH-DF systems. In case of R = 1, for and ideal protocols, the employed modulation is 4-QAM and independent of ρ while for protocol, α = 1/3 gives the optimum results for oth DH-AF and DH-DF systems and all values of d 1, where R = 1 corresponds to 8-QAM. From Figs. 7(a and 7(, it is concluded that protocol provides etter performance than for oth AF and DF cases. Fig. 8 shows the performance with respect to the channel parameter m h for two fixed m g values and R = 1, where the optimum ρ and α values are applied. From the theoretical and simulation results, it is concluded that the performances of the DH-AF and DH-DF systems are (c 18 IEEE. Personal use is permitted, ut repulication/redistriution requires IEEE permission. See for more information.

8 This article has een accepted for pulication in a future issue of this journal, ut has not een fully edited. Content may change prior to final pulication. Citation information: DOI 1.119/TWC , IEEE 8 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. XX, NO. X, XXXX (M-K -(M-QAM -(4-QAM -(4-QAM or Fig. 6. DH-DF system end-to-end performance versus ρ and α for SNR = 3 db, d 1 = d =.5 and R = 1. Fig. 8. DH system end-to-end performance versus m h for SNR = 3 db, d 1 = d =.5 and R = 1, (a AF and ( DF Fig. 7. DH system end-to-end performance versus d 1 for SNR= 3 db, R = 1 and (d 1 + d = 1. (a AF and ( DF. Fig. 9. DH system end-to-end performance versus R for SNR = 3 db, d 1 = d =.5 and M-QAM, (a AF and ( DF. approximately equivalent for m g = 1, however, for m g =, DH-DF system slightly outperforms DH-AF. protocol provides etter performance than since higher values of the channel parameters enale the relay to correctly decode the received signal and to harvest much more energy. The performances of DH-AF and DH-DF systems versus R for different system parameter values are given in Figs. 9(a and 9(, respectively. In this figure, M-QAM is considered since it outperforms M-K for M > 4. Also, the curve of the ideal protocol is depicted in this figure for comparison purposes. For each value of R, these curves are otained for corresponding optimum values of ρ and α. From Figs. 9(a and 9(, we oserve that outperforms for oth DH-AF and DH-DF systems, where the maximum difference etween two systems are otained when R =.5. Moreover, due to our approximation in (, increasing R results in increased modulation order for which the approximation in ( ecomes loose, especially when m h = m g = 1, for oth DH-AF and DH-DF systems. V. CONCLUSION In this paper, we have considered the energy harvesting issue in a conventional DH relaying network where the relay applies, and ideal protocols with AF/DF relaying tech (c 18 IEEE. Personal use is permitted, ut repulication/redistriution requires IEEE permission. See for more information.

9 This article has een accepted for pulication in a future issue of this journal, ut has not een fully edited. Content may change prior to final pulication. Citation information: DOI 1.119/TWC , IEEE BABAEI et al.: ANALYSIS OF DUAL-HOP RELAYING WITH ENERGY HARVESTING IN NAKAGAMI-M FADING CHANNEL 9 niques to harvest energy from the received RF source signal and to transmit it to the destination with the harvested energy. Tight closed-form analytical expressions for the BEP of oth DH-AF and DH-DF systems have een derived and approved y the computer simulations. Moreover, since IP time interval varies in protocol with respect to the parameter α, the mixture of modulations technique has een applied to maintain a constant spectral efficiency level. Finally, optimal values of the system parameters, which minimize BEP, have een otained for oth DH-AF and DH-DF systems. Our work has shed light on the performance of AF and DF-aided DH networks employing EH and provided guidelines for the system designer. An adaptive selection of time slots for EH systems can e considered as a future work. APPENDIX A PDF OF THE PRODUCT OF TWO CHI-SQUARE DISTRIBUTED RANDOM VARIABLES The PDF of random variale Z = h g is given in [3, 6.148] as 1 ( z f Z (z = x f h (xf g dx (5 x where for i {h, g}, [8,.3.1] ( mi mi x mi 1 f i (x = Γ(m i exp ( xm i/ω i. (6 Ω i Sustituting (6 in (5, after simplification and using [1, 3.478,4] we have ( Ω/ ( mg Ω h f Z (z = F z ɛ 1 mh m g K Ω z (7 Ω g m h Ω h Ω g where m h and m g are the Nakagami fading parameters and Ω h = E[ h ], Ω g = E[ g ], Ω = m h m g, ɛ =.5(m h + m g and F = (m h /Ω h m h (m g /Ω h mg Γ(m h 1 Γ(m g 1. APPENDIX B CDF OF THE SNR IN AF STRATEGY The received SNR at the destination for AF relaying is given as γ = A h 4 g B h g + C h + D (8 where the constants A, B, C and D differ for, and ideal protocols. For high SNR, taking D =, (8 can e rewritten as γ AXY (9 BX + C where Y = h and X = g. Using [3, Chap. 6], the CDF of γ can e calculated as ( ( γ F γ (γ = F Y B + C X f X (xdx. (3 A X Assuming that the channels are exposed to Nakagami-m fading, CDF of the channel gain is given in [8,.3.4] as F Y (y = 1 exp( ym h /Ω h ( k m h 1 1 ymh. (31 k= k! Ω h Sustituting (6 and (31 in (3 and using a inomial expansion [1, Eq ] and [1, Eq ], after some simplification, CDF of γ can e written as F γ (γ = 1 Γ(m g where 1 T (k, i = (k i!i! Λ(k, i, γ = exp mh 1 k ( mh k= Ω h A ( m hb Ω h A γ i= κ ( Cmg Ω g γ κ K mg i and κ = (m g i + k/, respectively. REFERENCES T (k, iλ(k, i, γ (3 mg +i B k i, ( m h m g C Ω h Ω g A γ [1] L. R. Varshney, Transporting information and energy simultaneously, in Proc. 8 IEEE Int. Symp. on Info. Theo., July 8, pp [] P. Grover and A. Sahai, Shannon meets Tesla: Wireless information and power transfer, in Proc. 1 IEEE Int. Symp. on Info. Theo., June 1, pp [3] A. A. Nasir, X. 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10 This article has een accepted for pulication in a future issue of this journal, ut has not een fully edited. Content may change prior to final pulication. Citation information: DOI 1.119/TWC , IEEE 1 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. XX, NO. X, XXXX 18 [18] Y. Gu, H. Chen, Y. Li, and B. Vucetic, Wireless-powered two-way relaying with power splitting-ased energy accumulation, in Proc. 16 IEEE Gloal Commun. Conf. (GLOBECOM, Dec 16, pp [19] N. T. P. Van, S. F. Hasan, X. Gui, S. Mukhopadhyay, and H. Tran, Three-step two-way decode and forward relay with energy harvesting, IEEE Commun. Lett., vol. 1, no. 4, pp , Apr. 17. [] Z. Ding, I. Krikidis, B. Sharif, and H. V. Poor, Wireless information and power transfer in cooperative networks with spatially random relays, IEEE Trans. Wireless Commun., vol. 13, no. 8, pp , Aug. 14. [1] A. Jeffrey and D. Zwillinger, Tale of Integrals, Series, and Products. Academic press, 7. [] M. Simon and M. Alouini, Digital Communication over Fading Channels, nd ed. Wiley, 5. [3] A. Papoulis and S. Pillai, Proaility, Random Variales, and Stochastic Processes, 4th ed. McGraw-Hill,. [4] R. H. Y. Louie, Y. Li, and B. Vucetic, Practical physical layer network coding for two-way relay channels: performance analysis and comparison, IEEE Trans. on Wireless Commun., vol. 9, no., pp , Fe. 1. [5] Wolfram. (1 The Wolfram functions site. Internet. [Online], http: //functions.wolfram.com. [6] V. S. Adamchik and O. I. Marichev, The algorithm for calculating integrals of hypergeometric type functions and its realization in reduce system, in Proc. of the Int. Symp. on Symolic and Algeraic Comput., ser. ISSAC 9, 199, pp [7] M. O. Hasna and M. S. Alouini, End-to-end performance of transmission systems with relays over Rayleigh-fading channels, IEEE Trans. Wireless Commun., vol., no. 6, pp , Nov. 3. [8] J. G. Proakis, Digital Communications, 5th ed. McGraw-Hill, Ertugrul Basar (S 9-M 13-SM 16 was orn in Istanul, Turkey, in He received the B.S. degree (Hons. from Istanul University, Turkey, in 7, and the M.S. and Ph.D. degrees from Istanul Technical University, Turkey, in 9 and 13, respectively. From 11 to 1, he was with the Department of Electrical Engineering, Princeton University, Princeton, NJ, USA, as a Visiting Research Collaorator. He was an Assistant Professor with Istanul Technical University from 14 to 17, where he is currently an Associate Professor of Electronics and Communication Engineering. His primary research interests include MIMO systems, index modulation, cooperative communications, OFDM, and visile light communications. Recent recognition of his research includes the Young Scientists Award of the Science Academy (Turkey in 18, Turkish Academy of Sciences Outstanding Young Scientist Award in 17, the first-ever IEEE Turkey Research Encouragement Award in 17, and the Istanul Technical University Best Ph.D. Thesis Award in 14. He is also the recipient of four Best Paper Awards including one from the IEEE International Conference on Communications 16. Dr. Basar currently serves as an Editor of the IEEE TRANSACTIONS ON COMMUNICATIONS and Physical Communication (Elsevier, and as an Associate Editor of the IEEE COMMUNICATIONS LETTERS and the IEEE ACCESS. Mohammadreza Baaei (S 11 received his B.S. degree from Tariz University, Tariz, Iran, in 11, and M.S. degree from Istanul Technical University, Istanul, Turkey, in 16. He is currently a Ph.D. student and a memer of Wireless communication laoratory in Istanul Technical University, Istanul, Turkey. He has served as a TPC memer for several IEEE conferences and as a reviewer for IEEE journals. His research interests include MIMO systems, cognitive radio, cooperative communications, spatial modulation, energy harvesting and NOMA. Ümit Ay golü received his B.S., M.S. and Ph.D. degrees, all in electrical engineering, from Istanul Technical University, Istanul, Turkey, in 1978, 1984 and 1989, respectively. He was a Research Assistant from 198 to 1986 and a Lecturer from 1986 to 1989, at Yildiz Technical University, Istanul, Turkey. In 1989, he ecame an Assistant Professor at Istanul Technical University where he ecame an Associate Professor and Professor in 199 and 1999, respectively. His current research interests include MIMO systems, cooperative communications, cognitive radio, spatial modulation, energy harvesting and NOMA (c 18 IEEE. Personal use is permitted, ut repulication/redistriution requires IEEE permission. See for more information.