Performance of Amplify-and-Forward Relaying with Wireless Power Transfer over Dissimilar Channels

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1 j.eee ELEKTRONIKA IR ELEKTROTECHNIKA ISSN 39-5 VOL. NO. 5 5 Performance of Amplify-an-Forwar Relaying with Wireless Power Transfer over Dissimilar Channels Dac-Binh Ha Duc-Dung Tran Vu Tran-Ha Een-Kee Hong Faculty of Electrical an Electronics Engineering Duy Tan University Danang Vietnam School of Electronic an Information Kyung Hee University Yongin South Korea tranucung@tu.eu.vn Abstract Relaying transmission is a promising approach for enhancing the performance of wireless networks meanwhile wireless power transfer is an emerging solution for prolonging the lifetime of energy constraine relay noes. In this framework the amplify-an-forwar (AF) relay network consisting of a power transfer an information source an energy constraine relay an a estination over issimilar faing channels is taken into account. First the relay employs the time switching-base relaying (TSR) protocol to harvest energy from the source. Accoringly the relay supports the source transmits information to the estination. By utilizing the statistical characteristics of signal-to-noise ratio (SNR) the close-form expressions of outage probability () an average symbol error probability (ASEP) are erive. By means of the obtaine result of we also investigate throughput of the system for elay-limite transmission moe. Moreover we accoringly evaluate the analysis in etails an assess the performance of the consiere system in various system parameters such as energy harvesting time energy harvesting efficiency an relay location. Finally Monte-Carlo simulation is also contribute to confirm the correctness of the analytical results. Inex Terms Wireless power transfer energy harvesting amplify-an-forwar outage probability average symbol error probability throughput. I. INTRODUCTION Raio frequency (RF) energy harvesting (EH) a technique to collect wireless energy from the surrouning environment for prolonging the lifetime of a wireless network has receive significant attention recently from both acaemia an inustry [] [5]. Since the harveste energy is typical in a small amount an also ranom it is ifficult to satisfy short-term performance. Relay methoology has a great potential to increase the iversity that can improve the performance of wireless networks [6] [9]. As a euction many researchers have pai attention on performance of EH relay networks in recent years [] [4]. For relate prominent works in [] a cooperative system in which EH noes volunteer evaluate as AF relays whenever they have sufficient energy for the transmission over frequency-flat block-faing Rayleigh channels is Manuscript receive May 6 5; accepte July consiere. The close-form expressions for the symbol error rate (SER) of the system an the asymptotic energy savings at the source from the exploit of EH relays are reveale. The analysis showe that the energy usage at an EH relay epens not only on the relay s energy harvesting process but also on its transmit power setting an the other relays in the system. Chalise et. al. [] eals with the performance limits of a two-hop multi-antenna AF relay system in the presence of a multi-antenna energy harvesting receiver. The source an relay noes of the two-hop AF system employ orthogonal space-time block coes for ata transmission. Moreover the trae-offs in information rate an energy transfer were characterize by the bounary of solving joint source an relay precoer optimization problems. In the paper [3] the researchers investigate a wireless energy harvesting an information transfer protocol in cognitive relay networks over the quasi-static Rayleigh faing channels. The seconary transmitter harvests energy from the receive primary signal an hence forwars the resulting signals along with the seconary signal. The seconary receiver can also collect the ambient energy an processes the remaining signal to remove the primary interference. Following this scenario they analytically erive the exact expressions of the outage probabilities for both primary an seconary networks. Base on the propose protocol they analyse the rate-energy trae-off between the maximum ergoic capacity an the maximum harveste energy in the seconary network. Taking into account the work [4] an AF cooperative network is consiere where an energy constraine relay noe harvests energy from the receive RF signals an then uses that harveste energy to forwar the source signal to the estination noe over Rayleigh faing channels. Analytical expressions for the outage probability an the ergoic capacity are inferre for the elay-limite an the elay-tolerant transmission moes. Due to the movement of wireless evices the channels of two hops may be subject to ifferent faing property. Especially in energy harvesting relay networks the relay shoul be close to energy station. Therefore the assumption of all above stuies that the channels of two hops in energy harvesting relay networks are subject to the same faing

2 ELEKTRONIKA IR ELEKTROTECHNIKA ISSN 39-5 VOL. NO. 5 5 property is weakene. Moreover ue to the relay is close to energy station the line-of-sight (LOS) wave shoul exist between the source an the relay. There have been many works consiering the heterogeneity faing characteristic between the channels in relay network appreciably however without the existence of EH scheme [6] [7]. In our paper we focus on the performance of power transfer system consisting of a power an information source an energy constraine relay an a estination that all of them are equippe with single antenna over issimilar Rayleigh/Rician faing channels. The main contributions of this paper fall in the erivations of the close-form expression of outage probability an average symbol error probability by utilizing statistical characteristics of the SNR. Aitionally by means of the result of we carry out evaluating the throughput at the estination. Moreover we also analyse the performance of the consiere system in various system parameters such as energy harvesting time energy harvesting efficiency an relay location. The rest of this paper is organize as follows. Section II presents the system an channel moel. Performance of the consiere system is analyse in Section III. In Section IV we show the numerical results. We conclue our work in Section V. II. SYSTEM AND CHANNEL MODEL We consier a two-hop AF communication system with energy harvesting illustrate in Fig.. Relay h sr h r Destination Power transfer & Information transmission channel Relay channel Source Fig.. System moel for ual-hop relay networks with energy harvesting. The network consists of one power transfer an information source enote by S one estination enote by D an one energy constraine relay noe enote by R. In this paper we consier the following scenario: Direct link between the source an the estination is not available ue to this link is in poor transmission conition an the communication from S to D is performe by the help of relay R. Relay harvests energy from the power transfer source S an helps the source convey information to the estination by using the TSR protocol []. The source transmits the power an information to the relay over Rician faing channel. Meanwhile the relay amplifies the receive signal an transmits information to estination over Rayleigh faing environment. This supposition is reasonable since the energy constraine relay noe usually is close to the power transfer station. In fact the channel between the source an relay has LOS whereas the channel between the relay an estination might not necessarily be the same. Note that Rician faing occurs when one of the paths typically a LOS signal is much stronger than the others. We also have suppose that in each block time T these channels are constant an inepenently an ientically istribute (i.i.). All transmitters an receivers are equippe with a single antenna. Compare to the power use for signal transmission from the relay to the estination the processing power require by the transmit/receive circuitry at the relay is insignificant. So it can be ignore. First the relay harvests energy from the power transfer source in the time uration of T which are [4] Eh hsr Pr a ( ) T / ( ) where is the energy conversion efficiency which epens on the rectification process an the energy harvesting circuitry; is the transmit power of the source; T is the block time in which a certain block of information is conveye from the source noe to the estination noe; is the fraction of the block time in which relay collects energy from the source signal. Consiering the link from the source to relay hsr is the channel power gain is the istance is the path-loss exponent; a ( ) h sr. In the uration of () T / the source transmits signal x(t) to the relay an the signal receive at relay as follows hsr y( t) x( t) nr () where nr is white complex Gaussian noise nr ~ ( N). In the remain uration of T / the relay amplifies the signal receive from the source an retransmits to the estination. Assume that the channel coefficient hsr is available to the relay. The receive signal at estination is given by P ( ) r hr z t y( t) n E y( t) where an are the istance an path-loss exponent from the relay to the estination respectively. n D is white complex Gaussian noise n ~ ( N). For simplicity we suppose N N N ; E is expectation operator. We rewrite z(t) as (3) 9

3 ELEKTRONIKA IR ELEKTROTECHNIKA ISSN 39-5 VOL. NO. 5 5 z( t) P P h h h x( t) r s sr r sr N P r s sr h P h N r n r n The instantaneous receive SNR at the estination can be given by Pr ee ( Pr ) N N a ( a ) N N h where sr h r. In high SNR region it hols that ee ap ~ S. ( a ) N The probability ensity function (PDF) of RV is [6] K ( K ) x ( K ) e K( K ) x f ( x) e I hsr E where. (4) (5) (6) (7) K is the Rician K-factor efine as the ratio of the powers of the LOS component to the scattere components an moifie Bessel function of the first kin. We can rewrite (7) as follows I is the zero-th orer l ( qk) l qx f ( x) p x e (8) l ( l! ) K l ( K ) e K x where p q an I( x) l l ( l!) [5]. The cumulative ensity function (CDF) of RV can be constitute as in [9] l l m p K q m q F ( ) ( ). f x x e (9) q l m l! m! The PDF an CDF of RV for PDF an for CDF as x ( ) are respectively given by: f x e () where / h r E. A. Outage Probability () ( ) x F x e () III. PERFORMANCE ANALYSIS Outage probability is an important performance metric that is generally use to characterize a wireless communication system. It is efine as the probability that the instantaneous en-to-en SNR - ee falls below the preetermine threshol given by a Pout F Pr e e ( a ) N where that ee () F is CDF of the instantaneous R en-to-en SNR R is fixe transmission rate at the source. We can erive the outage probability more etail in the Appenix A). B. Throughput ( ) P out as (6) (see At this point we analyse throughput ( ) at the estination noe for elay-limite transmission moe. It is foun out by evaluating at a fixe source transmission rate R bits/s/hz in which R log ( ). We observe that the source transmit information at the rate of R bit/s/hz an the effective communication time from the source noe to the estination noe in the block time T is ( ) T /. Thence throughput at the estination is efine as ( ) T / ( )( Pout ) R ( Pout ) R. (3) T C. Average Symbol Error Probability (ASEP) ASEP which is another prominent measure is very useful for system esigners to evaluate a wireless communication network. The ASEP of communication link over faing channels is given by ( e) Q f (4) ee t where Q( x) e / t is the Gaussian Q-function π x an are constants which is specific for moulation type. Accoring to [6] we can further express (3) as follows t t / ( e) F e t ee π t t/ / F e t t. ee (5) π 9

4 ELEKTRONIKA IR ELEKTROTECHNIKA ISSN 39-5 VOL. NO. 5 5 By using the calculation result of (6) we obtain as (7) (see Appenix B). IV. NUMERICAL RESULTS AND DISCUSSION In this section we provie simulation an analytical results for an ASEP to clarify the impact of parameters such as energy harvesting time ( ) energy harvesting efficiency ( ) an relay location ( ) on these two quantities. A. Verification of Analytical Results In this subsection the analytical results for an ASEP are evaluate an verifie through simulations. Figure plots an ASEP with respect to P S an the applie moulation types are BK an QK respectively. In general we can see that the superior match between analytical an simulation results occurs in the high SNR or in large region. In more clear explanation when P S hols low values the analytical an simulation results oes not match very well because we use approximate formulation of the receive SNR at the estination ( ee ) as (6). In aition Fig. also inicates obviously that an ASEP ecrease with the growth of ue to the increase level of ee an ASEP for BK moulation is lower than that of QK moulation ASEP - BK ASEP - QK P S (Bm) Fig.. an ASEP vs. transmit power with =.4 = = = K = 3 R = = = 3 N =.. B. Effect of Energy Harvesting Time ( ) In Fig. 3 an Fig. 4 the impacts of on ASEP (Fig. 3) an throughput (Fig. 4) are shown. Figure 3 epicts that when scales up an ASEP go own. This can be explaine by that there is more time for energy harvesting as grows. Therefore we may observe the smaller values of an ASEP at the estination noe when grows. For the throughput in Fig. 4 we can realize the existence of the specific value of (we can let it be * which is roughly equal to. in our consiere system) which helps to get peak value. Throughput is irectly proportional to in the range from to * however it starts with ecreasing from the * value in the entire range. The reason is that there is less time for energy harvesting when is smaller than * value. Consequently less energy is gathere which leas to higher can be obtaine an thence the smaller values of throughput are observe at the estination noe. In the other wors for the values of which is greater than * the more waste of time on energy harvesting is realize while less time is available for information transmission. Hence lower throughput values are achieve at the estination noe because of smaller value of ( - )/ ASEP - BK ASEP - QK Fig. 3. an ASEP vs. energy harvesting time with = W = = = K = 3 R = = = 3 N =.. Throughput or Fig. 4. Throughput vs. or with = W = - K = 3 R = 3 = = 3 N = ASEP - BK ASEP - QK Fig. 5. an ASEP vs. energy harvesting efficiency with = W =.4 = = K = 3 R = = = 3 N =.. 93

5 ELEKTRONIKA IR ELEKTROTECHNIKA ISSN 39-5 VOL. NO. 5 5 C. Effect of Energy Harvesting Efficiency ( ) ASEP - BK ASEP - QK Fig. 6. an ASEP vs. the istance from source to relay with = W =.4 = = - K = 3 R = = = 3 N =.. The effects of on ASEP an throughput shown in Fig. 4 ( ) an Fig. 6 ( an ASEP). Consiering Fig. 5 an ASEP ecrease with respect to the growth of. This can be explaine that the higher is the more energy is harveste. As a result the lower values of an ASEP at the estination noe are viewe. At the same time we attain the higher value of when increases ue to the egraation of. This result is shown in Fig. 4. D. Effect of Relay Location ( ) The effects of Relay location ( ) on ASEP an are shown in Fig. 4 an Fig. 6. In Fig. 6 contrary to two aforementione cases makes an ASEP grow when it scales up. In fact the higher values of lea to the smaller values of energy are collecte as well as the receive signal strength (y(t)) at the relay noe. Therefore we observe that the achievable values of fall own as in Fig. 4 ue to the reuction of receive signal strength at the estination. V. CONCLUSIONS are In this paper we have erive the close-form expressions of an ASEP. Base on the result of we have examine throughput for elay-limite transmission moe. The consiere system moel comprises a power transfer an information source an energy constraine relay an a estination over issimilar faing environments. Specifically the channels between the source to relay an the relay to estination are assume to unergo Rician an Rayleigh faing respectively. These analytical erivations have been valiate by Monte-Carlo simulation. Furthermore we have also istinctly evaluate the impact of system parameters such as energy harvesting time ( ) energy harvesting efficiency ( ) an relay location ( ) on stuie quantities in our work. APPENDIX A Here we calculate () as (6). Note that we have use the following relation in our calculation m m m mn n ( x y) x y n n t t / t e t t where are positive real values an moifie Bessel function of the secon kin an APPENDIX B. th is the orer. Here we employ two following equations (3.36.) an ( ) in [5] to yiel (7) where qt e π t t q t t e t t. exp is the Whittaker function. p q a P F Pr f out ee a / N a F f a / N m n q q l m l m t p m K q / N n t a / N e t e t q n l m n n l! m! a / N ( )/ m ( n )/ q l m l n K ( ) q / N q e l m ( n )/ n n l! n!( m n)! a / N a / N. (6) 94

6 ELEKTRONIKA IR ELEKTROTECHNIKA ISSN 39-5 VOL. NO. 5 5 t t/ / ( e) F ee e t t π ( )/ ( )/ qt l m l n m n p K ( ) qt P / / / S N qt t e ( )/ n e t t π q l m n n l! n!( m n)! a / N a / N t/ / e t t π ( )/ q l m l ( n)/ m n t p K ( ) q mn/ / N qt t e ( )/ n t q π l m n n l! n!( m n)! a / N a / N l m l n/ mn/ m( n)/ p K ( ) q q q π l m n n/ l! n! ( m n)! a / N / N 3 q q m n m exp m( n)/( n)/. (7) a ( q P S / N ) a ( q P S / N ) REFERENCES [] V. Raghunathan S. Ganeriwal M. Srivastava Emerging techniques for long live wireless sensor networks IEEE Commun. Mag. vol. 44 no. 4 pp [Online]. Available: [] P. Popovski A. M. Foulagar O. Simeone Interactive joint transfer of energy an information IEEE Trans. On Commun. vol. 6 no. 5 pp [Online]. Available: TCOMM [3] J. Xu R. Zhang Throughput optimal policies for energy harvesting wireless transmitters with non-ieal circuit power IEEE J. Sel. Area. Commun. vol. 3 no. pp [Online]. Available: [4] S. Luo R. Zhang T. J. Lim Optimal save-then-transmit protocol for energy harvesting wireless transmitters IEEE Trans. on Wireless Commun. vol. no. 3 pp [Online]. Available: [5] L. Liu R. Zhang K. C. Chua Wireless information transfer with opportunistic energy harvesting IEEE Trans. Wireless Commun. vol. no. pp [Online]. Available: [6] H. A. Suraweera G. K. Karagianniis P. J. Smith Performance analysis of the ual-hop asymmetric faing channel IEEE Trans. Wireless Communi. vol. 8 no. 6 pp [Online]. Available: [7] A. K. Gurung F. S. AI-Qahtani Z. M. Hussain H. Alnuweiri Performance analysis of amplify-forwar relay in mixe Nakagami-m an Rician faing channels in Proc. Int. Conf. Avance Technologies for Communications Ho Chi Minh City Vietnam pp [Online]. Available: ATC [8] L. Dong Z. Han A. P. Petropulu H. V. Poor Improving wireless physical layer security via cooperating relays IEEE Trans. Signal Processing vol. 58 no. 3 pp [Online]. Available: [9] M. R. Bhatnagar On the capacity of ecoe-an-forwar relaying over rician faing channels IEEE Communications Letters vol. 7 no. 6 pp [Online]. Available: [] B. Meepally N. B. Mehta Voluntary energy harvesting relays an selection in cooperative wireless networks IEEE Trans. on Wireless Commun. vol. 9 no. pp [Online]. Available: [] B. K. Chalise Y. D. Zhang M. G. Amin Energy harvesting in an OSTBC base amplify-an-forwar MIMO relay system in Proc. IEEE Int. Conf. on Acoustics Speech an Signal Processing (ICASSP) pp [Online]. Available: [] A. A. Nasir X. Zhou S. Durrani R. A. Kenney Relaying protocols for wireless energy harvesting an information processing IEEE Trans. Wireless Communications vol. no. 7 pp [Online]. Available: 4 [3] Z. Wang Z. Chen L. Luo Z. Hu B. Xia H. Liu Outage analysis of cognitive relay networks with energy harvesting an information transfer in Proc. IEEE ICC 4 - Wireless Communications Symposium Syney Australia 4 pp [Online]. Available: [4] A. A. Nasir X. Zhou S. Durrani R. A. Kenney Relaying protocols for wireless energy harvesting an information processing IEEE Trans. Wireless Communications vol. no. 7 pp [Online]. Available: 4 [5] I. Grashteyn I. Ryzhik Table of Integrals Series an Proucts. Acaemic Press 7. 95