Energy Efficiency Analysis and Power Allocation of Cooperative Communications in Wireless Sensor Networks

Transcription

1 Journal of Councatons Vol. 8, No. 12, Deceber 2013 Energy Effcency Analyss and ower Allocaton of Cooperatve Councatons n Wreless ensor Networks We u, Guangng, and n Zhu chool of Mechancal, Electrcal and Inforaton Engneerng, handong Unversty, Weha , Chna Eal: luwe1206.sw@163.co; gl@sdu.edu.cn; zhulngchna@126.co Abstract In order to prove the energy savng perforance of cooperatve councaton, a novel power allocaton soluton, naed Half Transsson ower Allocaton oluton (HTA, s proposed n ths paper. In ths soluton, the transsson power of the relay for forwardng the packet s half of the transsson power of the source. Based on the energy effcency analyss, HTA outperfors the equal transsson power allocaton soluton n energy savng of relay and cooperaton gan, eanwhle the proposed soluton s easy to be pleented. The nuercal results also show that the cooperatve transsson s ore energy effcent than the drect and ult-hop transsson when the source-destnaton dstances s larger than a sall threshold. Index Ters cooperatve councatons, energy effcency, power allocaton, wreless sensor networks I. INTODUCTION Energy-constraned networks, such as wreless sensor networks, are coposed of nodes typcally powered by batteres due to constrants n sze and cost, for whch replaceent or rechargng s very dffcult [1]. Wth fnte energy, only a fnte aount of nforaton can be transtted. Therefore, the energy consupton of the sensors s a key ssue n the desgn and realzaton of the wreless sensor networks. Mult-nput-Mult-output (MIMO technques based on antenna arrays can rearkably prove syste capacty, and reduce the requred transsson power under a certan throughput requreent due to spatal dversty, whch s studed to cobat the effects of ultpath fadng n wreless councatons. Even though t s practcal to ount ultple antennas due to the ltaton n sze of the nodes, ultple nodes could cooperate for forng a vrtual antenna array to acheve spatal dversty [2] [3]. Cooperatve councaton technques, no doubt, can be regarded as one of the potental solutons to nze the requred transts energy by explotng the dversty obtaned by the cooperaton aong the nodes n wreless sensor networks. Manuscrpt receved August 6, 2013; revsed October 26, Ths work n part was supported by cence and Technology Developent roject of handong under roject No.2011GF Addtonal support s provded by a grant fro Independent Innovaton Foundaton of handong Unversty. Correspondng author eal: gl@sdu.edu.cn. do: /jc ower allocaton can further prove the perforance of cooperatve councaton. The energy-effcent cooperatve councaton based on power control and selectve sng-relay has been studed n [4], whch confrs that cooperatve councaton can acheve sgnfcant energy savngs and prolongs the network lfete consderably. In [5], the cooperatve selectve decode-and-forward ( protocol has been nvestgated, n whch cooperatve transsson outperfors snglehop and ult-hop transssons. The energy effcency of the selectve decode-and-forward protocol and the ncreental decode-and-forward (IDF protocol have been studed n [6], where cooperaton ay be consderably ore energy effcent than non-cooperatve schees, by takng nto account the energy consupton of the F crcutry, especally f a feedback channel s avalable. The power allocaton of cooperatve councatons has been studed n [7]-[10], n whch the proposed optal power allocaton strateges outperfor the equal power allocaton to soe extent, except pleentng ore coplcated than the equal power allocaton. Based on the above cted works, the energy effcency analyss and a novel suboptal power allocaton schee are presented n ths paper. In order to odelng and analyzng accurately, the followng characterstcs are covered based on [6]: a the crcutry energy consupton for transttng and recevng; b the spectral effcency loss at the recever when eployng ult-hop and cooperatve councatons; c Nakaga- dstrbuton for descrbng the rado propagaton envronent. The reander of ths paper s organzed as follows. ecton II presents the syste odel and the outage analyss. The energy consupton and power allocaton analyss of the transsson schees are studed n ecton III. Fnally, nuercal results are dscussed n ecton IV, and conclusons are presented n ecton V. II. YTEM MODE As shown n Fg. 1, the cooperatve transsson syste odel conssts of three relevant nodes, whch are the source, the relay, and the destnaton. Cooperatve transsson takes advantage of the wreless edu broadcast nature. The cooperatve councaton s consdered n two slots. The frst te slot s the broadcast phase, when the packet sent by the source to the destnaton s also overheard by the relay. The second te slot s the cooperaton phase, when the relay 870

2 Journal of Councatons Vol. 8, No. 12, Deceber 2013 cooperates wth the source, forwardng the sae packet through a dfferent and ndependent channel, thus achevng the cooperaton dversty. In, the relay cooperates whenever the packet fro the source has been correctly receved at the relay. Dfferng fro, IDF consders the exstence of a feedback channel fro the destnaton, so that the relay cooperates only recevng a negatve acknowledgeent (NACK. In ths paper, cooperatve transsson s studed nstead of IDF, because that IDF produces delay due to the NACK sgnal, coparng to. And s easer to realze than IDF. In order to contrastvely analyss the energy effcency of the cooperatve councaton, another two transsson strateges are consdered, ncludng drect transsson and ult-hop transsson. In drect transsson schee, the source drectly councates wth the destnaton. In the ult-hop transsson schee, the councaton s generally carred out n two dfferent te slots. In the frst te slot, the source sends a packet to the relay, and the relay receves the packet. In the second te slot, the relay forwards the packet to the destnaton. The aylegh dstrbuton s one of the ost accepted odels to descrbe the behavor of the rado propagaton envronent. However, the Nakaga- dstrbuton ore closely atches wth the practcal wreless councaton envronent than the aylegh dstrbuton. Therefore, the Nakaga- dstrbuton s used for descrbng the wreless councaton envronent n ths paper. And the channel n long-ter quas-statc fadng s assued, whch eans that the channel s strongly correlated n te, reanng n the deep fade state for a long te. The syste perforance s characterzed n ters of outage probablty n ths paper. Outage s defned as the event that the receved N (gnal-to-nose ato falls below a certan threshold. Therefore, the probablty of outage III. In ths secton, the drect, ult-hop and transsson schees are foralzed. And a novel power allocaton soluton for cooperatve transsson s proposed. A. roble Forulaton hown n the syste odel, there are three councatng lnks n the cooperatve councaton schee. The receved packet for each lnk can be expressed as yj, j hj x nj (N. power for the source and relay respectvely, j s the path loss, hj s the Nakaga- quas-statc fadng coeffcent, x s the packet to be transtted, nj s the whte Gaussan nose (AWGN wth varance N 0. The receved N at the recevers are gven by [6] 2 Nj (3 N0 as [11] j G (4 dj M l N f where {, }, j {, D}, d j s the dstance n eters aong the source, the relay and the destnaton, s the path loss exponent, G s the total gan of the transt and receve antennas, s the wavelength, M l s the lnk argn and N f s the nose fgure at the (1 recever [6]. As dscussed before, an outage occurs when the N at the recever falls below a threshold whch allows error free decodng. Ths threshold s defned as 2 1, where Δ s the syste spectral effcency. However, the loss n spectral effcency nherent to the cooperatve transsson can degrade the syste perforance snce the end-to-end throughput wll be reduced to half [6]. Hence, the soluton that the nodes operate wth a spectral effcency ( = 2 tes greater than that of the drect transsson s assued, whch s 2 1 [6]. Hence, the outage probablty for each lnk, n Nakaga- fadng, s gven by [12] elay ( Destnaton (D ( Nj Fg. 1. Cooperatve transsson syste odel. hj j where {, }, j {, D}. And j can be expressed If the receved N s hgher than the threshold β, the recever s assued to be able to decode the receved essage wth neglgble probablty of error. If an outage occurs, the packet s consdered lost. Based on the derved outage probablty expressons, a constraned optzaton proble wth power allocaton strateges to nze the total consued power s llustrated n the next secton. ource ( (2 where {, }, j {, D}, s the transsson s defned as ENEGY EFFICIENCY ANAYI AND OWE AOCATION 871 N 1, ( j (5

3 Journal of Councatons Vol. 8, No. 12, Deceber 2013 where {, }, j {, D}, s the Nakaga- fadng fgure, (, b a1 exp( d 0 a b y y y s the ncoplete gaa functon and ( a1 exp( d 0 a y y y s the coplete gaa functon. At hgh N, a ( a, b (1/ a b [12]. Therefore, the outage probablty for each lnk can be expressed as, j 1 N (6 ( 1 The total outage probablty for the cooperatve transsson can be gven by, ( ND [ ( N (1 ( N ( N ] j D The total consued power n the cooperatve transsson s where tot ( N ( TX 2 X [1 ( N ] ( 2 2 and TX X (7 (8 are the transsson power of the are the source and the relay respectvely, TX and X power consued by the nternal crcutry for transttng and recevng, respectvely. Mnzng the total consued power of the cooperatve transsson s equvalent to nze the transsson power of the source and the relay due to the values of are fxed. and B. Half Transsson ower Allocaton oluton (HTA As shown n the equaton (8, the above optzaton probles of cooperatve schees are nonlnear and cannot adt a closed for soluton. Even though the optzaton soluton can lead to the best perforance, t s dffcult to pleent such a coplex optzaton proble due to the ltaton by the low coputng power of the nodes n a practcal scenaro. One of the sub-optzaton solutons s that the source and relay nodes utlze the sae power for transsson. In [6] and [9], t has been proved that the soluton of the equal transsson power of the source and relay nodes could eet the perforance of energy effcency. However, atheatcally speakng, the proportonal relaton between the transsson power and the dstance d are gven by [13] d K,2 K 4 (9 where K s a constant that depends on the propagaton edu and antenna characterstcs. Ths equaton eans the farther councatng dstance, the ore transsson power consued. In the cooperatve transsson scenaro, the relay node generally locates between the source node and the destnaton node. Hence, the transsson power of the relay node should be less than that of the source node. It s assued that there s a lnear relaton between the transsson power of the source node and that of the relay node as follows a, 0 a 1 (10 Fxng the outage probablty eet the Qo requreent, such that, whch s assued to, and substtutng n equaton (7. An equaton about s obtaned. The detaled dervaton work s gven n the Appendx. a ( ( a k k k k ( ( k k k 0 ( where ( N ( N k1, k 2 ( 1( ( 1( ( N k3 ( 1( Then, the sallest real and postve soluton of the equaton (11 s regarded as the optal transsson power of source. And the optal transsson power of relay s obtaned usng the equaton (10. In the next secton, the nuercal results prove that the proposed soluton perfors best when a 0.5, and s better than equal transsson power allocaton soluton. The soluton when a 0.5 s naed as Half Transsson ower Allocaton oluton (HTA n ths paper. In equal transsson power soluton, the transsson power of source and relay s assued to be sae. larly, the optal transsson power can be obtaned as the sall real and postve soluton of ( ( k k k k ( ( k k k 0 (12 3 D D Fro the equatons above, the coputng coplexty of the HTA and equal transsson power soluton can be derved. The coputng coplexty of the HTA s O(3, and the coputng coplexty of the equal transsson power soluton s also O(3. And n the process of pleentaton, the space coplexty of the HTA s O (1, the sae as the equal transsson power soluton. Then the concluson can be obtaned that the proposed HTA s also easy to pleent. C. Drect Transsson In the drect transsson, the source councates drectly wth the destnaton, wthout any nteredate 872

4 Journal of Councatons Vol. 8, No. 12, Deceber 2013 nodes. The outage probablty of drect transsson can be expressed as, DT 1 N (13 ( 1 where DT s the transsson power, and 2 1. The total consued power of the drect transsson s DT Dtot DT TX X (14 larly, fxng the outage probablty D, and substtutng n (13 leads to the optal transt power for the drect transsson: DT D N ( 1 (15 D. Mult-Hop Transsson The outage probablty for the ult-hop transsson s gven by O, MH ( N [1 ( N ] ( N D (16 Therefore, the total consued power n the ult-hop transsson s MHtot ( N ( MH TX X (17 [1 ( N ] (2 2 2 MH TX X where MH s the transsson power of ult-hop transsson schee. lar to the drect transsson, the outage probablty,mh s assued to be fxed, then substtutng n the equaton (16. The optal transsson power for the ult-hop transsson can be obtaned as the sallest real and postve soluton of ( ( k k ( ( k k 0 (18 3, MH MH 1 2 MH 1 2 sulatng plot s enlarged, as shown n Fg. 2. The reason that the stuaton of a 0.1 s not shown, s that the proposed power allocaton soluton perfors worst when a 0.1, hence, there s not necessary to show ths sulaton result. When =1.0, the proposed suboptzaton soluton s equal to the equal transsson power allocaton soluton. Fro ths sulaton result, t can be observed that the total consued power for the cooperatve transsson s least when a 0.5. In other words, the HTA perfors better than equal transsson power allocaton soluton. In the followng sulatons, the equal transsson power allocaton soluton and the HTA of the cooperatve transsson are consdered. Fg. 3 shows the optal transsson power of relay for the proposed power allocaton soluton. As entoned, the proposed sub-optzaton soluton when a 1.0 s equal to the equal transsson power allocaton soluton. As expected, the transsson power of relay for HTA s less than that for equal transsson power allocaton soluton. In other words, HTA decreases the energy consupton of relay and prolong the useful lfe of relay. tot [W] a=0.2 a=0.3 a=0.4 a=0.5 a=0.6 a=0.7 a=0.8 a=0.9 a= Dstance between and D [] Fg. 2. Total consued power of for the proposed power allocaton soluton. IV. IMUATION EUT In ths secton, soe sulatons are presented to prove the theoretcal analyss presented n the prevous secton. eferrng to [6], the lnk argn and the nose fgure are assued to be Ml 40 db and N f 10 db, respectvely. The total antenna gan s G 5 db, the carrer frequency s fc 2.5 GHz, and the path loss exponent s 2.5. Based on [14], The overall power consupton of the crcut for transttng and recevng are consued as TX 97.9 W and X W, respectvely. The Nakaga- fadng fgure s 1, 3 and the outage probablty s fxed as 10. The total consued power of cooperatve transsson wth the proposed power allocaton soluton s sulated whle assung a {0.2, 0.3,,1.0}. In order to observe the sulaton result clearly, a part of the [W] 10-2 a=0.5 a= Dstance between and D [] Fg. 3. Transsson power of relay for the proposed power allocaton soluton. A ore nsghtful coparson of the total consued power for each of the transsson schees s gven n Fg. 4. The sulaton results can be observed that the cooperatve transsson schee perfors better 873

5 Journal of Councatons Vol. 8, No. 12, Deceber 2013 than the drect and ult-hop transsson schees, whle the ult-hop transsson schee perfors worse than all the other schees. The drect transsson perfors better than cooperatve transsson only when the dstance between the source and the destnaton s less than about 25. The nuercal results reveal that for short dstance between the source and the destnaton, for exaple, below a threshold 25, the drect transsson s ore effcent than the cooperatve transsson. Above the threshold, the cooperatve transsson s useful for decreasng the total consued power n energy-constraned networks. The reason that the ult-hop transsson consues ore power than the drect transsson s consdered that the relay consued a part of power for forwardng the packets. tot [W] Drect Mult-Hop a=0.5 a=1.0 Dstance between and D [] Fg. 4. Total consued power of each transsson schees ( 3 10, 2 b/s/hz. consued power and hence the cooperaton gan trends to saturate. In addton, ths sulaton result obvously shows that the proposed power allocaton soluton HTA perfors a lttle better than the equal transsson power allocaton soluton. Hence, the concluson s obtaned that the cooperatve transsson wth the proposed power allocaton soluton HTA, n whch the transsson power of the relay s half of that of the source, can be energy effcent n energy-constraned networks when the dstance between the source and the destnaton s larger than 25. The varaton trend of the total consued power when 4 the outage probablty reduces to 2 10 s shown n Fg. 6. Accordng to the fgure, the cooperatve transsson perfors uch better than the drect transsson when the source-destnaton dstance s larger than 13. Hence, the concluson can be obtaned that the cooperatve transsson s ore and ore energy effcent whle the outage probablty decreases. When the requred syste spectral effcency s ncreased to 4 b/s/hz, the varaton trend of the total consued power s shown n Fg. 7. Fro ths sulaton result, t s llustrated that the advantage of energy effcency of the cooperatve transsson s reduced wth the syste spectral effcency ncreased. tot [W] Cooperaton Gan Drect Mult-Hop a=0.5 a=1.0 Dstance between and D [] Fg. 6. Total consued power of each transsson schees ( , 2 b/s/hz. Gan a=0.5 Gan a= Dstance between and D [] Fg. 5. Cooperaton gans of two dfferent power allocaton schees. eferrng to [9], the cooperaton gan that the rato between the power requred for the drect transsson and the cooperatve transsson s defned. Fg. 5 shows the nuercal results for the cooperaton gan of two dfferent power allocaton solutons. When the source-destnaton dstances s less than 25, the sulaton result reveals that the drect transsson s ore energy effcent than cooperatve transsson. For D 25, the cooperaton gan ncreases as the transsson power starts takng up a sgnfcant porton of the total consued power. Ths rato ncreases untl the transsson power becoes the an porton of the total tot [W] Drect Mult-Hop a=0.5 a=1.0 Dstance between and D [] Fg. 7. Total consued power of each transsson schees ( 3 10, 4 b/s/hz. V. CONCUION 874

6 Journal of Councatons Vol. 8, No. 12, Deceber 2013 In ths paper, the energy effcency of drect, ult-hop, and transsson schees are copared n energyconstraned networks. The nuercal results constranng the transsson schees to have the sae end-to-end throughput and outage probablty show that the cooperatve transsson s ore energy effcent than the drect and ult-hop transssons when the sourcedestnaton dstances s larger than a certan threshold. A novel power allocaton soluton (HTA for the cooperatve transsson s proposed. The sulatons of the transsson power of the relay and the cooperaton gan deonstrate HTA perfors a lttle better than the equal transsson power allocaton soluton, eanwhle t s also easy to be realzed. Ths s sgnfcant for applyng to the energy-constraned networks, such as wreless sensor networks. ACKNOWEDGMENT The authors would lke to thank Zunhua Guo and Chengyou Wang for ther help and valuable suggestons. The authors also thank the anonyous revewers and the edtor for ther valuable coents to prove the presentaton of the paper. AENDIX Fro the equaton (6, the outage probablty of the - D lnk, - lnk and -D lnk can be derved respectvely. 1 N ( ND ( 1 D 1 N ( N ( 1 1 N ( ND ( 1 D Fxng the outage probablty equaton (7. ( N [ ( N D (1 ( N ( N ] D,and substtutng n 1 N 1 N = [ ( 1 D ( 1 1 N 1 N 1 ] ( 1 ( 1 D plfyng the above equaton wth ( N ( N k1, k 2, ( 1( ( 1( ( N k3, ( 1( D D and replacng wth a, 0 a 1.The equaton (11 can be obtaned, a ( ( a k k k k ( ( k k k EFEENCE [1] I. F. Akyldz,. Welan, Y. ankarasubraana, and E. Cayrc, "A survey on sensor networks," IEEE Councatons Magazne, vol. 40, no. 8, pp , Aug [2]. Cu, A. J. Goldsth, and A. Baha, "Energy-effcency of MIMO and cooperatve MIMO technques n sensor networks," IEEE Journal on elected Areas n Councatons, vol. 22, no. 6, pp , Aug [3] J. N. anean, D. N. C. Tse, and G. W. Wornell, "Cooperatve dversty n wreless networks: Effcent protocols and outage behavor," IEEE Trans. on Inforaton Theory, vol. 50, no. 12, pp , Dec [4] Z. Zhong, Z. hengl, C. Jun-Hong, and C. huguang, "Energyeffcent cooperatve councaton based on power control and selectve sngle-relay n wreless sensor networks," IEEE Trans. on Wreless Councatons, vol. 7, no. 8, pp , Aug [5]. Ong and M. Motan, "Optal routng for decode-forward n cooperatve wreless networks," IEEE Trans. on Councatons, vol. 58, no. 8, pp , Aug [6] G. G. de Olvera Brante, M. T. Kaktan, and. Deo ouza, "Energy effcency analyss of soe cooperatve and noncooperatve transsson schees n wreless sensor networks," IEEE Trans. on Councatons, vol. 59, no. 10, pp , Oct [7]. Dong, "Outage probablty and power allocaton for cooperatve ultcast systes," IEEE Councatons etters, vol. 16, no. 7, pp , July [8] H. Alves, G. Brante,. ouza, and J. ebelatto, "Energy effcency and throughput perforance of power and rate allocaton on ncreental decode-and-forward relayng," Wreless Networks, vol. 18, no. 5, pp , July [9] A. K. adek, W. Yu, and K. J.. u, "On the energy effcency of cooperatve councatons n wreless sensor networks," ACM Trans. on ensor Networks, vol. 6, no. 1, Dec [10] [W. u, A. adek, and K. J. ay u, "Cooperatve councaton protocols n wreless networks: perforance analyss and optu power allocaton," Wreless ersonal Councatons, vol. 44, no. 2, pp , Jan [11] A. Goldsth, Wreless Councatons, 1st edton ed.: Cabrdge Unversty ress, [12] Z. Wang and G. Gannaks, "A sple and general paraeterzaton quantfyng perforance n fadng channels," IEEE Trans. on Councatons, vol. 51, no. 8, pp , Aug [13]. Banerjee and A. Msra, "Mnu energy paths for relable councaton n ult-hop wreless networks," roceedngs of the Thrd ACM Internatonal yposu on Moble Ad Hoc Networkng and Coputng, pp , Jun [14]. Cu, A. J. Goldsth, and A. Baha, "Energy-constraned odulaton optaton," IEEE Trans. on Wreless Councatons, vol. 4, no. 5, pp , ept

7 Journal of Councatons Vol. 8, No. 12, Deceber 2013 We u receved hs B.E. degree n councaton engneerng fro handong Unversty, Chna n Now he s studyng toward the M.. degree n sgnal and nforaton processng at handong Unversty. Hs current research nterests nclude wreless sensor networks and cooperatve councaton. n Zhu receved her B.E. degree n councaton engneerng fro handong Unversty, Chna n Now she s studyng toward the M.. degree n sgnal and nforaton processng at handong Unversty. Her current research nterests nclude wreless sensor networks. Guangng receved hs B.. degree fro handong Unversty, Chna, n 1996, hs M.. degree fro the tate Key aboratory of Crystal Materals, handong Unversty, n 1999, and hs h.d. degree fro the Unversty of Hong Kong, Hong Kong, n Now he s an assocate professor and supervsor of the Master n handong Unversty, Weha, Chna. Hs research nterest ncludes optcal networks and Internet of thngs. 876