Proceedings of the 2007 IEEE International Conference on Signal Processing and Communications (ICSPC 2007)

Transcription

1 Energy effcent wreless sensor networks Author M. Abbosh, Amn, Thel, Dav Publshe 2007 Conference Ttle Proceengs of the 2007 EEE nternatonal Conference on Sgnal Processng an Communcatons (CSPC 2007) DO Copyrght Statement 2007 EEE. Personal use of ths materal s permtte. owever, permsson to reprnt/ republsh ths materal for avertsng or promotonal purposes or for creatng new collectve works for resale or restrbuton to servers or lsts, or to reuse any copyrghte component of ths work n other works must be obtane from the EEE. Downloae from Lnk to publshe verson Grffth Research Onlne

2 EERGY EFFCET WRELESS SESOR ETWORKS Amn M. Abbosh (1) an Dav V. Thel (2), Senor Member, EEE (1) School of TEE, The Unversty of Queenslan, QLD 4072, Australa (2) Centre for Wreless Montorng an Applcatons, Grffth Unversty, QLD 4111, Australa ABSTRACT A theoretcal moel s presente to estmate the energy requrements of multple-nput multple-output (MMO) systems when use n wreless sensor networks (WS) assumng clustere channel moelng, wth Rcan strbuton an cochannel nterference. The effect of fferent propagaton envronments s smulate. Smulaton results show that the sngle-nput sngleoutput (SSO) can only be useful wth short range systems (less than 20m). The MMO system wth channel state nformaton has the best performance for applcatons that requre a range more than 20m an uner fferent propagaton contons. The results presente n ths paper ncate that ncreasng the number of antennas for MMO systems has a negatve effect on the performance uner free space propagaton, whereas t has a postve effect, especally for MMO wth channel state nformaton (CS), uner severe contons. nex Terms Energy effcency, multple-nput multple-output (MMO), wreless sensors networks. 1. TRODUCTO ew technologes allow wreless montorng systems to shrnk n sze, cost an energy requrements. One objectve s to bul a complete wreless unt (sensor, RF transcever, analogue to gtal converters ADC, gtal to analogue converters DAC an base ban processors) n a sngle chp wth lmte sze. Dsposable unts can be use n battery powere wreless sensng an montorng systems. One of the man ssues n usng those unts s how to maxmze ther operatonal lfetme. Recently, the multple-nput multple-output (MMO) technque has been propose to mnmze the power requrements of the wreless sensor networks [1]. Results obtane by smulaton n [1] show that ue to the relatvely hgh power requrements of the atonal crcutry, the overall performance of MMO system was nferor to that of SSO when workng n short range applcatons. All smulatons n [1] were carre out assumng a path loss exponent equal to two,.e. only free space propagaton was consere. Ths pont cannot be justfe because all measurements, whether noor or outoor, show that the square law relaton oes not gve a correct estmaton of the path loss. The path loss exponent was shown to vary n the range 2-4 [2]. Also, n [1] the assume Raylegh fang strbuton oes not ft the square law propagaton use n the analyss. One mportant category of MMO systems, MMO wth channel state nformaton ( MMO cs ), has not been smulate. The use of such systems may gve fferent results as t has been shown to gve hgher ata rates compare to other MMO systems,.e., t nees less power for the same ata throughput. Effect of cochannel nterference was also neglecte. n ths paper, clustere channel moelng s use wth a Rcan fang to compare the performance of SSO, MMO an MMO cs wreless sensor systems uner fferent propagaton contons. The comparson between the fferent systems assume a lmte array sze whch s the usual case n wreless sensors. The effect of cochannel nterference s also nclue n the propose moel conserng that many wreless systems may be locate n a nearby area an some mght use the same frequency ban. 2. PROPAGATO MODEL The propagaton channel moel use n ths paper s base on the EEE802.11n clustere channel moel. Ths moel escrbes propagaton paths as channel taps groupe n clusters. Each cluster s characterze by a mean angle-of-arrval (AOA) an conssts of multple paths, wth AOA values ranomly strbute. The power azmuth spectrum (PAS) wthn each cluster s assume to have a Laplacan strbuton as t conces wth many measurements [3]. The number of clusters, the values of PAS an ts stanar evaton use n ths calculaton, are assume accorng to moel F of EEE n [2] as t escrbes accurately most of the we area noor an outoor envronments n whch the wreless montorng system can be use. Durng smulaton, Rcan fang s assume n orer to take effect of lne-of-sght path nto conseraton. Ths s because when WS work n short range envronments there s a hgh possblty of lne of sght propagaton. The frst step when smulatng the performance of a MMO system s to fn the channel matrx. n ths paper we eal only wth arrays of length less than one wavelength an the channel matrx can be foun usng the followng metho [4]; r G Rt G = R (1) where s the channel matrx wth elements that are nepenent zero mean crcularly symmetrc complex Gaussan ranom varables, R r s the receve covarance matrx an R s the M M transmt covarance matrx, assumng receve antennas an M transmt antennas. These matrces are calculate usng the t

3 metho scusse n [] after makng the followng mofcatons so that t woul be sutable for the UCA shown n Fg. 1. ote that the angle of arrval φ UCA s measure relatve to the reference recton efne by elements an j n the UCA; 2π φuca = φula [ ( j )] (2) n where n s number of elements n the array, an j are the sequence of elements n the array (1, 2, 3 n). Also n ths smulaton, we wll assume a fxe ameter D for the array. Elements of the array are strbute unformly on the crcumference. The spacng between the an j elements n the array can be foun from the followng relaton, see Fg.1; 2π = D* sn[ ( j )] (3) n From the channel matrx, the nstantaneous recever sgnal to nose rato ( SR ) s calculate usng the followng equaton [4,]; k Egen SR * = 1 Eb = (4) M o where Eb s the requre energy per bt at the recever to acheve the requre bt rate, o s the nose energy, an Egen s the th egenvalue of the channel matrx an k s mn(, M). ote that for the SSO system M = 1 n (4). For MMO cs, the water-fllng algorthm can be use to maxmze the capacty an n ths case []; SR = k = 1 E b M o Egen where E b s the porton of energy allocate to the ata transmtte from the th antenna. The two-slope path-loss moel [2] s use to calculate the path loss L p. Ths moel assumes that the receve power s nversely proportonal wth the stance square up to the break-pont stance r br. At larger stances ( r >> ) the power falls by a rate proportonal rbr 3. to r. The break-pont stance epens on many parameters nclung the transmtter antenna heght, the recever antenna heght an the wavelength. n ths paper r s taken to be 10m whch s sutable for many WS. br 3. COCAEL TERFERECE Conser a MMO channel wth M antennas at the transmtter, antennas at the recever an K cochannel nterferng sgnals each equppe also wth M transmttng antennas. The receve sgnal at the esre recever can be moele as [6]; K y = x + = 1 P x + n where s the M normalze channel matrx for the esre user, x s the M 1 transmtte sgnal vector for the esre user. Smlarly, P s the average access path loss of the th nterferer sgnal compare wth that of the () (6) esre sgnal, s M normalze channel matrx of the -th nterferer, x s the M 1 transmttng sgnal vector of the th nterferer, an n s the atve Gaussan nose vector wth zero mean an covarance value ( o ). The channel matrces an are forme usng the metho scusse above. They nclue the effect of the Rcan fang, wth a Rce factor =10B whch means a strong lne-of-sght ray s present, an transmtter an recever correlaton as well as the effect of mutual couplng between elements of the transmttng an recevng array. From (6) the mutual nformaton can be calculate usng the followng equatons [7]; 1 = log ( et ( + R B )) (7) 2 o B = R P + (8) R = E( x x ) (9) where s entty matrx, s matrx whch s result of composton of the nterferers matrces where the frst M columns of comes from matrx of the frst nterferers an the secon M columns are channel matrx of the secon nterferer an so on. s the total number of nterferng antennas an t s equal to ( K M ).The agonal matrx P s forme from P where the frst M elements of the agonal comes from effect of the frst nterferer an so on. The agonal matrx R s forme by the same way from the elements; R = E( x x ) (10) The superscrpt () n (10) ncates the ermtan operaton. n ths paper, we have assume that there are many systems workng nearby to the system uner conseraton. Dstrbuton of the systems an frequency allocaton were chosen accorng to the 7-cell reuse system, although any other confguraton can be assume. Therefore, uner full loa contons the esre user wll suffer from sx cochannel nterferers [7],.e. K=6. The followng scenaros were consere n ths paper. The frst one s MMO wthout CS an the power s assume to be equally ve between elements of the array. ence, (9) an (10) can be wrtten as; E R = R 1 = R 2 = = R = b (11) M where E b s the total energy per bt transmtte from each sensor. The poston of the esre user s assume to be ranom wthn ts cell. ts poston relatve to the center of the cell s r where 0 r R assumng that the cell has a raus equal to R. The stance between center of the esre cell an center of any of the nterferng cells s D an ts value can be calculate as D = 21R [7]. Assumng that the -th cochannel sensor s at a stance r from the center of ts cell, the esre sensor an the -th nterferer are assume to be at angles θ an θ respectvely wth respect to D, (see Fg.2). The

4 stance between that nterferer an the esre sensor can be calculate geometrcally. The parameters r an r are assume to take any value between 0 an R wth unform strbuton whle the parameters θ an θ can take any value between 0 an 360 wth unform strbuton also. The two-slope path loss moel can be use to calculate the path loss between the clent an the esre sensor ( L p ) by usng the stance r as r, whereas the cochannel nterferer path loss, L p s calculate by replacng r wth. The average access path loss for the -th nterferer can now be foun as L L ), therefore; ( p p P = L L ) (12) ( p p n ths equaton, the same average path loss between any antenna element n transmtter of the nterferer an any antenna element n the esre recever s assume. Ths assumpton comes from the fact that the effect of fast fang was nclue n the channel matrx. The sgnal to nterference an nose rato (SR) can be calculate from (7) by summng all the postve egen values. Usng (7), (8), an (11); 1 SR MMO = eg( ( P + M o /E b ) ) (13) The secon scenaro s MMO cs. n ths case the water-fllng algorthm can be use,.e. non-unform strbuton of power between array elements. t has been shown that f the maxmum rato combnng MRC s use n the recever to maxmze the SR then [7]; 1 SR max eg( E B ) (14) cs = b 4. ELECTROC CRCUTRY n the smulaton, the SSO transmtter an recever electroncs use are as shown n Fg.3. For the MMO system there wll be parallel branches of the recever crcuts an M branches of the transmtter crcuts as shown n Fg.3. The power requrements for fferent parts of the electronc crcutry of SSO or MMO system are as gven n [8]. The followng equatons are use to estmate the energy requrements [1]. Mar * P E = ( α )[ ] + c b f c 1 + Eb * * L p (1a) GtGr Rb P MP + P + P = 2 (1b) t s r B e = Mean[ Q( 2* SR )] (1c) where the parameter to be mnmze s E b, the total energy consumpton per bt, α efnes the amplfcaton characterstcs of the power amplfer at the transmtter, M ar s the safety margn for the system, f s nose fgure of the recever, G t, Gr are the gans of an antenna element at the transmtter an recever se respectvely, s the transmtter-recever stance, λ s the wavelength, n s the path-loss exponent, R b s the bt rate. P c, Pt, Ps, Pr are the power consumpton values of the crcut sectons for one branch of the transmtter gtalto-analog converter, mxer an flter; the syntheszer; an the recever low-nose amplfer, mxer, ntermeate frequency amplfer, flter an analog-to-gtal converter. The Q functon n (1c) s the Gaussan error ntegral an B e s the bt error rate. The wor (Mean) n (1c) ncates that the estmaton shoul be average over all the channel matrx possbltes.. RESULTS AD DSCUSSOS The performance of the systems uner conseraton s smulate assumng that the frequency of operaton s 2.Gz, maxmum bt error rate s 0.001, an the bt rate s 10Kbps. Channel smulatons assume Rcan strbuton wth a rce factor of 10B. Elements of the MMO are strbute unformly on the crcumference of the crcle λ / 2 ameter value. The results ntrouce n Fgs. 4 an shows a comparson between the energy neee when usng SSO, MMO an MMO cs uner fferent propagaton contons. t s clear that the SSO system nees mnmum energy for operaton over very short stances,.e. less than 20m. Ths s because at short stances most energy s neee for the electronc crcutry. As the SSO has the mnmum harware, then t s expecte that t wll requre lttle energy. The next best system s the MMO cs when usng a two-antenna array. Ths s manly because ths system chooses propagaton through a channel that gves t the hghest possble SR. The four-antenna array the MMO system requres more harware an so more energy to actvate an when the stance s short enough the energy neee by the crcutry wll be a major part n the overall energy requrement. As the stance ncreases, the energy neee to compensate for the path loss ncreases untl t omnates the total energy requrement. At that stance MMO cs wll be the preferre system. Uner a severe propagaton conton,.e. when the path loss exponent ncreases, the energy neee to overcome the ncrease path loss wll be hgh compare to the case of a soft propagaton conton. n ths case the ablty of the MMO system n ffcult propagaton stuatons appears more obvous an the use of a four-antenna array mproves the performance even more. 6. COCLUSO A theoretcal moel has been presente to estmate the energy requrements of MMO systems when use n wreless sensor networks (WS) assumng clustere channel moelng, wth Rcan strbuton an cochannel nterference. The effect of fferent propagaton envronments has been smulate. Results from the smulaton have shown that the SSO s only useful wth short range systems (less than 20m). The MMO system wth channel state nformaton has the best performance for applcatons that requre range more than 20m an uner fferent propagaton contons. The results presente n ths paper have ncate that ncreasng the number of antennas for MMO systems has a negatve effect on the performance uner free space propagaton,

5 whereas t has a postve effect, especally for MMO wth channel state nformaton, uner severe contons. ACKOWLEDGMETS A. Abbosh acknowleges the fnancal support of the Unversty of Queenslan va ECR grant. REFERECES [1] S. Cu, A. Golsmth an A. Baha, Energy-effcency of MMO an cooperatve MMO Technques n sensor networks, EEE Journal on Selecte Areas n Comm., vol.22, no.6, pp , [2] V. Erceg et.al, TGn channel moels, EEE ocument 03/940r4, May [3] K. Peerson, P. Mogensen, an B. Fleury, Spatal channel characterstcs n outoor envronments an ther mpact on BS antenna system performance, Proc. Of EEE Vehcular Tech. Conf., Canaa, vol.2, 1998, pp [4] J. Kermoal, L. Schumacher, K. Peersen, an P. Mogensen, A stochastc MMO rao channel moel wth expermental valaton, EEE Journal on Selecte areas on Comm., vol.20, no.6, pp , [] L. Schumacher, K. Peersen, an P. Mogensen, From antenna spacngs to theoretcal capactes- guelnes for smulatng spatal correlaton n MMO systems, Proc. Of the 13 th EEE nt. Symp. on Personal noor Moble an Rao Comm., Portugal, [6] M. Kang, L. Yang, an M. Aloun, Certan computatons nvolvng complex Gaussan Matrces wth applcatons to the performance analyss of MMO systems, Chapter-3 n Space-Tme Processng for MMO Communcatons, John Wley & Sons, Canaa, 200. [7] B. Walke, Moble rao networks; etworkng, protocols an traffc performance, John Wley & Sons, 2n Eton, ew York, [8] S. Cu, A. Golsmth, an A. Baha, Energy-constrane moulaton optmzaton, EEE Trans. Wreless Communcaton, vol., pp , 200. π ( j ) Fg.3 Block agram of the transmtter (upper part) an the recever (lower part). Energy per bt (J) x Dstance between Tx an Rx (m) Fg.4 Comparson between the energy requre by fferent systems, assumng free space propagaton. Energy per bt (J) 10 x SSO 2X2 MMO 4X4 MMO 2X2 MMOcs 4X4 MMOcs SSO 2X2 MMO 4X4 MMO 2X2 MMOcs 4X4 MMOcs φ AOA(φ) Dstance between Tx an Rx (m) Fg. Comparson between the energy requre by fferent systems, assumng a two-slope propagaton moel. Fg.1 Unform crcular array confguraton. Fg.2 Schematc agram showng poston of the esre sensor an the cochannel nterferer, assumng a 7-cell reuse strbuton.