Experimental characterization of the outdoor MIMO wireless channel temporal variation

Transcription

1 Brgham Young Unversty BYU ScholarsArchve All Faculty Publcatons Expermental characterzaton of the outdoor MIMO wreless channel temporal varaton Mchael A. Jensen Karl F. Warnck See next page for addtonal authors Follow ths and addtonal works at: Part of the Electrcal and Computer Engneerng Commons Orgnal Publcaton Ctaton Wallace, J. W., et al. "Expermental Characterzaton of the Outdoor MIMO Wreless Channel Temporal Varaton." Vehcular Technology, IEEE Transactons on 56.3 (27): BYU ScholarsArchve Ctaton Jensen, Mchael A.; Warnck, Karl F.; Wallace, Jon W.; Gummalla, Ajay; and Lee, Harry B., "Expermental characterzaton of the outdoor MIMO wreless channel temporal varaton" (2007). All Faculty Publcatons. Paper Ths Peer-Revewed Artcle s brought to you for free and open access by BYU ScholarsArchve. It has been accepted for ncluson n All Faculty Publcatons by an authorzed admnstrator of BYU ScholarsArchve. For more nformaton, please contact scholarsarchve@byu.edu.

2 Authors Mchael A. Jensen, Karl F. Warnck, Jon W. Wallace, Ajay Gummalla, and Harry B. Lee Ths peer-revewed artcle s avalable at BYU ScholarsArchve:

3 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 56, NO. 3, MAY Expermental Characterzaton of the Outdoor MIMO Wreless Channel Temporal Varaton Jon W. Wallace, Member, IEEE, Mchael A. Jensen, Senor Member, IEEE, Ajay Gummalla, Member, IEEE, and Harry B. Lee, Member, IEEE Abstract Tme-varant multple-nput multple-output (MIMO) channels are measured n an outdoor campus envronment at 2.45 GHz wth drectonal patch arrays and omndrectonal monopole arrays. A number of useful metrcs are proposed for quantfyng tme varaton n MIMO channels: egenvalue level crossng rate, egenvector angular devaton, and capacty loss for delayed transmt and receve channel state nformaton (CSI). Measurements n four dfferent envronments confrm the strong correlaton between angular spread of multpath and MIMO channel tme varablty. The rate of tme varaton s also strongly nfluenced by the type of array, ndcatng that drectonal elements may be advantageous for hghly moble envronments. The proposed metrcs ndcate that although the physcal communcaton layer may need to update CSI several tmes per wavelength, the requred rate of adaptaton n transmt rate, modulaton, and power allocaton s much less severe. Index Terms Informaton theory, multple-nput multpleoutput (MIMO) systems, tme-varyng channels. I. INTRODUCTION ANALYTICAL studes and measurement campagns have demonstrated the dramatc capacty ncrease enabled by explotng the multpath spatal structure wth multplenput multple-output (MIMO) communcatons [1], [2]. However, realzaton of these gans depends crtcally on the avalablty of channel state nformaton (CSI) [3], whch s typcally obtaned by perodcally transmttng known tranng sequences. When the channel vares rapdly, the requred frequency of tranng can dmnsh and eventually offset the capacty mprovement enabled by MIMO technology. Although sgnalng strateges for rapdly varyng MIMO channels exst Manuscrpt receved January 4, 2006; revsed May 19, 2006 and July 5, Ths work was supported n part by the Defense Advanced Research Projects Agency under Phase 2 SBIR Award #HR C-0029, by the Natonal Scence Foundaton under Informaton Technology Grants CCR and CCF , and by the U.S. Army Research Offce under the Mult- Unversty Research Intatve Grant W911NF The revew of ths paper was coordnated by Dr. K. Dandekar. J. W. Wallace was wth the Department of Electrcal and Computer Engneerng, Brgham Young Unversty, Provo, UT USA. He s now wth the School of Engneerng and Scence, Jacobs Unversty Bremen (formerly Internatonal Unversty of Bremen), Bremen, Germany (e-mal: wall@eee.org). M. A. Jensen s wth Brgham Young Unversty, Provo, UT USA (e-mal: jensen@ee.byu.edu). A. Gummalla was wth San Dego Research Center, Inc., San Dego, CA USA. He s now wth Rayspan Corporaton, San Dego, CA USA (e-mal: ajayg@eee.org). H. B. Lee s wth San Dego Research Center, Inc., San Dego, CA USA. Dgtal Object Identfer /TVT [4], such methods typcally provde modest capacty ncrease relatve to the gans assocated wth methods explotng full CSI [5], [6]. Snce the rate of tme varaton effectvely lmts the achevable MIMO capacty, an understandng of the degree of tme varaton n real-world channels s very mportant. Such knowledge helps n determnng the type of MIMO technology to apply for specfc applcatons. Prevously reported MIMO measurements have shown that a movng person can temporarly nhbt a sngle ndoor channel egenmode [7], and that the coherence tme of outdoor channels s about twce that predcted by Jakes model [8]. Furthermore, recent work demonstrates the effect of delayed receve CSI on the bt error rate of MIMO systems n an ndoor envronment [9]. However, to date there does not appear to be a comprehensve analyss provdng metrcs for MIMO channel varaton combned wth real-world channel measurements wth the goal of demonstratng how the varaton mpacts performance n practce. Also, the effect of drectonal and dual-polarzaton elements on channel tme varaton has receved lttle attenton. In ths paper, we evaluate the channel tme varaton from narrowband measurements taken at 2.45 GHz n several representatve outdoor locatons. Instead of smply plottng egenvalues of tme-varyng channels or applyng prevous sngle-nput sngle-output (SISO) metrcs, we present true MIMO metrcs that quantfy the rate of channel tme varaton, thus allowng the channels to be classfed based on ther tme varablty. Combnng outdoor measurements wth useful tme-varaton metrcs llustrates general lmtatons mposed by tme-varyng channels and serves as a benchmark for later studes. II. NARROWBAND MIMO MEASUREMENT SYSTEM In ths secton, we brefly descrbe the MIMO channel sounder employed, wth an emphass on parameters specfc to ths measurement campagn. We refer the reader to [10] for addtonal detals on the measurement system. A. Channel Sounder Fgs. 1 and 2 depct a hgh-level block dagram of the narrowband MIMO channel sounder and the actual transmt/receve subsystems, respectvely. The channel s probed by transmttng a hgh-frequency carrer on N T dfferent transmt antennas, each modulated wth an ndependent code word. The recever smultaneously samples the ntermedate frequency waveforms /$ IEEE Authorzed lcensed use lmted to: Brgham Young Unversty. Downloaded on February 6, 2009 at 11:01 from IEEE Xplore. Restrctons apply.

4 1042 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 56, NO. 3, MAY 2007 Fg. 1. Hgh-level block dagram of narrowband MIMO channel sounder used n ths paper. Fg. 2. Photographs of (a) transmt and (b) receve subsystems. Equpment s placed on carts for moble outdoor measurements. TABLE I MEASUREMENT PARAMETERS FOR MEASUREMENT CAMPAIGN receved on N R dfferent receve antennas, thus allowng the formaton of an N R N T narrowband channel matrx. B. Measurement Parameters Table I lsts the mportant parameters of the system for ths measurement campagn common to all measurement locatons. The nomnal 30-kHz bandwdth allowed a sngle tone n the 2.4-GHz ndustral, scentfc, and medcal band to be measured. Each transmt channel used a repeated 31-bt sequence consstng of a unque 16-bt Walsh code combned wth a common 15-bt algnment code. The algnment code was chosen to have favorable autocorrelaton propertes, allowng correct algnment of the waveforms to be acheved n postprocessng. Although the system produced channel snapshots for each 2.5 ms of measurement tme, the data were smoothed by a factor of 10 n tme to mprove sgnal-to-nose rato (SNR). C. Antenna Arrays Fg. 3 depcts the two basc array types used n ths paper, namely: 1) a unform lnear array (ULA) of eght vertcally polarzed monopole antennas and 2) a lnear array of four dualpolarzed patch antennas. The monopole antennas of length Fg. 3. Two types of antenna arrays employed n ths paper. (a) λ/4 monopole antennas mounted on a reconfgurable ground plane. (b) Dual-polarzaton patch antennas. Arrows pontng out of the page ndcate orentaton drecton for the two arrays. λ/4, where λ s the free space wavelength, exhbt nearly unform radaton patterns n the azmuthal plane. Each patch element has two ndependent feeds for vertcal and horzontal polarzatons, wth the polarzatons exhbtng 3-dB azmuthal beamwdths of approxmately 90 and 120, respectvely. The use of the two array types allows the nvestgaton of the effect of drectvty and polarzaton on the rate of channel varaton. III. CHANNEL METRICS An mportant part of ths paper s the dentfcaton of metrcs that quantfy the tme varaton of the measured channel responses. Each channel metrc can be computed from the channel transfer matrx elements H (n) j, where n s a channel measurement tme ndex, and and j are the receve and transmt antenna ndces, respectvely. Snce the temporal varaton of measured channels results largely from recever movement, tme-varaton metrcs are gven n terms of dstance, whch can readly be converted to tme gven a recever moton velocty. Many of the metrcs presented make use of the noton of parallel spatal channels enabled by the array and the multpath propagaton. As way of background, let the sngular value decomposton of the channel matrx at tme ndex n be gven as H (n) = U (n) S (n) V (n)h, where U (n) and V (n) are untary matrces of sngular vectors, S (n) s a dagonal matrx of real sngular values, and { } H s the Hermtan operator. If we precode the vector x (n) 0 of transmt symbols by the rght sngular Authorzed lcensed use lmted to: Brgham Young Unversty. Downloaded on February 6, 2009 at 11:01 from IEEE Xplore. Restrctons apply.

5 WALLACE et al.: EXPERIMENTAL CHARACTERIZATION OF THE MIMO WIRELESS CHANNEL TEMPORAL VARIATION 1043 vectors usng x (n) = V (n) x (n) 0 and weght the resultng receved sgnal vector by the left sngular vectors, we obtan y (n) 0 = U (n)h y (n) = U (n)h H (n) x (n) + U (n)h η (n) = S (n) x (n) 0 + η (n) 0 (1) where η (n) s the nose at the nth tme ndex. Throughout ths dscusson, t wll be assumed that the nose vector conssts of zero-mean Gaussan random varables and has covarance σ 2 I, where I s the dentty matrx. Snce the receved sgnal vector s now a scaled (and nosy) verson of the transmtted vector, ths weghtng effectvely creates a set of ndependent spatal modes over whch the data are communcated. In the followng, we wll refer to the th columns of U (n) and V (n), symbolzed by u (n) and v (n) respectvely, and γ (n),astheth receve and transmt egenvectors, = S (n)2 as the th channel egenvalue. A. Capacty Metrcs The Shannon capacty, whch s the upper bound of achevable rates for error-free transmsson, s a key fgure of mert for MIMO channels. In ths paper, we consder narrowband MIMO capacty under the condtons where the transmtter s nformed and unnformed about the CSI. All numercal values of capacty are gven n terms of bts per second per hertz. Note that snce ths paper analyzes tme-varant channels, and notons of capacty usually assume an nfnte tme wndow for codng, the tme-varant capacty n our context represents a fgure of mert as opposed to a truly achevable capacty. These values serve as a bound that becomes tght as ether the velocty vanshes or the symbol rate grows large. 1) Informed Transmt Capacty C WF : A transmtter wth perfect CSI may dagonalze the channel as outlned above and subsequently use water-fllng on the parallel Gaussan channels to obtan the capacty,.e., C (n) WF = ( ) log 2 1+ p(n) γ (n) σ 2 (2) ( ) + p (n) = ν σ 2 /γ (n) (3) { z, z 0 (z) + = (4) 0, otherwse where p s the power delvered to the th parallel channel, ν s determned usng the constrant p(n) = P T, and P T s the total transmt power. Typcally, H (n), σ 2, and P T are scaled to obtan a prescrbed average SISO SNR that s reasonable for a realstc system. In ths paper, a SISO SNR of 10 db was assumed for all capacty computatons. 2) Unnformed Transmt Capacty C UT : When the transmtter has no knowledge about channel state, rank, or statstcs, the best strategy nvolves delverng equal power n ndependent streams to the transmt antennas. In ths case, the channel capacty s gven by C (n) UT = log P T H (n) H (n)h 2 N T σ 2 + I. (5) Fg. 4. Example plot of the tme varaton of the frst four channel egenvalues, llustratng the meanng of the ELCR metrc. B. Egenchannel Metrcs Snce achevng capacty nvolves transmttng ndependent nformaton on the parallel channel egenmodes, t s nterestng to study the temporal behavor of these modes. The followng metrcs represent possble mechansms for quantfyng the temporal varablty of the channel egenvalues and egenvectors. 1) Egenvalue Level Crossng Rate (ELCR): ELCR s the number of tmes γ (n), whch represents the power gan of the th egenmode, drops below a specfed threshold dvded by the total dstance traveled. Ths concept s llustrated n Fg. 4. In ths paper, a threshold of 2 db below the mean s assumed, and ELCR s specfed as the average number of crossngs per wavelength. ELCR s nterestng from the pont of vew of an adaptve MIMO physcal layer (PHY) and a medum access layer (MAC) that must adapt transmsson rate and modulaton to the tmedependent channel qualty. Ths metrc also ndcates the level of codng that may be requred to overcome channel fades for constant rate/modulaton transmsson. 2) Egenvector Angular Devaton (EAD): EAD quantfes how quckly the transmt and receve egenvectors rotate n complex multdmensonal space. We defne EAD for the transmt space as θ k = 1 N k cos 1 v (n)h N k n=1 v (n+k) (6) where k s the dstance between two channel snapshots, and N s the total number of snapshots, wth an analogous defnton for the recever EAD. EAD drectly mpacts how quckly the PHY must update transmsson weghts to track the tme-varant MIMO channel. However, snce the nformaton n ths metrc s somewhat redundant wth the nformaton provded by the capacty degradaton metrcs n Secton III-C, t wll not be used n the followng data analyss. Authorzed lcensed use lmted to: Brgham Young Unversty. Downloaded on February 6, 2009 at 11:01 from IEEE Xplore. Restrctons apply.

6 1044 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 56, NO. 3, MAY ) Egenvalue Spread (ES): ES ndcates the amount of multpath n the channel, rangng from large values for nearly lne-of-sght (LOS) channels to lower values for channels wth rcher multpath. ES n ths campagn s defned as ES = 10 log 10 (γ 1 ) 10 log 10 (γ 3 ), where γ s the mean of the th egenvalue. C. Capacty Degradaton Metrcs Although the egenchannel metrcs are useful for system specfcaton and desgn, they do not ndcate the loss of channel qualty n an nformaton-theoretc sense. Furthermore, the tme-varant capacty metrcs only provde an nstantaneous measure of capacty (wthn the lmts outlned n Secton III-A). Here, we defne smple metrcs for quantfyng the loss n capacty due to channel tme varaton. 1) Transmt CSI Delay: Frst, consder the case where the recever has perfect CSI but the transmtter only has the delayed channel estmate Ĥ. We may defne capacty for delayed transmt CSI as C (n) (n) H Q(Ĥ)H(n)H T = log 2 σ 2 + I (7) where H s the true channel, σ 2 s the recever nose varance, Q(Ĥ) s the optmal transmt covarance gven by the water-fllng soluton (assumng Ĥ represents the true channel), Tr{Q} P T, and P T s total transmt power. As the estmate Ĥ becomes ncreasngly outdated, C (n) T wll tend to decrease. When C (n) T falls below the unnformed transmt capacty (C (n) T wth Q = I), whch occurs at the moton dstance d T,the transmt CSI s no longer useful. 2) Receve CSI Delay (RCD): Next, consder the case where both transmtter and recever have outdated CSI. Wth mperfect channel estmates Ĥ = ÛŜ V H, we can rearrange the receved sgnal as y (n) = Ĥx(n) +[H (n) Ĥ]x(n) + η (n) (8) where x (n) (n) = Vx 0. Detecton of the receved waveform usng the outdated CSI leads to a modfcaton of (1) gven by ŷ (n) 0 = ÛH y (n) = Ŝx(n) 0 + M (n) x (n) 0 + ÛH η (n) (9) where M (n) = ÛH [H (n) Ĥ] V. Ths procedure therefore constructs parallel channels wth gans Ŝ but wth selfnterference (or crosstalk ) controlled by the matrx M (n). We make no assumptons about the dstrbuton of the channel, whch n turn leads to unknown statstcs for M (n). Unfortunately, defnng the capacty of ths channel rgorously s dffcult, and we therefore construct a lower bound for the capacty by computng the mutual nformaton of a smplfed system. Specfcally, t s realstc to assume that the recever knows the level of self-nterference on the parallel subchannels but s unaware of the cross correlaton. Mathematcally, we assume the nterference vector z (n) = M (n) x (n) 0 conssts of ndependent zero-mean Gaussan elements wth varance (at tme sample n)of{r (n) z R (n) x system s s the covarance of x (n) 0 C (n) R } = {M (n) R (n) x M (n)h }, where. The mutual nformaton of ths log 2 ( 1+p (n) γ (n) ) /q (n) (10) = { q (n) = M (n) R (n) x M (n)h} + σ2 (11) where R (n) x = dag(p (n) ) wth p (n) found accordng to waterfllng (assumng H (n) = Ĥ and q(n) = σ 2 ). We defne d R as the dstance at whch C R drops to 50% of ts maxmum value. We note that ths RCD capacty s very smlar to the capacty defned n [11], whch has been appled to ray-tracng smulatons of tme-varyng urban channels. Snce the capacty degradaton metrcs are a functon of delay between the ponts n tme when the channel CSI s obtaned and eventually used, these metrcs may be averaged over many startng ponts to obtan a more general understandng of the effect of tme varaton on capacty. D. Spatal Spectra It s ntutve that the rate of channel tme varaton s lnked to the angle spread of the multpath feld, motvatng a study of the channel spatal structure. The channel spatal spectrum represents the relatve power transfer through the channel as a functon of transmt or receve angle. A smple Bartlett (or Fourer) beamformer estmates the transmt and receve spectra as P (φ) =a H (φ)ra(φ) (12) a (φ) =f (φ)exp[jk 0 (x cos φ + y sn φ)] (13) where a s the array steerng vector, R s a transmt or receve covarance matrx, f (φ) s the far-feld radaton/recepton pattern of the th antenna n the horzontal plane, k 0 s the freespace wavenumber, and x and y are the coordnates of the th antenna. Covarance matrces for transmt and receve are, respectvely, estmated usng R T,j1,j 2 = 1 NN R R R,1, 2 = 1 NN T N R N =1 n=1 N T N j=1 n=1 IV. CHANNEL MEASUREMENTS H (n) j 1 H (n) j 2 (14) H (n) 1 j H(n) 2 j. (15) Measurements were taken n four dfferent envronments. In all cases, the transmtter remaned statonary durng the measurement tme. In the followng, the desgnaton 8P refers to the eght-port (four-element) dual-polarzed patch array wth an element spacng of 0.5 λ. The desgnaton nm refers to the n-element monopole ULA, where the nterelement spacng s 0.44 λ unless otherwse noted. Authorzed lcensed use lmted to: Brgham Young Unversty. Downloaded on February 6, 2009 at 11:01 from IEEE Xplore. Restrctons apply.

7 WALLACE et al.: EXPERIMENTAL CHARACTERIZATION OF THE MIMO WIRELESS CHANNEL TEMPORAL VARIATION 1045 TABLE II ARRAY CONFIGURATIONS AND METRICS FOR DT FIELD (ENVIRONMENT 1) Fg. 5. Map of Envronment 1 (DT feld). Transmtter and recever were placed n a large open feld to the east of a sngle large buldng, smulatng a low-scatterng envronment. Dstances are n meters. A. Deseret Towers (DT) Feld Intal measurements were taken at the DT feld, whch s a large open area, surrounded by a 1.5-m-hgh fence composed of vertcal metal rods and brcks, wth a sngle large buldng nearby. The transmtter and recever were placed about 70 m to the east of the buldng, as shown n Fg. 5. The monopole array spacng was set to 0.4 λ for these experments. Furthermore, a reflectng plate was placed on the sde of the monopole transmt array to block the LOS component. Two experments were run to determne a sutable spatal sample rate for the movng recever. The recever frst traveled approxmately 2.5 cm/s over a dstance of 75 cm, wth a sample acqured every λ. Ths experment was then repeated for moton at 30 cm/s over a dstance of 9 m, wth a sample acqured every 0.06 λ. Comparson of these results revealed that the channel varaton could be captured wth nsgnfcant error usng the hgher recever speed. The array orentatons, recever moton path (relatve to Fg. 5), and metrcs resultng from the acqured data are lsted n Table II. The metrcs confrm that ths envronment has relatvely slow temporal varaton. The egenvalue varaton ndcates that the MAC should optmally adapt at a rate less than once per wavelength. However, snce the RCD capacty degradaton s sgnfcant for dstances on the order of λ/4, the receve PHY must adapt at a hgher rate. The results also show that the monopole antennas exhbt hgher channel varaton than the patch antennas. Ths concept s renforced by Fg. 6, whch plots a sample tme evoluton of the frst four egenvalues for Set 1 (patches) and Set 4 (monopoles). The rapd varaton observed for the monopole array s lkely due to the wde angular spread of arrvals collected by omndrectonal elements. In contrast, the dual- Fg. 6. Sample temporal evoluton of egenvalues from Envronment 1 for (a) Set 1 wth patches and (b) Set 6 wth monopoles. polarzed patches have more drectve patterns, resultng n reduced senstvty to poston. Fg. 7 plots the egenvalue probablty densty functons (pdfs) for channels obtaned wth four vertcal patch elements and four monopoles (from Sets 1 and 4). These results show that the egenvalues (and therefore capactes) are nearly dentcal for the two antennas. Ths observaton suggests that antennas wth more spatal selectvty may be advantageous for MIMO systems n envronments wth hgh moblty snce they offer hgh capacty whle exhbtng lower temporal varablty. Fg. 8 plots spatal spectra for Sets 1 and 2. The spectra for Set 1 are narrow due to a domnant reflecton from the buldng (Conference Center) to the west, correspondng to farly slow varaton as quantfed by the metrcs. In contrast, for Set 2, the recever ponts south toward more dstant buldngs, and snce no sngle-bounce propagaton mechansm s present, the spectra are much wder, resultng n faster channel varaton. B. Clyde Buldng (CB) Trees In the second measurement campagn, the system nodes were placed n the mdst of sparse trees near the CB, as shown n Fg. 9. The envronment was nfluenced by occasonal passng pedestrans. The transmtter was placed n front of the buldng Authorzed lcensed use lmted to: Brgham Young Unversty. Downloaded on February 6, 2009 at 11:01 from IEEE Xplore. Restrctons apply.

8 1046 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 56, NO. 3, MAY 2007 Fg. 7. Egenvalue pdfs of four patches (Set 1) compared wth four monopole elements (Set 6). Fg. 9. Map of Envronment 2 (CB Trees). Transmtter was placed behnd sparse trees, and the recever assumed three dfferent postons on the opposte sde of the trees. Dstances are n meters. TABLE III ARRAY CONFIGURATIONS AND METRICS FOR CB TREES (ENVIRONMENT 2) Fg. 8. Transmt and receve spectra for data sets 1 and 2, ndcatng much hgher angular spread for set 2. behnd two trees, whereas the recever assumed a number of possble postons. For each measurement, the recever was ether statonary (to observe the effect of pedestrans) or moved 9 m along a straght path. The crossng rates for the statonary measurements were all zero except for the thrd egenvalue on a sngle data set. Therefore, we wll assume the effect of pedestrans to be neglgble and focus on the movng cases. Table III summarzes the array confguratons and metrcs n ths envronment. These data exhbt even less varaton than the DT feld measurements, partcularly for patch arrays. As wth DT feld, the locaton wth the hghest varaton (Set 3) has very wde angular spread of multpath at transmt and receve. For sets wth very low varaton (Sets 4 and 8), the spatal spectra are much narrower, suggestng a strong nonfadng path through the trees. Gven the varaton rates, t appears reasonable that the MAC adapt at a rate less than once per wavelength. The receve PHY, however, may stll need to update recepton weghts on the λ/4 scale. C. Coal Yard The thrd envronment conssted of a parkng lot wth parked cars surrounded by many metal buldngs, as depcted n Fg. 10. The transmtter assumed one of three possble lettered postons n the dagram, and the recever assumed one of two possble numbered postons. The recever was ether statonary or moved along a straght 9-m path at 30 cm/s. For the statonary measurements, the crossng rates were agan almost always zero, showng that any cars movng n the channel had a nearly neglgble effect. Table IV summarzes the measurement parameters and metrcs for the movng cases. The metrcs reveal that the varaton s only slghtly hgher (on average) than the varaton seen at the DT feld. However, certan postons (Set 1, for example) Authorzed lcensed use lmted to: Brgham Young Unversty. Downloaded on February 6, 2009 at 11:01 from IEEE Xplore. Restrctons apply.

9 WALLACE et al.: EXPERIMENTAL CHARACTERIZATION OF THE MIMO WIRELESS CHANNEL TEMPORAL VARIATION 1047 Fg. 10. Map of Envronment 3 (Coal Yard). Transmtter was at one of the lettered postons, whereas the recever was placed at one of the numbered postons. For Sets 7 and 8, a coal truck was parked n the coal yard as ndcated. Dstances are n meters. TABLE IV ARRAY CONFIGURATIONS AND METRICS FOR COAL YARD (ENVIRONMENT 3) Fg. 11. Map of Envronment 4 (CB Corrdor) showng postons and orentatons of arrays. The transmtter was at three dfferent locatons, and the recever was moved along a 27-m path (dotted lne) n a corrdor between two buldngs or rotated (Rot.). Patches were used for Sets 1 3 and monopoles for Sets 4 6. The orentaton for the recever monopole array (M) was shfted by 45 relatve to the patches (P). exhbt much more varaton, revealng that the same physcal scenaro can produce channels wth both hgh and low varatons. Addtonal analyss not ncluded here agan reveals that Sets 3, 5, and 7, whch represent the channels wth hgh tme varaton, are characterzed by larger angular spread as compared to Sets 4, 6, and 8. D. CB Corrdor Fg. 11 shows a map of measurements taken when the nodes sat n corrdors between buldngs. For all sets, the transmtter assumed a fxed poston and the recever was ether moved along a 27-m path or rotated two tmes. Large-scale movement and rotaton led to much more pronounced changes n the channel than had been seen prevously. However, large transtons led manly to changes n the path loss as opposed to changes n the amount of multpath present. Fg. 12 shows the spatal spectra for Set 1 as the recever s moved along a corrdor between the buldngs. Snce the path s qute long, the spatal spectra have been computed separately at the begnnng (B), mddle (M), and end (E) of the path. Interestngly, when the recever s the most obscured (B), the Fg. 12. Transmt/receve spectra for Envronment 4, Set 1 for the begnnng (B), mddle (M), and end (E) of the path. spectra look the most drectonal, and when the recever moves out nto the open, the spectra become wder. These results can possbly be explaned by a wavegudng phenomenon, snce a wavegude would exhbt only a few strong propagaton drectons. The effect of the large-scale movement and rotaton on the egenvalues s depcted n Fg. 13 for Set 1. These results show a change n the overall egenvalue levels (due to path loss) rather than a change n the ES. Table V(a) and (b) summarzes the Authorzed lcensed use lmted to: Brgham Young Unversty. Downloaded on February 6, 2009 at 11:01 from IEEE Xplore. Restrctons apply.

10 1048 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 56, NO. 3, MAY 2007 TABLE V METRICS FOR CB CORRIDOR (ENVIRONMENT 4) (a) LARGE-SCALE MOVEMENT (b) ROTATION (ELCR IN CROSSING 110 ) TABLE VI AVERAGE METRICS VERSUS ENVIRONMENT Fg. 13. Varaton of the frst four egenvalues for Envronment 4, Set 1 for (a) recever movement and (b) recever rotaton, ndcatng manly changes n the path loss. metrcs for ths locaton for movng and rotatng measurements. For rotatng measurements, ELCR s measured n number of egenvalue crossngs per 10 of rotaton, and d R s measured n degrees. Metrcs for the movng case show that the rate of varaton here was lower than that for DT feld. Although surprsng, perhaps the wavegudng effect of the buldngs partally accounts for ths effect. Varaton of the channels for patch antennas and monopoles s qute smlar, n contrast to other measurements where the monopoles exhbt hgher varaton. Ths can be explaned by the fact that the drectonal arrays were usually ponted where the maxmum power transfer would occur (.e., down the corrdor), and therefore, t s unlkely that the monopoles would collect sgnfcantly more multpath than the patches. E. Dscusson Table VI summarzes average values of the metrcs for monopole and patch arrays across all of the envronments n ths paper. Ths paper ndcates that the physcal scatterng envronment has much less of an effect on the tme varablty of channels than the array confguratons and orentatons of the MIMO system. Dual-polarzed drectonal patch antennas produced channels wth consderably lower temporal varaton than omndrectonal monopoles, ndcatng that spatally selectve elements may be advantageous for hghly moble systems. Ths dea s also supported by the fact that throughout the measurements, a very strong correlaton between the angular spread of spatal spectra and the temporal varaton was evdent. The measurements also ndcate the level of adaptaton requred of advanced moble MIMO archtectures. Table VI gves average egenvalue crossng rates on the order of 0.4/λ and 0.2/λ for monopoles and patches, respectvely, ndcatng that an advanced adaptve MIMO MAC/PHY would need to update ts modulaton and rate a few tmes per wavelength. On the other hand, values for d R are about 0.2 λ and 0.5 λ for monopoles and patches, respectvely, suggestng that tranng must be performed rapdly at the receve PHY to acheve hgh capacty. Although d T can be qute large, ndcatng that transmt CSI s useful for long dstances, the ncrease n capacty when the transmtter knows the channel was farly modest for our measured channels. Authorzed lcensed use lmted to: Brgham Young Unversty. Downloaded on February 6, 2009 at 11:01 from IEEE Xplore. Restrctons apply.

11 WALLACE et al.: EXPERIMENTAL CHARACTERIZATION OF THE MIMO WIRELESS CHANNEL TEMPORAL VARIATION 1049 V. C ONCLUSION Ths paper presents MIMO channel measurements conducted n an outdoor campus envronment at 2.45 GHz and analyzes the data behavor n terms of channel temporal varaton. A number of useful metrcs are developed to quantfy MIMO tme varaton and ts effect on system performance. The results ndcate that rates of system adaptaton are on the order of λ/4 for the PHY and 1 λ for hgher level adaptaton of the transmsson rate and modulaton. The analyss should be useful for the desgn of MIMO systems for moble envronments. REFERENCES [1] M. A. Jensen and J. W. Wallace, A revew of antennas and propagaton for MIMO wreless communcatons, IEEE Trans. Antennas Propag., vol. 52, no. 11, pp , Nov [2] L. Zheng and D. N. C. Tse, Dversty and multplexng: A fundamental tradeoff n multple antenna channels, IEEE Trans. Inf. Theory, vol. 49, no. 5, pp , May [3] A. J. Goldsmth, S. A. Jafar, N. Jndal, and S. Vshwanath, Capacty lmts of MIMO channels, IEEE J. Sel. Areas Commun., vol. 21, no. 5, pp , Jun [4] B. M. Hochwald and W. Sweldens, Dfferental untary space-tme modulaton, IEEE Trans. Commun., vol. 48, no. 12, pp , Dec [5] B. Hassb and B. M. Hochwald, How much tranng s needed n multple-antenna wreless lnks? IEEE Trans. Inf. Theory, vol. 49, no. 4, pp , Apr [6] J. Baltersee, G. Fock, and H. Meyr, Achevable rate of MIMO channels wth data-aded channel estmaton and perfect nterleavng, IEEE J. Sel. Areas Commun., vol. 19, no. 12, pp , Dec [7] D. P. McNamara, M. A. Beach, and P. N. Fletcher, Expermental nvestgaton of the temporal varaton of MIMO channels, n Proc. IEEE 54th Veh. Technol. Conf., Atlantc Cty, NJ, Oct. 7 11, 2001, pp [8] H. Xu, M. Gans, D. Chzhk, J. Lng, P. Wolnansky, and R. Valenzuela, Spatal and temporal varatons of MIMO channels and mpacts on capacty, n Proc. IEEE Int. Conf. Commun., New York, Apr. 28 May 2, 2002, vol. 1, pp [9] V. Pohl, P. H. Nguyen, V. Jungnckel, and C. von Helmolt, How often channel estmaton s needed n MIMO systems, n Proc. IEEE Global Telecommun. Conf., San Francsco, CA, Dec. 1 5, 2003, vol. 2, pp [10] J. W. Wallace, M. A. Jensen, A. L. Swndlehurst, and B. D. Jeffs, Expermental characterzaton of the MIMO wreless channel: Data acquston and analyss, IEEE Trans. Wreless Commun.,vol.2,no.2,pp , Mar [11] J. Maurer, C. Waldschmdt, T. Kayser, and W. Wesbeck, Charactersaton of the tme-dependent urban MIMO channel n FDD communcaton systems, n Proc. IEEE 57th Veh. Technol. Conf., Jeju, Korea, Apr , 2003, vol. 4, pp Mchael A. Jensen (S 93 M 95 SM 01) receved the B.S. (summa cum laude) and M.S. degrees n electrcal engneerng from Brgham Young Unversty (BYU), Provo, UT, n 1990 and 1991, respectvely, and the Ph.D. degree n electrcal engneerng from the Unversty of Calforna, Los Angeles (UCLA), n From 1989 to 1991, he was a Graduate Research Assstant n the Lasers and Optcs Laboratory, BYU. From 1991 to 1994, he was a Graduate Student Researcher n the Antenna Laboratory, UCLA. Snce 1994, he has been wth the Electrcal and Computer Engneerng Department, BYU, where he s currently a Professor and Department Char. Hs man research nterests nclude antennas and propagaton for personal communcatons, mcrowave crcut desgn, radar remote sensng, numercal electromagnetcs, and optcal fber communcatons. Dr. Jensen s a member of Eta Kappa Nu and Tau Beta P. He s currently a member of the Admnstratve Commttee and the Jont Meetngs Commttee for the IEEE Antennas and Propagaton Socety, s an Assocate Edtor for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, and has served the socety as Vce Char and Techncal Program Char for several symposa. He s the recpent of the H. A. Wheeler Paper Award n the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION n 2002 and the Best Student Paper Award at the 1994 IEEE Internatonal Symposum on Antennas and Propagaton. Ajay Gummalla (S 96 M 00) receved the B.Tech. degree from Indan Insttute of Technology, Madras, Inda, n 1996 and the M.S. and Ph.D. degrees n electrcal engneerng from Georga Insttute of Technology, Atlanta, n He has worked extensvely n broadband wreless and wred communcaton systems. He recently joned Rayspan Corporaton, San Dego, CA, as the Drector of Communcaton Systems. Pror to ths, he was a Prncple Member of Techncal Staff at San Dego Research Center, where he led the research, desgn, development, and successful demonstraton of Moble MIMO technology. Prevously, he made sgnfcant contrbutons to the IEEE 802.3ah Ethernet n the Frst Mle study group and was a key contrbutor n the development of Propane technology at Broadcom (Dgtal Furnace). He has authored numerous journal and conference papers. He s the holder of eght patents and s a Conventor on 12 patent applcatons. Hs current research nterests nclude MIMO wreless communcatons, wreless mesh/ad hoc networks, and broadband access technologes. Jon W. Wallace (S 99 M 03) receved the B.S. (summa cum laude) and Ph.D. degrees n electrcal engneerng from Brgham Young Unversty (BYU), Provo, UT, n 1997 and 2002, respectvely. From 1995 to 1997, he was an Assocate at Novell, Inc., Provo. Durng 1997, he was a member of Techncal Staff at Lucent Technologes, Denver, CO. He receved the Natonal Scence Foundaton Graduate Fellowshp n 1998 and was a Graduate Research Assstant at BYU untl From 2002 to 2003, he was wth the Moble Communcatons Group, Venna Unversty of Technology, Venna, Austra, where he pursued a collaboratve research n the area of wreless channel measurement and modelng. From 2003 to 2006, he was a Research Assocate at the Wreless Communcatons Laboratory, BYU, where he developed platforms for wdeband MIMO channel soundng and real-tme space tme codng. He s currently an Assstant Professor n the School of Engneerng and Scence, Jacobs Unversty Bremen (formerly Internatonal Unversty of Bremen), Bremen, Germany. Hs research nterests nclude wreless channel soundng and modelng, real-tme MIMO mplementaton, optcal devce modelng, and remote sensng. Harry B. Lee (S 61 M 63) was born n Chcago, IL, on July 27, He receved the Ph.D. degree n electrcal engneerng from Massachusetts Insttute of Technology (MIT), Cambrdge, n From 1963 to 1967, he was an Assstant Professor of Electrcal Engneerng at MIT. He s currently wth San Dego Research Center, Inc., San Dego, CA. He has cofounded three successful hgh-tech companes, namely: 1) Applcon (1969), 2) Atlantc Aerospace Electroncs Corporaton (1985), and 3) San Dego Research Center, Inc. (2001). Hs professonal nterests nclude geolocaton, drecton fndng, MIMO, LPD/AJ, and adaptve technques. Dr. Lee s the recpent of the IEEE Browder J. Thompson Award n 1964 for the best paper by an author under age 30 and the IEEE Russel Baker Award n 1968 for the best paper by an author of any age. Authorzed lcensed use lmted to: Brgham Young Unversty. Downloaded on February 6, 2009 at 11:01 from IEEE Xplore. Restrctons apply.