ADAM: An Adaptive Beamforming System for Multicasting in Wireless LANs

Transcription

1 ADAM: An Adaptve Beamformng System for Multcastng n Wreless LANs Ehsan Aryafar 1,Mohammad(Amr)Khojastepour 2,KarthkeyanSundaresan 2 Sampath Rangarajan 2,andEdwardW.Knghtly 1 1 Rce Unversty, Houston, TX 2 NEC Laboratores Amerca, Prnceton, NJ Abstract We present the desgn and mplementaton of ADAM, the frst adaptve beamformng based multcast system and expermental framework for ndoor wreless envronments. ADAM addresses the jont problem of adaptve beamformer desgn at the PHY layer and clent schedulng at the MAC layer by proposng effcent algorthms that are amenable to practcal mplementaton. ADAM s mplemented on an FPGA platform and ts performance s compared aganst that of omn-drectonal and swtched beamformng based multcast. Our expermental results reveal that () swtched multcast beamformng has lmted gans n ndoor mult-path envronments, whose defcences can be effectvely overcome by ADAM to yeld an average gan of three-fold; () the hgher the dynamc range of the dscrete transmsson rates employed by the MAC hardware, the hgher the gans n ADAM s performance, yeldng upto nne-fold mprovement over omn wth the rate table; and () fnally, ADAM s performance s susceptble to channel varatons due to user moblty and nfrequenhannel nformaton feedback. However, we show that tranng ADAM s SNR-rate mappng to ncorporate feedback rate and coherence tme sgnfcantly ncreases ts robustness to channel dynamcs. I. INTRODUCTION Wreless multcastng s becomng ncreasngly mportant for applcatons such as vdeo/audo streamng. Whle the nherent broadcast nature of the wreless medum allows for a sngle multcast transmsson to cover a group of users smultaneously, ts performance s determned by the clent wth the weakeshannel (SNR). On a parallel front, beamformng antennas have recently ganed a lot of attenton n ndoor wreless networks [1], [2]. These are multple-element arrays that are able to focus ther sgnal energy n specfc drectons and hence form a natural soluton to mprove the channel to the weakeslent and hence the multcast system performance. Beamformng could be ether adaptve where the beam patterns are computed on the fly based on channel feedback from clents, or swtched, where precomputed beams thaover the azmuth of 36 o are used. Recent work advocated the use of swtched beamformng to mprove multcastng [3], [4], [5]. However, the beamformng gan (from restrcted sgnal footprnt) comes at the cost of reduced broadcast advantage, thereby requrng multple beamformed transmssons to cover all the clents unlke an omn-drectonal transmsson. Addressng ths tradeoff n turn requres the use of composte beams that are generated by combnng ndvdual beams so as to effectvely balance between beamformng gan and coverage [3]. Be t ndvdual or composte beams, we expermentally show that the performance of swtched beamformng s lmted for multcastng n ndoor wreless networks. The reasons are two fold: () usng a pre-determned set of beam patterns lmts performance when smultaneously caterng to a multtude of clents n multpath envronments; () snce the resultng SNR on a composte beam s not avalable a pror, t s modeled based on the measured SNR from ts consttuent beams; however, such modelng s naccurate n multpath envronments, resultng n lmted performance when a composte beam s appled. To address these defcences, we advocate the use of adaptve beamformng for multcastng n ndoor wreless networks. Translatng the potental of adaptve beamformng nto practcally realzable benefts for multcastng s a hghly challengng task. Specfcally, () gven the channel nformaton of clents, an optmal soluton needs to dentfy f and how asetofclentsmustbeparttonedntoseparategroups (schedulng) and how to desgn an adaptve beamformer that smultaneously caters to all clents wthn the same group; () f such a soluton can be realzed and mplemented n practce to overcome the defcences of swtched beamformng and provde gans n ndoor multpath envronments, and what are the factors affectng ts performance; and () n practcal scenaros the rate of channel feedback from a clent may not be suffcenompared to the coherence tme of ts channel ether due to lmted feedback (for reducng overhead) or small coherence tmes (due to clent moblty). In such cases, the adaptve beamformer must ncorporate robust mechansms to compensate for the lack of tmely channel feedback not only to retan ts benefts, but also to avod degradng to worse than omn. Towards addressng these challenges, we present ADAMthe frst adaptve beamformng based system for multcastng n ndoor wreless networks. ADAM decouples the jonlent schedulng and beamformer desgn problem nto two ndvdual sub-problems n a manner that allows ther solutons to renforce each other, whle also makng them amenable to practcal mplementaton. It frst parttons the set of clents nto groups based on the closeness of ther channels. Ths allows t to later determne an effcent adaptve beamformer for clents wthn the same group, wheren a greedy, one-shot algorthm yeldng near-optmal performance s employed. ADAM s mplemented on the WARP platform and ts performance s extensvely evaluated n ndoor envronments. Our expermental results reveal that () whle swtched beamformng provdes lmted gans for multcastng n ndoor multpath

2 envronments, ADAM s able to address these defcences to yeld a three-fold average gan; () ADAM s gans are more wth a hgher dynamc range of the (dscrete) transmsson rates employed by the MAC, yeldng gans as hgh as nnefold over omn wth the rate table. Fnally, wth controlled experments performed wth a channel emulator, we show that the performance of ADAM s strongly dependent on both the coherence tme ( )ofthe channel as well as the channel feedback tme scale (t f )and more specfcally on the s-rato, where s = t f.hence,adam categorzes the clents based on ther s parameter and employs clent-specfc rate tables n determnng the beamformed transmsson rate, thereby ncreasng ts robustness to both clent moblty and lmted channel feedback. The rest of ths paper s organzed as follows: Secton II provdes a background on beamformng along wth related work. Sectons III descrbe the challenges n realzng a practcal adaptve beamformng system for multcast. Secton IV descrbes the components of ADAM. Secton V descrbes ts mplementaton followed by detaled evaluaton n Sectons VI and VII. Fnally, we conclude the paper n Secton VIII. A. Prelmnares II. BACKGROUND AND RELATED WORK Beamformng: Beamformng rados consst of an array of omn-drectonal elements and sophstcated sgnal processng capabltes to control the sgnals that are sent/receved from each of these antennas. The sgnals that are fed to each of these elements can be weghted n both ampltude and phase to produce a desred beam pattern that ncreases the SNR at the recever. These weghts are appled at the Tx antenna array and can be wrtten as w =[w w 1... w N 1 ] T.Dependngon the level of sophstcaton n adaptng these weghts, there are two man types of beamformng: swtched and adaptve. In swtched beamformng, a set of pre-determned beam patterns s avalable. Each of these beams has a man lobe of maxmum gan and some sde lobes representng leakage of energy. In swtched beamfomng, a Tx normally chooses a beam that provdes the strongest sgnal strength at the clent, wthout requrng fne-graned channel nformaton. Such a beam may nooncde wth the physcal drecton of the Rx dependng on the multpath scatterng n the envronment [6]. In adaptve beamformng, channel estmaton from the Rx s used to adapt the beam pattern n the sgnal doman at the Tx. The resultng beam pattern may not have the sngle man lobe structure (pontng n the drecton of the Rx) of a swtched beam, but s optmzed to renforce the multpath components of the sgnals arrvng at the Rx from the dfferent Tx antenna elements. Multcast and Beamformng: The soluton to address the beamformng-coverage tradeoff wth swtched beamformng s to employ ndvdual beams sequentally or form a composte beam by combnng multple ndvdual beam patterns so as to cover multple clents smultaneously [3]. However, snce the energy s conserved, the net power n a composte beam s dstrbuted among ts consttuent beams, and hence the resultng beamformed SNR at the clents s reduced. Hence, t becomes mportant to ntellgently choose composte beam patterns that tradeoff user coverage and beamformng gan [3]. In adaptve beamformng, the channel to each of the clents s estmated and fed back to the AP. Wth the complete channel nformaton, the AP determnes and apples a beamformer that maxmzes the mnmum SNR among all the clents. B. Related Work Beamformng and Multcast: Beamformng has receved alotofattentonrecentlynuncast[7],[8]andmultcast[9], [1], [11], [4], [3] applcatons. The problem of multcastng wth adaptve beamformng has receved sgnfcant attenton n the physcal layer communty [9], [1], [11] from a theoretcal perspectve. Whle these works target the contnuous (power, rate) verson of the problem wthout addressng the schedulng aspect, we consder both. Further, our focus s on buldng a practcal system that realzes the benefts of adaptve beamformng for multcast. The jont problem of schedulng and beamformng has been consdered n theory wth swtched beamformng antennas [4], [3]. In addton to swtched beamformng solutons beng less effectve n practcal ndoor multpath envronments (shown expermentally later), the problem formulaton and hence solutons are sgnfcantly dfferent when omes to adaptve beamformng. MU-MIMO Protocols: MU-MIMO mplementatons has been explored n [2], [12] for uncast. In uncast, dfferent streams cause mutual nterference to one another. However, n multcastng a common stream needs to be optmzed for all the clents. Thus, MU-MIMO technques for uncast do not apply to the multcast problem, necesstatng redesgn of the beamformng algorthms along wth schedulng for multcast. III. DESIGN CHALLENGES In ths secton, we descrbe the system model and challenges n realzng a practcal adaptve-beam multcast system. A. System Model We consder a sngle-cell envronment, where a smart antenna AP s equpped wth N antennas and transmts to K clents each equpped wth a sngle antenna. Once a multcast sesson has been selected, our goal s to determne: () how to group (schedule) the clents that belong to a multcast sesson, nto one or multple transmssons, () how to calculate the adaptve beamformer for each of the transmssons, and () the transmsson rate for each of the groups. We consder a narrowband system model, where the receved baseband sgnal y k of the k-th user s gven by: y k = h k x + z k, k =1,..., K (1) here x s the transmtted symbol from the base staton antennas, h k = [h 1k h 2k...h Nk ] s the channel gan for the k th user, and z k represents the crcularly symmetrc addtve whte Gaussan nose at the recever. In ths model, the base staton transmtter s subject to a total power constrant P,.e., x x P (x s the conjugate transpose of x). The total transmt power does not depend on the number of transmt

3 antennas and remans the same for all the schemes studed n ths paper. Wth beamformng, the transmtted sgnal x s gven by x = ws,wherew s the beamforer vector and s s the ntended symbol. When beamformng s appled, the resultng SNR at a clent k s equal to h k ww h k. B. Addressng the Beamformng-Multcastng Problem Solvng the jont beamformng-multcastng problem s challengng at two levels: () determnng an adaptve beamformer caterng to a set of users smultaneously; () determnng f and how asetofusersmustbeparttonednto sub-groups, where beamformng s executed separately n each group. Adaptve Beamformer Desgn: Consder the objectve of maxmzng the mnmum rate of the users n a sngle multcast group under constant transmt power constrant. The rate of the k th user can be wrtten as R k = log 2 (1 + h k ww h k) (2) The multcast beamformng problem s then max w mn{log 2 (1 + h k ww h k )} k s.t. w w P Wthout loss of generalty we assume s 2 = 1.Here, optmzng the rate s equvalent to optmzng the mnmum SNR of the multcast group. Hence, the problem can be alternatvely presented as the maxmzaton of the mnmum receved SNR of all users,.e. P 1 : max w mn{w h k kh k w} s.t. w w P The problem formulaton n P 1, s a quadratcally constraned quadratc optmzaton program (QCQP), whch s a non-convex problem and ts dscrete verson s NP-hard as well [9]. Desgnng an effcent algorthm to address ths problem, whle beng amenable to mplementaton s all the more challengng. User Parttonng: We perform an experment n whch we ncrease the number of users n the multcast group from one to fve n the topology of Fg. 3(a). The adaptve beamformer s determned for each group and the gan of the resultng mnmum SNR of the beamformed transmsson over omn s plotted n Fg. 1(a). Ian be seen that as the sze of the group ncreases, the adaptve beamformng benefts tend to decrease wth ts performance tendng to that of an omn transmsson. Ths n turn advocates the need to restrct beamformng to small multcast groups and hence to partton users n a large multcast group nto smaller groups, where beamformng s executed separately wthn each group. The need for such parttonng s exacerbated n the presence of dscrete rate tables. For example, consder two users that each acheves a5dbsnrwhenjontlybeamformedto.wth82.11rate table of Fg. 2(b), the transmsson rate would be 1Mbps. Now, f sequental beamformng of the users ncreases each user s SNR by 3 db, the resultng data rate of each clent would be 9 Mbps. Snce multple transmssons are requred, the performance metrc shfts to latency (schedule length) - total tme requred to transmt L bytes of multcast data to all users. Thus, whle jont beamformng ncurs a tranmsson tme of L 1,sequentalbeamformngwouldncur L 9 + L 9 = L 4.5, whch s latency reducton of over four-fold. Note that when users are parttoned nto sub-groups, there s a (tme) multplexng loss wth dfferent sub-groups recevng transmssons sequentally. Hence, there s a tradeoff between operatng on low rates (low mn SNR) by beamformng to all the users n one shot or operate on hgher rates n each sub-group but ncur the multplexng loss. Problem Formulaton: Assume K users n the system, and amultcastdataszeofl bytes. The objectve s to partton the users nto J groups and transmt L bytes sequentally on each group usng adaptve beamformng, such that the total schedule length to delver L bytes to all users s mnmzed. The problem can now be formally stated as: P 2 : mn J j=1 L R(SNR j ) s.t. wj w j P ; and SNR j = mn(h k w j wj h k) k S j where J s the number of parttons, S j s the set of user ndces and w j s the beamformer for partton j. Therate functon R(SNR) maps SNR nto the approprate rate based on a codng-modulaton scheme and s dscrete n practcal systems. J, S j,andw j are the outputs of the problem. C. Robustness to Channel Dynamcs and Feedback Rate The above two challenges are wth respect to determnaton of a soluton under the assumpton of nstantaneous channel nformaton from clents. However, n any practcal system, channel state feedback consttutes overhead and may not be avalable for every sngle packet. The moblty of clents further reduces the coherence tme of the channel, thereby requrng ncreased feedback frequences, the absence of whch could render the feedback both outdated and naccurate. We conduct an experment n whch the AP transmts 1 pkts/sec to a statc clent at nght. The clent estmates the channel from the preambles. The varaton n the channel magntude and phase s plotted as a functon of the nterval sze n Fg. 1(b),(c). The experment s then repeated for a moble clent and the results are also ndcated. Ian be seen that the channel dynamcs are almost neglgble for a statc clent, ndcatng a large coherence tme for the channel as well as ts ablty to wthstand reduced feedback frequences. However, wth a moble clent, the stuaton s qute the contrary, where the mean channel magntude and phase varatons are around 1 db and 3 o,ndcatngthesmallcoherencetmeofthechannel and thereby the need for hgh feedback frequency. Hence, t s mportant to understand the senstvty of the adaptve beamformng multcast soluton to such channel dynamcs, and hence ncorporate robustness nto ts desgn. IV. DESIGN OF ADAM We now present our adaptve-beam multcast system (ADAM) that addresses the dentfed challenges. We present our soluton to the beamformng-multcastng problem that s

4 Adaptve Omn (db) # of Users a) Impact of User Sze b) Channel Magntude Varaton c) Channel Phase Varaton Fg. 1. Adaptve beamformer challenges ((a), (b), (c)), and WARP board SNR-rate relaton (d). Delvery Rato (%) BPSK 1/2 BPSK 3/4 QPSK 1/2 QPSK 3/4 16 QAM 1/2 16 QAM 3/4 64 QAM 2/3 64 QAM 3/ RSS (dbm) d) WARP board SNR-rate relaton amenable to a practcal mplementaton, whle ts extenson to handle channel dynamcs s deferred to Secton VII. A. Operatons n ADAM Once the AP receves data to be dssemnated for a multcast sesson, ADAM operates as follows: () AP sequentally transmts tranng symbols on each of ts antennas; () Each clent measures the channel ampltude and phase for each of the transmttng antennas; () Clents sequentally feedback channel nformaton to the AP; (v) AP runs algorthms whch partton the clents to dfferent groups and fnd the beamformer for each group; (v) AP selects the approprate rate for each group based on a rate table, and transmts multcast data. The algorthmc component of ADAM (step v) s responsble for desgnng an effcent user parttonng and multcast beamformer algorthm. B. Algorthm Overvew The optmal user parttonng n problem P 2 depends on the rate acheved by each group (partton), whch depends on the beamformer used for that group (NP-hard), whch n turn depends on the set of users grouped together. To address ths cyclc dependency, we decompose the problem nto two subproblems n a manner that they re-nforce each other and propose the followng algorthm (JPB-A). For a gven number of parttons, we frst partton the users based on the closeness of ther channels. Ths allows us to employ a greedy, oneshot algorthm to provde a near-optmal multcast beamformer wthn each partton. Based on the clent membershp and beamformer employed, the resultng rate n each partton s determned to obtan the net schedule length. The procedure s repeated for all number of parttons (up to K) and the one (j )yeldngthemnmumschedulelengthschosenalong wth ts correspondng beamformers and clent membershps. The above algorthm needs to address two sub-problems: () gven a number of parttons, how to assgn the clents to the gven number of parttons; and () desgn an approprate beamformer for the clents wthn each group. These two components are dscussed next. C. User Parttonng We use the noton of chordal dstance [13] between two vectors as our metrc for user parttonng. Gven two users wth channels h and h j,thechordaldstancebetweenthem s defned as: d c (h, h j )= 1 h h j 2 h 2 h j 2 (3) The multcast beamformer can be effcently desgned for agroupofchannelswthlowchordaldstancebetweeneach other. Ths s because of two reasons. Frst, a beamformer w that has a low chordal dstance from one channel n such agroup,wouldhavealowchordaldstancefromanyother channel n the group due to the followng property of chordal dstance d c (h, w) d c (h j, w) d c (h, h j ) (4) Second, based on Eq. 3, mnmzng d c (h j, w) s equvalent to maxmazng w h j h j w (SNR) where w,and h j are the normalzed beamformng and channel vectors. Hence, when we subsequently desgn a beamformer for clents that are grouped together based on ther chordal dstance, the beamformer would effcently ncrease the SNR across all the clents. Algorthm 1 Multcast user parttonng GM-UP. 1: Input: 2: Channel vectors h k, 1 k K 3: Number of parttons n and number of teratons Q 4: Output: 5: AparttonngofK clents nto n sets (S 1,...,S n) 6: Normalze the channel vectors h k = h k, 1 k K h k 7: Randomly assgn clents to parttons s.t. S () 8: Let M () = 1 S () k S () h k h k 9: Fnd partton centrod: m () =largestegenvectorm () 1: for t =1to Q do 11: j = 1,...,n : Let Sj t = {k : d c(h k,m (t 1) j ) d c(h k,m (t 1) ), k =1,...,K, =1,...,n,j } 12: Let M (t) 1 h k h k = S (t) k S (t) 13: Fnd partton centrod: m (t) 14: end for 15: S = S Q {1,...n} =largestegenvectorm (t) Algorthm 1 summarzes the procedure for groupng of users nto a gven number of parttons. The algorthm s manly composed of two steps:

5 Step 1: Parttonng (Lne 11): users are assgned to parttons whch have the leashordal dstance from the centrod or mean of the partton. Step 2: Fndng the centrod (Lne 13): new mean of each partton s calculated. Algorthm 1 takes the maxmum number of teratons as nput and converges to a parttonng wthn a small number of teratons. D. Multcast Beamformer Desgn The remanng component n algorthm JPB-A s that for a gven set of users that are grouped together, how to desgn a beamformer that maxmzes the mnmum SNR of the users (problem P 1 ). The soluton to the optmzaton problem n P 1 s equvalent (up to a scalng constant) to the soluton to the followng problem P 3 : mn w w w s.t. mn w h k kh k w α, k [1,K] Ths s because the optmal soluton to P 1 wll be gven by the product of α and a scalng constant. Based on the KKT optmalty condtons of P 3, we make the followng two observatons whch serve as the bass for our beamformer desgn algorthm. Observaton 1: The multcast beamformer w s a lnear combnaton of h k, k [1,K]. Observaton 2: Gven a permutaton of the users (π), the optmal soluton can be represented as a functon of the orthogonalzed channels of each user wth respect to the channels of users precedng t n the permutaton (h π,π(k) ).,.e. w = K k=1 β π,kh π,π(k). Leveragng these observatons, the key steps of our proposed greedy algorthm can be summarzed as follows. Step 1: For a gven permutaton of users, orthogonalze the user channels wth respect to the channels of users precedng t n the permutaton. Step 2: Wth the help of the orthogonalzed channels determned, each weght β π,k s obtaned successvely as a functon of the orthogonalzed channels of users [1,k]such that they mnmze the norm of w. Step 3: Steps 1 and 2 are repeated for every permutaton π (or a randomly selected number of permutatons to reduce complexty) to obtan the correspondng beamformng vector w π.thefnalbeamformngvectorsobtanedastheonethat has the mnmum norm over all permutatons. Note that snce the man focus of ths paper s on the mplementaton and expermental evaluaton of adaptve beamformng for multcastng, we have omtted detals of the beamformer algorthm (dervaton, pseudo-code, etc.) and presented them n [14]. A. Hardware and Software V. EXPERIMENTAL SETUP Our mplementaton s based on the WARPLab framework [15]. In ths framework, all WARP boards are connected to a host PC through an Ethernet swtch. The host PC s responsble a) WARPLab PHY Parameters. b) SNR-Rate table. Fg. 2. WARPLab (a) and SNR-Rate Table. for baseband PHY sgnal processng, whle WARP boards act as RF front-ends to send/receve packets over the ar. Fg. 2(a) specfes the PHY parameters used n our evaluaton. Our APs use four rados connected to 3 db antennas. The antennas are mounted on a crcular array structure wth a half-wavelength ( λ 2 )dstancebetweenadjacentantennas(6.25cmat2.4ghz). B. Multcastng Framework We mplemented three multcast mechansms on our testbed. Omn. Ths mechansm obtans SNR feedbacks from all of the clents n the multcast group and transmts packets wth the rate supported by the weakeslent. Ths mechansm always uses the frst (fxed) antenna for transmsson. Multcastng wth Swtched Beam Antennas. We have consdered Lnear and Crcular arrays for swtched-beam multcastng wth 3 and 4 orthogonal beams respectvely. Our mplementaton s accordng to [3], whose solutons consders both ndvdual and composte beams, and shows consderable reducton n schedule length compared to schemes usng ndvdual beams alone. In ths approach, the base staton transmts tranng symbols for each of ts beams sequentally. Next, the clents feedback the beam ndex on whch the strongest sgnal was receved, together wth the correspondng beam ndex. The base staton then constructs a set of optmal composte beams to cover all of the clents. However, when a composte beam s used, the total power s equally dstrbuted among ts consttuent beams. In such cases, the algorthm predcts the resultng SNR of the clents assocated to a composte beam and selects a rate supported by the clent wth the lowest SNR. ADAM. Our proposed adaptve beam multcast system. C. System Implementaton We now descrbe the components of our mplementaton. Channel Tranng Durng the channel tranng, the transmtter sends a known preamble. The preamble s composed of atranngsequenceandaplottone.thetranngsequences used to acheve frequency and phase synchronzaton between the transmtter and recever. The plot s used for actual channel estmaton. In omn, the preamble s sent over the fxed antenna. For each of the beam patterns n swtched beamformng, the preamble s multpled by the correspondng beam weght. The weghted preambles are next transmtted sequentally. In ADAM, the base staton transmts the preamble sequentally on each of ts antennas. Thus, clents can correctly measure the channel for each transmttng antenna.

6 Channel Estmaton. Durngthechannelestmaton,each clent measures the h or SNR and sends t to the host PC. In omn, each of the clents measures the preamble s SNR and feeds back ts value. In swtched beamformng, each beam s SNR s measured and the value of the hghest SNR together wth ts beam ndex s fed back. In ADAM, h s measured and fed back by each of the clents. Modulaton and Codng Scheme (MCS) Selecton. All of the studed protocols n ths paper select a MCS accordng to the resultng SNR. Thus, we need to quantfy the SNRrate relaton for the WARP boards. We have used the Azmuth ACE 4WB channel emulator [16] to fnd the WARP board s rate table. We connect one sngle antenna transmtter and one sngle-antenna recever to the emulator and vary the SNR accross the full range of allowable receved power for the WARP rado board. The channel profle parameters used by the channel emulator are adapted from the 82.11n task group (TGn) models for a small offce envronment. The channel profle s composed of 14 Raylegh fadng channels wth multpath RMS delay spread of 3 ns, andmaxmumdelay of 2 ns. Fg.1(d)showsthepacketdelveryrato(PDR)as afunctonofrecevedpowerforvarousmcss.weselectthe rate of an SNR value, as the hghest MCS such that the gven SNR acheves 1% PDR. Multcast Packet Transmsson. In ths step, the AP sends the multcast packet wth the approprate parameters. D. Performance Metrcs All of our ndoor experments are conducted durng nght and wth statc nodes. Experments were conducted on the GHz channel 14, whch consumer devces are not allowed to use n the USA. As observed n Fg. 1(b),(c), the varatons n channel n such condtons are such that the channel remans coherent durng the experments. Ths allows for vald comparson among multple multcastng schemes. Each data pont n our ndoor over-the-ar experments s an average of ffty samples. In our channel emulator based experments, we take 1 SNR measurements for each data pont. We consder the receved sgnal strength (dbm), schedule length (delay), packet delvery rato (PDR), and throughput as our metrcs of comparson. We defne PDR and throughput for aclent,basedonthenumberofpacketsthatarereceved correctly by thalent over all the transmtted packets. Next, we defne the multcast PDR and throughput as the average of PDRs and throughputs over all of the clents. VI. GAINS OF ADAPTIVE BEAMFORMING In ths secton, we compare the performance of ADAM to omn and swtched beamform multcastng. Scenaro. Fg. 3(a) depcts our expermental setup n whch we deployed 6 nodes n an offce envronment. Nodes 1 and 2 each have four antennas and thus, can be used as transmtters or sngle-antenna recevers. We frsonsder node 1 as our transmtter, and amongst the remanng fve nodes, consder all subsets of two, three, four, and fve nodes as our dfferent clent sets for generatng dfferent topologes. We repeat the experment wth node 2 as our transmtter, leadng to a total of 52 topologes. For each of these topologes, we measure the schedule length for all of the multcastng systems. A. ADAM s performance characterzaton Performance Gans: Fg. 3(b) shows the schedule length of ADAM when the rate s selected accordng to the WARP SNR-rate relaton of Fg. 1(d). Topology ndces 1-1, 21-3, 41-45, and 51 are respectvely 2,3,4, and 5 clent topologes wth node 1 as the transmtter. Topology ndces 11-2, 31-4, 46-5, and 52 correspond to node 2 as the transmtter. Fg. 3(b) shows that for some of the topologes wth node 1 as the transmtter, ADAM provdes neglgble gans compared to omn. For these topologes, the mnmum rate that s supported by omn s hgh. Thus, the ncrease n SNR due to adaptve beamformng does not provde hgh throughput gans. However, n topologes where at least one clent has a weak channel, the gans of adaptve beamformng are much hgher. In such topologes, omn would choose the lowest rate such that all clents can successfully receve the packet. A smlar ncrease n the SNR would then result n hgh gans due to the nonlnear mappng of SNR-rate of WARP boards. On average, n ths experment ADAM reduces the schedule length by a factor of 2.8 compared to omn. Sub-optmalty of Parttonng: Fg. 3(b) also compares the performance of ADAM s user parttonng (JPB-A) to the optmal partton. We fnd the optmal partton of a gven topology, by consderng all possble parttons of ts correspondng clent set and selectng the one wth the mnmum schedule length. Accordng to Fg. 3(b), JPB-A has a performance that s very close to that of the optmal partton. On average, JPB-A ncreases the schedule length only by 7% compared to that of the optmal partton. Dynamc Range of Rate Tables: ADAM s user parttonng and ts overall schedule length s dependent on the SNRrate mappng of ts hardware. We now explore ADAM s performance when we select the rates accordng to s rate table. The SNR-rate mappng of 82.11a s shown n Fg. 2(b). Fg. 3(c) depcts the schedule length of ADAM as well as omn. In order to measure the schedule length, we measure the beamformed multcast packet s SNR at the correspondng clents. Next, we map the measured SNR to rate table of Fg. 2(b) and calculate the resultng schedule length for each of the schemes. Fg. 3(c) shows that ADAM has sgnfcantly reduced the schedule length wth an average reducton factor of a uses OFDM modulaton wth rates of 6 to 54 Mbps. It also supports basc rates of 1 and 2 Mbps wth DSSS modulaton. Thus ADAM has the potental to provde gans as hgh as 54. Ths n turn results n addtonal decrease n schedule length as compared to WARP board s SNR-rate table. Fndng: ADAM wth four antennas can reduce the schedule length by about 2.8 tmes compared to omn. As the SNR of the weakeslent ncreases, ADAM s gan decreases. ADAM s gans are also hghly dependent on the SNR-rate table used by the specfc hardware and can sgnfcantly ncrease when the dynamc range of a rate table s hgh.

7 !"#$ %"#+ %"#*!"#$#%"#& %"#)!"#$#%"#' %"#( a) Map of the envronment. Schedule Length (msec) Omn JPB A Optmal Partton 2 4 Topology Index b) Schedule length wth WARP Fg. 3. Gans of ADAM. Schedule Length (msec) Omn JPB A Optmal Partton 2 4 Topology Index c) Schedule length wth rates B. Adaptve vs. Swtched beamformng In ths secton, we compare the performance of ADAM to that of swtched beamformng. We have used the same expermental setup of Fg. 3(a). For each topology, we frst perform adaptve beamformng. Next, wthouhangng the antenna array, we perform swtched multcast beamformng by usng the pre-determned beams for the crcular array. Fnally, we change the antenna array to a lnear array and perform swtched multcast beamformng wth ts correspondng beam weghts. Whle changng the antenna array, we keep the frst antenna at ts former locaton. Snce the performance of omn s only dependent on the frst antenna, ts schedule length remans smlar to that of Fg. 3(b)). Relatve Gans: We now compare the schedule length of swtched beamformng to that of adaptve beamformng. Fg. 4(a) shows that ADAM provdes an average gan of 1.8 and 2.1 over swtched beamformng wth crcular and lnear arrays respectvely. Further, ADAM consstently outperforms swtched beamformng n every topology. Ths can be attrbuted to the fact that swtched beam uses only a fnte set of pre-determned beams whch mght even have a lower gan compared to an omn transmsson n the presence of multpath. Indeed, by comparng Fg. 3(b) and Fg. 4(a) we observe that n many scenaros swtched beamformng would not be used and nstead the swtched beam algorthm would end up usng omn transmsson. Drawback of Swtched Beamformng: Fg. 4(b) shows the drawback of swtched beamformng when employng composte beams. The resultng PDR of swtched beamformng could be a lot lower than the predcted 1%, andcouldbeequalto zero for many topologes. Ths s due to the composte beam constructon of swtched beamformng. For example when two beams are combned and the power allocated to each beam s dvded n half (so that total power s conserved), the nherent assumpton s that the resultng SNR n each beam reduces by 3dBandaMCSsselectedaccordngly. We have performed an experment to show the naccuracy of such a modelng assumpton n ndoor multpath envronments. For each of the clents n the topology of Fg. 3(a), we fnd the beam that acheves the hghest SNR for both lnear and crcular array structures. Next, for each clent we construct a two-lobe composte beam by combnng ts best beam, wth every other beam of that partcular antenna array. Fnally, we measure the resultng SNR of the constructed composte beam, and subtract t from the SNR obtaned by usng the best beam alone. Fg. 4(c) shows that when combnng two beams, the resultng SNR could be sgnfcantly hgher or lower than the predcted SNR. Ths s because, even when the consttuent beams are orthogonal, when a composte beam s used n an ndoor multpath envronment, the resultng energy at each clent not only depends on ts chosen consttuent beam but also on other beams due to reflectons and multpath scatterng. Dependng on whether the resultng effect s constructve or destructve, the resultng SNR could be hgher or lower, makng t hard to leverage composte beams n ndoor multpath envronments. Fndng: Swtched beamformng has lmted performance for multcastng n ndoor multpath envronments, whle ADAM benefts from ndoor multpath by choosng approprate weghts that renforce the multpath components at the recever. VII. IMPACT OF CHANNEL DYNAMICS The experments so far were conducted wth perfechannel nformaton at the transmtter. However, n any practcal system the rate of channel feedback that s avalable from a clent may not be suffcenompared to the coherence tme of ts channel. The channel feedback tme scale could be nherently lmted n the system for overhead reducton, and/or the channel coherence tme could be small due to hgh varatons n the envronment or clent moblty. Ths would cause naccurate channel nformaton at the transmtter whch can sgnfcantly reduce the gans of ADAM and may even degrade ts performance to worse than omn. In ths secton, we frst explore the relaton between channel feedback rate and coherence tme on the performance of ADAM. Next, we propose solutons to compensate for the lack of tmely channel feedback, such that the benefts of ADAM are retaned. Scenaro. In order to have precse and repeatable channel condtons, we use a channel emulator for the experments wthn ths secton. We use the same channel emulator confguraton setup of Secton V. However, our topology s composed of a four-antenna transmtter, and three sngle-antenna recevers. The three recevers consttute a sngle multcast group to whom the the transmtter jontly beamforms. A. Feedback Rate and Coherence Tme We now evaluate the gans of beamfomng n changng channel condtons as a functon of feedback rate. Specfcally, we vary the tme scale of channel nformaton feedback (t f )

8 Schedule Length (msec) Swtched Crcular Swtched Lnear ADAM Topology Index a) Schedule length Delvery Rato (%) Swtched Crcular Swtched Lnear Topology Index b) PDR Commulatve Fracton Crcular Lnear SNR Combnaton SNR Best Beam (db) c) Impact of beam combnng. Fg. 4. Evaluaton of swtched beamformng ((a), (b), (c)), and WARP SNR-rate for s = 5 8. Delvery Rato (%) 1 5 BPSK 1/2 BPSK 3/4 QPSK 1/2 QPSK 3/4 16 QAM 1/2 16 QAM 3/4 64 QAM 2/3 64 QAM 3/ RSS (dbm) d) SNR-Rate for s = 5 8. that s avalable at the transmtter. Once the transmtter obtans the channel nformaton, t jontly beamforms towards the clents and transmts back-to-back multcast packets untl the nexhannel nformaton feedback s avalable. We repeat ths experment for four coherence tme ( )valuesof12,64, 16, and 8 ms. The12and64ms values are assocated wth a fxed wreless endpont n slowly and hghly varyng envronments, respectvely. The 16 and 8 ms values are assocated wth a typcal pedestran clent n slowly and hghly varyng envronments. Couplng between t f and : Fg. 5(a) shows the average PDR as a functon of channel feedback tme scale for dfferent coherence tmes. We observe that the PDR of multcast beamformng drops as the tme scale of channel feedback ncreases for a gven coherence tme, or as the coherence tme decreases for a fxed feedback tme scale. Ths drop n PDR s sgnfcant for smaller coherence tmes (16 and 8 ms) assocated wth user moblty. We also observe that for 8 ms coherence tme, the tme scale of 1 ms for channel feedback results n approxmately 8% drop n PDR, whereas 1% PDR s acheved for all of the other. To understand the reason for the drop n PDR, we evaluate the varaton n the receved average SNR of clents n the multcast group n Fg. 5(b) as a functon of channel feedback tme scale. In these experments, we measure the SNR value for every packet over all of the clents and plot the average SNR and ts standard devaton. We observe that the average SNR drops as the tme scale of channel feedback ( )ncreasesfora gven coherence tme (t f ), or the coherence tme decreases for afxedfeedbackrate,therebycorroboratngthecorrespondng trend observed n PDR. Ths also ndcates the strong couplng between t f and (specfcally the rato of s = t f )thatkeeps track of channel dynamcs and hence mpacts the multcast performance of a group. Impact on Performance: We nexompare the performance of ADAM to omn. In omn, the transmtter selects a rate that s supported by the weakeslent. Ths rate s used for all of the multcast packets untl the next SNR feedback s avalable. Omn wth base rate uses the lowest MCS wthout any feedback requrement from the clents. Ths approach s currently mplemented n for multcastng. Fg. 5(c) depcts the throughput results for 16 and 64 ms coherence tmes. Whle both ADAM and omn are hghly senstve to accurate channel nformaton, the senstvty s hgher n ADAM as expected due to ts stronger dependence on channel nformaton. Further, at extremely reduced feedback rate (t f =5ms) and small coherence tme ( =16ms),.e. large s values, both the schemes degrade to perform even worse than omn wth base rate. Fndng: Channel varatons reduce the effectve SNR of a multcast group, whch n turn depends on both t f and,and more specfcally on s = t f.inaccuratechannelnformaton, characterzed by large s values, can sgnfcantly reduce the multcast throughput to even lower than omn wth base rate. B. Reduced Feedback and Moblty In any multcast system, the requred PDR s dependent on the applcaton. As seen n Fg. 5(a), for a gven PDR requrement, clents wth smaller coherence tmes requre more frequent feedback. Ths could result n sgnfcant tranng and feedback overhead especally wth a hgh number of clents and/or transmt antennas. Also, when clents n a multcast system have dfferenoherence tmes, a sngle clent wth a small coherence tme s suffcent to sgnfcantly ncrease the tranng overhead. Ths s because the frequency at whch the AP should transmt tranng symbols on each of ts antennas depends on the clent wth the smallesoherence tme. Thus, for any practcal system t s desrable to reduce the feedback rate and hence the overhead. Snce we have no control over of clents and would lke to keep t f fxed to a desred value to mnmze the overhead, the resultng nfrequent feedback (for clents wth small ) reduces the effectve SNR of the multcast system as seen n Fg. 5(b). Hence, to account for the reduced effectve SNRs, we propose to tran ADAM s operatonal SNRs based on both t f and. Snce the naccuracy n channel nformaton s drectly related to s = t f,tranngherereferstoobtanngthe SNR-rate profles that are specfc to dfferent s values. ADAM then categorzes clents based on ther s value and apples the approprate s-rate table for each clent n determnng the effectve multcast rate. Thus, accountng for t f and of each clent helps buld robustness nto ADAM s operaton aganst nfrequent feedback and clent moblty. s-valued Rate Tables: To tran a rate table correspondng to a gven s = t f,weperformanexpermentwthchannel emulator wth one sender and one recever. For each SNR value, the transmtter sends back-to-back packets to the recever for a duraton of t f,measuresthepdrandrepeatsths experment for a thousand trals. The emulator uses the same confguraton parameters of Secton V. However, nstead of

9 a) PDR b) SNR c) Throughput d) Traned throughput. Fg. 5. Impact of coherence tme and feedback rate on ADAM ((a), (b), (c)), and tranng mpact on throughput (d). usng a statc channel ( = ), ts value s based on the s parameter. Fg. 4(d) shows the acheved PDR as a functon of the SNR (dbm) for each of the WARP MCSs for an s = 5 8 (t f =5, =8ms). Comparng Fg. 4(d) wth Fg. 1(d), we observe that the requred SNR for 1% PDR s now ncreased. In other words, a hgher average SNR s requred to sustan a gven MCS so as to compensate for the nfrequent feedback avalable to track the channel dynamcs. Impact on Robustness: We now quantfy the gans of tranng ADAM based on s-rate tables. To acheve ths, we use the same expermental setup of Fg. 5. However, we obtan our rate table accordng to Fg. 4(d) for s = 5 8.Fg.5(d)shows the performance of ADAM both wth and wthout tranng for coherence tmes of 8 and 16 ms. Ian be seen that the gans of tranng are dependent on the tme scale of channel update. Wth a 1 ms update rate, the untraned system s capable of trackng channel dynamcs to yeld hgh throughput. However, tranng becomes crtcal to sustan hgh throughput when channel update rates are equal or hgher than t f for the correspondng s. Snceatraned multcast system selects a lower MCS to account for channel varatons, ts resultng throughpuompared to an untraned system would be lower for feedback tme scales smaller than t f,andhgherforthetmescaleslargerthant f.notethat apart from throughput, PDR s another metrc that should be consdered n selectng between a traned vs. untraned rate table. In the above experment, 1% PDR s acheved by the traned system for two data ponts, whose (,t f ) s (8,5) ms and (16,1) ms respectvely. However, ther s value s the same (s = 5 8 ), thereby ndcatng the performance dependence on the s value as opposed to the ndvdual t f and values. Fndng: Tranng a rate table based on coherence tme and feedback rate allows ADAM to effectvely accommodate clents wth vared ( ) values. The clent specfc SNR-rate mappng can be ncorporated n the user schedulng optmzaton problem to further reduce the overall schedule length, whch s an nterestng avenue for future research. VIII. CONCLUSIONS In ths paper, we presented the desgn and mplementaton of ADAM, an adaptve beamfomng system for multcastng n wreless LANs. We proposed effcent algorthms to solve the jont schedulng and beamformng problem. We also mplemented ADAM on the WARP platform, and through extensve ndoor measurements showed sgnfcant gans compared to swtched-beam and omn. We also evaluated the performance of ADAM wth respect to feedback rate and user moblty, and proposed solutons to ncrease ts robustness to channel dynamcs. IX. ACKNOWLEDGEMENTS Ths research was supported n part by NSF grants CNS , CNS , and CNS REFERENCES [1] X. Lu, A. Sheth, M. Kamnsky, K. Papagannak, S. 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