CSI-SF: Estimating Wireless Channel State Using CSI Sampling & Fusion

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1 CSI-SF: Estimting Wireless Chnnel Stte Using CSI Smpling & Fusion Riccrdo Crepldi, Jeongkeun Lee, Rul Etkin, Sung-Ju Lee, Robin Krvets University of Illinois t Urbn-Chmpign Hewlett-Pckrd Lbortories Abstrct One of the key fetures of high speed WLAN such s 8n is the use of MIMO (Multiple Input Multiple Output) ntenn technology The MIMO chnnel is described with fine grnulrity by Chnnel Stte Informtion (CSI) tht cn be utilized in mny wys to improve network performnce Mny complex prmeters of MIMO system require numerous smples to obtin CSI for ll possible chnnel configurtions As result, mesuring the complete CSI spce requires excessive smpling overhed nd thus degrdes network performnce We propose CSI-SF (CSI Smpling & Fusion), method for estimting CSI for every MIMO configurtion by smpling smll number of frmes trnsmitted with different settings nd extrpolting dt for the remining settings For instnce, we predict CSI of multi-strem settings using CSI obtined only from single strem pckets We evlute the effectiveness of CSI-SF in vrious scenrios using our 8n testbed nd show tht CSI-SF provides n ccurte, complete knowledge of the MIMO chnnel with reduced overhed from trditionl smpling We lso show tht CSI-SF cn be pplied to network lgorithms such s rte dpttion, ntenn selection nd ssocition control to significntly improve their performnce nd efficiency I INTRODUCTION While the deployment of 8 WLANs (Wireless Locl Are Networks) is continuously incresing, the demnd for relible high bndwidth WLANs is exploding due to the demnds of pplictions such s HD (High Definition) video streming Additionlly, with the incresing populrity of smrtphones, Wi-Fi offloding [] llevites the lod on low throughput cellulr links, but increses the bndwidth demnd for Wi-Fi In response to this growing demnd of pplictions nd services, the new IEEE 8n [] nd the emerging IEEE 8c [3] stndrds im to provide very high throughput WLANs by improving on the existing 8 stndrds Some of the key enhncements used for incresing the PHY throughput re using wider, bonded chnnels (4 MHz in 8n nd up to 6 MHz in 8c) nd MIMO (Multiple Input Multiple Output) ntenns [4], [5] Currently vilble 8n devices support up to three MIMO sptil strems To chieve improved performnce t MAC nd ppliction lyers, lgorithms nd protocols for WLANs now need to consider these new fetures offered by the use of multiple ntenns For instnce, while before rte dpttion only selected the modultion nd coding rte, it now needs to consider the number of concurrent sptil dt strems trnsmitted Essentilly, optiml WLAN performnce required detiled knowledge of the wireless link Such informtion is vilble through the use of Chnnel Stte Informtion (CSI), which describes the current condition of the chnnel, nd consists of the ttenution nd phse shift experienced by ech sptil strem to ech receive ntenn in ech of the OFDM subcrriers CSI is determined in the 8n hrdwre by nlyzing received pckets using trining sequences in the pcket heders For network lgorithms such s rte selection, AP ssocition nd chnnel ssignment, timely optiml decisions require ccurte CSI estimtes under vrious settings (eg, different number of sptil strems, trnsmission ntenns used, trnsmission powers, etc) However, some settings might not hve been smpled for recently received pckets nd so dditionl frme trnsmissions re necessry to obtin complete nd fresh CSI These extr trnsmissions consume bndwidth nd increse ltency, nd ultimtely degrde system performnce if over used To enble the effective use of CSI, we present CSI-SF (Chnnel Stte Informtion with Smpling nd Fusion), CSI processing technique tht predicts the CSI of non-smpled MIMO configurtions, using smll number of smples Protocols using CSI-SF cn predict the CSI of 3 3 chnnel using CSI mesured from pckets sent using 3 configurtion We evlute the ccurcy of CSI-SF by compring its CSI estimtes ginst the ctul mesured chnnel conditions in our 8n testbed We lso describe the prcticl chllenges of ccurtely estimting CSI nd ssess CSI-SF without the knowledge of hrdwre specific chrcteristics We demonstrte how network lgorithms such s rte dpttion, ntenn selection, nd ssocition control cn utilize CSI-SF to enhnce the efficiency nd hence improve network performnce The rest of this pper is orgnized s follows In Section II, we survey the relted work nd describe the motivtions tht led us to the development of CSI-SF In Section III, we provide the nlyticl foundtions of our technique, nd in Section IV, we present results of its ppliction in rel-world trces tht we collected in the evlution of CSI-SF on our 8n testbed In Section V, we discuss ppliction uses of CSI-SF nd Section VI concludes the pper A Relted Work II CHANNEL QUALITY METRIC Wireless network lgorithms mximize the network performnce by using chnnel qulity informtion to fine tune protocol configurtions (eg, modultion, coding rte, number

2 of strems, set of trnsmit ntenns, trnsmission power, etc) For exmple, mny rte dpttion lgorithms such s ARF [6], AARF [7] nd SARA [8] probe the chnnels to collect sttisticl informtion t different bitrtes These probing-bsed schemes incur excessive messging overhed when there is lrge number of configurtions to probe Additionlly, it tkes long to converge, especilly when the gp between the rte of the probed pckets nd the optiml rte is lrge Moreover, optiml bitrte selection requires the differentition of losses from wireless errors nd losses from collisions/congestion [9], [], [] Mny lgorithms tke n lterntive pproch nd use Signl to Noise Rtio (SNR) s the chnnel qulity metric (eg, RBAR []) SNR is esy to compute nd is lredy provided by current 8 hrdwre However, it ws shown tht wireless networks hve complex error distributions nd SNR does not well-represent chnnel qulity [3], [4] In prticulr, the uthors of [5] show tht SNR is not the right metric to determine chievble throughput, in lrge prt due to the fct tht the frequency selectivity of the widebnd 8 chnnel is not cptured by SNR Moreover, in OFDM modultion, subcrriers with low SNR hve stronger effect on the overll probbility of error Recent stndrds such s IEEE 8n [] nd 8c [3] utilize MIMO trnsceivers [4], [5], which increse the degrees of freedom nd so the complexity of rte selection Essentilly, long with selecting modultion nd coding schemes, rte selection lgorithms must now choose the correct number of concurrent dt strems Optimiztions cn be bsed on the CSI red from the 8 hrdwre In [6], [5], [7], the detiled informtion in the CSI report is used to determine the SNR vlue for ech subcrrier ( s), s opposed to single verge vlue s in the generl SNR metric The subcrrier-specific SNR is then ggregted into globl metric, effectivesnr (esnr), which better chrcterizes chnnel performnce We next provide n introduction to CSI B Chnnel Stte Informtion Wireless signls experience trnsformtions such s mplitude nd phse chnges while trveling over the ir from the trnsmitter to the receiver For exmple, simple model is y[t] = h x[t]+z[t], () where t is time index, y is the received signl, x is the trnsmitted signl, h is the chnnel gin, or more often complex vlue representing both chnnel gin nd phse component, nd z is dditive noise More complex models incorporte multipth fding, time-vrying chnnels, multiple ntenns, etc Coherent receivers require knowledge of CSI (h in the simple model () bove) for successful demodultion CSI cn lso be used for dt rte selection, ntenn selection, power control nd lloction cross trnsmit ntenns, etc One method of obtining CSI is to use pilot sequences within the dt pcket These sequences re predetermined sequences (ie, they do not crry informtion) tht re sent within the dt pcket to help the receiver estimte CSI For exmple, in the chnnel model (), setting x = in the first k symbols of the dt pcket llows the receiver to compute ĥ = α k y[t] = α h+ α k z[t] () k k t= t= where the constnt α is chosen ppropritely depending on the SNR The 8n protocol llows the use of MIMO to obtin improvements in dt rte nd relibility In ddition, 8n uses OFDM modultion to convert widebnd chnnel into multiple nrrowbnd chnnels to void inter-symbol interference (ISI) The simple model () cn be extended for MIMO OFDM system s follows: y[w,t] = H[w]x[w,t]+z[w,t] (3) where for n trnsmit nd m receive ntenns, x is n n- dimensionl vector, y nd z re m-dimensionl vectors, H is n m n mtrix, nd w is n index specifying the OFDM frequency chnnel In MIMO OFDM systems, the CSI H is n m n W dt structure, where W is the number of OFDM chnnels used in the system (W = 56 in 8n for MHz bndwidth, nd W = 4 in 8n for 4 MHz bndwidth with chnnel bonding) Note tht in (3) the column index of H[w] indictes the trnsmit ntenn index, while the row index of H[w] corresponds to the receive ntenn index C CSI Estimtion in 8n Mny implementtions of 8n require successful decoding of dt pcket to obtin CSI In ddition, it is required to send pcket using n trnsmit ntenns over bndwidth W, nd receive it over m receive ntenns to obtin the complete m n W CSI dt structure In the following, we denote ny type of communiction scheme tht involves n trnsmit ntenns, m receive ntenns, nd spns bndwidth W s n m n W configurtion In current CSI estimtion pproches, obtining CSI for ll possible configurtions of 3 3 system requires seven smples: -strem Modultion nd Coding Schemes (MCS) require three probes, one per ech TX ntenn Similrly, -strem MCSs require three probes to collect CSI for ech combintion of two ntenns Finlly, 3-strem MCSs require single probe using trnsmission from ll three trnsmit ntenns The number of required smples increses drmticlly when the system supports 4 4 communiction or lrger chnnel widths Moreover, common hrdwre only provides CSI reports for unicst pckets, thus limiting the possibility of opportunisticlly collecting CSI mtrices by evesdropping; node must be connected to n ccess point to ctively send or receive probing pckets In the rest of this pper, we discuss the problem of estimting p q R CSI dt structures using pckets encoded with m i n i W i schemes, where p m i, q n i, R W i, nd (p,q,r) (m i,n i,w i ), where i is the pcket index We then show how CSI dt structures obtined from multiple pcket trnsmissions cn be used to to estimte lrger CSI dt structures We describe this problem in the context of n

3 8n system However, similr ides cn be pplied to CSI estimtion in other MIMO OFDM systems (eg WiMAX) III CSI-SF CSI-SF reduces the overhed of chnnel probing by ggregting the CSIs obtined from multiple pckets from smller chnnel to derive the CSI corresponding to lrger chnnel For exmple, CSI-SF enbles the determintion of 56 CSI mtrix by combining the CSI informtion derived from two pckets trnsmitted using 56 configurtion, s long s different trnsmit ntenns re used to send the two pckets Combining the CSI from multiple pckets cn be used to: estimte lrger multi-ntenn m q W CSI mtrix using pckets sent/received with smller multi-ntennm n W configurtion (ie, q > n); estimte lrger bndwidth m n R CSI mtrix using pckets sent/received with n smller bndwidth m n W configurtion (ie, R > W ); estimte CSI mtrix combining the bove two cses (ie enlrge the number of ntenns nd bndwidth in the combined CSI) A Enlrging the Number of Antenns or Bndwidth in the CSI Mtrix The key benefit of CSI-SF is in combining CSI from multiple pckets to crete CSI mtrix corresponding to more trnsmit ntenns thn those used in the given pckets To cpture the spce of this combintion, let N i be the set of ntenns used in pcket i, of size N i, nd let N be the set of trnsmit ntenns in the combined CSI mtrix We ssume tht N > N i for ll i I, where I is the set of pckets used to combine the CSI We require N i N i so tht we hve CSI for ll trnsmit ntenns in N Combining CSI from smller set of trnsmit ntenns to infer CSI mtrix for lrger set of ntenns requires tht the trnsmitter chnges the set of trnsmit ntenns used in ech pcket In ddition, the set N i of trnsmit ntenns used in pcket i needs to be identified within the pcket This cn be done, for exmple, by dding metdt bout N i to the heder or pylod of the pcket Similrly, CSI combining used to enlrge the number of frequency subchnnels in the CSI mtrix (eg, to go from MHz to 4 MHz bndwidth) needs different pckets trnsmitted in different chnnels (eg, chnnels 36 nd 4 of the 5 GHz bnd) so tht CSI derived from those pckets cn be combined to estimte the CSI mtrix of the bonded chnnel 36+4 B Power Scling The CSI estimtes produced by the receivers re dependent on the trnsmission power used for the pcket However, if trnsmission power is constnt, CSI combining does not depend on trnsmission power Essentilly, if the chnnel gins remin constnt during the trnsmission of the two pckets nd P = γp, where P i is the trnsmission power of pcket i, i = {,} nd γ is scle fctor, then CSI = γcsi, where CSI i is the CSI estimte produced for pcket i x x x n Precoding Q Chnnel H Fig MIMO chnnel with precoding mtrix Q The dependency on time or frequency is omitted Due to regultions nd prcticl limittions, trnsmitted signls hve totl power constrint When the trnsmission spns multiple trnsmit ntenns, ssuming tht the signls in the different ntenns nd OFDM sub-chnnels re sttisticlly independent, the totl trnsmitted power is given by P = W n w= i= P i[w], where P i [w] is the power in the signl trnsmitted in ntenn i, i =,,n nd frequency sub-chnnel w, w =,,W In order to stisfy the totl power constrint, P i [w] my vry for different configurtions with different bndwidths or number of trnsmit ntenns, even when the power settings specified by the driver is the sme These power considertions hve importnt implictions for CSI combining Since the trnsmission powers my not be known t the receiver (see Model (3)), the CSI estimte for entry (i, j) in sub-chnnel w of the chnnel mtrix H my be n estimte of H i,j [w] P j [w] Since P j [w] my vry for communiction schemes involving different numbers of trnsmit ntenns nd different trnsmission bndwidths, CSI estimtes must be ppropritely scled during CSI combining If the totl power setting is not chnged between pckets, this scling is bsed only on the number of strems, nd no informtion bout the power settings t the trnsmitter is required C Precoding Sptil multiplexing is chieved by sending different dt strems in the different entries of x (see Model (3)) The 8n stndrd llows the use of precoding mtrix Q to mp x into the chnnel Typiclly, Q is unitry mtrix (ie Q Q = Q Q = I, where denotes conjugte trnspose nd I is the identity mtrix) Eqution (3) represents the soclled direct mpping mode, in which Q = I nd ech dt strem is sent in different trnsmit ntenn More generlly, the received signl vector cn be written s (see Fig ) z + z + z m y[w,t] = H[w]Qx[w,t]+z[w,t] (4) Typiclly, the precoding mtrix Q does not need to be known t the receiver, nd the chnnel estimtion lgorithm provides n estimte of H[w]Q The CSI-SF combining technique requires the receiver to know Q nd post-multiply the chnnel estimtes Ĥ[w] by Q or Q if Q is not unitry (ie, Ĥ = Ĥ Q ) However, Q vries bsed on the chipset used, nd my lso be chnged dptively In the rest of this section, we ssume tht Q is known In Section IV, we investigte the loss in performnce of implementing Q-gnostic estimtor To understnd the combining process, consider the following exmple illustrting how to combine CSI from two pckets + y y y m

4 pilot sequence 44 3 pcket pcket 56 3 Q 56 CSI 3 Q 56 3 CSI Q 3 _ /3 * combined CSI SNR [db] MCS MCS 5 MCS 6 MCS 7 3 Fig Schemtic representtions of the opertions used to combine CSI from multiple pckets TX Power [dbm] sent/received with n 3 56 configurtion nd precoding mtrix Q to form CSI estimte for configurtion (see Fig ) We ssume tht N = {,}, N = {,3} nd N = {,,3} Similr opertions re performed for the remining 55 sub-chnnels After successful reception of pcket i, i {, }, the receiver genertes CSI estimte for sub-chnnel w, Ĥ i [w], which my be dependent on the trnsmission power in ech ntenn nd frequency sub-chnnel Next, the receiver post-multiplies Ĥ i [w] by Q obtining Ĥ i [w] = Ĥi[w] Q = [ĥ,i[w],ĥ,i[w]], where ĥi,j[w] C, i,j, The combined CSI for sub-chnnel w, fter power scling, is given by Ĥ 3 [w] = 3 [ĥ,[w],ĥ,[w],ĥ,[w]] Q 3 Note thtĥ,[w] ndĥ,[w] contin CSI tht cn be used to generte Ĥ3[w] CSI-SF only used ĥ,[w] in the combined CSI estimte becuse wireless chnnels often experience vritions over time nd the most recent CSI is often the most suitble to mke future estimtes However, more generl combining functions cn be used to blnce the effects of chnnel vritions nd chnnel estimtion errors due to, for exmple, noise One such exmple is Ĥ 3 [w] = 3, 3 [ĥ,[w],(βĥ,[w]+( β)ĥ,[w]),ĥ,[w]] Q where β [, ]is some constnt chosen ppropritely D Trnsmission Power Compenstion In most WLAN deployments, dynmic trnsmission power is used in combintion with rte control to reduce energy consumption Commodity hrdwre llows the user to choose trnsmission power level If the trnsmitted power closely follows the level chosen by the user, scle fctor cn be pplied to the CSI of pcket trnsmitted t specific power level to estimte the CSI of different power level For exmple, if receiver receives pcket sent t 7 dbm nd is interested in the estimted CSI for trnsmission with the sme ntenn configurtion t 5 dbm, it is enough to subtrct db from the mgnitude of the originl CSI to obtin the new one Fig 3 SNR for different tx power levels for four -strem MCSs However, prcticl limittions influence the power control cpbilities of rel trnsceivers Power mplifiers re not perfectly liner, producing incresing distortion s they re driven closer to their mximum rted power The distortion introduced by the trnsmitter mplifiers hs bigger impct on MCSs with lrger coding rtes nd higher order modultions As result, mny trnsceivers limit the output power used for high rte MCSs through vrious power cps Figure 3 shows these power cps for QAM-64 trnsmissions with different coding rtes The sme behvior is present for - nd 3-strem MCSs, but the liner region extends to higher power settings This is most likely result of the fct tht for multiple strem pckets the power is split mong the multiple strems, reducing the power tht ech mplifier is required to output An ccurte power profiling cn prevent two erroneous outcomes in the CSI estimtion procedure First, when using the CSI derived from pcket with specific MCS to estimte the CSI of different MCS, not being wre of the power cps might introduce estimtion errors This hppens not only when combining CSI to produce estimtes for different number of strems, but lso when using the CSI from given MCS to estimte the CSI for some other MCS with the sme number of strems Additionlly, this informtion must be considered when estimting the effect of power dpttion For exmple scling the nominl trnsmission power from dbm to 5 dbm hs no effect on the ctul trnsmitted power (nd power consumption) in MCS7 To correct power scling requires two pieces of informtion: The power profile for the specific hrdwre instlled in the trnsmitter This informtion cn be hrd coded in the receiver or sent on demnd by the trnsmitter The power level t which ech pcket is sent This informtion cn be specified explicitly by the trnsmitter with d control pcket or ttching it to dt pckets, or inferred from the pcket type (eg, becons re generlly trnsmitted t the lowest dt rte nd the highest power level) The 8n stndrd provides n optionl feture clled stggered sounding by which the trining sequence in the pcket heder is trnsmitted over more strems thn those used in the pylod of the pcket This feture would enble

5 us to lern lrger CSI structure without risking decoding error in the pylod of the pcket While this feture would solve the sme problem tht we re ddressing, it presents number of drwbcks nd prcticl limittions First, being n optionl feture, it my not be supported cross different chipset vendors In ddition, it does not llow estimting CSI structures for lrger bndwidth thn tht used for the given pcket Finlly, it is not supported during becon trnsmissions, hence it cnnot be used in pplictions such s AP selection during ssocition When stggered sounding is supported, it cn be used jointly with CSI-SF to further reduce the number of smples required to obtin complete knowledge of the MIMO chnnel We next evlute the performnce of CSI-SF, nd lso investigte the impct of pproximtions tht my be necessry due to the lck of knowledge of the hrdwre-specific Q mtrix nd power profile IV EVALUATION We evluted the performnce of CSI-SF using CSI informtion collected on our 8n testbed We deployed five nodes, equipped with n Intel 53 chipset tht supports up to 3 3 MIMO configurtions A modified chipset firmwre nd kernel [8] were used to obtin the CSI mtrices of successfully received 8n dt frmes nd trnsfer the mtrices to userspce for further nlysis We deployed the nodes in cubicle office environment At different times, ech node took turns to serve s n AP on free chnnel in the 5 GHz spectrum nd sent pckets t vrious MCS rtes nd trnsmission powers, while the other nodes, ssocited to the AP, collected the CSI for received pckets We performed the tests multiple times with different plcements of nodes thus collected dt from 3 different links in totl For ech power level nd trnsmission ntenn combintion, we chnged the MCS fter ech pcket, nd collected CSI for, pckets t ech MCS, with n verge inter pcket rrivl time of ms, which is the time necessry for the driver to chnge the hrdwre settings We performed the sme experiments in the 4 GHz bnd, nd obtined similr results tht we omit for spce constrints The Intel hrdwre only reports CSI for subset of the OFDM subcrriers, s defined by the grouping option in the 8n stndrd More specificlly, it reports CSI for 3 subcrriers in either the MHz or the 4 MHz bonded chnnel (grouping nd 4, respectively) A Single Strem to Multi Strem Combining CSI-SF s min gol is to predict the CSI of chnnel configurtions tht hve not been smpled, by using proper combintion of pckets sent with smller number of sptil strems We first compre the CSI obtined from combining the CSI of two -strem pckets sent over two different trnsmission ntenns ginst the ctul CSI of the -strem configurtion, smpled immeditely fter the two -strem smples were collected For -strem pcket, the Intel 53 s CSI structure is 3 3 mtrix, nd for -strem pcket it is 3 3 mtrix In Figure 4, we plot the mgnitude of ech element of the CSI mtrices of the two -strem pckets (top) nd mgnitude [db] tx: A rx: A tx: A rx: B tx: A rx: C tx: B rx: A tx: B rx: B tx: B rx: C Mesured Combined Subcrrier Index Fig 4 Mgnitude of ech CSI element for two -strem pckets (top) nd their -strem combintion, compred with n ctul -strem pcket (bottom) compre the resulting combined CSI with the ctul -strem CSI (bottom) The combined nd ctul CSI re only slightly different probbly due to smll chnnel vritions between the time t which the three pckets were smpled However, the difference is smll, nd when CSI is used to compute ggregte metrics such s esnr, it becomes negligible More detils re provided in the following subsections The ccurcy of combined estimte depends on the freshness of smples used in the combining lgorithm The office environment in which we collected the smples does not show significnt chnnel vritions over time, nd therefore n estimte from ged pckets could be used In more dynmic environment, the ccurcy of the CSI-SF estimtes would degrde, but so would the ccurcy of ny probing mechnism B e SNR: estimted effectivesnr While complete chrcteriztion of given chnnel by looking t every element of its CSI mtrix might be useful t times, in most pplictions (eg, bitrte dpttion) n ggregte metric obtined from the CSI is sufficient Hence we use the effective SNR (esnr) vlue, s described in [5], to evlute the ccurcy of CSI-SF esnr first computes the SNR nd bit-error rte (BER) of ech OFDM subcrrier From the subcrrier-specific informtion, chnnel-wide BER is computed nd trnslted into esnr The ccurcy of esnr in terms of describing the qulity of OFDM MIMO chnnel compred with the per-pcket SNR metric tht 8 drivers usully provide in the form of Received (or Reltive) Signl Strength Indictor (RSSI) is shown in [5] In the rest of this section, we use the term, SNR, to indicte the per-pcket SNR directly given by drivers We evlute the ccurcy of CSI-SF by compring the esnr obtined from the rel CSI informtion ginst esnr obtined using CSI-SF, which we cll estimted effective SNR (e SNR) Figures 5 nd 6 show the reltion between ech metric (SNR, esnr nd e SNR) nd the mximum supported rte on 3 links we tested on vrious environments nd configurtions We sy tht bitrte is supported by given link when the pcket error rte t tht bitrte is mesured to be smller thn

6 Rte [Mbps] Rte[Mbps] Rte[Mbps] SNR [db] esnr [db] 5 SNR Worst SNR Best esnr Worst esnr Best e SNR Worst e SNR Best e SNR [db] Fig 5 Link rtes (Mbps, y-xis) for the best nd the worst links s function of vrious metrics (SNR, esnrnd e SNR) for -strem MCSs using MHz chnnel % We define link rte the mximum supported bitrte for link For rte dpttion lgorithms nd similr pplictions, it is impertive tht the link qulity metric shows predictble behvior However, for ech metric, it is possible tht links with the sme metric vlue support different link rtes For ech vlue of SNR, esnr nd e SNR we find the link with the highest nd the lowest link rte nd denote them s the best nd the worst links, respectively For ech metric we plot the link rte for the best nd the worst link A good metric should exhibit two properties: smll gp between the best nd the worst links (idelly the two lines should overlp) to enble n ccurte prediction of the link rte; monotonic reltion between the metric vlue nd the link rte, so tht we cn lwys consider higher metric vlue s better link qulity indictor In both Figures 5 nd 6, ech from MHz nd 4 MHz chnnel widths respectively, the use of pcket SNR (the top grphs) results in significnt gps between the bitrtes supported by the best nd the worst links with the sme SNR vlue A rte selection lgorithm bsed on SNR could choose to be conservtive nd select low bitrte, nd then increse the rte until the link rte is reched, or be optimistic nd strt from the bitrte supported by the best link with the sme SNR vlue nd then fllbck to lower rte if the selected one is not supported In both cses the lgorithm tkes time to converge to the optiml rte The bottom prt of the figures show the results of using esnr nd e SNR metrics For the most prt, the best nd the worst link overlp or show smll gp limited to one MCS difference, which suggests tht n ccurte estimte of the supported bitrte for link is possible Additionlly, e SNR from combined CSI exhibits promising bitrte predictbility, which is comprble to tht of esnr of ctul CSI C Effect of Unknown Q Mtrix For the hrdwre we used in the experiments, we hd complete knowledge of the sptil mpping mtrix (Q) for the -strem settings In Section III, we described why knowing Rte [Mbps] Rte[Mbps] Rte[Mbps] SNR [db] esnr [db] 5 SNR Worst SNR Best esnr Worst esnr Best e SNR Worst e SNR Best e SNR [db] Fig 6 Link rtes (Mbps, y-xis) for the best nd the worst links s function of vrious metrics (SNR, esnrnd e SNR) for -strem MCSs using 4 MHz chnnel Q is necessry for computing the correct CSI for combining However, hrdwre vendors might not lwys disclose this informtion nd even when it is known t the trnsmitter, informing the receiver would require dditionl overhed We investigted the effect of using inccurte Q mtrix through MATLAB simultions Our gol is to evlute the effect of pplying n inccurte Q to the received CSI on the finl metric (e SNR) We rndomly generted, H mtrices, with 3 subcrriers ech The elements of the mtrices re generted with circulrly symmetric complex Gussin distribution with vrince, CN(,) For ech of these chnnels we computed the CSI pplying TX power rnging from db to 4 db (this vlue is normlized with the noise level) nd using the identity mtrix s sptil mpping mtrix (ie, ech dt strem is independently trnsmitted by ech ntenn) We lso generted 5 rndom Q mtrices (unitry) nd for ech of the CSI mtrices we computed the esnr using ll the different Q mtrices The stndrd devition of the esnr vlues obtined using the 5 different vlues of Q, verged over, H is smller thn db Considering tht db is the grnulrity tht ll the metrics ssume, nd difference of db mens t most n error of one MCS, the metric without knowledge of Q cn still be used, lthough the precision of the fine grnulrity estimtion in Figure 4 is lost We lso tested the effect of using wrong Q mtrix lso with our rel testbed, using four different vlues of Q (ie, the correct one, the identity mtrix, nd two rndomly generted mtrices) The results, which we omit for spce constrints, showed none or very smll differences compred with those in Figures 5 nd 6 In contrst to -strem cses, the exct Q mtrix for the 3- strem MCSs is not known to us nd thus we use the identity mtrix insted The results using the identity mtrix for 3- strem is shown in Figure 7 The sme remrks we mde for the -strem experiments cn be pplied for this experiment s well, with the ddition tht in this cse not only the gp between the worst nd the best link for the pcket SNR metric is very

7 Rte [Mbps] Rte[Mbps] Rte[Mbps] SNR [db] esnr [db] 5 SNR Worst SNR Best esnr Worst esnr Best e SNR Worst e SNR Best e SNR [db] Fig 7 Link rtes (Mbps, y-xis) for the best nd the worst links s function of vrious metrics (SNR, esnrnd e SNR) for 3-strem MCSs using MHz chnnel lrge, but in some cses (eg, between db nd 6 db) the reltion between SNR nd the supported rte is non-monotonic The results for esnr nd e SNR re once gin very similr The supported rte is monotoniclly incresing nd the gp between the best nd the worst link is never lrger thn MCS steps (in fct, two MCS gp is shown only for vlues of esnr nd e SNR 7 db) There is no significnt difference in the performnce of the two metrics These results show tht CSI-SF chieves high ccurcy while reducing the probing overhed D Chnnel Width Expnsion CSI-SF not only cn be used for estimting MIMO configurtion with lrger number of ntenns, but lso for chnnel tht is bonding two or more nrrower chnnel which hve been smpled independently Bonding of two djcent chnnel is used in 8n to increse the bndwidth, nd the new 8c stndrd llows bonding of non-djcent chnnels up to bndwidth of 6MHz We tested the ccurcy of CSI-SF on bonded chnnels by compring the e SNR obtined from combining two MHz link sent on different chnnels, nd the ctul esnr of pckets sent on the bonded chnnel, on severl different links The mximum vlue for the stndrd devition is lower thn db The distnce between the synthetic e SNR nd the rel esnr cn be explined with the lrge time between the rrivl of pckets on the different chnnels in our experiments, due to hrdwre configurtion constrints Note tht the reported CSI hs only subset of the OFDM frequencies For the 4MHz chnnel, three out of four subcrrier re not reported from the Intel hrdwre This lck of informtion cuses the esnr itself to be imprecise A more ccurte evlution using hrdwre cpble of reporting CSI for entire subcrriers is our future work E Power Compenstion In Section III, we described the non-liner reltion between the power settings nd the trnsmitted power t different MCSs When the hrdwre-specific power profile is known, the receiver cn compenste it when pplying CSI-SF For exmple, when combining two -strem pckets sent t MCS 7 with power setting of 5 dbm, we must consider tht the rel Rte [Mbps] Rte [Mbps] e SNR Worst e SNR Best e SNR [db] Fig 8 Reltion between e SNR link rte for the best nd the worst links, when pplying power compenstion (top) or ignoring it (bottom) trnsmitted power is dbm (Figure 3) If the combined CSI is used to compute the e SNR of -strem MCS with no power cp, for exmple MCS 8, we must compenste for 4 db offset or the qulity of the combined CSI will be underestimted However, s the power profile is property of the hrdwre, there might be situtions in which the receiver does not know wht is the proper compenstion to pply In Figure 8 we compre the e SNR performnce with the proper power compenstion (top) ginst the sme metric, computed ignoring the power profile (bottom) We combined only pckets sent with MCS6, using trnsmission power settings between dbm nd 5 dbm, to see the difference more clerly The most visible effect of the lck of power compenstion is the compression of the vlues in the x-xis, due to the fct tht the combining lgorithm tends to overestimte the power t which the originl pckets re sent, which in relity is lower thn the level specified by the driver Our power compenstion lgorithm dds the offset to the CSI before using it in the combining lgorithm, to correct this behvior However, we observe tht even when power compenstion is not pplied, lthough e SNR nd esnr curves differ, e SNR still shows the two desirble chrcteristics of good chnnel qulity metric However, the x-xis shift, cused by the lck of power compenstion, requires trining to identify the shifted metric-to-mcs mpping Fortuntely, even in this cse, the reltion between e SNR nd the supported rte depends on the hrdwre but not on individul link Thus, in cse of downlink MCS dpttion, receiver must trin only once when it ssocites with n AP bsed on specific hrdwre, nd use tht informtion for ny other link s long s the AP uses the sme hrdwre Once the trining is performed nd the mpping is stored, no dditionl overhed is required V CSI-SF APPLICATION CSI-SF cn be used to obtin complete chrcteriztion of the chnnel, without incurring the sme overhed of trditionl probing The estimted CSI cn be used to improve network performnce in mny wys In this section, we describe possible uses of CSI-SF in three common WLAN protocol pplictions

8 Fig 9 -strem TX ntenn Best MCS (bitrte) -strem TX ntenn Best MCS (bitrte) 3-strem TX ntenn Best MCS (bitrte) 7 (65 Mbps) b 4 (7 Mbps) bc 8 (585 Mbps) b 7 (65 Mbps) bc 3 (4 Mbps) c 6 (585 Mbps) c (78 Mbps) () Best MCS for different TX ntenn combintions of given link Probing-bsed (eg, MiRA) esnr-bsed CSI-SF 8 b b 3 8 bc c 4 8 c 4 b 5 6 bc 6 4 b 7 (b) Probing overhed b 3 b 4 b 5 b MCS # TX ntenn MCS # TX ntenn bc drops 4 b probing pcket dt pcket Probing overhed comprison on n exmple 3 3 link A Optiml MCS nd Antenn Selection Bitrte dpttion is necessry to mximize the chievble throughput in dynmic wireless link In legcy SISO chnnels, the spce to serch for the best bitrte is limited to the number of modultion nd coding schemes, which is eight in the cse of 8/g systems The use of multiple ntenns nd MIMO chnnel coding dds one more dimension With the conventionl probing-bsed pproch tht relies on pcket error sttistics for every possible bitrte, the probing overhed (or the serch spce size) is symptoticlly O(n ck), where n is the number of possible strems (usully equl to the number of TX ntenns), c is the number of modultion & coding schemes for ech strem (8 in 8 systems) nd k is the number of required probings for ech rte to obtin enough sttistics The n overhed stems from the number of possible TX ntenn combintions If the optiml ntenn selection is not supported, the symptotic overhed becomes O(nck) but the chnce of finding the best bitrte decreses The use of CSI for MCS dpttion, s shown in [5], [7] by using the esnr metric, gretly reduces probing overhed nd lso convergence time becuse single CSI mtrix cn directly indicte the best MCS supported by the chnnel from the MCSs using the sme number of MIMO strems, thus removing the c nd k fctors Hence, the overhed of esnrbsed dpttion schemes is O(n ) Furthermore, CSI-SF does not need to probe ll possible TX ntenn combintions to compute e SNR for ll MCSs It only needs n -strem CSI smples, with ech smple from the n TX ntenns Figure 9 illustrtes the probing overhed of three different pproches: probing-bsed MIMO link dpttion scheme (eg, MiRA [9]), n esnr-bsed scheme nd CSI-SF Since [5] does not describe n dpttion mechnism for chnging MCS over different numbers of strems nd ntenns over timevrying chnnel, we simulte the best possible behvior of n esnr-bsed dption scheme Figure 9() shows the best MCSs for ll TX ntenn combintions tht we observed from one exmple 3 3 link of our testbed The -strem MCS 4 on two TX ntenns b (out of three ntenns, b nd c ) exhibited the best throughput performnce on tht link Next consider chnge in the environment where chnnel qulity hs improved from the cse when MCS ws the best MCS Figure 9(b) shows tht the probing-bsed scheme probes ll - strem MCSs bove the current rte nd ll the -strem MCSs tht provide higher rtes thn MCS 7 MCS 5 fils becuse this chnnel cn only support up to MCS 4 MCS is lso probed becuse this is the lowest 3-strem MCS tht could provide higher rte thn MCS 4 but this MCS lso fils since MCS 8 is the highest 3-strem MCS supported by this link As result, totl of probes re required nd the ctul probing overhed would be much lrger for sttisticlly meningful outcome As mentioned in [9], 8n AMPDU ggregtion cn be used to mitigte the probing messge overhed but the overhed is still much lrger thn the CSI-bsed schemes Unlike MiRA, where the pylod size impcts the pcket error rtes, the probing pckets to obtin CSI mtrices do not need ny dt pylod 8n s optionl null dt pcket sounding cn be used to obtin CSI smples with miniml messge overhed Figure 9(b) clerly illustrtes tht the esnr-bsed scheme nd CSI-SF incur much smller probing overhed nd quickly find the best MCS We hence expect them to perform even better in mobile environments In this exmple, the esnr-bsed scheme must probe ll three TX ntenn combintions of - strems to discover MCS 4 trnsmitted over b is the best one The 3-strem MCS 6 is lso probed to check if there is ny 3-strem MCS tht provides better bitrte thn MCS 4; thus four probings re used in totl In contrst, CSI-SF uses only two probings nd combines their CSI mtrices with the one from the -strem dt pcket nd decides the best MCS nd the ntenn combintion If we expnd this exmple to 4 4 MIMO, the probing overhed reduction of CSI-SF from esnr is from to 3 B Chnnel Bonding in 8c The new IEEE 8c stndrd, currently being defined, is exploring the option of using up to eight MHz chnnels for the bonding feture Similr to 8n, the proposed scheme defines one of the MHz chnnel s the primry chnnel, while the others re secondry chnnels, nd cn be dynmiclly used if necessry A sttion cn choose to operte (i) using only the primry chnnel, (ii) leverging the whole 6 MHz bndwidth or (iii) selecting one or three secondry chnnels to be used in conjunction with the primry chnnel Note tht the secondry chnnels re not required to be djcent Bsed on the bonding scheme currently discussed in the stndrd group [], [], there re totl of 44 possible chnnel combintions tht probing-bsed mechnism should exmine Using the chnnel expnsion mechnism in CSI-SF, only eight smples re necessry, one per MHz chnnel, to compute complete chrcteriztion of ll the possible bonding combintions For simple illustrtion, we ssume this probing-bsed scheme does not select ntenns optimlly but uses ntenn combintions of, b, nd bc, which fvor this exemplry scheme since the best MCS is from b

9 esnr std [db] 5 5 Night Dy Window size [s] Fig Averge stndrd devition of esnr vlue for different sizes of sliding window We compre two different links mesured t different times of the dy C AP Assocition Another cse where CSI-SF is useful is when client must decide which AP to ssocite with Our experiments confirmed tht the AP tht hs the strongest SNR might not be the one with the highest supported rte CSI nd esnr for the MIMO configurtions would be better metric, but - nd 3-strem pckets cn only be received fter ssociting with n AP However, three -strem becons, sent from ech AP on its three ntenns, would suffice for our lgorithm to compute the e SNR of ll MIMO configurtions for ech AP To support this ppliction, n AP must simply switch the ntenn from which the becons re sent, n esy vrition on trditionl AP behvior with no effect on clients tht do not implement CSI-SF Of course this mesurement is only vlid s long s the chnnel qulity is stble, but this limittion pplies to ll AP selection lgorithms For our experimentl settings, we studied the verge stndrd devition of the esnr of pckets received in temporl windows of vrious sizes for the links tht we used in our experiments We compre the results of two links in Fig The trces were collected in the sme office environment, one of them during dytime, with no node mobility but people freely moving in the spce surrounding the two nodes, nd the other during the night when the office ws empty The night environment is quite stedy, lthough interestingly it shows certin mount of vrition, independent from the length of the window However, in both cses, the verge stndrd devition is below db for up to 5ms, nd does not exceed db even for the lrgest window tested This is n indiction tht even in busy office environment, when nodes re not mobile, the link rte estimted before the ssocition is likely to remin constnt for long period VI CONCLUSION This pper presents CSI-SF, method for estimting CSI using smll number of frme trnsmissions nd extrpolting dt to settings tht hve not been smpled We implemented nd evluted CSI-SF on our 8n network testbed nd lso discussed the prcticl chllenges of CSI-SF In our experiments in vrious network scenrios, CSI-SF showed high efficiency nd effectiveness by chieving high ccurcy in CSI estimtion with reduced smpling overhed CSI-SF cn be utilized not only for estimting CSI for lrger number of strems, but lso for wider chnnels nd different trnsmission power levels We lso showed tht CSI-SF provides ccurte estimtes even without knowledge of hrdwre specific chrcteristics such s non-liner response to the power settings nd unknown sptil mpping mtrix We believe the lgorithm designers for rte dpttion, bemforming, ssocition control cn tke dvntge of CSI-SF to improve their performnce We lso rgue tht CSI-SF will be even more beneficil in future networks with more ntenn configurtions nd wider bonded chnnels REFERENCES [] A Blsubrmnin, R Mhjn, nd A Venktrmni, Augmenting mobile 3G using WiFi, in Proceedings of ACM MobiSys, [] IEEE 8n-9 Amendment 5: Enhncements for Higher Throughput, IEEE-SA 9 October 9 [3] IEEE 8c: Very High Throughput < 6 GHz, IEEE Stndrds [4] A J Pulrj, D A Gore, R U Nbr, nd H Bolcskei, An overview of MIMO communictions - key to gigbit wireless, Proceedings of IEEE, vol 9, no 5, 4 [5] A Goldsmith, S A Jfr, N Jindl, nd S Vishwnth, Cpcity limits of MIMO chnnels, IEEE Journl on Selected Ares in Communictions, vol 5, no 5, 3 [6] A Kmermn nd L Montebn, WveLAN-II : A High-Performnce Wireless LAN for the Unlicensed Bnd, Bell Lbs Technicl Journl, pp 8 33, July 997 [7] M Lcge, M H Mnshei, nd T Turletti, IEEE 8 rte dpttion: prcticl pproch, Proc of MSWiM, p 6, 4 [8] T Joshi, D Ahuj, D Singh, nd D Agrwl, SARA: Stochstic Automt Rte Adpttion for IEEE 8 Networks, IEEE Trnsctions on Prllel nd Distributed Systems, vol 9, no, pp , Nov 8 [9] J Choi, J N, Y-s Lim, K Prk, nd C-k Kim, Collision-wre design of rte dpttion for multi-rte 8 WLANs, IEEE Journl on Selected Ares in Communictions, vol 6, no 8, pp , Oct 8 [] J Kim, S Kim, S Choi, nd D Qio, CARA: Collision-Awre Rte Adpttion for IEEE 8 WLANs, in Proc of IEEE INFOCOM IEEE, Apr 6, pp [] S H Y Wong, H Yng, S Lu, nd V Bhrghvn, Robust rte dpttion for 8 wireless networks, Proc of ACM MOBICOM, p 46, 6 [] G Hollnd, N Vidy, nd P Bhl, A rte-dptive MAC protocol for multi-hop wireless networks, Proc of ACM MOBICOM, [3] K LCurts nd H Blkrishnn, Mesurement nd nlysis of relworld 8 mesh networks, in Proc of ACM IMC, Nov [4] A Willig, M Kubisch, C Hoene, nd A Wolisz, Mesurements of wireless link in n industril environment using n IEEE 8- complint physicl lyer, IEEE Trnsctions on Industril Electronics, vol 49, no 6, pp 65 8, Dec [5] D Hlperin, W Hu, A Sheth, nd D Wetherll, Predictble 8 pcket delivery from wireless chnnel mesurements, in Proc of ACM SIGCOMM, [6] S Nnd nd K Rege, Frme error rtes for convolutionl codes on fding chnnels nd the concept of effective eb/n, IEEE Trnsctions on Vehiculr Technology, vol 47, no 4, pp 45 5, 998 [7] T To nd A Czylwik, Performnce nlysis of Link Adpttion in LTE systems, in Interntionl ITG Workshop on Smrt Antenns (WSA) IEEE,, pp 5 [8] D Hlperin et l, 8n CSI Tool bsed on iwlwifi nd Linux-6, [9] I Pefkinkis, Y Hu, S H Wong, H Yng, nd S Lu, MIMO Rte Adpttion in 8n Wireless Networks, in Proc of MOBICOM, [] M Prk, IEEE 8c : Dynmic Bndwidth Chnnel Access, in Proc of IEEE ICC, [] L Criou nd J Benko, Multi-chnnel trnsmissions, c-multi-chnneltrnsmissionsppt

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