Wireless Link SNR Mapping Onto An Indoor Testbed

Transcription

1 Wirele Link SNR Mapping Onto An Indoor Tetbed Jing Lei, Roy Yate, Larry Greentein, Hang Liu WINLAB Rutger Univerity 73 Brett Road, Picataway, NJ 8854, USA {michelle, ryate, ljg, Abtract To facilitate a broad range of experimental reearch on novel protocol and application concept, we conider an indoor wirele tetbed to emulate the performance of realworld network. A fundamental iue for emulation i the replication of communication link of pecified quality. In particular, we need to replicate on the tetbed, for every link in the real world, a communication link whoe received ignal-to-interference-and-noie-ratio (SINR) matche the correponding link ignal-to-noie-ratio (SNR). In thi paper, we focu on the downlink SNR mapping aociated with a network with a ingle acce point (AP). Four indoor wirele propagation model (commercial building with/without line-of-ight path and reidential building with/without line-of-ight path) and two type of patial ditribution (uniform ditribution inide a circular cell and uniform ditribution along a line) have been invetigated. Baed on the characteritic of the indoor tetbed, we propoe a mapping method with one AP and one interferer, which eparate the tak into two phae: In the firt phae, the bet location and tranmiion power for the interferer node are determined; in the econd phae, the topology of receiver node i configured by a minimum weight matching algorithm. Through analyi and imulation, we find that when the interferer node i located on the corner acro from the AP, we can achieve a mapping range on the order of 57dB and an average rootmean-quare (RMS) mapping error le than db. Keyword Indoor Tetbed, Path Lo, Downlink, SNR, Minimum Weight Matching Wirele Network (ORBIT) project ha been initiated. It focue on the creation of a large-cale wirele network tetbed which will facilitate a broad range of experimental reearch on novel protocol and application concept []. The propoed ORBIT ytem will employ a two-tier laboratory emulator/field trial network to achieve reproducibility of experimentation, and upport evaluation of protocol and application in real-world etting illutrated in Fig. (a). A hown by Fig. (b), the laboratory-baed wirele network emulator i to be contructed with a large two-dimenional array of 82.x radio node (~4 node), which are uniformly paced on a grid of 2 meter by 2 meter, and which can be dynamically interconnected into pecified topologie for reproducible wirele channel model. (a) Real world outdoor/indoor environment. INTRODUCTION The powerful technology and market trend toward portable computing and communication imply an increaingly important role for wirele acce in the next-generation Internet. New enor and pervaive computing application are expected to drive large-cale deployment of embedded computing device interconnected via new type of hortrange wirele network. Motivated by the goal to advance the technology innovation in the wirele networking field, the Open Acce Reearch Tetbed for Next-Generation Thi reearch i upported by the NSF ORBIT Tetbed Project (NRT Grant # ANI ) (b) ORBIT tetbed with 4 node uniformly ditributed on a grid of 2m by 2m Fig. Mapping of real world environment onto the ORBIT indoor tetbed

2 A fundamental iue for emulation i the replication of communication link of pecified quality. In particular, we need to map the actual link ignal-to-noie-ratio (SNR) onto the indoor tetbed. The difficultie of thi tak lie in the fact that on the grid, due to the limited path lo gain, we can only obtain a link SNR range of approximately 26 db. In addition, the path lo between the grid node can only take on dicrete value. Conequently, we dedicate one or more node on the grid to the radiation of noie-like interference, which ha the effect of increaing the dynamic range of received ignal-to-interference-and-noie-ratio (SINR) value among the other grid node. Thi permit the et of grid SINR obtained by our mapping method to better match the et of real-world link SNR. We recognize that the grid tetbed doe not capture all radio channel effect []. For example, the radio channel will have no ignificant multipath. For phyical layer radio teting, the abence of multipath would be unacceptable; however, for a wirele network tetbed, the difference are le ignificant. At the network layer, a combination of channel impairment and multiuer interference reulting in the failure of the phyical layer to provide a reliable link will reult in an abence of network connectivity. Uing programmable interference and grid mobility, the propoed emulator will create imilar variation in network connectivity. In thi paper, our dicuion focue on the downlink SNR mapping for a real-world network with a ingle acce point (AP) and multiple wirele terminal. In order to avoid a time conuming, brute-force earch over the entire grid, we have propoed a two-phae mapping method baed on minimum weight matching [2] between the real-world link SNR and the grid SINR. A for the mapping of uplink SNR, it can be eaily realized by adjuting the tranmiion power of each mapped grid node within it 2+ db dynamic range. The ret of thi paper i organized a follow: Section 2 introduce the link SNR model for real-world indoor WLAN application; Section 3 formulate the propoed mapping algorithm; and Section 4 preent the imulation reult. Section 5 conclude thi paper. 2. Link SNR OF INDOOR WLAN 2. Pathlo Model In a wirele network, the propagation environment can vary from a imple line-of-ight (LOS) path to one that i attenuated by variou obtruction [3]. To obtain the link SNR ample for indoor environment, we extend the path lo model developed for ultra-wide-band (UWB) communication [4] to WLAN application. Similar to [4, 5], we eparate the indoor path lo model into commercial (COM) and reidential (RES) building, a well a line-ofight (LOS) and non-line-of-ight (NLS) path. To capture the difference in building material, tructure and age, we treat both the path lo exponent and the tandard deviation of hadowing a random variable, which are given by α = µ α + xασα () and = y( µ + xσ ), (2) repectively, where µ α, σ α, µ and σ are buildingdependent contant, while x, x and yare mutually independent Gauian random variable of zero mean and unit α variance. The value for x and x α vary from building to building, but y varie from location to location inide each building. Table lit the model parameter for four different indoor environment. Subtituting () and (2) into the generic path lo formula [3] yield PL( d ) = PL + µ log ( d / d ) + x σ log ( d / d ) + yµ + yx σ α α α average path lo hadowing deviation from average value (3) Table. Parameter for link SNR model [4] Propagation Model LOS Commercial NLS Commerical LOS Reidential NLS Reidential PL (db) d = m Pathlo Exponent σ µ α α Shadowing σ µ Conidering the limitation of practical environment, it i more realitic to model the ditribution of x, x and ya α truncated Gauian variate. Therefore, we introduce the following truncation: x α.3, (4.) x.5, (4.2) y.5. (4.3) The contraint (4.) yield a truncated path lo exponent falling within the th to 9th percentile of the Gauian ditribution, while (4.2) and (4.3) lead to truncated ditribution for the mean and deviation of the hadowing that fall within the 7th to 93rd percentile. 2.2 Noie and Interference Given the tranmiion power and path lo model, it i the received noie and interference that determine the.

3 minimum acceptable received power. Generally, natural background noie and device internal noie can be minimized by good ytem deign. Beyond thi, level of artificial noie/interference may et the enitivity limit of a receiver. Source of artificial noie/interference include other communication ytem operating in the ame frequency band, or operating in other frequency band but unintentionally generating RF ignal in the band of interet. For example, microwave oven operate at a natural frequency of the water molecule of approximately 2.45 GHz, which fall in the middle of the Wi-Fi band. Alo, the ocillator ued in ome microwave oven have poor tability and have been oberved to vary by MHz around their nominal frequencie. In addition, due to the limited frequency pectrum reource, communication frequencie are reued the world over, leading to multiple acce interference. A a reult, the formula for calculating the ratio of ignal-tointerference-and-noie (SINR) i PSβ S SINR = (5) Γ η + PI β l Il l = where η i the noie power, P S and P I l denote the tranmiion power of the deired uer and the k-th interferer, repectively, Γ i the number of interferer, and β S and βi l repreent the path lo of the receiver k to the deired tranmitter and to the interferer tranmitter k, repectively. Following [3], the noie power can be calculated via η = NW, (6) where W i the equivalent noie bandwidth and N i the power pectral denity of thermal noie, which can be expreed by N = ktf, (7) where k i Boltzmann contant, F i the noie figure and T i the abolute temperature. In our link SNR model, the contribution of external interference i ignored due to the interference uppreion mechanim of the MAC layer, and we take F= and T= 29 K. 2.3 Spatial Ditribution of Receiver In a wirele network, the receive terminal can be ditributed in quite different way. In the following, we will conider the probability denity function aociated with two form of patial ditribution: Receiver are uniformly ditributed inide a circular cell, with the AP at the center: 2d fd ( d) =, d 2 2 d R R d ; (8) Receiver are uniformly ditributed along a line, with the AP at one end: fd ( d) =, d d R R d ; (9) where R repreent the coverage radiu of the AP, d i the reference ditance a in (3), and d tand for the T-R eparation. 3. Link SNR Mapping by Grid SINR Vertical Axi (a) Arrangment of Grid Node Horizontal Axi Location of grid node Horizontal Axi In thi ection, our dicuion i focued on the cae of downlink SNR mapping for a WLAN with a ingle acce point (AP). A an abtract of Fig. (b), Fig.2 (a) how a total of 4 node uniformly paced inide a quare. We aume the path lo on the grid i the ame a that in free pace. To map the link SNR onto the grid channel, we can claify the node into three categorie: AP, interferer, and receive terminal. Baically, the freedom of grid node that can be exploited for SNR mapping include the following: Tranmiion power of AP Number, location and tranmiion power of interferer Topology of AP, interferer and receive terminal Obviouly, we only have a finite number of grid node and their path loe can only take on dicrete value. Therefore, for a given etting of the AP tranmiion power, we cannot find a perfect match for arbitrary link SNR and have to develop mapping technique to minimize the difference between the target SNR and the mapped grid SINR. In order to avoid a time conuming, brute-force earch over the entire grid of node, we have developed a mapping method baed on the minimum weight matching algorithm. Aume there are M link SNR required to be mapped onto the grid and the baic idea of our approach can be formulated a follow: Pick one node a the AP and fix it to a grid corner. Chooe another node a the interferer tranmitter and poition it along a diagonal of the grid (with the AP at one end of thi diagonal); Vertical Axi AP (b) SNR Mapping Baed on Grid SINR Poible location of interferer Fig. 2 Illutration of propoed mapping methodology

4 From the remaining 398 grid node, elect a ubet of M node a the receive terminal. Configure the topology of thee receiver node to make the vector of grid SINR bet match the vector of link SNR in the mean quare ene. Fig.2(b) illutrate the propoed mapping methodology. The pentagon on the corner repreent the AP whoe poition i fixed, and the filled quare on the diagonal tand for the poible location of the interferer. For implicity, we can chooe one diagonal node a the interferer and leave the remaining 4-2=398 node a candidate for the M receive terminal. Roughly, the mapping tak can be eparated into two phae: Coare Mapping: chooing the location of the interferer node and configure it tranmiion power; Fine Mapping: determining the location of the receiver. CDF SIR: 5/..3 SIR: 5/.5 SIR: 5/. SIR: 5/.5.2 SIR: 2/.5 SIR: /.5. SIR: SIR:.5/.5 SIR:.5/5 SIR:./ SINR, db Grid SINR CDF of Interferer Node 5 for Different TX Power (Pathlo Exponent = 2) (a) Node 5 Grid SINR CDF of Interferer Node 9 for Different TX Power (Pathlo Exponent = 2) SINR ditribution on grid channel, db In the firt phae, we can figure out a bet poition and power level for the interferer. In the econd phae, we do the "fine mapping" by invoking the minimum weight aignment algorithm to determine the receiver topology. Subtituting Γ = into (5) and auming η << β ( kp ), I I where P denote the tranmiion power of the interferer, I and β ( k) tand for the path lo between receiver k I ( k 398 ) and the interferer, the SINR of node k can be implified into P β ( k) β ( k) S S S SINR( k) = SIR, () P β ( k) β ( k) I I I where SIR = PS PI i the tranmiion power ratio between the AP and the interferer. The econd term on the right hand ide of () i the ratio of path loe. For a pecified SIR, the SINR ditribution i determined by the poition of the interferer only. In other word, if the hitogram of the grid SINR i plotted a a function of the SIR parameterized on the interferer, we can oberve that the pattern of the hitogram depend on the poition of the interferer while the relative tranlation of the hitogram for a given interferer i dependent on the SIR. Without lo of generality, Fig.3 (a)-(b) preent the cumulative ditribution function (CDF) of the grid SINR for interferer node 5 and 9, repectively, with SIR (tranmiion power of AP v. tranmiion of interferer) a a parameter. It can be een from thee figure that the hape of the CDF curve correponding to the ame interferer are identical, and the tranlation among thee curve depend on the SIR Fix 5 mw AP on the corner & move.5 mw interferer along the diagonal Lower bound Upper bound CDF.5.4 SIR: 5/..3 SIR: 5/.5 SIR: 5/. SIR: 5/.5.2 SIR: 2/.5 SIR: /.5. SIR: SIR:.5/.5 SIR:.5/5 SIR:./ SINR, db (b) Node 9 Fig.3 CDF of grid SINR for interferer node 5 and 9 with different tranmiion power etting Ditance between AP and interferer (m) Fig. 4 Ditribution of grid SINR for different location of the interferer Fig.4 how the et of all poible grid SINR correponding to different location of the dedicated interferer when we fix the AP power at 5mw, and move a.5mw interference ource along the diagonal of the grid. From thi figure, we can ee that the mapping range i determined by the location of the interferer. The farther away the inter-

5 ferer i from the AP, the larger the mapping range. Since the larget mapping range i approximately 57 db, which i ufficient for mot application of interet, we can implify the iue of the interference ource by fixing it location to node 9, which i located on the farthermot corner acro from the AP. A a reult, the tak of coare mapping reduce to the power etting for node 9 only. Finally, the tep for coare mapping can be generalized a follow: Fix the poition of the AP to a grid corner, with power P. Fix the poition of the interferer to the grid corner acro from the AP. Compute the median of the target link SNR ample. Make the value of SIR equal to that median and et the tranmiion power of the interferer node at P /SIR. After the tranmiion power of the interferer i determined, the fine mapping can be implemented by invoking a bipartite weighted matching algorithm [2]. In our cae, we regard the M target link SNR and the K grid SINR a two M γ = et of vertice, whoe db value are given by et { m} m K and { ρ k}, repectively. For each element in et { } M k = γ, m m= we need to aign it to a ditinct element in{ ρ k } k =, and the rule governing the aignment i given by: Minimizing mk, m, k K ( ) mk, m k 2 µ mk, = m { M} () ubject to,,2 where µ k = µ γ ρ, γ m i aigned to ρk =, otherwie 4. Reult Figure 5 and Fig. 6 how reult for link SNR in NLS/RES environment when the receive terminal are uniformly ditributed inide a circle and along a line, repectively. The SNR ample are generated by the tatitical model given by (3) and (4.)-(4.3). Obviouly, even under the aumption of the ame propagation and the ame geographical ditribution, there i ignificant difference in the range and ditribution of link SNR due to the randomne of path lo exponent and hadowing. Fig.7 how the root-mean-quare (RMS) mapping error veru the number of uer (target link SNR ample) under four indoor environment (LOS/COM, NLS/COM, LOS/RES, NLS/RES) and two patial ditribution ( RX along a line and RX inide a circle). Under each cenario, we conider M, the number of real-world node whoe SNR are to be mapped onto the grid, to be 3, 4, 5, 6, 7 and 8. In our experiment, we have oberved link SNR range over 8 db, and the mapping error i dominated by K the outlier, i.e. link with extremely low or high SNR. Since the grid can cover a dynamic range of 57dB, which i ufficient to quantify the link qualitie of interet, we can hard limit the extreme to appropriate level and make the range of the trimmed link SNR commenurate with that of the grid SINR. We did that here for the NLS cae with uer ditributed along a line to obtain Fig. 7. It can be oberved from thi figure that NLS environment have larger mapping error than LOS environment becaue the path lo exponent for the LOS cae come cloer to that of free pace propagation. Alo, the RX inide a circle cae can achieve better mapping accuracy than the RX along a line cae becaue, in the latter ituation, it i more probable to get large SNR beyond the coverage of the grid SINR. Therefore, of the eight cenario conidered, the NLS/COM/Line and NLS/RES/Line cae have larger RMS mapping error than their counterpart. 5. Concluion Baed on the characteritic of the ORBIT indoor tetbed, we have propoed a downlink SNR mapping method for the cae of an AP cenario. Through analyi and imulation, we have found that when a noie-like interferer node i located on the corner acro from the AP, we can achieve a mapping range on the order of 57 db and a RMS mapping error le than db. Our future work include the link SNR mapping for a meh network, which i more complicated than the AP cae due to the multiple contraint impoed on the grid node. Reference [] D. Raychaudhuri, ORBIT: Open-Acce Reearch Tetbed for Next-Generation Wirele Network, propoal ubmitted to NSF Network Reearch Tetbed Program, May 23. [2] C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithm and Complexity, Prentice Hall, 982. [3] T. S. Rappaport, Wirele Communication: Principle and Practice, Prentice Hall, 995. [4] S. S. Ghaemzadeh, L. J. Greentein, A. Kavcic, T. Sveinon and V. Tarokh, An Empirical Indoor Path Lo Model for Ultra-Wideband Channel, Journal of Communication and Network, Vol. 5, pp , Dec. 23. [5] V. Erceg, L. J. Greentein, S. Y. Tjandra, S. R. Parkoff, A. Gupta, B. Kulic, A.A. Juliu, R. Bianchi, An empirically baed path lo model for wirele channel in uburban environment, IEEE Journal on Selected Area in Communication, Volume 7, pp. 25 2, July 999.

6 6 4 Link SNR v T-R Separation for Different Pathlo Exponent α=2.39 α= α= α= α= Link SNR v T-R Separation for Different Pathlo Exponent α=3.289 α=3.368 α=3.495 α= α= T-R Separation, m T-R Separation, m.9.8 CDF of Link SNR.9.8 CDF of Link SNR α=3.289 α=3.368 α=3.495 α= α= Empirical CDF Empirical CDF α=2.39 α= α= α= α= Fig.5 Simulated link SNR for NLS/RES environment when receiver are along a line Fig.6 Simulated link SNR for NLS/RES environment when receiver are inide a circle RMS Mapping Error, db (a) Commercial Building.9 LOS/COM/CIRCLE LOS/COM/LINE.8 NLS/COM/CIRCLE NLS/COM/LINE RMS Mapping Error, db (b) Reidential Building LOS/RES/CIRCLE LOS/RES/LINE.9 NLS/RES/CIRCLE NLS/RES/LINE Number of Uer Number of Uer Fig. 7 RMS mapping error v. number of uer under eight cenario (a) inide commercial building (b) inide reidential building