Collision Detection in IEEE Networks by Error Vector Magnitude Analysis

Transcription

1 Collson Detecton n IEEE 80. Networks by Error Vector Magntude Analyss Muhammad Naveed Aman, Wa Kn Chan, and Bplab Skdar Department of ECSE, Department of ISE Rensselaer Polytechnc Insttute, Troy, NY 80 USA Abstract There are two causes of packet losses durng a wreless transmsson: losses caused by collsons and losses caused by poor channel condtons. The throughput and spatal reuse of IEEE 80. based wreless networks, as well as the effectveness of the rate adaptaton algorthms they use, s adversely affected by ther nablty to determne the real cause of a packet loss. To address ths ssue, ths paper proposes a mechansm based on Error Vector Magntude EVM) to dscern random channel errors from collsons n wreless networks. The proposed mechansm s based on frst developng an analytc model to characterze the EVM of a packet n the presence and absence of a collson. A threshold based classfer s then proposed that selects the threshold value such that the crossover error rate s acheved. Smulaton results are presented to demonstrate the accuracy of the proposed collson detecton mechansm. I. INTRODUCTION Wred networks lke Ethernet IEEE 80.3) use carrer sense multple access wth collson detecton CSMA/CD) as the bass for medum access control. A wred network can detect collsons because of ts ablty to lsten at the same tme t transmts. The wreless envronment brngs wth t dfferent challenges, one of them beng the dffculty to transmt and receve at the same tme. Moreover, whle a node n a wred network can receve every other node s transmssons, a node on a wreless network may be too far or hdden) from certan other nodes to receve ther transmssons and vce versa) [6]. Thus, wreless networks lke IEEE 80. use a mechansm called carrer sense multple access wth collson avodance CSMA/CA) at the MAC layer. The physcal layer of IEEE 80. delvers a packet to the MAC layer only f t has been receved correctly, otherwse the packet s dscarded. A fundamental ssue wth the use of CSMA/CA based protocols s that upper layers are unaware of the reason why a packet was dscarded at the physcal layer. In general, a packet may be dscarded due to two causes: a weak sgnal due to attenuaton and multpath characterstcs of the envronment) or nterference due to concurrent transmssons from other neghborng devces. However, the MAC layer of IEEE 80. s unaware of the cause of the packet loss, resultng n loss of performance. The nablty to detect collsons and dstngushng them from channel errors causes a waste of bandwdth due to the colldng transmsson), and an unnecessary delay due to performng a backoff. To address ths ssue, ths paper ntroduces a mechansm to detect the cause of a packet loss n wreless networks usng IEEE 80. as the MAC protocol. Determnng the actual cause of packet loss n wreless networks helps the MAC layer n makng ntellgent decsons. If a packet loss occurred due to a collson, an exponental backoff should be performed. Whereas, f a packet loss was the result of channel errors then a data rate adaptaton algorthm should be nvoked - possbly reducng the data rate and/or ncreasng the transmt power. It has been shown n [] that knowledge of the cause of a packet loss can ncrease the throughput by 0-60% whle reducng the retransmssons by 40%, dependng upon the channel condtons. From the above dscusson t s clear that the cause of a packet loss should be used by the MAC layer to mprove performance n wreless networks. A small number of technques have been proposed n lterature for collson detecton n wreless networks. A mechansm for collson detecton called CARA has been proposed n [3], and s based on the use of multple RTS/CTS packets. RRAA [] uses the CARA based RTS/CTS scheme to nfer whether a packet loss s due to a collson or weak sgnal. A method to solate physcal packet errors from collson packet errors usng RTS/CTS and packet fragmentaton s gven n [4]. These approaches requre the observaton and transmsson of multple RTS/CTS packets, thus requrng a long tme to solate the cause of a packet loss. In contrast, our approach to collson detecton s more drect and s based on a metrc that can be obtaned mmedately from the receved packet, thus gvng us mmedate results n real tme. In [] a scheme for collson detecton s proposed usng three channel qualty related metrcs and a metrc vote. Smulaton results presented n ths paper show that our proposed technque leads to sgnfcant reducton n the false postve rates and comparable detecton accuracy. A. Key Contrbutons The followng are the major contrbutons of ths work. ) Characterzaton of EVM n the presence of collsons: In ths paper, we present an analytc model for the statstcal behavor of EVM for the purpose of collson detecton n wreless networks. Usng a realstc model for wreless communcaton, we evaluate the probablty dstrbuton functon PDF) of EVM. Ths model s then used to derve analytcal expressons that relate key parameters characterzng the cause of a packet loss to the statstcal behavor of EVM. ) Mechansm for Collson Detecton: Ths paper proposes a mechansm to detect collsons usng EVM. The collson

2 TABLE I ALLOWED EVM VALUES VERSUS DATA RATE IN IEEE 80. Data rate Mbts/s) EVM db) EVM %) Fg.. Illustraton of Error Vector detecton mechansm s based on usng a threshold for the EVM to classfy packets nto collson or non-collson packets. To obtan the threshold, we frst develop an analytc model to characterze the EVM n the presence and absence of collsons. The optmum EVM threshold for classfcaton s then determned by dervng the threshold that leads to equal false postve and false negatve rates. We evaluate the effectveness of our collson detecton mechansm by usng extensve smulatons. The rest of ths paper s organzed as follows. Secton II presents an analytc model for the EVM under dfferent nterference scenaros. The model for EVM s used n Secton III to determne the threshold for classfyng the cause of a packet loss. Fnally, Secton IV presents the detals of the smulaton model, Secton V presents the smulaton results and Secton VI concludes the paper. II. ANALYSIS OF EVM FOR COLLISION DETECTION In ths secton we present a model to characterze the PDF of EVM n the presence and absence of collsons. Ths model s then used n the next secton to develop a classfer for determnng the cause of each packet loss. An error vector s the dfference between the complex voltage value of an deal symbol and the actual receved symbol. The root-mean-squared value of the error vector s defned as EVM. If X k denotes the reference or transmtted sgnal and Y k denotes the receved dstorted) sgnal, then Fgure shows the error vector E k = Y k X k. Then the EVM s defned as [0]: N k=0 EV M RMS = Y k X k N k=0 = E k P 0 P 0 ) where P 0 s the average power of all the symbols for a gven modulaton, and N s the number of receved symbols. P 0 normalzes the EVM so that t does not depend on the modulaton order. A transmtted OFDM sgnal may experence varous dstortons durng transmsson, resultng n hgh values of EVM. The standards specfy lmts on the EVM to ensure satsfactory n-band performance [5]. The thresholds for EVM, as specfed n the IEEE 80. standard [9], are gven Table I. Let us denote the transmtter by T x, the recever by R x, and the nterference by ζ J where J s the number of nterferers). Let us consder an OFDM system wth N subcarrers. We assume a frequency flat multpath Raylegh fadng channel. The receved tme doman OFDM sgnal y n s gven by y n = H n x n + η n + ζ n ) where H n denotes the Raylegh dstrbuted channel coeffcents, η n s the addtve whte Gaussan nose wth zero-mean and varance ση, and ζ n s the nterference due to a collson). x n s the n th tme doman OFDM sgnal, 0 n N. Then x n can be obtaned from X k, the M-QAM modulated symbol at the k th subcarrer as [7], x n = IDF T {X k } = k=0 X k e jπkn/n 3) where k = 0,,, N. If the number of subcarrers N s large, the real and magnary parts of x n are approxmately..d. Gaussan dstrbuted wth zero-mean and varance σ x [5]. If we assume frequency flat fadng, we can replace the convoluton operator n Equaton ) wth a multplcaton and rewrte Equaton ), as y n = H n x n + η n + ζ n. 4) Let us ntroduce a random varable Z defned as Z = E k. 5) N P 0 k=0 Let e n denote the error vector n the tme doman.e., e n = y n x n. We also know that e n = IDFT{E k } and y n = IDFT{Y k }. Therefore, applyng Parseval s theorem, we can rewrte Equaton 5) as Z = e n. 6) N P 0 Observng Equatons 5) and 6), we see that Z s composed of the sum of N..d. random varables. Applyng the central lmt theorem for large N typcally N = 5 for IEEE

3 80.a), we can approxmate Z by a Gaussan dstrbuton wth probablty densty functon PDF) f Z z) = e z µz ) σ Z. 7) πσ Z To obtan the pdf f Z z) of Z, we need to fnd ts mean µ Z ) and varance σz ). µ Z and σz wll have dfferent values for dfferent types of dstortons, and we are nterested n fndng them for packets nvolved n a collson. We frst evaluate µ Z and σz for the case when there s no collson. In ths case the error vector s gven by e n = H n x n + η n x n = x n H n ) + η n. 8) We assume the standard path loss law lr) = r, and take r α α as the mean power for a Raylegh dstrbuted channel H n ). To fnd µ Z, we have ε{z} = µ Z = N P 0 = P 0 [σ x ε{ e n } ) ] π + r α + ση 3) where ε{e n} s gven by Equaton 9). To fnd the varance of Z, we need to evaluate ε{z } gven as follows: ) Z = e n = NP 0 N P0 e n e n. 4) n =0 n =0 We now assume block fadng wth a block length of m symbols. Then Equaton 4) can be re-wrtten as [ Z = m ) m m N P0 e n 4 + e n e n + n =0 n =0 n =0 n =m m ) m m m m e n 4 + e n e n + e n e n n =m n =m + + n =β n =β n =mn =0 e n 4 + n =β n =0 n =mn =m β e n e n. 5) where β = N m. Takng the expectaton of Equaton 5), we get ε{z } = [ NP0 mε{e 4 n} + N m) ε{e n} ) ] 6) where ε{e n} and ε{e 4 n} are gven by Equatons 9) and 0), respectvely. Combnng Equatons 3) and 6), we can obtan the varance of Z as σ Z = ε{z } µ Z ). Now consder the case when a packet s corrupted due to the nterference caused by collson from other concurrent transmssons. We assume a wreless network wth J nterferers at dstance r j > 0 from R x, that transmt wth a probablty p ndependent of each other. We assume that the startng locaton of a collson wthn a packet s unformly dstrbuted between 0 and N. If a collson starts at OFDM symbol n 0, the error vector can be wrtten as { e en n < n n = 0 7) e n + ζ J n n 0 where ζ J s gven as follows ζ J = J B H r W. 8) =0 Here B s are..d. Bernoull random varables wth parameter p, H r s Raylegh dstrbuted wth mean power /r α, and W s the OFDM symbol transmtted by nterferer, whch s approxmately..d. Gaussan dstrbuted wth zero-mean and varance σx. We can then rewrte Equaton 6) as follows: Z = NP 0 n0 e n + n=n 0 e n + ζ J ) ). 9) Takng the expectaton of Equaton 9), we get ε{z } = µ Z = { } ) π σx P 0 r α + r α + ση ) J N + + pσx. 0) N P 0 r α j=0 j Smlarly, to get the varance of Z, we need to evaluate ε{z }, whch s gven by Z = = N P 0 N P 0 n =0 n =0 [ n0 n =n 0 n =0 n 0 n =0 n =0 n 0 e n e n e n e n + e n e n + n =n 0 n 0 n =0 e n e n + n =n 0 ] n =n 0 e n Takng the expectaton of Equaton ), we get ε{z } = N P 0 e n [ n 0.mε{e 4 n} + n 0 n 0 m) ε{e n} ) +.) n 0 N n 0 )ε{e n}ε{e n } + mn n 0 )ε{e n4 } + ) ] N n 0 )N n 0 m) ε{e n }. ) Takng the expectaton of Equaton 3) w.r.t. n 0, we get ε{z }= [ N P0 mn )ε{e4 n}+ 3 N ) ) ε{e mn ) n} ) + )) N + N ) ε{e 3 n}ε{e n }+ mn + )ε{e n4 } + N +N + ) ) ) ] 3 m N + ) ε{e n }. 3)

4 ε{e n} = σ x { ε{e 4 n} = 3σ 4 x) } π + r α + ση 9) ) 8 r α 4 r 3 α + π + { } ε{e n π } = σx + + ση + pσx ε{e n4 } = [ 3σ 4 x) [ { 6 σx r α 8 r α 4 + r 3 α r α π + J r α j=0 j + 3σ η + 6σ xσ η ) π + + 3ση + 6σxσ η } ] + ση pσx J r α j=0 j + 6pσx 4 J j=0 r α j ) π r α + )] π r α + + 0) ) ) where ε{e n} and ε{e 4 n} are gven by Equatons 9) and 0), respectvely, whle ε{e n } and ε{e n } are gven by Equatons ) and ), respectvely. Thus, we can now obtan the varance of Z as σ Z = ε{z } µ Z ). III. THRESHOLD BASED COLLISION DETECTION In ths secton we descrbe our threshold based mechansm for collson detecton and present the methodology for obtanng the threshold. The proposed collson detecton method s based on notng the dfference n the pdf of EVM n the presence of a collson. To classfy the cause of each packet loss, we frst calculate the EVM of each receved packet. Ths calculated EVM value s then compared aganst a threshold value. If the calculated EVM value s greater than the threshold, the packet s classfed as a collson, and vce versa. The optmum value of the threshold s determned by choosng the threshold value that leads to equal false postve and false negatve rates.e., the threshold that leads to the crossover error rate). The probablty of a false postve s defned as the probablty that the cause of a packet loss s attrbuted to a collson, whle the actual cause was a weak sgnal not a collson). If we denote the threshold by γ, then the probablty of a false postve s gven by γ ] P Z [Z > γ] = P e [ f Z z) dz 4) where P e s the symbol error rate for an M-QAM system. Smlarly the probablty of a false negatve s defned as the probablty that the cause of a packet loss s attrbuted to a weak sgnal, whle the actual cause was a collson. The probablty of a false negatve can be expressed as follows: [ γ ] P Z [Z γ] = P e f Z z ) dz. 5) To obtan the threshold that leads to the crossover error rate, we can fnd γ by equatng Equatons 4) and 5). Thus, to get the threshold we need to solve the followng equaton numercally: γ TABLE II PARAMETERS FOR FINDING THE THRESHOLD Parameter Value P 0 QPSK), 06QAM), 464QAM) σx 0.5 ση r meters) 3 r j meters) 3, 0, 5, 0, 30 α N 3 m 6 TABLE III THRESHOLDS FOR DETECTING COLLISIONS Modulaton Type Threshold for Z Threshold db) QPSK Mbps) QAM 4Mbps) QAM 48Mbps) γ f Z z) dz + f Z z ) dz =. 6) Usng the parameter values gven n Table II, the numercal solutons for the threshold γ absolute value and n db scale) for Mbps QPSK), 4Mbps 6QAM), and 48Mbps 64QAM) are gven n Table III. IV. SIMULATION MODEL In ths secton we descrbe the smulaton model used to evaluate the proposed collson detecton mechansm. The smulator was created n MATLAB/Smulnk. The transmtter and recever models were desgned accordng to the IEEE 80.a specfcatons [9]. The wreless nodes n the smulaton are connected through a frequency flat multpath Raylegh fadng channel. The channel s realzed through the Jake s model [8]. OFDM s used at the physcal layer. The modulaton related

5 Data rate Mbts/s) TABLE IV MODULATION PARAMETERS Modulaton Codng rate R) Coded bts per subcarrer N BP SC ) Coded bts per OFDM symbol N CBP S ) 6 BPSK / BPSK 3/ QPSK / QPSK 3/ QAM / QAM 3/ QAM / QAM 3/ Data bts per OFDM symbol N DBP S ) Fg. 3. Comparson of False Postve Rates Parameter TABLE V TIMING RELATED PARAMETERS Value N SY M : Samples per OFDM symbol 80 N F F T : FFT Length 64 N SD : Number of data subcarrers 48 N SP : Number of plot subcarrers 4 N ST : Number of total subcarrers 5 N SD + N SP ) N T RAIN : Number of tranng symbols F : Subcarrer frequency spacng 0.35 MHz =0 MHz/64) T F F T : IFFT/FFT perod 3.µs/ F ) T P REAMBLE : Preamble duraton 8µs T GI : Guard Interval GI) duraton 0.8µs T F F T /4) T GI : Tranng symbol GI duraton 8µs T SY M : Symbol nterval 4µs T GI + T F F T ) T LONG : Tranng sequence duraton 8µs T GI + xt F F T ) parameters are gven n Table IV, whle the OFDM tmng related parameters are gven n Table V. The network topology used n our smulatons s shown n Fgure. We have two transmtters T and T ) and one recever R) n our network. T acts as the nterferer and ntroduces collsons nto the network. The frame sze for T s fxed at 3 OFDM symbols, whle the frame sze of T s unformly dstrbuted between and 3 OFDM symbols. By varyng the frame sze of the nterferer T ) we can smulate collsons occurrng between packets of dfferent sze. The smulator also allows us to change the probablty of collson n the network, gvng us flexblty n terms of controllng our experment. Fg.. Scenaro for ntroducng collsons To model hgh moblty usage scenaros, the wreless channel assumes a maxmum Doppler frequency of 00Hz. A hgh Doppler frequency also ncreases the probablty of packet loss due to a weak sgnal. From the dscusson n Secton II t s clear that EVM does not depend on the modulaton order, therefore we do not need to consder all the possble data rates. We smulate data rates of Mbps QPSK), 4Mbps 6QAM), and 48Mbps 64QAM). V. RESULTS In ths secton we present smulaton results to evaluate the performance of the proposed collson detecton mechansm. We also compare the performance of the proposed mechansm wth the most accurate detecton mechansm n exstng lterature: a scheme proposed n [] that uses three metrcs, receved sgnal strength, bt error rate and errors per symbol, to classfy packets. The mechansm proposed n [] uses a metrc vote,.e., whenever at least one of the metrcs ndcates a collson, the cause of packet loss s classfed as a collson. The performance of the proposed detecton mechansm s evaluated n terms of two metrcs: the false postve rate defned as the proporton of the number of channel losses that were classfed as collson losses) and the accuracy defned as the proporton of the total number of classfcatons that were correct). The smulaton settngs used for obtanng the results are gven n Secton IV. Fgure 3 compares the false postve rates of the proposed mechansm and the mechansm from [] as a functon of the dstance between the nterferer and the recever. We observe that the proposed mechansm has very low false postve rates and outperforms the classfer proposed n []. The correspondng accuraces for the two schemes s shown n Fgure 4. We observe that whle the scheme from [] has better accuracy when the dstance between the recever and the nterferer s small, our method performs better as ths dstance ncreases. However, t s mportant to note that the accuracy of the mechansm n [] depends on the tranng data that s used to set ts thresholds. In the smulaton results reported here, the tranng and evaluaton scenaros were qute smlar, and the hgh accuracy s not surprsng. In contrast, our mechansm

6 VI. CONCLUSIONS Ths paper proposed a mechansm based on EVM to determne the root cause of a packet loss n a wreless lnk. The proposed methodology s based on evaluatng the EVM value assocated wth a packet and comparng t aganst a threshold value. An analytc model s proposed to determne the threshold value such that the crossover error rate s acheved. The proposed mechansm s compatble wth exstng OFDM based IEEE 80. hardware and protocol specfcatons. The accuracy of the proposed mechansm was evaluated and establshed through extensve smulaton results. Fg. 4. Comparson of Accuracy does not depend on any tranng data and s thus expected to be more robust n a varety of envronments. In addton, the mechansm n [] needs three metrcs and thus has a hgher complexty and overhead. The proposed scheme, however, s based on only one metrc. Overall, the proposed mechansm outperforms the mechansm n [] n terms of the false postve rates and has comparable performance n terms of the accuracy, and ths performance s acheved at lower complexty and greater robustness. Fnally we note that another metrc for comparng the performance of the classfers s the false negatve rate, defned as the proporton of collsons that were ncorrectly classfed as channel errors. Compared to the false negatves, the false postves have a more sgnfcant effect on the performance of a collson detecton mechansm. A hgher false postve rate wll result n an ncrease n the number of backoffs and retransmssons. Thus t s desrable to keep the false postve rate as low as possble and the results show that the proposed mechansm s better at achevng ths objectve, as compared to the mechansm n []. REFERENCES [] S. Rayanchu, A. Mshra, D. Agrawal, S. Saha, S. Benerjee, Dagnosng Wreless Packet Losses n 80.: Separatng Collson from Weak Sgnal, Proc. IEEE INFOCOM, Phoenx, AZ, Aprl 008. [] S. H. Wong, H. Yang, L. Lu, and B. Bhargavan, Robust Rate Adaptaton n 80. Wreless Networks, Proc. ACM MOBICOM, Los Angeles, CA, September 006. [3] J. Km, S. Km, S. Cho, and D. Qao, CARA: Collson-aware rate adaptaton for 80. WLANs, Proc. IEEE INFOCOM, Barcelona, Span, March 006. [4] M. A. Y. Khan, and D. Vetch, Isolatng Physcal PER for Smart Rate Selecton n 80., Proc. IEEE INFOCOM, Ro de Jenero, Brazl, Aprl 009. [5] C. Zhao, and R.J. Baxley, Error Vector Magntude Analyss for OFDM Systems, Sgnals, Systems and Computers, 006. ACSSC 06. Forteth Aslomar Conference on, October 006. [6] L. L. Peterson, and B. S. Dave, Computer Networks - A systems Approach, Elsever Inc., 007. [7] Y. S. Choo, J. Km, W. Y. Yang, and C. G. Kang, MIMO-OFDM Wreless Communcatons wth MATLAB, IEEE press, 00. [8] W. C. Jakes, Mcrowave Moble Communcatons, IEEE press, 974. [9] IEEE Standard 80.a-999, Hgh-speed Physcal Layer n the 5 GHz Band, 999. [0] S. Forester, P. Bouysse, R. Quere, A. Mallet, J. M. Nebus, and L. Laperre, Jont Optmzaton of the Power-Added Effcency and the Error-Vector Measurement of 0-GHz phemt Amplfer through a New Dynamc Bas-Control Method, IEEE Transactons on Mcrowave Theory Tech., vol.5, no.4, pp.3-4, 004.