A MAC and PHY Cross-Layer Analytical Model for the Goodput and Delay of IEEE a Networks Operating Under Basic Access and RTS/CTS DCF Schemes

Transcription

1 JOURNAL OF COMMUNICATIONS, VOL, NO 6, SEPTEMBER 2006 A MAC and PHY Cross-Layer Analytical Model for the Goodput and Delay of IEEE 802a Networks Operating Under Basic Access and RTS/CTS DCF Schees Roger Pierre Fabris Hoefel University La Salle - Canoas - Brazil E-ail: roger@unilasalleedubr Abstract We have developed a theoretical cross-layer odel that allows assessing the goodput and delay of IEEE 802 local area networks (WLANs operating siultaneously under the distributed coordination function (DCF basic access (BA and request-to-send/clear-to-send (RTS/CTS ediu access control (MAC protocols under saturated traffic over correlated fading channels A coparison between nuerical and siulation results is carried out assuing the IEEE 802a PHY layer Index Ters 802, Cross-layer, Goodput, Delay, Fading I INTRODUCTION AND RELATED WORKS The release of the first IEEE 802 standard (that specifies the MAC and the original slower frequencyhopping and direct sequence PHY layers in 997 paved the way for a world wide developent of a standardized cost-effective scalable technology for WLANs Since then, intensive research activities have been carried out on analyze, design, ipleentation, and optiization issues of IEEE 802 networks In 997, B P Crow et al [] published one of the first papers to explain the IEEE 802 specification (with particular ephasis on the MAC layer and to show siulation results for packetized data and a cobination of packetized data and voice over WLANs In 2000, G Bianchi [2] proposed an analytical bi-diensional Markov odel to estiate the perforance of IEEE 802 networks operating under saturated traffic conditions over ideal channels (ie only collisions were taken into account and, therefore, the fraes were not corrupted due to noise and interference This Bianchi s odel has been recently used as a fraework to analyze others IEEE 802 technologies, as in [3] where it is proposed an analytical odel to assess the perforance of quality of service (QoS schees for IEEE 802 WLANs operating under saturated traffic conditions over ideal channels In 2002, S D Qiao and et al [4] derived an analytical odel that takes the non-ideal channel into account on the perforance of IEEE802a WLANs However, they assued an additive white Gaussian noise (AWGN channel and a siple analytical odel to odel the MAC layer issues Therefore, due to the properties of the rando ultipath radio channel and the use of advanced PHY layer techniques, there was also a necessity to develop an accurate joint MAC and PHY theoretical odel to estiate the perforance of IEEE 802based networks Hence, based on the ethodology proposed by Bianchi in [2], we have developed a cross-layer saturation goodput theoretical odel that allows assessing the perforance of IEEE 802a WLANs over uncorrelated [5] and correlated fading channels [6] We have also have noticed a lack in the literature on theoretical analyzes of IEEE 802 WLANs when both the BA and RTS/CTS access schees are siultaneously operational, even when it is assued an ideal PHY layer Therefore, in the present contribution we have iproved our previous theoretical results by: ( developing a MAC and PHY cross-layer odel that allows to estiate the goodput and delay of IEEE 802a WLANs operating siultaneously under the basic and RTS/CTS access schees; (2 carrying out a unified coparison between the perforance of IEEE 802a WLANs over uncorrelated and correlated fading channels when both schees are operational The present contribution is organized as follows In Sections II and III, we briefly present eaningful aspects regarding the IEEE 802 MAC and IEEE 802a PHY layers, respectively The analytical results for the goodput and average delay are developed in Sections IV and V, respectively In Sections VI, we present analytical results to estiate the IEEE 802a frae success probability over correlated fading channels In Section VII, we briefly describe an IEEE 802 MAC and PHY layer siulator that have been developed to assess the perforance of IEEE 802based networks In Section VIII, we show a eaningful set of IEEE 802a analytical and siulation results for the goodput and average delay over distinct environents Finally, our conclusions are carried out in Section IX

2 2 JOURNAL OF COMMUNICATIONS, VOL, NO 6, SEPTEMBER 2006 II IEEE 802 MAC LAYER The IEEE PHY standards 802, 802a and 802b use the sae MAC layer protocols To accoplish it, a MAC service unit (MSDU is segented into a MAC protocol data unit (MPDU that, on its turn, it is apped to the physical layer using a standardized physical layer convergence procedure (PLCP As the IEEE 802 MAC protocol is widely known, we only show at Figures and 2 the tie diagra for the atoic transission used by the DCF BA and RTS/CTS echaniss [7, pp 57-58] Notice that DIFS stands for DCF interfrae spacing (IFS, PIFS for point coordination IFS, SIFS for short IFS and NAV for network allocation vector Figure The atoic cycle for the BA schee Figure 2 The atoic cycle for the RTS/CTS schee III IEEE 802a PHYSICAL LAYER The IEEE 802a, see Tab, is based on orthogonal frequency division odulation (OFDM using a total of 52 subcarriers, of which 48 subcarriers carry actual data and 4 subcarriers are pilots used to facilitate coherent detection [8] The OFDM sybol interval (ts is set to 4µs, and the sybol rate R s is of 2 Msybols/sec TABLE I The IEEE 802a PHY odes [4]: BpS eans Bytes per Sybol Mode p Modulation Code Rate R c Data Rate BpS BPSK /2 6 Mbps 3 2 BPSK 3/4 9 Mbps 45 3 QPSK /2 2 Mbps 6 4 QPSK 3/4 8 Mbps QAM /2 24 Mbps QAM 3/4 36 Mbps QAM 2/3 48 Mbps QAM 3/4 54 Mbps 27 Considering the IEEE 802a convolutional codes generator polynoials, g 0 (33 8 and g (7 8, of rate R c /2 and constrain length K7, then the union bound on the probability of decoding error is given by [9] Pe ( γ b, p < P0( γb, p + 38 P2( γb, p + 93P4( γb, p +, ( where the notation ephasizes the dependence of P d with the received signal-to-interference-plus-noise (SINR per bit γ b, and the PHY ode p The union bound on the probability of decoding error for the higher code rates of 2/3 and 3/4 (which are obtained by puncturing the original rate-/2 code, are given by (2 and (3, respectively [0] Pe ( γ b, p < P6 ( γ b, p + 6 P7 ( γ b, p + 48 P8 ( γ b, p + (2 Pe ( γ b, p < 8P5 ( γ b, p + 3 P6 ( γ b, p + 60 P7 ( γ b, p + (3 Assuing that the convolutional forward error correcting code (FEC is decoded using hard-decision Viterbi decoding, then (4-5 odel the probability of selecting incorrectly a path when the Haing distance d is even and odd, respectively The average bit error rate (BER for the PHY ode p is denoted by ρ p d d d / 2 d 2 d k d k P d ( γ b,p p p ( p p ( p 2 d 2 ρ + k d 2+ k ρ ρ (4 d d k d k P d ( γ b,p p ( p k (d+ 2 k ρ ρ (5 The nuber of octets of the PHY layer protocol data unit (PDU for the RTS frae is given by 6 6 Nrts N pre + Nsrv + lrts + Ntail , (6 8 8 where N pre, N srv and N tail denote the nuber of octets of the preable, service and tail fields, respectively The nuber of octets used to carry the logical control inforation sent by the RTS, CTS and ACK control fraes is labelled by l rts, l cts and l ack, respectively Notice that 6 tail bits, N tail, are used to flush the convolutional code to the zero state The nuber of octets of the PPDU that transport the CTS and ACK control frae is given by 6 6 Ncts Nack Npre + Nsrv + l + Ntail , (7 8 8 where ll cts l ack 4 octets The MAC PPDU length is given by 6 6 Np Npre+ Nsrv+ Nh+ lpl + Ntail lpl +, (8 8 8 where the MPDU header and the cyclic redundant checking (CRC fields have together a length of 34 bytes (N h 34 [7, pp 46] l pl labels the MPDU payload The RTS and CTS control fraes ust be transitted using the basic service set (BSS basic rate (ie PHY odes, 3 and 5 The ACK control fraes ust be transitted using the BSS basic rate that is less than or equal to the rate of the data frae it is acknowledging The length of RTS, CTS and ACK control fraes are given by (9-, respectively The PHY layer convergence procedure (PLCP preable duration, tpclp_pre, is equal to 6 µs The PCLP header is always transitted using PHY and its duration, tpclp_sig, is equal to 4µs [4] lrts + ( 6+ 6 /8 Trts( prts tpclp_ Pre+ tpclp_ SIG+ ts BpS ( prts (9

3 JOURNAL OF COMMUNICATIONS, VOL, NO 6, SEPTEMBER ( 6 6 / lcts Tcts( pcts tpclp_ Pre+ tpclp_sig+ ts BpS( pcts (0 ( 6 6 lack + + / 8 Tack( pack tpclp_pre+ tpclp_sig+ ts BpS( pack ( The tie period spent to transit a MPDU with a payload of l pl octets over the IEEE 802a using the PHY ode p p is given by Tp( pp tpclp _ Pr e + tpclp _ SIG + ( 6 6 N pl BpS( pp / 8 ts IV ANALYTICAL RESULTS: SATURATION GOODPUT (2 Fig 3 shows a discrete bi-diensional Markov chain (s i (t,b i (t for a IEEE 802 STA The present analytical odelling, that odels the backoff window size and the non-ideal channel conditions, assues that: there is a fixed nuber of n STAs that operate in saturation conditions, ie each STA has a MPDU to transit after finishing each successful transission; 2 a MPDU frae is transitted using the BA and RTS/CTS schees with probability P ba and P rts, respectively; 3 s i (t is a stochastic process that odels the ith backoff stage at tie t, where i (0,,; 4 b i (t is a stochastic process that odels the backoff tie counter for the backoff stage i at tie t; 5 the window size at backoff stage i is W i 2 i W, where W is the MAC contention window (CW size paraeter, CW in The axiu window size for the STA is denoted as W CW ax 2 W ; 6 the MPDUs transitted by the STAs collide with a constant and independent conditional collision probability p; 7 the capture effect is neglected as such as the lost of fraes due to collisions is independent of the lost of fraes due to noise and interference; 8 the post backoff procedure [3] is not taken into account The probability that a transitted MPDU is successful depends upon the following events: ( no collision and successful transission using the BA schee; (2 no collision and successful transission using the RTS/CTS access schee Thus, { P ( S + P ( S } Ps ( p ba p ack rts rts cts p ack, (3 where S cts, S rts and S ack denote, respectively, the probability that the RTS, CTS and ACK control fraes be transitted with success S p denotes the probability the transission of a MPDU frae is successful Eq (4 and (5 odel the probability that a MPDU is transitted using the BA and RTS/CTS schees, respectively Notice that these probabilities depend upon the MAC payload length l pl and the RTSThreshold defined at the Manageent Inforation Base (MIB P P l RTSThreshold (4 ba pl < { } { l RTSTheshold} P pl (5 Eq (6 details the events that cause an unsuccessful MPDU transission: ( collision; (2 no collision, but a corrupted frae on the basis access schee (see 7; (3 no collision, but a corrupted frae on the RTS/CTS access schee (see 8 ( p ( P P + P P Pf p + ba f,ba rts f,rts (6 Pf,ba (- Sp + Sp (- Sack (7 - Sp ( S (- Srts + Srts cts + Pf,rts Srts (- Sp + Srts Sp (- Sack - Srts p ack (-p {P ba (S p S ack + P rts (S rts S cts S p S ack } 0, 0 0, 0, W 0 -, 0, ', W - [p+(-p (P ba P f,ba + P rts P f,rts ]/ W - cw, 0 cw,, cw, W cw - [p+(-p (P ba P f,ba + P rts P f,rts ]/ W (8 [p+(-p (P ba P f,ba + P rts P f,rts ]/ W - Figure 3 Bi-diensional Markov chain (s(t,b(t odel for the backoff window size and a non-ideal channel A Packet Transission Probability Equations (9 to (22 odel the null one-step transition probabilities of the bi-diensional Markov chain depicted at Fig 3, where it is used the notation i,k /i 0,k o } s(t+i,b(t+k s(ti o,b(tk o } The decreasing of the backoff tier at the beginning at each slot tie of size σ is odeled as { i,k i,k } for k ( 0,W 2 and i ( 0, P + i (9 Eq (20 takes into account that a new PHY layer PDU (PPDU starts at the backoff stage 0 and that the backoff is uniforly distributed into the range (0, W 0 - after a successful PPDU transission { i,0 } [ p] P 0,k Pba rts for k 0 ( Sp + ( S S S S cts p ack ( 0,W and i ( 0, / W0 (20 The property that a new backoff value is uniforly chosen in the range (0,W i after an unsuccessful transission at the backoff stage i- can be odeled as P { i,k i 0, } p+ [ p] P ( S + ( Srtspack ba p ack { }/W i (2

4 4 JOURNAL OF COMMUNICATIONS, VOL, NO 6, SEPTEMBER 2006 Eq (22 odels the fact that the backoff is not increased in subsequent frae transissions once the backoff stage has reached the value Pba ( Spack +,k 0, } { p+ [ p] }/W ( Srts pack (22 The MPDU transission occurs when the backoff tier counter is equal to zero Therefore, using an algebraic procedure siilar to that one developed in [5] we can show that the probability that a STA transits in a randoly chosen slot tie is given by (23, where, the stationary probability of a given STA be in the tie slot 0 for first contention window is given by (24 The average frae success transission probability is denoted by S, as indicated by (25 b00, τ bi, ( p P S + P S b 0,0 i W [ ( ( ] ba p ack rts rts cts p ack (23 2 ( p [ + 2 ( p ] [ + ( + p ] + ( + p 2+ W+ 2 W [ + ( + p ] { } (24 S Pba ( Sp + ( Srts Scts Sp (25 For an ideal channel (ie S rts S cts S p S ack, Eq (24 resues to (26, which agrees with (6 of [2] 2( 2 p ( p b0,0 (26 2 p W + + pw 2 p ( ( ( ( Each STA transits with probability τ Therefore, the conditional probability that a transitted PPDU encounters a collision in a given slot tie can be stated as n p ( τ (27 The nonlinear syste represented by (23 and (27 can be solved using nuerical techniques in order to estiate the transission probability τ and the conditional collision probability p B Goodput The goodput (net throughput in bits per second (bps can be odeled as the ratio of the payload bits transitted with success to the average cycle tie, ie Pba Nba + Nrts Gbps (28 Pba Tba + Trts The average nuber of payload bits transitted with success for the BA and RTS/CTS schees are given by (29 and (30, respectively The nuber of payload octets when is used the BA and RTS/CTS schees are denoted by l pl,ba and l pl,rts, respectively Nba 8 l pl,ba Ptrp (29 Nrts 8 l pl,rts Ptrrts p ack (30 The probability that there is no collision on the channel conditioned to the fact that at least one STA transits is given by n n ( τ τ n n n τ ( τ n τ ( τ Ps (3 P P n ( τ tr where P tr is the probability that there is at least one transission in the considered slot tie The average cycle tie for the basic access and RTS/CTS schee is given by (32 and (33, respectively T ba Bs,ba + B f,ba + B f 2,ba + B f 3,ba + I (32 Trts Bs,rts + Bf,rts + Bf 2,rts, + Bf 3,rts + Bf 4,rts + Bf 5, rts + I (33 For the BA schee, the average busy tie when the atoic positive ACK basic access transission is successful is given by tr ( p DIFS + T p p + a + B s, ba Ps Ptr Sp Sac (34 SIFS + Tack ( pack + a where a is the propagation delay T p (p p is the tie period necessary to transit a MPDU when it is used the PHY ode p p (see 2 T ack (p ack is the tie period spent to transit a positive ACK control frae using the PHY ode p ack (see The average busy tie when the transission is successful using the RTS/CTS schee is given by Bs Ps Ptr rts p ac DIFS+ Trts( prts + a + SIFS+ Tcts( pcts + a + SIFS+ Tp( pp + a + SIFS+ Tack( pack + a] (35 where T rts (p rts and T cts (p cts denote the tie necessary to transit the RTS and CTS control fraes when it is used the PHY ode p rts and p cts, respectively (see 9 and 0 B f, ba odels the average aount of tie that the channel is busy due to collisions of a MPDU fraes when it used the BA schee (see 36 However, for the RTS/CTS MAC schee the waste tie occurs due to RTS control frae collisions, as odeled by (37 ( P ( DIFS + T ( p a B f,ba Ptr s p p + (36 ( P ( DIFS + T ( p a B f,rts Ptr s rts rts + (37 B f 2, ba and B f 3, ba odel the average lost tie due to an unsuccessful transissions due to noise and interference of data and ACK fraes, respectively, when it is used the BA schee ( S ( DIFS + T ( p a B f 2, ba Ptr p p p + (38 DIFS+ Tp( pp + a + Bf,ba Ptr Ps Sp ( Sack SIFS Tack( pack a ( B f 2, rts, B f 3, rts, B f 4, rts and B f, rts [ 5 odel the average tie that the channel is busy with unsuccessful transissions due to noise and interference, of RTS, CTS, data and ACK fraes, respectively, when it is used

5 JOURNAL OF COMMUNICATIONS, VOL, NO 6, SEPTEMBER the RTS/CTS access schee Finally, the average tie that a slot tie is idle is given by (39, where s is the slot tie length ( S [ DIFS + T ( p a] B f 2,rts Ptr rts rts rts + (40 DIFS + Trts( prts + a + B f 3,rts Ptr Srts ( Scts (4 SIFS + Tcts( pcts + a B f 4,rts Ptr Srts Scts ( S [ DIFS + Trts ( prts + a + SIFS + Tcts ( pcts + a + SIFS + Tp ( pp + (42 B f 5,rts Ptr Srts Sp p ( S [ a] DIFS + Trts ( prts + a + SIFS + Trcs ( pcts + a + SIFS + Tp ( pp + a + SIFS + Tack ( pack + a] (43 I ( Ptr σ (44 ack V ANALYTICAL RESULTS: AVERAGE DELAY The average delay between the tie that a MPDU arrived at the queue until the tie that an positive ACK for this MPDU is received can be odeled as the average nuber of cycle ties necessary to accoplish a successful MPDU transission, as odeled by (45 The average cycle tie for the BA and RTS/CTS schees is given by (32 and (33, respectively The average nuber of tie slots spent for a successful transission is given by (46, where the average probability that an atoic transission is not successful, P f, is given by (6 D P Pba T ba+ T rts (45 i W ( i i W P ( P P f f i i 2 (46 VI ANALYTICAL RESULTS: FRAME SUCCESS PROBABILITY OVER BLOCK FADING CHANNELS In this Section, we assue that the fading is correlated at each atoic cycle (see Fig and 2 and uncorrelated aong distinct atoic cycles Assuing hard decision Viterbi decoding, then the upper bound for a successful frae transission over an uncorrelated fading channel can be estiated by (47 for a frae with l octets [] For a block-fading channel, this upper bound ust be odified to take into account the channel eory Eq (48 estiates the average probability that a hard decision Viterbi decoder decodes successfully a frae with l octets transitted using the PHY ode p when the ulitpath fading with average SINR per bit γ b reains the sae during the whole frae transission Notice that p(g b is the probability distribution function (pdf of the SINR per bit at the Viterbi decoder input and g inf is chosen to satisfy the inequality (49 S( l, γ, p < P ( γ, p 8 (47 [ ] l b e b 8l S( l, γ b, p < [ Pe( γ b, p ] p( γ b dγ b (48 γ inf Pe ( γ inf, p (49 We have assued a flat fading Nakagai- channel [2, pp 47] Therefore, considering a axiu ratio cobining (MRC receiver atched with the channel diversity and that the sae average power is received at each diversity branch, then pdf of the SINR per bit at the Viterbi decoder input is of gaa kind [5], ie L n p n ( γb b Γ( L n γb γ γb ( γ L n exp n b if γ > 0, 05, (50 where n is the fading figure, γ b is the average SINR per bit at the at Viterbi decoder input and L is the nuber of independent diversity branches Notice that n odels a Rayleigh channel A PHY Mode (BPSK@6Mbps For the PHY ode, the union bound on the decoding error can be estiated using ( and (4, where the average BER ρ p is given by (5 with code rate R c /2 Q(x is the copleentary Gaussian cuulative distribution function [2, pp 269] ( 2γ ρ (5 Q brc Since all fraes are transitted using the PHY ode, then S rts, S cts, S p and S ack can be estiated using (52-58 with p Srts( prts S( Nrts, γ b, prts ; (52 Scts ( pcts CTS is ack / RTS was ack}; (53 S( N N,, p S ( p rts + cts γ b cts cts cts ; (54 Srts ( prts Sp ( pp MPDU is correct / RTS,CTS were correct}; (55 S( N rts + N cts + N p, γ b, pp Sp ( pp ; (56 Srts ( prts Scts ( pcts Sack ( pack ACK is correct / RTS,CTS, MPDU were correct}; (57 S( Nrts + Ncts + Np + Nack, γb, pack Sack( pack (58 Srts( prts Scts( pcts Sp( pp B PHY Mode 2 (BPSK@9Mbps When the MPDU is transitted using the PHY ode 2, then all control fraes are transitted using the PHY ode Thus, the S rts and S cts are still given by (52 and (54, respectively, with p The union bound on the decoding error can be estiated using (3 and (5, where ρ p is given by (5 with R c 3/4 The probability that the MPDU is transitted with success can be stated as S( N p, γ b,2 S( N p, γ b,2 Sp ( 2 Srts ( Scts ( S( N rts + N cts, γ b, (59 Notice that the 3 octets of the preable were not taken into account in (59 since they are transitted using the b n

6 6 JOURNAL OF COMMUNICATIONS, VOL, NO 6, SEPTEMBER 2006 PHY ode (ie a ore robust signaling schee We also have used the following approxiation: MPDU, RTS, CTS } MPDUis ack/ RTS and CTS wereack} RTS,CTS } MPDU} RTS,CTS} (60 since N p >>(N rts +N cts, and the MPDU is transitted using the PHY ode 2 (ie a signaling schee with lesser iunity to noise and interference than the signaling schee used to transit the control fraes The ACK control frae is transitted using the PHY ode, while the MPDU is transitted using the PHY ode 2 (ie a signaling schee ore suitable to the decoding errors Thus, the ACK control frae success probability can be approxiated by (6 for block fading channels Notice that, usually, N ack <<N p Sack ( p ACK is ack / RTS,CTS and MPDU were ack (6 C PHY Mode 3(QPSK@2Mbps In this case all control and data fraes are transitted using the PHY ode 3 Therefore, S rts and S cts are given by (52 and (54, respectively, with p3 Correspondingly, S d and S ack are given by (56 and (58, respectively, with p3 The union bound on the decoding error can be estiated using ( and (4, where ρ p is given by (5 with R c /2 for coherent deodulation [2] D PHY Mode 4 (QPSK@8Mbps Here, all the control fraes are transitted using the PHY ode 3 and the MPDU is transitted using the PHY ode 4 Consequently, S rts and S cts are given by (52 and (54, respectively, with p3 Using siilar reasoning developed for PHY ode 2, then S d is given by (62 and S ack is given by (6 The union bound on the decoding error can be estiated using (3 and (5, where ρ p given by (5 with R c 3/4 for coherent deodulation [2] S( Npd, γ b,4 S( Npd, γ b,4 Spd( 4 (62 Srts( 3 Scts( 3 S( Nrts + Ncts, γ b,3 E PHY Mode 5 (6QAM@24Mbps In this case all control and data fraes are transitted using the PHY ode 5 Therefore, S rts and S cts are given by (52 and (54, respectively, with p5 Correspondingly, S d and S ack are given by (56 and (58 with p5 The union bound on the decoding error can be estiated using ( and (4 ρ p for QAM signaling is given by (63 with M6 and R c /2 [3] ρ p + M erfc M log M 2 M 2 erfc M log2 M 2log2M γ b R c 2( M 3log2M γ b R c 2( M (63 F PHY Mode 6 (6QAM@36Mbps, PHY Mode 7 (64QAM@48Mbps and PHY Mode 8 (64QAM@64Mbps For all these PHY odes the control fraes are transitted using the PHY ode 5 and the MPDU is transitted using the PHY odes 6, 7, or 8 Thus, the S rts and S cts are still given by (52 and (54 with p5 The S d is given by S( Npd, γ b, p S( Npd, γ b, p Spd ( p Srts( 5 Scts( 5 S( Nrts + Ncts, γ b,5 (64 where p6, 7 and 8 The S ack can be estiated by (6 since the control fraes are transitted using 6QAM with R c /2 while the MPDU is transitted using 6QAM with R c 3/4 (, 64QAM with R c 2/3 ( or 64QAM with R c 3/4 ( VII JOINT MAC AND PHY LAYERS SIMULATOR The C ++ IEEE 802 joint MAC and PHY layers siulator has the following ain characteristics: It ipleents an ad hoc IEEE 802a WLAN It ipleents the MAC state achine that fulfills the IEEE 802 DCF BA and RTS/CTS schees The OFDM PHY layer is ipleented assuing perfect synchronis The PHY layer signal processing algoriths ipleents the axiulikelihood hard decision detection for the PHY ode to PHY ode 8 The convolutional hard-decision decoding is ipleented using a sei-analytic approach as follows The short-ter average BER is estiated at a frae basis using on-line statistics collected at the deodulator output Then the average BER is used in (-5 to estiate the probability that the hard decision Viterbi decoding algorith produces a decoding error It is assued the IEEE 802a PHY layer paraeters [7, pp 279]: slot tie σ9µs, SIFS6µs, DIFS34µs, CW in 6, CW ax 023, 6 The propagation delay a is set to µs The correlated fading (tantaount for block fading is generated using the Jakes odel with carrier frequency of 55 GHz and velocity of 3 k/h [4] It is assued a confidence interval of 98% VIII ANALYTICAL AND SIMULATION RESULTS In this section, assuing correlated and uncorrelated flat fading Rayleigh channels, we shall show siulation and analytical results for the following syste configurations: ( IEEE 802a networks operating only under the RTS/CTS access schee: P ba 0 and P rts in (3 and subsequent equations; (2 IEEE 802a networks operating only under the BA ode: P ba and P rts 0; (3 joint operation of BA and RTS/CTS schees A Single Operation of RTS/CTS Access Schee Over Correlated Fading Channels In this subsection, we assue an uncorrelated flat fading Rayleigh channel, P ba 0, P rts The MAC

7 JOURNAL OF COMMUNICATIONS, VOL, NO 6, SEPTEMBER payload l pl is set to 023 octets Fig 4 copares the goodput as a function of the SINR per bit for a syste without spatial diversity (L First, we ephasize a good agreeent between analytical andsiulation results Second, we can conclude that the PHY ode 3 (QPSK with R c /2 and PHY ode 4 (QPSK with R c 3/4 allows, respectively, a superior perforance in relation to that one obtained with the PHY ode (BPSK with R c /2 and PHY ode 2 (BPSK with R c 3/4, since the QPSK signalling has a better spectral efficiency when it is ipleented coherent deodulation Fig 5 shows a reasonable agreeent between nuerical and siulation results for the average MPDU delay Saturation Goodput in bps 240M 200M 60M 20M 80M 40M 00 Flat Rayleigh Channel; L Jakes' Model (f c 55 GHz, v3 k/h RTS+CTS+Data+ACK schee 0 STAs PHY in db Figure 4 Coparison between analytical (straight lines and siulation (arks results for the goodput in bps over a correlated fading channel Average Delay [s] 00 0 Flat Rayleigh Channel; L Jakes' Model (f c 55 GHz, v3 k/h RTS+CTS+Data+ACK schee 0 STAs PHY Figure 5 Coparison between analytical (straight lines and siulation (arks results for the delay over a correlated fading channel L B Coparison of the Perforance of RTS/CTS Schee Over Correlated and Uncorrelated Fading Channels In this subsection, we assue that the MAC payloads of 023 octets are transitted by the RTS/CTS schee Analytical results for uncorrelated fading channels can be found in [5] Fig 6 shows that for teporally uncorrelated flat fading Rayleigh channel there is a well-defined short range of SINR per bit where the syste perforance is acceptable On the other hand, when the fading is strongly correlated there is a wide and sooth variation of the goodput with SINR per bit Fig 6 also shows that the spatial diversity (assued uncorrelated at each diversity branch provides a greater gain in the required SINR per bit, γ b, on environents where the fading is teporally uncorrelated However, the diversity gain is also substantial on environents where the fading is both teporally and frequency correlated Saturation Goodput in bps 240M 200M 60M 20M 80M 40M 00 Flat Rayleigh Channel RTS+CTS+Data+ACK 0 STAs Uncorrelated Fading L L3 Correlated Fading L L3 Uncorrelated Fading L L3 Correlated Fading L L Average γ b Figure 6 Coparison between analytical (straight lines and siulation (arks results for the average goodput Hereafter, we shall present results for IEEE 802a networks operating siultaneously under the BA and RTS/CTS access schees It is generated MAC payloads of 255 and 023 octets with equal probability (ie P ba P rts 05 The RTSThreshold is set to 256 octets C Joint Operation of BA and RTS/CTS Access Schees Over Correlated Fading Channels In spite of the coplexity of the MAC and PHY layers, we can verify a good agreeent between analytical and siulation results for the goodput (Fig 7 and delay (Fig 8 for the joint operation of BA and RTS/CTS schees over correlated flat fading Rayleigh channels Saturation Goodput in bps Average Delay [s] 200M 80M 60M 40M 20M 00M 80M 60M 40M 20M 00 PHY Flat Rayleigh Channel 0 STAs; L (no spatial diversity Figure 7 Goodput in bps versus the average SINR per bit 00 0 Flat Rayleigh Channel 0 STAs; L (no spatial diversity PHY Figure 8 Average delay in seconds versus the average SINR per bit

8 8 JOURNAL OF COMMUNICATIONS, VOL, NO 6, SEPTEMBER 2006 D Joint Operation of BA and RTS/CTS Access Schees Over Uncorrelated Fading Channels Figures 9 and 0 are siilar to figures 7 and 8, respectively, except that in this section it is assued an uncorrelated Rayleigh fading channel Notice that the PHY ode 5 (6QAM with R c /2 has a better perforance than the PHY ode 2 (BPSK with R c 3/4 and PHY ode 4 (QPSK with R c 3/4 This interesting characteristic is due to the high coding gain allowed on channels where the Rayleigh ultipath fading is teporally independent at sybol level, as postulated in this ite PHY ode 7 (64QAM with R c 2/3 has a better perforance in relation to the PHY ode 6 (6QAM with R c 3/4 since the higher coding gain overwhel (in the assued channel odel the greater noise iunity of 6QAM in relation to the 64QAM signaling schee The results shown in Fig 9 indicate a different interrelation between axiu perforance and the PHY ode, since the correlated fading channel assued in Fig 8 decreases the net effect of coding gain due to lack of teporal and frequency diversity Saturation Goodput in bps Average Delay [s] 200M Flat Rayleigh Channel Uncorrelated Fading 50M 00M 50M 00 0 STAs; L (no spatial diversity PHY Figure 9 Goodput in bps versus the average SINR per bit 00 0 Flat Rayleigh Channel Uncorrelated Fading 0 STAs; L (no spatial diversity PHY Figure 0 Average delay in seconds versus the average SINR per bit correlated at sybol level and dependent across the OFDM carriers REFERENCES [] B P Crow et al, IEEE 802 wireless local area networks, IEEE Counications Magazine, vol 35, no 9, pp 6-26, Sept 997 [2] G Bianchi, Perforance Analysis of the IEEE 802 Distributed coordination function, IEEE Journal on Selected Areas of Counications, vol 8, no 3, pp , March 2000 [3] J W Robinson and J W and Randhawa, Saturation throughput analysis of IEEE 802e enhanced distributed coordination function, IEEE J on Select Areas on Counications, vol 22, no 5, pp , June 2004 [4] S D Qiao, S Choi and K G Shin, Goodput analyzes and link adaptation for the IEEE 802a wireless LANs, IEEE Trans Mobile Cop, pp , 2002 [5] R P F Hoefel A Cross-Layer saturation goodput analysis for IEEE 802a networks, Proc of IEEE Vehicular Technology Conference 2005-Spring (IEEE VTC 2005-Spring, Stockhol, 2005 [6] R P F Hoefel Goodput and delay analysis of IEEE 802a networks over block fading channels, Proc of IEEE Consuer Counication and Networking Conference 2006 (IEEE CCNC 2006, Las Vegas, 2006 [7] M S Gast, 802 Wireless Networks, Sebastopol, CA: O Reilly, 2005 [8] IEEE 802a, Part : Wireless LAN Mediu Access Control (MAC and Physical Layer (PHY Specification Aendent : High-speed Physical Layer in the 5 GHz band, suppleented to IEEE 802 standard, New Jersey, NY: IEEE Press, Sept 999 [9] J Conan, The weight spectra of soe short low-rate convolutional codes, IEEE Transactions on Counications, vol 32, pp , Sept 984 [0] D Haccoun and G Bégin, High-rate punctured convolutional codes for Viterbi and Sequential decoding, IEEE Transactions on Counications, vol 37, n, pp 3-20, Nov 989 [] M B Puersley and D J Taipale, Error Probabilities for Spread-Spectru Packet Radio with Convolutional Codes and Viterbi Decoding, IEEE Transactions on Counications, vol 35, n, pp -2, Jan 987 [2] J G Proakis, Digital Counications, New York, NY: MacGraw-Hill, 200 [3] L Yang and L Hanzo, A recursive algorith for the error probability evaluation of M-QAM, IEEE Counications Letters, vol 4, pp , Oct 2000 [4] W C Jakes, Microwave Mobile Counications, New York, NY: Wiley, 974 IX CONCLUSIONS In this paper, we have derived and validated a joint MAC and PHY cross-layer odel that can be confidentially used to estiate first order results for the goodput and the delay of IEEE 802a ad hoc networks operating siultaneously under the BA and RTS/CTS MAC protocols We have considered the following environents: ( a flat fading Rayleigh channel that is uncorrelated at sybol level and independent across the OFDM carriers; (2 a flat fading Rayleigh channel that is Roger Pierre Fabris Hoefel was born in Porto Alegre, Brazil, on July 9, 965 He received the BS degree in electrical engineering fro Pontific University Catholic, Porto Alegre, Brazil, in 990, a Master degree in coputer science fro Federal University of Rio Grande do Sul, Brazil, in 995, and a doctor degree in electrical engineering fro State University of Capinas, Brazil, in 2000 He is currently the coordinator of Telecounications Engineering Departent at the University La Salle, Canoas, Brazil His research interests are in the areas of wireless counications, MAC protocols and signal processing