A Joint MAC and Physical Layer Analytical Model for IEEE a Networks Operating under RTS/CTS Access Scheme

Transcription

1 A Joint MAC and Physical Layer Analytical Model for IEEE 80211a Networks Operating under RTS/CTS Access Schee Roger Pierre Fabris Hoefel Departent of Telecounications Engineering - University La Salle Canoas - RS - Brazil roger@lasalletchebr Abstract It is proposed an analytical cross-layer saturation goodput odel for the IEEE 80211a physical (PHY) and ediu access control (MAC) layers It is assued an ad hoc network operating under the distributed coordination function (DCF) using the request-to-send/clear-to-send (RTS/CTS) operational ode The proposed analytical expressions, which are validated by siulation, allow assessing the effects on the syste perforance of channel load, contention window resolution algorith, distinct odulation schees, forward error corrector (FEC) coding schees, receivers structures and channel odels Resuo Neste artigo é proposto u odelo teórico que perite analisar de aneira integrada o desepenho das caadas de enlace e física de redes locais se fio IEEE 80211a As expressões analíticas propostas perite verificar os efeitos no desepenho do sistea da carga no canal, do algorito de resolução da janela de contenção, de esqueas de odulação, integrados co códigos corretores de erro, das estruturas do receptor e de odelos de canal 1 Introduction In [BIANCHI 2000], it is carried out a theoretical analysis of the IEEE DCF MAC protocol in the assuption of ideal channel conditions In [QIAO 2002], considering a network loaded with two stations (STAs) that generate deterinistic traffic, it is developed an analytical odel to jointly evaluate the perforance of IEEE 80211a MAC and PHY layer protocols In [HOEFEL 2004], we developed a theoretical cross-layer odel for MAC and PHY layer protocols for networks based on the IEEE faily of specifications The analytical expressions derived allow estiate the effects of distinct odulation schees, channel odels and an adaptive link level schee on the syste perforance However, in [HOEFEL 2004] the MAC contention window (CW) resolution was not ipleented (ie the packets are dropped after the first non-successful transission attepted) in order that the siulated offered traffic follows strictly the Poisson statistics, as analytically postulated In this contribution, we use the ethodology proposed by Bianchi in [BIANCHI 2000] in order to develop a theoretical cross-layer goodput analysis for IEEE 80211a networks The proposed odel takes into account the effects of backoff schee and non-ideal channel

2 conditions (ie MAC and PHY layer issues) Siulation results, obtained using a joint C ++ IEEE syste level and link level siulator, are used in order to validate the proposed theoretical odel This paper is divided as follows Section 2 presents a brief description of the IEEE DCF ediu MAC protocol The developent of analytical expressions for the net saturation throughput (or goodput) is done at Section 3 Section 4 presents a coparison between nuerical and siulation results, while the final rearks are drawn in Section 5 2 The IEEE DCF RTS/CTS access schee The DCF ipleents the Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) protocol [IEEE ], ie a andatory rando access protocol where physical and virtual carrier sensing functions indicates if the channel is busy or idle The virtual carrier sensing is ipleented using the network allocation vector (NAV) This tier, which is updated by a control field transitted in data and control fraes, sets the aount of tie the channel is reserved to provide uninterrupted atoic transissions The DCF can be used on Infrastructure Base Service Set (IBSS) networks, where access points (APs) and wired backbones are ipleented, and on Independent BSS (or ad hoc) networks, where counication is done at peer-to-peer basis The DCF has the following distributed access polices [IEEE ]: (1) basic positive acknowledgent (ACK); (2) RTS/CTS clearing technique In this paper, we only analyze the second one due to space constraints Fig 1 shows the clearing technique used at atoic RTS/CTS operational ode The station 1 (STA1) only accesses the channel after ipleenting the physical carriersensing and virtual carrier-sensing functions If the channel is idle, then the transission of a RTS control frae can begin iediately, as long as the channel reains idle for a tie longer than the DCF interfrae spacing (DIFS) If the channel is busy, the STA1 ust backoff its transission until the channel becoes idle for the DIFS period After this DIFS period: (1) it starts to treat the channel in units of tie slot; (2) it ipleents a binary exponential backoff period (EBP) to deterine the access tie in tie slots; (3) it keeps checking the channel to verify if it is busy or idle The STA1 decreents the EBP while the channel is idle If the channel is busy, the decreent of backoff interval stops and it only resues after the channel is detected idle for a DIFS period If the channel reains idle when the EBP becoes zero, then the STA1 transits a RTS control frae If the RTS frae transission is successful, the peer station (STA2) sends a CTS control frae to confir the reservation After that, it is transitted a MAC protocol data unit (MPDU) unicast frae If the MPDU transission is successful, then the peer station ust transit an ACK control frae after a short interfrae spacing (SIFS) period The sender STA ust use the extended interfrae spacing (EIFS) to set the tie for new physical channel sensing if either data or control fraes are corrupted or due to the tieout of tier that controls the axiu expected delay It is again used a binary EBP to set the tie slot, but now the CW is doubled at each unsuccessful transission The CW is reset after a successful transission The data frae is dropped after a given nuber of transission attepts 3 Analytical results for the net saturation throughput Fig 2 shows a discrete bi-diensional Markov chain (s(t),b(t)) for the backoff window size assuing the RTS/CTS schee with positive ACK of data, where s(t) is the

3 stochastic process of the backoff stage (0,,) of the STA at tie t and b(t) is the rando process that odels the backoff tie counter for a given STA This odel assues that each packet collides with a constant and independent conditional collision probability p It is also assued a fixed nuber of n STAs operating in saturation conditions, ie each STA has a packet to transit after the copletion of each successful transission Figure 1 The clearing technique used at atoic RTS/CTS schee (1- S rts S cts S p S ack /W , 0 0, 1 0, W , 0 1, 1 { p+(1- [ (1-S rts )+S rts (1-S cts )+ S rts S cts (1-S p ) + S rts S cts S p (1-S ack ) ] }/ W 1 ' 1 1, W 1-1 { p+(1- [ (1-S rts )+S rts (1-S cts )+ S rts S cts (1-S p ) + S rts S cts S p (1-S ack ) ] }/ W 1 1, 0, 1, W -1 { p+(1- [ (1-S rts )+S rts (1-S cts )+ S rts S cts (1-S p ) + S rts S cts S p (1-S ack ) ] }/ W Figure 2 Bi-diensional Markov chain (s(t),b(t)) odel for the backoff window size and a non-ideal channel 31 Packet Transission Probability Using the short notation P{i 1,k 1 /i 0,k o }=P{s(t+1)=i 1,b(t+1)=k 1 s(t)=i o,b(t)=k o }, equations (1) to (4) odel the null one-step transition probabilities of the Markov chain depicted at Fig 2 { i k i, k + 1} = 1 for k ( 0,W 2) and i ( 0,) { 0, k i,0} = ( 1 SrtsSctsSpSack / W0 for k ( 0,W 1) and i ( 0,) P, i (1) P 0 (2)

4 {, k i 1,0 } = { p + (1 [ P i (1 Srts) + Srts(1 Scts) + SrtsScts(1 S + SrtsSctsSp(1 Sack) ]} / Wi k (0,W i -1) and i (1,) (3) {,,0} = { p + (1 [ P k (1 Srts ) + Srts(1 Scts) + SrtsScts(1 S + SrtsSctsSp(1 Sack ) ]} / W k (0,W -1) (4) The window size at backoff stage i is labeled as W i = 2 i W, where i (0,) is the backoff stage and W is the MAC CW size paraeter CW in The axiu window size is denoted as W =2 W 1=CW ax - 1 Eq (1) odels the decreasing of the backoff tier at the beginning at each slot tie of size σ Eq (2) takes into account that a new physical layer convergence procedure (PCLP) protocol data unit (PPDU) starts at backoff stage 0 and that the backoff is uniforly distributed into the range (0, W 0-1) after a successful PPDU transission 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 that the transission of a MPDU (ie a MAC PDU) is successful Eq (3) odels the fact that a new backoff value is uniforly chosen in the range (0,W i ) after an unsuccessful transission at the backoff stage i-1 The capture effect is neglected in such way that the lost of fraes due to collisions is independent of the lost of fraes due to noise and interference Eq (4) odels the fact that the backoff is not increased in subsequent frae transissions once the backoff stage has reached the value The closed-for solution for the stationary distribution for this Markov chain can be obtained as follows For 0 < i <, we have that (1- Srts ) + Srts(1- Scts) + SrtsScts(1- S + b i-1,0 p + ( 1 = bi,0, (5a) SrtsSctsSp(1- Sack ) { p + 1 [ 1- S S S S ]} b, b i-1,0 ( rts cts p ack = i,0 (5b) i [ 1 + S S S S ( p )] b bi,0 rts cts p ack 1 0,0 = (5c) We also have that (1-S ) + S (1-S ) + S S (1-S ) +, (6a) SrtsSctsSp(1-Sack) rts rts cts rts cts p [ b 1,0 + b,0] p+ ( 1 = b, 0 [ b 1,0 + b,0] { p+ ( 1 [ 1 SrtsSctsSpSack } = b, 0, (6b)

5 [ 1+ S S S S ( p 1) ] rts cts p ack b,0 = b0,0, (6c) ( 1 Scts Srts Sp Sack where it is used (5c) in (6b) for =i Due to the Markov chain regularities, for each k (0,W -1), we have that [ p + (1- ( 1- S S S S ) ]( b + b ) ( 1 Srts Scts Sp Sack b j,0 j= 0 W k b = i i,k bi-1,0 [ p + (1- rts rts p ack Wi ( 1- S S S S ) ] rts rts p ack -1,0 Using (5b) and (6b), then (7) can be rewritten as Wi k bi, k bi,0 Wi,0 for i = 0 for 0 < i < (7) for i = =, (8) since (see 5c and 6c) 1 [ 1 + Srts Scts Sp Sack ( p 1) ] bi,0 = i= 0 i= 0 b0,0 = Srts Scts SpSack ( 1 i b0,0 + b,0 (9) We can ipose the following noralization condition: Wi 1 = i= 0 k= 0 i= 0 bi,k = bi,0 = Wi 1 W + i i k Wi 1 2 W + 1 bi,0 = bi,0 k= 0 Wi i= 0 2 i= (10) Using (5c), (6c) and (9), then (10) can be siplified to [ 1+ S S S S ( p 1) ] 1 i i 2 rts cts p ack + b0,0 i= 0 1 1= W + (11) 2 [ + S S S S ( p )] Srts Scts Sp Sack( 1 rts cts p ack ( ) 1 p Srts Scts Sp Sack b0,0= 1+ 2 W Using S=S rts S cts S p S ack, we can show that 21 ( S [ 1+ 2 S ( p 1) ] [ 1+ ( 1+ S] + ( 1 + S 2+ W+ 2 W [ 1+ ( 1+ S] { } Notice that for an ideal channel (ie S rts =S cts = S p = S ack =1), Eq (12) resues to b0,0 2 ( 1 2 (1 ( 1 2 ( W + 1) + pw 1 ( 2 [ ] (12) =, (13) which is in agreeent with Eq (6) of [BIANCHI 2000]

6 Any transission occurs when the backoff tier counter is equal to zero, then the probability that a STA transits in a randoly chosen slot tie is (see 9) b0,0 b0,0 τ = bi,0 = = (14) i= 0 S ( 1 Srts Scts Sp Sack ( 1 When there is no exponential backoff, then using (13) with =0, we have that 2 τ =, (15) W + 1 in according with Eq (8) of [BIANCHI 2000] Each STA transits with probability τ Therefore, the probability that a transitted PPDU encounters a collision in a given slot tie can be stated as n 1 p = 1 (1 τ ), (16) The nonlinear syste represented by (14) and (16) can be solved using nuerical techniques 32 Goodput The net throughput in bits per second (bps) can be stated as the probability that a MAC payload with N pl octets be transitted with success in the average cycle tie T, ie N pl Ps Ptr Srts Scts Sp Sack Gbps = 8 (17) T 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 1 τ ( 1 τ ) 1 n 1 n 1 n τ ( 1 τ ) n τ ( 1 τ ) Ps = = =, (18) P n tr Ptr 1 (1 τ ) where P tr is the probability that there is at least one transission in the considered slot tie Notice that it is assued in (17) and (19) that the lost of fraes due to collisions is independent of the lost of fraes due to noise The average cycle tie is given by T = Bs + B f1 + B f 2 + B f 3 + B f 4 + B f 5 + I, (19) The average busy tie when the transission is successful is given by: [ Bs = Ps Ptr Srts Scts Sp Sack DIFS + Trts ( prts ) + a + SIFS +, (20) Tcts ( pcts ) + a + SIFS + Tp ( pp ) + a + SIFS + Tack ( pack ) + a] where a is the propagation delay T rts (p rts ), T cts (p cts ) and T ack (p ack ) denote the tie necessary to transit the RTS, CTS and ACK control fraes when it is used the PHY ode p rts, p cts and p ack, respectively T p (p p ) is the tie necessary to transit a MPDU payload when it is used the PHY ode p

7 B odels the average aount of tie in which the channel is busy due to f 1, collisions at the transission of RTS control fraes, whereas B f 2, B f 3, B f 4 and odel the average tie that the channel is busy with unsuccessful transissions, B f 5 due to noise and interference, of RTS, CTS, data and ACK fraes, respectively ( 1 P ) [ EIFS + T ( p a] B f 1 = Ptr s rts rts ) + (21) ( 1 S ) [ EIFS + T ( p a] B f 2 = Ptr Ps rts rts rts ) + (22) ( 1 S )[ EIFS + T ( p ) + a + SIFS + T ( p ) ] B f 3 Ptr Ps Srts cts rts rts cts cts + a = (23) ( 1 S ) [ B f 4 = Ptr Ps S rts Scts p EIFS + Trts ( prts ) + a + SIFS + Tcts ( pcts ) + a + SIFS + Tp ( pp ) + a] B f 5 = Ptr Ps Srts Sp SIFS + Tack ( pack ) + a] ( 1 S )[ ack EIFS + Trts ( prts ) + a + SIFS + Trcs ( pcts ) + a + SIFS + Tp ( pp ) + a + where a is the propagation delay, T p is the tie necessary to transit a MAC PDU, DIFS is the DCF interfrae spacing (IFS), SIFS is the short IFS and EIFS is the extended IFS The average tie that a slot tie is idle is given by ( P ) (24) (25) I = 1 tr σ (26) For an ideal channel (ie S rts =S cts = S p = S ack =1), (17) resues 8 N pl Ps Ptr G =, (27) Bs + Bf1 + I in according with (13) of [BIANCHI 2000] 33 Frae Success Probability for 80211a The IEEE 80211a is based on Orthogonal Frequency Division Modulation (OFDM) using a total of 52 subcarriers, of which 48 subcarriers carry actual data and four subcarriers are pilots used to facilitate coherent detection [IEEE 80211a 1999] The OFDM sybol interval, tsybol, is set to 4µs Therefore, the channel sybol rate R s is of 12 Msybols/sec Tab 1 shows the OFDM PHY characteristics, where BpS eans Bytes per Sybol For instance, the PHY ode 1 carries 3 bytes per sybol, ie 6 Mbps* tsybol/80=3 BpS The convolutional encoders use the industry-standard generator polynoials, g 0 =(133) 8 and g 1 =(171) 8, of rate r=1/2 and constraint length K=7 [IEEE 80211a 1999] The transfer function, using the data tabulated in [CONAN 1984], is given by (28)

8 Tab 1 The IEEE 80211a PHY odes Mode Modulation Code Rate R c Data Rate BpS 1 BPSK 1/2 6 Mbps 3 2 BPSK 3/4 9 Mbps 45 3 QPSK 1/2 12 Mbps 6 4 QPSK 3/4 18 Mbps QAM 1/2 24 Mbps QAM 3/4 36 Mbps QAM 2/3 48 Mbps QAM 3/4 54 Mbps T1/ 2( D) = 11D + 38 D + 193D D (28) D D D + The higher code rates of 2/3 and 3/4 are obtained by puncturing the original rate- 1/2 code [IEEE 80211a 1999] The transfer function, using the data tabulated in [Haccoun 1999], for the code rate 2/3 is given by (29), whereas the transfer function for the code rate 3/4 is given by (30) T2/3( D) = D + 16 D + 48 D D D D D D + (29) T3/4 ( D) = 8D + 31D + 160D + 892D D + (30) D D D + Fig 3 shows the PLCP Protocol Data Unit (PPDU) of the IEEE 80211a: (1) the PLCP preable duration, tpclppreable, is equal to 12 µs; (2) the PCLP field duration, tpclp_sig, is equal to 4 µs Both MPDU fraes and RTS, CTS and ACK control fraes are encapsulated in the PPDU as shown at Fig 3 Figure 3 PPDU frae forat of the IEEE 80211a [IEEE 1999b] The RTS and CTS control fraes ust be transitted at one of the rates of the basic service set (BSS) so that they can be decoded by all the STSs in the sae network The andatory BSS basic rate set is {6 Mbps, 12 Mbps, 24 Mbps} The ACK control frae ust be transitted using the BSS basic rate that is less than or equal to the rate of the data frae it is acknowledging As shown at Fig 3, that the SERVICE field has 16 bits and that 6 tail bits are used to flush the convolutional code to the zero state Therefore, the duration of RTS and CTS fraes are given by (31) and (32), respectively The RTS and CTS have l rts= 20 bytes and l cts =14 bytes, respectively [IEEE 80211a 1999]

9 Trts( rts) = tpclppreable+ tpclp_ SIG + ( 16 6) / lrts + + BpS( prts) ( 16 6) 8 tsybol Tcts( cts) = tpclppreable+ tpclp_ SIG + lcts + + /8 tsybol BpS( pcts) The transission period to transit a MPDU with a payload of l octets over the IEEE 80211a using the PHY ode is given by (33) The MPDU header and the cyclic redundant checking (CRC) fields have together a length of 34 bytes [IEEE , pp 52] The ACK transission tie, whose length is of l ack =14 bytes [IEEE , pp 64], is given by (34) assuing the PHY ode ack Tp( ) = tpclppreable+ tpclp_ SIG + ( 16 6) l BpS( p ( 16 6) /8 tsybol Tack ( ack ) = tpclppreable+ tpclp_ SIG + lack + + /8 tsybol BpS( pack ) Assuing that the convolutional forward error correcting code (FEC) is decoded using hard-decision Viterbi decoding, then (35) and (36) odel the probability of incorrectly selecting a path when the Haing distance d is even and odd, repesctivly The used notation ephasizes the dependence of P d with the received signal-tointerference-plus-noise (SINR) per bit γ b, and the PHY ode p [QIAO 2002] The bit error rate (BER) for the PHY ode odulation schee is denoted by ρ (31) (32) (33) (34) 1 d d d/2 d 2 d k d k Pd ( γ b, ) = (1 ) + (1 ) (35) 2 d 2 k= d 2+ 1 k Pd d d k= ( d+ 1) 2 k k d k ( b, ) = (1 ) γ (36) Considering the IEEE 80211a generator polynoials, g 0 =(133) 8 and g 1 =(171) 8, of rate r=1/2 and constrain length K=7 [IEEE , pp16] and using (28), then the union bound on the probability of decoding error is given by (37) Correspondingly, using (29) and (30), then the union bound on the probability of decoding error for the code rates 2/3 and 3/4 are given by (38) and (39), respectively Pe ( γ b, ) < 11 P10( γ b, ) + 38 P12( γ b, ) P14 ( γ b, ) + (37) Pe ( γ b, ) < P6 ( γ b, ) + 16 P7 ( γ b, ) + 48 P8 ( γ b, ) + (38) Pe ( γ b, ) < 8P5 ( γ b, ) + 31P6 ( γ b, ) P7 ( γ b, ) + (39)

10 Postulating that the errors inside of the decoder are interdependent, then Pursley and Taipale have shown that the upper bound for a successful transission of a frae with l octets is given by [PURSLEY 1987] 8 [ 1 P ( γ, )] l S( l, γ b, ) < e b (40) 34 Bit Error Rate (BER) for Uncorrelated Fading Channel It is assued a Rayleigh fading teporally independent at sybol level and independent across of the OFDM carriers Using the uncorrelated channel assuption and considering that the PCLP header with 24 bits is always transitted using PHY ode 1 (see Fig 3) Then, the successful MPDU transission is given by Sp( l, γ b, ) = S(24/8, γ b,1) S(34 + (16 + 6)/8 + N pl, γ b, ), (41) where the MPDU header and the CRC fields have together a length of 34 bytes, the SERVICE field has 16 bits and 6 bits are used to set the convolutional coder to the zero state Correspondingly, the RTS, CTS and ACK control fraes success probabilities are given by (42), (43) and (44), respectively Srts ( l, γ b, ρrts ) = S(24/8, γ b,1) S(20 + (16 + 6) /8, γ b, ρrts ) (42) Scts ( l, γ b, ρcts) = S(24/8, γ b,1) S(14+ (16+ 6)/8, γ b, ρcts) (43) Sack ( l, γ b, ρack) = S(24/8, γ b,1) S(14+ (16+ 6)/8, γ b, ρ ack) (44) Considering a axiu ratio cobining (MRC) receiver atched with the channel diversity and that the sae average power Ω is received at each diversity branch, then the probability distribution function (pdf) of the SINR per bit at the receiver is of gaa kind [HOEFEL 1999], ie L 1 1 p( γ b ) = b b > L Γ( ) γ b γ b L 1 γ b ( γ ) exp if γ 0, (45) where Γ is the gaa function, γ b is the average SINR per bit at the receiver output and L is the nuber of diversity branches The average BER for BPSK and QPSK signaling is given [PROAKIS 2001] Pe = ρ = Q 0 ( Rcγ b ) p( γ b ) dγ b 2, (46) where Q(x) is the copleentary Gaussian cuulative distribution function and R c is the code rate The average BER for M-QAM signaling is given by [Yang 2000]

11 M 1 2log2M Rc γ b Pe = ρ = erfc p M log2 M 2( M 1) 0 M 2 3log2M R erfc c γ b + p b M log2 M 2( M 1) 0 where erfc(z) is the copleentary error function ( γ ) b ( γ ) dγ, b dγ b (47) 4 Model Validation The C ++ IEEE 80211a MAC and PHY layer siulator (ie an integrated syste level and link level siulator) ipleented in this paper has the following ain characteristics: It is assued an ad-hoc network, as such as the DCF MAC protocol is used It is ipleented the MAC state achine that fulfills the RTS/CTS clearing technique (Fig 1) specified at the IEEE anageent inforation base (MIB) The OFDM PHY layer is ipleented assuing perfect synchronis The physical layer signal processing algoriths ipleents the axiu-likelihood hard decision detection for the PHY ode 1 to PHY 8 The convolutional hard-decision decoding is constructed using a sei-analytic approach as follows The average BER is estiated at a frae basis using on-line statistics collected at the deodulator output Then the average BER is used in (40) to estiate the probability of the successful MPDU transission The used odular software design perits that the Viterbi convolutional decoding can be ipleented as a plug-in function This ethodology, besides speeding-up the coputational tie, offers powerful insights on the syste perforance as well as on the fundaental issue of software validation It is assued the following paraeters: slot tie σ=9µs, SIFS=16 µs, DIFS=EIFS=34 µs, CW in =16, CW ax =1023, =6, a=1µs, N pl =1023 octets Fig 4 shows a good agreeent between nuerical and siulation results when the syste is lightly (10 STAs) and heavily (30 STAs) loaded Here, it is assued that all STAs are transitting using the PHY ode 1 Fig 4 also shows the goodput does not change significantly when the nuber of STAs is increased fro 10 to 30 This occurs because the increase of collisions, besides to be restricted to the short lenght RTS control fraes, is counterbalanced by the diinishing of the average idle tie (see 26) when the channel load is increased Fig 5 shows again a good agreeent between nuerical and siulation results for the BSS PHY odes It is noticed, as theoretically expected, that the net effect of increasing the nuber of received antennas on the syste perforance follows the law of decreasing gains Fig 6a copares the goodput as a function of the SINR per bit for a syste without spatial diversity Fig 6a perit to drawn soe interesting rearks on the effects of SINR per bit on the syste perforance First, we can verify that the PHY ode 3 (QPSK with R c =1/2) allows a superior perforance in relation to that one obtained with the PHY ode 1 (BPSK with R c =1/2) since the QPSK signalling has a better spectral efficiency when it is ipleented coherent deodulation Notice that this also explains the better perforance of PHY ode 4 (QPSK with R c =3/4) in relation to the PHY ode

12 2 (BPSK with R c =3/4) signalling schee Second, PHY ode 5 (16QAM with R c =1/2) 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 occurs due to the high coding gain allowed in environents where the Rayleigh ultipath fading is teporally independent at sybol level (see 45, 46 and 47), as postulated in this contribution Third, PHY ode 7 (64QAM with R c =2/3) has a better perforance in relation to the PHY ode 6 (16QAM with R c =3/4) since the higher coding gain overwhel (in the assued channel odel) the greater noise iunity of 16QAM in relation to the 64QAM signalling schee Finally, Fig 6b shows that when the net effect of the fading is less severe due to spatial diversity, then we can deterine (differently of observed at Fig 6a) a range of γ b where the perforance of PHY ode 4 is superior in relation to the perforance obtained with the PHY ode 5 and a region where the perforance of PHY ode 6 superior in relation to the perforance observed with the PHY ode 7 5M Saturation Goodput in bps 4M 3M 2M 1M 0 Flat Rayleigh Channel RTS+CTS+Data+ACK schee PHY Mode 1 (BPSK, 6 Mbps) 10 STAs 30 STAs L=1 L=2 L=3 L=1 L= Average γ per Antenna in db b Figure 4 Analytical (straight lines) and siulation (arks) results for the saturation goodput in bps for the PHY ode 1 as a function of SINR per bit Results paraeterized by the nuber of STAs and received antennas 160M Saturation Goodput in bps 140M 120M 100M 80M 60M 40M 20M 00 Flat Rayleigh Channel RTS+CTS+Data+ACK schee 10 STAs PHY Mode 1 (BPSK, 6 Mbps) L=1 L=2 L=3 PHY Mode 3 (QPSK, 12 Mbps) L=1 L=2 L=3 PHY Mode 5 (16QAM, 24 Mbps) L=1 L=2 L= γ per Antenna in db b Figure 5 Analytical (straight lines) and siulation (arks) results for the saturation goodput in bps of the andatory BSS rate as a function of SINR per bit and the nuber of received antennas

13 Saturation Goodput in bps 240M 220M 200M 180M 160M 140M 120M 100M 80M 60M 40M 20M 00 Flat Rayleigh Channel RTS+CTS+Data+ACK schee 10 STAs; L=1 (no spatial diversity) PHY 1 PHY 2 PHY 3 PHY 4 PHY 5 PHY 6 PHY 7 PHY 8-20M Average γ b per Antenna in db Figure 6a No spatial diversity (L=1) Saturation Goodput in bps 240M 220M 200M 180M 160M 140M 120M 100M 80M 60M 40M 20M 00 PHY 1 PHY 2 PHY 3 PHY 4 PHY 5 PHY 6 PHY 7 PHY 8 Flat Rayleigh Channel RTS+CTS+Data+ACK schee 10 STAs; L=3-20M Average γ b per Antenna in db Figure 6b Spatial diversity with 3 receiving antennas (L=3) Figure 6 Coparison between analytical (straight lines) and siulation (arks) results for the saturation goodput in bps for all IEEE 80211a PHY odes as a function of SINR per bit 5 FINAL REMARKS In this contribution we have derived and validated a joint MAC and PHY crosslayer goodput saturation odel that can be confidentially used to assess the perforance of IEEE 80211a ad hoc networks operating under the RTS/CTS operational ode We have assued a flat fading Rayleigh channel that is uncorrelated at sybol level and independent across of the OFDM carriers In a future work we are going to present the perforance of IEEE 80211a networks

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