Sateite Link Layer Performance Using Two Copy SR-ARQ and Its Impact on TCP Traffic Jing Zhu and Sumit Roy Department of Eectrica Engineering, University of Washington Box 352500, Seatte, WA 98195, USA {zhuj,roy}@ee.washington.edu Abstract. The paper focuses on improving performance of and mobie sateite channes (LMSC) at higher frequencies such as K or EHF band, where shadowing is the primary impediment to reiabe data transmission. Compared with short-term mutipath fading, shadowing is characterized by onger time constants so that intereaving is not desirabe as it introduces unacceptaby arge deays. To combat error bursts, an adaptive two-copy SR-ARQ scheme is proposed that uses a suitabe deay between every retransmission. Cosed-form soutions for metric of interest:mean transmission time, success probabiity, andresidua oss probabiityare derived and vaidated by simuation. An optima choice of the deay is determined and the performance of TCP traffic over such a ink ayer is evaauted by simuation and compared to norma SR-ARQ in terms end-to-end throughput. 1 Introdu ction Currenty, there is a great dea of interest in extending sateite communications to higher bands (K or EHF band)in order to achieve more transmission bandwidth. In [3] it was shown that the primary impediment to the and mobie sateite channe at K or EHF bands is shadowing due to bockage rather than mutipath fading. In such cases, the channe can be represented by a two-state Markovprocessasin[1]. In bad (shadowed)states, the average SNR is too ow to correcty transmit signas even with powerfu forward error correction (FEC) codes whie in good (unshadowed)states, the arge vaue of Rice factor corresponding to the ine-of-sight component guarantees reiabe signa transmission even without much FEC protection. As is we known, intereaving is widey used with FEC to resist fading and improve the reiabiity of a wireess channe with burst errors. However, with increasing average ength of error bursts, the intereaving depth needed may ead to unacceptabe end-to-end deays. Therefore, a mutipe copy (re)transmission scheme was proposed in [2], that inserts a suitabe deay between copies of the transmitted packet. This paper extends the idea to a sateite channe with shadowing by modifying how the number of copies is varied with retransmission number in the interest of stabiity. For the two-copy H.-K. Kahng (Ed.): ICOIN 2003, LNCS 2662, pp. 909 917, 2003. c Springer-Verag Berin Heideberg 2003
910 Jing Zhu and Sumit Roy case, simpe expressions for the metrics of interest (i.e. mean transmission time, transmission success probabiity, and residua oss probabiity)are obtained. Such adaptive transmission schemes [4] have naturay been considered since most wireess sateite channes such as LMSC are time-varying. In such methods, the coding rate, packet ength and retransmission mode parameters etc. can be varied to match the transmitter for current channe conditions. Nevertheess, their performance depends criticay on the efficiency and accuracy of channe state estimation (CSE)at the receiver that is fed back to the transmitter. Obviousy,the ong propagation deay of a sateite ink impies that a variations ess than one round trip time cannot be tracked. However, when average shadowing periods typicay exceed a round-trip time, a ong-term estimate of the average ength of shadowing periods may be used to determine the optima deay of our proposa. The paper is organized as foows. In the next section, expressions for success probabiity for each transmission, mean transmission time, and residua oss probabiity are derived for deayed two-copy (DTC)SR-ARQ. Section 3 contains numerica resuts to quantify the improvements of the proposa. The impact of this improved LL design on end-to-end TCP throughput is assessed by comparing with norma SR-ARQ as we under the assumption of the same aowabe copy number. Finay, we concude the paper in Section 4. 2 Deayed Two-Copy (DTC) SR-ARQ The protoco empoys the basic seective repeat (SR-ARQ)strategy, except that two identica copies of a packet with a deay D is sent at each attempt (note that an attempt consists of transmissions or retransmissions of the packets). Ony when both copies in an attempt are ost, a negative acknowedgment is produced and retransmission occurs. Compared with a norma 1-copy scheme, theequivaentcoderateisthus0.5. The parameters used in the subsequent anaysis are as foows: X: Good-state time share parameter; Peg: Packet error rate in good states; Peb: Packet error rate in bad states; m: The Mean ength of bad states; RT T : Round trip time of sateite channe; Bw: Bandwidth of a sateite channe. The usua aternating two-state Markov mode is assumed to represent the channe state evoution in time; the duration of a bad or shadowed state (i.e. the error burst ength)is exponentiay distributed with mean m. In the bad or shadowed state, it is reasonabe to assume Peb 1, impying that no successfu transmission is possibe during shadowing. Further, Peg << Peb and for anaytica purposes, may be assumed equa to zero, i.e. a packet transmissions during
Sateite Link Layer Performance Using Two Copy SR-ARQ 911 good or un-shadowed state are successfuy received. This eads to the important simpification that the sequence of packet success and faiures is a Markov process 1. First we consider transmission of any two successive packets with a genera deay (d)in between. We define an attempt to impy transmission of two copies (of the same packet)as per our scheme. We now identify two important situations: (i)the success/faiure of the second copy in an attempt is reated to that of the first copy in the same attempt; (ii)the success/faiure of the first copy in current attempt is reated to success/faiure of the second copy in the previous attempt. Hence there are two reevant vaues of d for consideration - D and RT T. Since the packet error rate is negigibe in good states, packet osses take pace in ony bad states. If the previous copy is ost, the probabiity of correcty receiving the current one can be written as: P {S F } = P {B E,G}P{S G } = P {B E }P {G B E }P {S G }, (1) where the notations represent the foowing events: S: Success on the current copy; F : Faiure on the previous copy; B E : The bad state during transmission of the previous copy is competed before transmission of the current copy; G: The current copy is transmitted in a good state; S G : Success of the current copy in a good state. Since the duration of bad state is exponentiay distributed with the mean of m and the inter-duration between two copies is d, wehave P {B E } =1 e d m. (2) and ceary, P {S G } =1 Peg. (3) An exact expression for P {G B E } is difficut and therefore an intuitive approximation is given next. We know that P {G B E } is a function of d. Let s consider two extreme cases: For d 0, i.e., two copies are sent next to each other with no deay. Since the end of the bad state for the previous transmission is foowed by a good state, the current copy wi be sent in the good state with probabiity 1, eading to P {G B E } 1. (Here we ignore the event that the good state ends before one LL packet duration because the good state mean duration is significanty onger than a LL packet duration). For d, the correation between the channe states for the two copies vanishes, eading to P {G B E } P{G}, wherep {G} = X. 1 In genera, the sequence of packet success and faiures is a Hidden Markov process, and not stricty a Markov process.
P (N) =(1 P Sr ) N 1 (1 P St )(10) 912 Jing Zhu and Sumit Roy We define the above two extreme cases as two mutuay excusive events: the channe state for the current copy is competey correated (CC) or competey un-correated (CU) to that for the previous { one. The probabiity of CC is given by the correation function of e d m 1,d=0 (= ), and the probabiity of CU 0, d= is 1 e d m. The desired resut for P {G B E } is given by the statistica average of the above, i.e., P {G B E } 1 e d m + X (1 e d m ). (4) In concusion, the probabiity of correcty receiving the current copy given that the previous is ost is expressed as P Se (d) =(1 e d m )(e d m + X(1 e d m ))(1 Peg), d= {D, RTT}. (5) We next consider the success probabiity for transmission and retransmission, denoted by P St and P Sr respectivey. There are foowing events invoved: S 1 : Success on the first copy; F 1 : Faiure on the first copy; S 2 : Success on the second copy; F 2 : Faiure on the second copy; F o : Faiure on a previous attempts. Obviousy, P {S 2 F 1 } = P Se (D), (6) and the state for the current copy ony depends on that for the previous copy, eading to P {S 1 F o } = P Se (RT T )(7) The first copy of the transmission has probabiity of X(1 Peg)of being correcty received. Therefore, Then P St = P {S 1 } + P {F 1 }P {S 2 F 1 } = X(1 Peg)+(1 X(1 Peg))P Se (D). (8) P Sr = P {S 1 F o } + P {F 1 F o }P {S 2 F 1,F o } = P {S 1 F o } + P {F 1 F o }P {S 2 F 1 } = P Se (RT T )+(1 P Se (RT T ))P Se (D). (9) If the maximum number of attempts aowed is N, the packet oss probabiity P (N) after N attempts is
Sateite Link Layer Performance Using Two Copy SR-ARQ 913 Denote by T the time from the first transmission to receipt of the acknowedgement. We have the foowing resuts of probabiity distribution function of T : 1)Correcty receiving the second copy: { (1 X(1 Peg))PSe (D) i =1 P[T = i(rt T + D) ]= (1 P St )(1 P Sr ) i 2 (1 P Se (RT T ))P Se (D) i 2 (11) 2)Correcty receiving the first copy: P[T = irt T +(i 1)D] = { X(1 Peg) i =1 (1 P St )(1 P Sr ) i 2 P Se (RT T ) i 2 (12) Thus, the mean vaue of T is given beow 1 N E[T ]= {(irt T +(i 1)D)P[T = irt T +(i 1)D]+ (1 P (N) ) i=1 i(rt T + D)P[T = i(rt T + D)]} (13) As N, P (N) 0 and we get a cosed-form soution for (13)as foows: im N E[T ]= (1 P St) [RT T + D + RTTP Sr + D(1 P Se (RT T ))P Se (D)] P Sr +X(1 Peg)RT T +(1 X(1 Peg))P Se (D)(RT T + D)(14) The anaytica expressions of Eq.10 and Eq.14 are most usefu as they provide performance estimate for appications with specia QoS requirements. Of course, the mean error burst ength must be obtained a-priori in practice using a suitabe ong-term channe estimator. In the foowing, we wi assume that m is known. 3 Nu merica Resu ts In a simuations and anaysis reported here, a ink ayer packet duration is chosen as the unit of time. Wireess channe bandwidth (Bw)is fixed at 1Mbps. 3.1 Performance Comparison of DTC-SR-ARQ to Intereaving In this section, we consider an error burst with fixed ength m (packets)foowed by a sufficienty ong error-free period. The metric of interest is additiona deay, defined as the extra deay introduced by the method empoyed to resist fading (DTC-SR-ARQ or Intereaving). For DTC-SR-ARQ, the minimum deay inserted between two copies of a packet for a successfu transmission is m 1. The additiona deay of the first copy is zero whie that of the second one is m. Since either of them are equay ikey to be transmitted during an error burst, the average additiona deay introduced by DTC-SR-ARQ is m 2.
914 Jing Zhu and Sumit Roy Error Burst... Fading Channe... Intereaving Depth = mn/ packets symbos n symbos a) Intereaving with FEC code (n, k, ) #3 #2 #1 #3 #2 #1 b) Deayed Two Copy SR-ARQ D = m-1 packets Error Correct Fig. 1. Deay Comparison of DTC-SR-ARQ to Intereaving in terms of Additiona For intereaving with RS(n, k, ), the minimum intereaving ength for error free transmission is n m (packets), where n is the ength of codeword, k is the number of information symbos in a codeword, and is the maximum number of correctabe symbos in a codeword. De-intereaving starts at receiver ony after receiving a n m packets, thus the additiona deay is n m for the first packet, and zero for the ast one. The consequent average additiona deay introduced by intereaving is n 2m.Fig.2 demonstrates that the additiona deay as a function of m is shorter for DTC-SR-ARQ than intereaving, with difference increasing for onger error bursts. 3.2 Deay Optimization of DTC-SR-ARQ Fig.3 shows the success probabiity of the first transmission as a function of the deay D - our anaytica resuts match simuations quite we. From Fig.3, we Average Additiona Deay 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 RS(255, 102, 76) with Intereaving (R=0.4) Deayed Two Copy (R=0.5) 10 20 30 40 50 60 70 80 90 100 m Fig. 2. Deay Comparison of Intereaving and DTC-SR-ARQ
Sateite Link Layer Performance Using Two Copy SR-ARQ 915 Transmission Success Probabiity (P St ) 0.90 0.88 0.85 0.80 0.75 0.70 m=10 m=20 m=40 Anaysis Simuation X=0.7, Peg=0.01, Peb=1, RTT=100 0 20 40 60 80 Deay (D) Fig. 3. Success Probabiity of Transmission aso see that onger error bursts need onger deay to achieve the same success probabiity. Fixing the maximum number of attempts at 3, we study the residua oss probabiity after retransmission in Fig.4a); the residua oss probabiity is dramaticay reduced by increasing deay. Fig.4b)investigates the mean transmission time T and indicates that there exists an optima vaue of deay yieding the minimum mean transmission time. The optima deay for achieving the minimum average transmission time, using the first-order necessary conditions, is given by dt dd = 0. However, it is tedious to expicity sove. Figs.1-3 show that D = 2m is a good pragmatic choice considering P Ts, P (N), andt. Therefore, in our foowing simuation on TCP performance, we wi use D =2m. Fig.5 studies the ink ayer performance of DTC-SR-ARQ with D =2m in terms of residua packet oss probabiity and mean transmission time. Anaytica resuts indicate that onger average burst error ength eads to higher residua packet oss probabiity and onger mean transmission time. We aso compare these resuts with norma SR-ARQ for the same maximum copy number (MCN) Packet Loss Probabiity (P (N) ) 0.1 0.01 1E-3 m=10 m=40 m=20 Anaysis Simuation X=0.7, Peg=0.01, Peb=1, RTT=100, N=3 0 20 40 60 80 100 Deay (D) Mean Transmission Time E(T) 150 145 140 135 130 125 120 115 m=10 m=20 m=40 Anaysis Simuation X=0.7, Peg=0.01, Peb=1, RTT=100, N=3 0 20 40 60 80 100 Deay (D) a) Fig. 4. Packet Loss Probabiity a)and Mean Deay b)after N attempts (N = 3) b)
916 Jing Zhu and Sumit Roy Residua Packet Loss Probabiity 0.1 0.01 1E-3 MCN = 2 MCN=4 MCN=6 DTC-SR-ARQ (D=2m) Norma SR-ARQ MCN: Maximum Copy Number 0 10 20 30 40 50 a) Residua Packet Loss Probabiity After N Attempts m Mean Transmission Time E(T) 150 140 130 120 110 DTC-SR-ARQ (D=2m) Norma SR-ARQ 0 10 20 30 40 50 m b) Mean Transmission Time (N= ) Fig. 5. Performance for D =2m (RT T = 100,X =0.7,Peg =0.01) so that the maximum transmission number is MCN (say 4)for SR-ARQ and MCN/2 (say 2)for DTC-SR-ARQ. It is seen that by using DTC-SR-ARQ the mean transmission time is significanty reduced at the expense of a sma increase in residua packet oss probabiity. Furthermore, shorter the average ength of error bursts, the more the improvement in mean transmission time. In addition, by using DTC-SR-ARQ instead of norma SR-ARQ, we can reduce maximum (RT T +D) transmission time from MCN RT T to MCN 2.Ifm<<RTT, we have RT T >> D because of D =2m, eading to amost 50 % reduction in maximum transmission time. 3.3 On TCP Performance In this section, we study the performance of TCP over two-copy deayed SR- ARQ. The deay is bounded by haf the RTT and set as D = min(2m, RT T 2 ). Assuming a fixed maximum number of retransmission attempts(say 8), the maximum transmission time for norma is 7 and 3 RTTs respectivey for reguar SR- ARQ and our two-copy deayed SR-ARQ. Fig.6 shows that the TCP end-to-end throughput is improved by using our scheme, especiay when the average error burst ength is short. When the error burst ength increases, the performance improvement using our proposa is reduced. In other words, the two-copy deayed SR-ARQ is more suitabe for the fast shadow fading channe with much shorter error burst ength compared to the round trip time. 4 Concusion In this paper, we proposed an optimized two-copy deayed SR-ARQ scheme for the shadowed sateite channe in the K or EHF bands. Shadowing eads to onger fade durations compared with mutipath fading; consequenty mutipe copy transmission with a deay was suggested in pace of intereaving to combat burst errors. Anaytica resuts showed that success probabiity of each transmission is significanty improved, and mean transmission time is reduced as we.
Sateite Link Layer Performance Using Two Copy SR-ARQ 917 TCP End-to-End Throughput 0.35 0.30 0.25 0.20 0.15 0.10 Norma SR-ARQ Two-Copy Deayed SR-ARQ TCP Packet Length=500 Bytes, LL Packet Length =50 Bytes, RTT=400, Peg=0.01, Peb=1, X=0.7, Bw=1Mbps. 20 40 60 80 100 120 Average Length of Error Burst Fig. 6. TCP End-to-End Throughput Comparison (Buffer Size=20000 bytes) Simuations performed to compare our scheme with norma SR-ARQ in terms of TCP end-to-end throughput indicate that our proposa achieves noticeabe performance improvement especiay for the fast shadowing channes with error burst onger than a ink ayer packet but shorter than one round trip time. References [1] E. Lutz, D. Cygen, M. Dippod, F. Doainsky, and W. Papke, The Land Mobie Sateite Communication Channe - Recording, Statistics, and Channe Mode, IEEE Trans. on Vehicuar Tech., Vo. 40, No. 2, May 1991, pp.375-386. 909 [2] J. Zhu, Z. Niu, Y. Wu, A deayed mutipe copy retransmission scheme for data communication in wireess networks,proc. Ninth IEEE Internationa Conference on Networks, 2001 pp. 310-315. 909 [3] J. B. Schodorf, EHF Sateite Communications on The Move: Baseband Considerations, MIT Lincon Lab Technica Report 1055, Feb. 2000. 909 [4] A. Annamaai, V. K. Bhargava, Anaysis and Optimization of Adaptive Muticopy Transmission ARQ Protocos for Time-Varying Channes, IEEE Trans. on Commu., vo. 46, no. 10, pp. 1356-1368 910