On the Performance of TCP over Free-Space Optical Atmospheric Turbulence Channels

Transcription

1 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO. 1, JANUARY 7 1 On the Perormance o TCP over Free-Space Optical Atmospheric Turbulence Channels Vuong V. Mai, Truong C. Thang, and Anh T. Pham Abstract This paper presents an analytical study on the perormance o transmission control protocol (TCP) over ree-space optical (FSO) turbulence channel when the automatic-repeat request, selective repeat (ARQ-SR) scheme is used by the link layer. Dierent TCP versions, including Tahoe, Reno and selective acknowledgement (SACK), are considered. In the analysis o TCP throughput, a threedimensional (3-D) Markov model is used. In addition, to analyze the joint eect o ARQ-SR and FSO turbulence channel in terms o both TCP throughput and the energy consumption, a newly deined energy-throughput eiciency parameter is analytically derived. In the numerical results, we discuss cross-layer designing strategies or the selection o FSO system parameters and ARQ-SR scheme in order to maximize the TCP throughput, and to achieve the tradeo between the energy consumption and the throughput in various conditions o the FSO turbulence channel. Index Terms FSO Communications; Atmospheric Turbulence; TCP; ARQ-SR. I. INTRODUCTION Free-space optical (FSO) communications is a transmission technology in which the optical signal is transmitted through the atmosphere. FSO has been considered as an alternative solution or a wide range o applications thanks to its advantages such as license-ree, high data rate, quick and easy deployment, and cost-eectiveness [1]. In FSO systems, one o major issues is the high error rate due to the impact o the atmospheric turbulence []. Over the past decade or so, there have been many studies ocusing on the eect o atmospheric turbulence on the perormance o physical layer in FSO systems [3] [7]. In the transport layer, to oer a reliable transmission, the popular Transmission Control Protocol (TCP) is employed to carried many internet applications, including FTP, TELNET, , etc. However, it has been proven that the TCP perormance is severely degraded when it is operating over high error-rate environments, including both radio and optical wireless (e.g. FSO) communications [1] [13]. Thereore, such environments pose ormidable challenges to maintain the TCP reliability. In radio wireless communications, many proposals to overcome the degradation o TCP perormance have been reported [8] [1]. These proposals can be categorized into two groups. The irst one includes methods to modiy the TCP congestion operation to adapt to the multiple segment loss in wireless transmission [8]. In another group, the TCP perormance is enhanced by employing new schemes in the link layer. For example, in [9], the explicit loss notiication (ELN) scheme has been proposed to provide TCP with the ability to classiy wireless link losses and congestion losses. The TCP-sender thereore can react appropriately with each case o losses. In addition, error recovery schemes in the link The authors are with the Computer Communications Lab., The University o Aizu, Aizuwakamatsu, Fukushima, Japan ( pham@u-aizu.ac.jp). layer, such as the automatic-repeat request (ARQ)-based retransmission o the error data [1] [11] and the orward error correction (FEC) [1], have also been introduced. It is seen in these studies that, the interaction between the designs o link layer and wireless physical layer plays an importance role to improve the TCP perormance at the transport layer. Regarding the FSO communications, there have been recently several studies ocusing on the perormance o transport and link layers over the FSO turbulence channels [13] [16]. In [13], Lee et al. ocused solely on the transport layer and analyzed the TCP throughput over the clear atmospheric turbulence channels. It is seen that the TCP throughput strongly depends upon the atmospheric turbulence and the channel distance. In [14] [16], the outage probability o FSO systems when the ARQ and FEC schemes are used in the link layer has been studied taking into account the FSO lognormal turbulence channels. In these studies, the impact o FSO channel conditions on the perormance o either link or transport layer has been separately studied. Similar to the radio wireless communications, the understanding o the combined impact o both link and physical layers on the perormance o TCP would result in more eicient cross-layer optimization. This is especially critical to the design o the FSO networks due to the harsh condition o atmospheric channels. In this paper, we thereore develop an analytical ramework or cross-layer perormance analysis o transport layer perormance considering the eects rom both FSO channel and link layer design. In our study, dierent TCP versions are considered and a three-dimensional (3-D) Markov chain model that includes the exponential back-o phase is used or modeling the TCP operation. It is important to include the exponential back-o phase as the probability o this event is considerably high in FSO link due to the burst loss caused by the atmospheric turbulence. In the link layer, we also employ the automatic-repeat request, selective repeat (ARQ-SR) scheme thanks to its ability to oer both loss-recovery eiciency and simplicity [14] [16]. In the physical layer, the sub-carrier binary phase-shit keying (SC-BPSK) system, as described in [7], is employed and both FSO log-normal and gamma-gamma turbulence channels are considered or the case o weak-to-moderate and strong turbulences, respectively. In addition, we deine a new parameter, the joint throughput-energy eiciency, which is the the ratio between the TCP throughput and the average energy or transmitting an unit data o TCP. Using this parameter, we can optimize FSO system parameters or the trade-o between the energy consumption and the TCP throughput in various contexts o ARQ-SR and FSO turbulence channels. The remainder o the paper is organized as ollows. The system descriptions, including the network model, FSO channel model and ARQ-SR scheme, are detailed in Section II. In Section III, TCP segment-loss probability and end-to-

2 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO. 1, JANUARY 7 where σs is the log intensity variance that depends on the channel characteristics as given by [5] [ σs.49σr = exp ( ) 7/ d +.56σ 1/5 R ].51σR + ( ) 5/6 1. () 1 +.9d +.6d σ 1/5 R Fig. 1. Network scenario with a TCP connection over FSO link. Here, d = kd /4L, k = π/λ is the optical wave number, L is the channel distance, and D is the receiver aperture diameter. σ R is the Rytov variance, and in case o plane wave propagation, it is given by σ R = 1.3C nk 7/6 L 11/6, (3) end transmission delay are derived considering the impact o link and physical layers. The TPC Markov chain model is presented in Section IV. The TCP perormance analysis and numerical results are given in Section V and VI, respectively. Finally, Section VII concludes the paper. A. Network Model II. SYSTEM DESCRIPTIONS Figure 1 illustrates the network scenario with an endto-end TCP connection between a source (server) and a destination (client) over a FSO link and wired networks. At the physical layer o the FSO link the optical signal is transmitted over ree space under the impact o atmospheric turbulence. We apply SC-BPSK as modulation scheme or the physical layer transmission. In addition, the log-normal and gamma-gamma models are assumed or the weak and strong atmospheric turbulence conditions, respectively. In the data link layer each TCP segment o size L T CP is divided into N smaller data units, i.e. rames, beore transmitting over the FSO link. Under the impact o atmospheric turbulence, the rame error on FSO-link may happen requently. Thus, the purpose o ARQ-SR is to retransmit the corrupted rames. In the transport layer, we employ one o TCP versions such as TCP-Reno, TCP-Tahoe and TCP- SACK; we assume that the reader is amiliar with those TCP versions and thus neglect the description o TCP operation. Details o TCP operation can be ound in [18]. B. FSO Channel Models FSO channels, under the inluence by the atmosphereinduced turbulence, can be modeled as ading channel. In case o weak turbulence, it is generally accepted that the inluence o turbulence is modeled as a random process with log-normal distribution whose the probability density unction (p.d.) is given as ( 1 ln x + σ X(x) = [ exp s / ) ], (1) πσsx σ s where Cn is the altitude-dependent index o the reractive structure parameter determining the turbulence strength. Typically Cn varies rom 1 17 to 1 13 accordingly to the strength o atmospheric turbulence. When the atmospheric turbulence becomes stronger (the strength is higher than 1 14 ), it can be characterized by a stationary random process with gamma-gamma distribution whose p.d. is described as X(x) = (αβ)(α+β)/ x (α+β)/ 1 K α β ( ) αβx, (4) Γ(α)Γ(β) where Γ(.) is the gamma unction, and K α β (.) is the modiied Bessel unction o the second kind and order α β. α and β are the p.d. parameters describing the turbulence experienced by waves, and in the case o zero-inner scale they are given by [3] 1 α = exp.49σr ( ) 7/6 1, β = exp ( σ 1/5 R.51σ R σ 1/5 R ) 5/ (5) Here, both σ R and d are also deined as in case o the lognormal channel mentioned above. C. ARQ-SR Scheme Basically, we can explain the operation o ARQ-SR as the activity o re-transmission o the corrupted rames. The maximum number o re-transmissions is determined by parameter M. I ater M attempts o re-transmission, and the rame does not get through the FSO link, ARQ- SR gives up and the corresponding TCP segment is lost. In this Section, we analyze the perormance o TCP taking into account the combined eect o the FSO link and ARQ-SR scheme. In particular, the TCP segment-loss probability and the average end-to-end transmission delay, which are two key TCP perormance indicators, will be analytically derived. III. TCP SEGMENT LOSS AND TRANSMISSION DELAY A. TCP Segment-Loss Probability Let P F SO and P wire denote the segment-loss probabilities in the FSO link and wired network, respectively, the probability o having exactly i losses out o w segments, P w(i), can

3 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO. 1, JANUARY 7 3 be expressed as ( ) w P w(i) = [1 (1 P F SO)(1 P wire)] i (6) i [(1 P F SO)(1 P wire)] w 1. The TCP segment-loss probability on the FSO link under ARQ-SR scheme can be written as ( ) P F SO = 1 N, (7) in which P is the rame-error probability on the FSO link, and it can be given by P = 1 (1 P e) L, (8) where L = [L T CP /N ] is the rame length and P e is biterror probability. In FSO systems employing SC-BPSK, P e is given as [7] ( ) P e = Q SNR x X(x)dx, (9) where Q(.) is the Gaussian Q-unction with Q(y) = 1 π y exp( y )dy, (1) and SNR is the signal-to-noise ratio, which can be expressed as SNR = ( mrpsa 4σ N ), (11) where P s is the peak transmitted power o the laser beam, m is the modulation index, R is the responsivity o the photodetector at the receiver, σn is the receiver noise variance and a = D (φl) exp( βl) is channel attenuation, in which D, L, φ and β are the receiver aperture diameter, the channel distance, the angle o divergence in radian, and the atmospheric extinction coeicient, respectively. When the turbulence is modeled by log-normal channel, the system BER can be expressed as ( ) P e = Q SNR x [ 1 exp (ln x + ] σ s/) dx. (1) πσsx σs Making the change o variable y = (ln x+σ s /) σs P e = 1 π we have [ ] Q SNR exp( σsy σs/) exp( y )dy. (13) Using the approximation g(y) exp( y )dy N i= N;i w ig(y i), (14) where w i and y i, in which i = ( N, N +1,..., 1,,..., N), are the weight actors and the zeros o the Hermite polynomial, respectively, we can obtain a tractable expression o P e, that is P e 1 π N i= N;i [ ] w iq SNR exp( σsy i σs/). (15) For gamma-gamma channels the BER expression is given by P e = ( ) Q SNR x (αβ)(α+β)/ x (α+β)/ 1 K α β ( ) αβx dx. (16) Γ(α)Γ(β) This integral can be solved by use o a series expansion or modiied Bessel unction [6], K v(y), with K v(y) = π sin(πv)) (y/) p v [ Γ(p v + 1)p! p= (y/)p+v ], v / Z, y <. (17) Γ(p + v + 1)p! Based on the derivation in [4], we can substitute Eq. (17) into Eq. (16) in order to obtain the close orm o P e as ollows: P e = A(α, β) [a p(α, β)b( 1, p + β + 1 )( SNR p+β ) p= a p(β, α)b( 1, p + α + 1 )( SNR p+α ) ], (18) where B(x, y) = a p(x, y) are given by Γ(x)Γ(y) Γ(x)+Γ(y) A(α, β) = a p(x, y) = is the Beta unction. A(α, β) and 1 4Γ(α)Γ(β)sin[(α β)π], (19) (xy)p+y Γ( p+y ) Γ(p x + y + 1)p!. () B. Average TCP End-to-End Transmission Delay The average end-to-end transmission delay or the average round-trip time, E[RT T ], can be deined as the average o time period rom the time when TCP source transmits a segment to the time when the corresponding ACK comes back to the source. It is derived as ollows: E[RT T ] = T wire + (L /R + T CRC)(M + 1)N, (1) where T wire is the one way transmission time in the wired part. R is the transmission rate o FSO link. T CRC is the error detection time that data-link layer spends to check the CRC ield and recognize the corrupted rame. L /R is the time needed or the transmission o one rame. M is the average number o re-transmissions or one rame, which depends on the operation ARQ-SR and the rame loss probability on FSO link and is determined as M M = m P m (1 P ) = P (1 P ) m= ( ) = P (1 P ) 1 P M+1 P 1 P = P (1 P ) = P 1 P M m=1 mp m 1 (M + 1)P M (1 P ) + ( ) (1 P ) M+1 (M + 1)P. ()

4 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO. 1, JANUARY 7 4 Fig.. Markov chain model or W max = 8 and the number o increasing timeouts is limited by 6. IV. TCP OPERATION MODEL In this section, we present the 3-D Markov chain model, which includes the exponential back-o phase, to analytically study the perormance o TCP over FSO link with ARQ-SR. It is necessary to note that the exponential backo phase was omitted in [13]. In FSO link, it is necessary to include the exponential back-o phase in the TCP analysis. The reason is that the temporal correlation time o the atmospheric turbulence process is on the order o several milliseconds, burst error oten occurs in the FSO link. In addition, in order to study the perormance o dierent TCP versions, we irst create the Markov chain model or TCP- Reno and then expand it or TCP-Tahoe and TCP-SACK. A. 3-D Markov Chain Structure The behavior o the TCP-Reno can be modeled as a 3-D Markov chain as shown in Fig.. In this igure, the three axes (i, j, k) represents the congestion window size, the value o slow-start threshold and the number o increasing timeouts in the exponential back-o phase, respectively. Here we assume that the maximum window size W max = 8, the number o increasing timeouts is limited by 6. Furthermore, the timeout increasing actor o is selected (i.e. we have the binary exponential back-o), and thereore the equivalent maximum timeout duration is 6 T. In the igure, the TCP-Reno operation can be separated into our sections according to the our operating phases: slow-start, congestion avoidance, timeout, and exponential back-o. Initially, the congestion window is set to one segment and in slow-start phase (Ss), i there is no loss event, the congestion window is doubled ater each RTT. Its growth continues until it reaches the current slow-start threshold (W t); then TCP-Reno changes into the congestion avoidance phase (Ca). In Ca, i there is no loss occurring, the window size will increase by one segment per RTT. This increase in window size continues until either the congestion window reaches the maximum window size (W max), or there is a loss event. I the loss event is a triple-duplicate ACK, TCP-Reno will reduce the congestion window size to a hal, and continues staying in the Ca phase. I a timeout occurs, TCP-Reno will all into time-out phase (T o) and set the slow-start threshold to a hal o the current congestion window size. TCP will wait or a timeout duration, T, beore trying to transmit a segment. I this segment is lost again, TCP will double the timeout period. This doubling is known as the exponential back-o phase (Bo). Bo continues up to a maximum timeout value o 6 T beore exiting and coming back to T o. Finally, the general state space E o the Markov chain can be expressed as E = Bo T o Ss Ca where Bo = {(1, j, k) j [W max/], 1 k 6}, T o = {(1, j, ) j [W max/]}, Ss = {(i, j, ) i < j [W max/]}, Ca = {(i, j, ) j < i W max, j [W max/]}. (3) B. State-Transition Probabilities In the Markov chain operation, ater every transmission period, there is a state transition. This transition depends on the events occurring in the network. In TCP-Reno, there are two kinds o loss events deined as timeout (T.O) and threeduplicate ACKs (T.D). We denote the probability o T.O and T.D at congestion window sizes w are P T.O(w) and P T.D(w), respectively. It is noted that a state transition also depends on the phase where the state belongs to. For the Bo and T o phases, because the congestion window is ixed by one, the loss events are always expressed as T.O with congestion window size w = 1. In addition, at the last state in Bo phase, when the timeout duration reaches the maximum value (i.e. 6 T ), the state transition deinitely

5 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO. 1, JANUARY 7 5 equals one because Bo will be back to T o whether or not a loss event occurs. P (1,j,k) (1,j,k+1) = P T.O(1), P (1,j,k) (1,j,) = 1 P T.O(1), P (1,j,6) (1,j,) = 1, P (1,j,) (1,j,1) = P T.O(1), P (1,j,) (,j,) = 1 P T.O(1). (4) In the Ss and Co phases, there are three cases that can happen at a state: a loss is detected as T.O (P T.O) or T.D (P T.D), and no loss (1 P T.O P T.D). It is also denoted that, when the congestion window size reaches the maximum value, W max, it will stay there i no loss happens. Consequently, the transition matrix in the Ss phase can be expressed as P (i,j) (1,max([i/],)) = P T.O(i), P (i,j) (max([i/],),max([i/],)) = P T.D(i), P (i,j) (i,j) = 1 P T.D(i) P T.O(i). (5) Similarly, the transition matrix in the Co phase can be given by P (i,j) (1,max([i/],)) = P T.O(i), P (i,j) (max([i/],),max([i/],)) = P T.D(i), P (i,j) (i+1,j) = 1 P T.D(i) P T.O(i), P (Wmax,[ Wmax ]) (W max,[ Wmax ]) = 1 PT.D(Wmax) P T.O(W max). (6) From Eqs. (4) (6), the complete transition matrix o the Markov chain cam be obtained i P T.O(w) and P T.D(w) are known. As master o act, loss-event detection o T.O or T.D is based on the number o losses occurring at a given congestion window size. Based on the study in [18], P T.O(w) and P T.D(w) can be approximately calculated as unctions o the probability o i losses out o a congestion window size o w (e.g., P w(i) in Eq. (6)). P Re T.O = P Re T.O = w i=3 w i= P w(i); P Re T.D = P w(1) + P w(), w 1, P w(i); P Re T.D = P w(1), 4 w < 1, P Re T.O =1 P w(); P Re T.D =, w < 4. (7) Finally, our model is expanded or TCP-SACK and TCP- Tahoe. The detailed operation o these TCP versions can be ound in [18] []. The main dierence between TCP- SACK and Reno is that selective retransmissions are used by TCP-SACK when multiple segments are lost within a RTT. While in TCP-Tahoe, loss events are observed by timeout or all cases o loss. Our Markov chain thereore can be easily expanded or TCP-SACK and Tahoe by modiying transition probabilities. For example, or TCP-Tahoe we will set PT.D T a and PT.O T a by zero and (PT.O Re +PT.D), Re respectively. Meanwhile, or TCP-SACK a closed orm expression o transition probabilities has been derived in [] or w 4 as ollows w 3 PT.O SA = P w(i)(1 (1 P 1(1)) i ) + i=1 w 3 PT.D SA = P w(i)(1 P 1(1)) i + i=1 w i=w w i=w P w(i), P w(i), (8) in case o w < 4, transition probabilities o TCP-SACK and TCP-Reno are the same. V. TCP PERFORMANCE In the Markov chain model, we denote N as the total number o states (e.g. N = 7 in Fig. ). Let P = [p 1 p... p N ] be the matrix o steady-state probabilities, where p i is the probability o the i-th state in the equilibrium. Generally, ollowing Markov chain theory, we have { P = P Q N i=1 pi = 1, (9) where Q = [q ij] N N is the transition matrix o the Markov chain with an element q ij being the transition probability rom the state i to the state j. In our analysis, the transition matrix has been obtained in Section IV. We can transorm Eq. (9) into a basic set o linear equations ormed as: Ax = b and then solve it by using standard Gaussian elimination. Here, x = [p 1 p... p N ] T, b = [... 1] T and A = [a ij] N N where a ij is given as a ii = q ii 1, 1 i N, a ij = q ij, 1 i N 1, 1 j N and i j, (3) a Nj = 1, 1 j N. A. TCP Throughput Let W = [w 1, w,..., w N ] and T = [t 1, t,..., t N ] be the matrices o congestion window sizes and time durations that the TCP spends in N states, respectively. Elements o the irst vector are values o the irst dimension (i) o Markov chain that we mentioned in Eq. (3). Elements o T can be obtained rom the average end-to-end transmission delay (e.g., E[RT T ] in Eq. (1)) as ollows. { tn = E[RT T ], n (T o, Ss, Ca), t n = k (31) T, n Bo, 1 k 6, where T is the minimum value o timeout, and generally T = 5 E[RT T ] is chosen [19]. According to the Little s law, the TCP throughput, which is the ratio between the average congestion window size and the average value o the window holding time, can be given by B. Joint Throughput-Energy Eiciency Λ = W x T x. (3) From the previous Section, it is seen that the TCP throughput can be described as a unction o the peak transmitted power and the maximum number o re-transmissions: Λ = (P s, M). Thereore, or a given FSO link, i other parameters are ixed, P s and M can be set by the transmitter side to increase Λ. Obviously, the higher P s and M could result in the higher Λ. This, however, also causes extra energy consumption. In order to analyze combined eect o power management and ARQ-SR on both TCP throughput and energy consumption, we consider a new parameter called joint throughputenergy eiciency, denoted as J Λ,E. J Λ,E is deined as the ratio between the TCP throughput and the average value o the energy consumed or transmitting a data unit o TCP, and can be given as J Λ,E = Λ E[energy]. (33)

6 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO. 1, JANUARY 7 6 For SC-BPSK modulation, the bit power equals to a hal o the peak-transmitted power. Moreover, by applying the previous calculation o the average number o re-transmissions (e.g., Eq. (14)), the average value o the energy consumed or transmitting a TCP segment can be obtained by E[energy] = (M + 1)L T CP P s/ (34) P = ( 1 P (M + 1)P M+1 + 1)L T CP P s/. VI. NUMERICAL RESULTS AND DISCUSSIONS In this Section, using the previously derived ormulations, we analyze the TCP perormance over FSO turbulence channels when the ARQ-SR scheme is used at the link layer. Table I shows the system parameters and constants used in the numerical analysis. To ocus on the impact o the FSO link on TCP perormance, we assume that there is no segment loss in the wired network part (P wire = ). Also, the one-way transmission time in the wired network part, T wire, is ixed by 6 ms. Regarding the FSO link, we assume the log-normal and gamma-gamma models or the weak-to-moderate and strong turbulence conditions, respectively. In the bit-error probability calculation (i.e., Eqs. (15) and (18)), we assume the receiver noise variance, σn = so that SNR can be obtained by Eq. (11). TABLE I SYSTEM PARAMETERS AND CONSTANTS Name Symbol Value TCP segment size L T CP 536 bytes Frame size L 68 bytes Wired part transmission time T wire 6 ms CRC checking time T CRC 1 ms Transmission rate R Gb/s Modulation index m 1 Responsivity R 1 Receiver aperture diameter D. m Atmospheric extinction coeicient β.1 db/km Angle o divergence φ 1 3 radian First, in Fig. 3, we compare the perormance o TCP-Tahoe, TCP-Reno and TCP-SACK when ARQ-SR is not used. We set the turbulence strength Cn = m /3 and channel distance L = 1 m or two values o maximum window size (W max = 16 and 1 segments). It is seen that when the peak transmitted power increases, the throughput increases until it reaches a limit. This maximum throughput, Λ max, is determined by the value o W max. The systems with higher W max obviously achieve the higher maximum throughput. For instance, Λ max equals 18 kb/s and 68 kb/s when W max = 16 and W max = 1 segments, respectively. In addition, we observe that, compared to TCP-Tahoe, both TCP-Reno and TCP-SACK have signiicantly better perormance. This is thanks to the selective re-transmission algorithm used by TCP-SACK and the classiication o loss events employed by TCP-Reno, by which a loss can be accurately detected as either T.O or T.D [18] []. In remaining discussions, we employ the TCP-Reno due to its popularity and ability to oer the high perormance. The value o Throughput, Λ (kb/s) TCP-Tahoe TCP-Reno TCP-SACK W max =16 W max = Fig. 3. Throughput versus the peak transmitted power (P s) or dierent TCP versions when Cn = m /3, L = 1 m and no ARQ-SR. maximum window size W max = 16 segments, which is widely used in related studies, is also selected. Figures 4, 5 and 6 show the system throughput versus the peak transmitted power with dierent maximum number o re-transmissions and channel distances or weak, moderate and strong turbulence regimes, respectively. The turbulence strength Cn is selected as ollows: Cn = m /3 or the weak turbulence, Cn = m /3 or the moderate turbulence, and Cn = m /3 or the strong turbulence. Two channel distances o 1 m and 15 m are considered. Using these igures, the impact o ARQ-SR, turbulence strength, channel distances and the peak transmitted power on TCP throughput can be comprehensively analyzed. As is evident, the increase o turbulence strength results in the increase o the required peak transmitted power to achieve the same throughput. For example, in the case o no ARQ-SR and L = 1 m, in order to obtain the maximum throughput (Λ max = 18 kb/s), the required P s are 6 dbm, dbm and 1 dbm or weak, moderate and strong turbulences, respectively. Additionally, the system perormance also depends strongly on the channel distance. More speciically, an increase in L by 5 m leads to an increase o the required peak transmitted power by approximately 1 db to achieve the same Λ max. This phenomenon can be observed in Fig 5. Next, we highlight the advantage o ARQ-SR scheme to improve the TCP throughput by comparing the perormance o the system in various cases o M. It is seen that when ARQ-SR is employed, lower P s is required to achieve the maximum throughput. For example, in Fig. 6 i ARQ-SR with M = is employed, the maximum throughput can be achieved even when P s = dbm whereas the FSO system without ARQ-SR requires P s = 1 dbm to reach that throughput. More importantly, the increase o M also urther improves TCP throughput. As a result, the required P s to reach the maximum throughput decreases as M increases, especially

7 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO. 1, JANUARY Weak turbulence 1 Strong turbulence 1 1 Throughput, Λ (kb/s) L = 1 m L = 15 m No ARQ-SR ARQ-SR, M = Throughput, Λ (kb/s) No ARQ-SR ARQ-SR, M = ARQ-SR, M = 4 ARQ-SR, M = 6 ARQ-SR, M = 7 ARQ-SR, M = 4 ARQ-SR, M = 6 ARQ-SR, M = 7 L = 1 m L = 15 m Fig. 4. Throughput versus the peak transmitted power (P s) or dierent values o M and L when Cn = m /3. Fig. 6. Throughput versus the peak transmitted power (P s) or dierent values o M and L when Cn = m /3. Throughput, Λ (kb/s) 1 Moderate turbulence 1 8 L = 1 m L = 15 m 6 4 No ARQ-SR ARQ-SR, M = ARQ-SR, M = 4 ARQ-SR, M = 6 ARQ-SR, M = Joint throughput energy eiciency, J Λ,E (kb/s/j) C n = C n = C n = Fig. 5. Throughput versus the peak transmitted power (P s) or dierent values o M and L when Cn = m /3. in case o strong turbulence as shown in Fig. 6. However, this required power remains unchanged when M becomes higher than 6. This is because while the use o ARQ-SR decreases the TCP segment-loss probability, it signiicantly increase the average end-to-end transmission delay caused by the retransmission. It is thereore recommended that M = 6 is the optimized value or analyzed systems. In Figs. 7 and 8, we analyze the joint throughput-energy eiciency, J Λ,E when the optimal value o maximum number o re-transmissions, M = 6, is used. The purpose is to ind the range o transmitted powers at which the acceptable throughput-energy eiciency is attained under the impact o dierent turbulence strengths, channel distances and the peak transmitted powers. More speciically, Fig. 7 shows J Λ,E vs. the peak transmitted power, P s, or dierent turbulence Fig. 7. Joint throughput-energy eiciency versus the peak transmitted power (P s) or dierent turbulence strengths when L = 1 m and M = 6. strengths, when L = 1 m; J Λ,E vs. P s or various channel distances with Cn = m /3 is shown in Fig. 8. It is intuitively clear in all Figures that there exists an optimal value o peak transmitted power, P op, at which the joint throughput-energy eiciency is maximized. The presence o P op is due to the act that when the peak transmitted power becomes high enough, the TCP throughput saturates, and the urther increase o P s only results in additional energy consumption. In Fig. 7, it is seen that as the turbulence strength increases, the optimal peak transmitted power P op increase whereas the joint throughput-energy eiciency J Λ,E decease. For instance, when Cn = m /3, we have P op = 7 dbm and the maximum joint throughput-energy eiciency

8 JOURNAL OF L A TEX CLASS FILES, VOL. 6, NO. 1, JANUARY 7 8 Joint throughput energy eiciency, J Λ,E (kb/s/j) L = 1 m L = 11 m L = 1 m L = 15 m Fig. 8. Joint throughput-energy eiciency versus the peak transmitted power (P s) or dierent channel distances when C n = m /3 and M = 6. Optimal Peak transmitted power, P op (dbm) C n = C n = C n = Channel distances, L (m) Fig. 9. The optimal peak transmitted power versus the channel distance (L) or dierent turbulence strengths when M = 6. transmitted power also varies between -5 dbm and dbm. Moreover, i we continue to increase the peak transmitted power (higher than dbm), the joint throughput-energy eiciencies start decreasing, and they are the same or dierent channel distances. This is because in this case when the transmitted power is high enough, the TCP throughput reaches the maximum or any channel distances and the joint throughput-energy eiciency takes the same value or dierent distances. Finally, we combine results o Fig. 7 and Fig. 8 in Fig. 9. Using this igure, we can ind the optimal peak transmitted power or a speciic turbulence strength and channel distance. Again, it is conirmed that to achieve the maximum joint throughput-energy eiciency, the optimal peak transmitted power should be increased when the channel distance increases. The higher turbulence strength requires the higher value o P op. This igure allows us to select the range o optimal transmitted power or a given the channel distance. For example, when the channel distance is 13 m, the range o o optical transmitted power is rom 6 to 5 dbm. VII. CONCLUSIONS We have analytically studied the perormance o TCP over FSO links with ARQ-SR used in the link layer. A 3-D Markov chain model with the exponential back-o phase was used to derive the TCP throughput and joint throughputenergy eiciency or TCP-Tahoe, Reno and SACK. Various physical and link layers parameters, including turbulence strength, channel distance, transmitted power, and the ARQ- SR maximum number o re-transmissions, were taken into account in the TCP perormance analysis. Numerical results showed that the impact o turbulence and channel distance on the TCP throughput are severe. However, using ARQ- SR scheme could signiicantly reduce the required transmitted power to reach the maximum throughput. It was also shown that the recommended value o the maximum number o re-transmissions is 6 or the link layer o the analyzed system. In addition, the optimal peak transmitted power or the physical layer was investigated by considering the joint throughput-energy eiciency under the impact o atmospheric turbulence and channel distance. The results revealed the relation between the channel distance, the turbulence strength and the optimal peak transmitted power or the joint throughput-energy eiciency. REFERENCES J Λ,E = 195 kb/s/j can be achieved. However, at Cn = m /3, the transmitted power o -4 dbm is required to achieve the maximum J Λ,E o approximately 9 kb/s/j. The reason is that, as the turbulence strength increases, higher transmitted power is required to reach the SNR value at which the maximum throughput can be achieved. In addition, as the system P s increases, additional energy is also required or transmitting an unit data o TCP. As a result, the joint throughput-energy eiciency is decreased. The eect o channel distances on the joint throughputenergy eiciency is analyzed in Fig. 8. Obviously, the optimal peak transmitted power changes requently when the channel distances varies. When the channel distance increases rom 1 m to 15 m, it is seen that the optimal peak [1] O Brien, D., and Katz, M., Optical wireless communications within ourth-generation wireless systems, J. Opt. Netw., 5, 4, pp [] Xiaoming Zhu; Kahn, J.M., Free-space optical communication through atmospheric turbulence channels, Communications, IEEE Transactions on, vol.5, no.8, pp , Aug. [3] Uysal, M., Li, J.T., and Yu, M., Error rate perormance analysis o coded ree-space optical links over gamma-gamma atmospheric turbulence channels, IEEE Trans. Wireless Commun., 6, 5, (6), pp [4] Xuegui Song; Mingbo Niu; Cheng, J., Error Rate o Subcarrier Intensity Modulations or Wireless Optical Communications, Communications Letters, IEEE, vol.16, no.4, pp , April 1. [5] W. Popoola, Z. Ghassemlooy, H. Haas, E. Leitgeb, and V. Ahmadi, Error perormance o terrestrial ree space optical links with subcarrier time diversity, IET Commun. 6, 499 (1).

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