On the Performance of Millimeter Wave-based RF-FSO Links with HARQ Feedback

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1 On the Perforance of Millieter Wave-based -FSO Links with HARQ Feedback Behrooz Makki, Toy Svensson, and Mohaed-Sli Alouini Chalers University of Technoy, Gothenburg, Sweden, {behrooz.akki, King Abdullah University of Science and Technoy KAUST, Thuwal, Saudi Arabia, arxiv:163.88v1 [cs.it] 6 Mar 16 Abstract This paper studies the perforance of hybrid radiofrequency and free-space optical FSO links in the cases with and without hybrid autoatic repeat request HARQ. Considering illieter wave wave characteristics in the link and pointing errors in the FSO link, we derive closed-for expressions for the essage decoding probabilities as well as the throughput and the outage probability of the -FSO setups. We also evaluate the effect of various paraeters such as power aplifiers efficiency, different transission techniques in the FSO link, pointing errors in the FSO link as well as different coherence ties/sybol rates of the and the FSO links on the throughput and outage probability. The results show the efficiency of the -FSO links in different conditions. Moreover, the HARQ can effectively iprove the outage probability/energy efficiency, and copensate the effect of hardware ipairents in -FSO links. I. INTRODUCTION The deand for high data rates raises the question of spectru availability. Thus, for future counication systes, ore spectral resources are andatory. Of the any popular solutions, free-space optical FSO counication systes have gained significant research attention as effective eans of transferring data at high rates over short distances. In the radio frequency doain, on the other hand, it is ainly concentrated on illieter wave wave counication as a key enabler to obtain sufficiently large bandwidths so that it is possible to achieve data rates coparable to those in the FSO links. In this perspective, the link reliability and the service availability can be considerably iproved via the cobination of FSO and wave-based links. This is particularly because both the FSO and the wave-based links are highly susceptible to atospheric effects. However, the good point is that these links are copleentary because the resp. the FSO signal is severely attenuated by rain resp. fog/clouds while the FSO resp. the signal is not. The perforance of -FSO systes is studied in different papers, e.g., [1] [3], where the and the FSO links are considered as separate links and the link acts as a backup when the FSO link is down. On the other hand, in [4] [8] the and the FSO links are cobined to iprove the syste perforance. Moreover, the ipleentation of hybrid autoatic repeat request HARQ in -based resp. FSObased systes is investigated in, e.g., [9] [13] resp. [14] [18], while the HARQ-based -FSO systes have been rarely studied, e.g., [19] [1] /14/$31. c 14 IEEE Encoder link FSO link HARQ feedback Decoder Figure 1. Channel odel. The data is jointly transitted by the and the FSO links and, in each round of HARQ, the receiver decodes the data based on all received signals. To have realistic insights about the perforance of - FSO links, it is necessary to take the non-ideal link properties into account. Particularly, considering the FSO link, theral expansion, dynaic wind loads, and weak earthquakes result in the building sway phenoenon that causes vibration of the transitter bea leading to a isalignent between the FSO transitter and receiver known as pointing error 1. The pointing error ay lead to significant perforance degradation and is a serious issue in urban areas, where the FSO equipents are placed on high-rise buildings [], [3]. In the link, on the other hand, the power aplifiers PAs efficiency is the ain hardware proble affecting the syste perforance [4], [5]. These are the ain otivations for our paper analyzing the perforance of HARQ-based -FSO links with pointing errors and iperfect PAs. In this paper, we study the data transission efficiency of -FSO systes fro an inforation theoretic point of view. The contributions of this paper are twofold. 1 Taking the pointing errors in the FSO link and the wave characteristics of the link into account, we derive closedfor expressions for the essage decoding probabilities as well as the syste throughput and outage probability. Our results are obtained in different cases with and without HARQ. Particularly, we show the HARQ as an effective technique to copensate the non-ideal properties of the -FSO links and iprove the hybrid link reliability. Then, we analyze the effect of various paraeters such as the FSO link pointing errors, the PAs efficiency, different heterodyne detection- and intensity odulation with direct detection IM/DD-based data transission techniques of the FSO link, and different sy- 1 In general, the wave-based links also suffer fro pointing errors in cases with narrow beaforing and obility. However, here we focus on static links e.g., wireless backhauling, in which pointing errors of the link are negligible.

2 bol rates/coherence ties of the and FSO links on the throughput/outage probability. In contrast to [1] [3], we consider joint data transission/reception in the and FSO links. Moreover, our paper is different fro [4] [6] because we derive new analytical/nuerical results on the essage decoding probabilities, and outage probability/throughput of HARQ-based -FSO links which have not been presented before. The differences in the proble forulation and the channel odel akes our analytical/nuerical results and conclusions copletely different fro the ones in the literature, e.g., [1] [6]. The nuerical and the analytical results show the efficiency of -FSO links in different conditions. Moreover, the HARQ protocols can effectively iprove the outage probability/energy efficiency, and copensate the effect of hardware ipairents in -FSO links. For instance, with the coon paraeter settings of the -FSO links, outage probability 1 and code rate 1 nats-per-channel-use npcu, the ipleentation of HARQ with a iu of 3 retransissions reduces the required power by 8 db, copared to the cases with open-loop counication. II. SYSTEM MODEL Consider a joint -FSO syste, as deonstrated in Fig. 1. The data sequence is encoded into parallel FSO and bit streas. Then, the FSO and the signals are siultaneously sent to the receiver. At the receiver, the received FSO signal is down-converted to baseband resp. collected by an aperture and converted to an electrical signal via photodetection and the signals are sent to the decoder which decodes the received signals jointly. We denote the instantaneous realizations of the fading coefficient of the link and the turbulence coefficient of the FSO link in tie slot i by H,i and H FSO,i, respectively, and for siplicity we refer to both of the as channel coefficients. These channel coefficients are assued to be known at the receiver which is an acceptable assuption in block-fading conditions [9] [15], []. Also, we define G,i = H,i, G FSO,i = H FSO,i which are referred to as channel gain realizations in the following. We then assue no channel state inforation CSI feedback to the transitter, except for the HARQ feedback bits. The feedback channel can be an, an FSO or an -FSO link, and is supposed to be errorand delay-free. Finally, we assue perfect synchronization between the links in harony with, e.g., [4] [8], [19], []. As the ost proising HARQ approach leading to highest throughput/lowest outage probability [9] [1], we consider the increental redundancy INR HARQ with a iu of M retransissions, i.e., the essage is retransitted a iu of M ties. Using INR HARQ, K inforation nats are encoded into a parent codeword of length ML channel uses. The parent codeword is then divided into M sub-codewords of length L channel uses which are sent in the successive transission rounds. Thus, the equivalent data rate, i.e., the K code rate, at the end of round is L = R npcu where R = K L denotes the initial code rate. In each round, the receiver cobines all received sub-codewords to decode the essage. The retransission continues until the essage is correctly decoded or the iu peritted transission round is reached. Note that setting M = 1 represents the cases without HARQ, i.e., open-loop counication. The FSO link is assued to follow a unified Gaa- Gaa fading distribution with pointing errors for which the probability distribution function PDF of the channel gain is given by f GFSO x = ξ 1 x r rxγαγβ G3, 1,3 hαβ µ r ξ +1 ξ,α,β. 1 This is a well-established odel for pointing errors in FSO links, e.g., [], [3]. Also, Γ denotes the Gaa function. Then, r represents the paraeter specifying the detection technique type, where r = 1 accounts for heterodyne detection and r = represents IM/DD technique. Also, h = ξ ξ +1 denotes the ratio between the equivalent bea radius at the receiver and the pointing error displaceent standard deviation jitter at the receiver [3] i.e. for negligible pointing errors, ξ. Then, α and β are the fading/scintillation paraeters related to the atospheric turbulence conditions, and G,, is the Meijer s G function as defined in [7, Eq.9.31]. Finally, µ r stands for the average electrical signal-to-noise ratio SNR where µ 1 = µ heterodyne = E[G FSO ] and µ = µ IM/DD = E[G FSO]αβξ ξ + α+1β+1ξ +1 []. Finally, we denote the transission power of the FSO link by P FSO. While the odeling of the wave-based links is well known for line-of-sight wireless backhaul links, it is still an ongoing research topic for non-line-of-sight conditions [8]. Particularly, different easureent setups have ephasized the non-/near-line-of-sight propagation and the non-ideal hardware as two key challenges of such links. Since we target a hybrid wave-based -FSO link, we consider Rician channel odel for the link, which is an appropriate odel for near line-of-sight conditions. With a Rician odel, the channel aplitude G and gain G, respectively, follow the PDFs f x = x e x +ν xν ω ω I ω, and f G x = 1 f x x, where ν and ω denote the fading paraeters andi is the zero-th order odified Bessel function of the first kind. Finally, to take the non-ideal hardware into account, we consider the state-of-the-art odel for the PA efficiency in the link which is given by [4], [5] ϑ P P P cons = ǫ P P = 1 ϑ ǫp cons P ϑ. 3 Here,P,P and P cons are the output, the iu output and the consued power of the PA, respectively, ǫ [,1] denotes the iu power efficiency achieved at P = P and ϑ [,1] is a paraeter depending on the PA classes.

3 N fading blocks of FSO channel in each retransission Transission 1 Retransission Retransission.. Retransission M One fading block of channel Tie Figure. Tie scales. The link reains constant in the retransissions quasi-static channel [1], [11] while in each retransission round of HARQ N different channel realizations are experienced in the FSO link. III. ANALYTICAL RESULTS As shown in [9] [13], for different channel odels the throughput of HARQ protocols can be written as η = R1 φ M 1+ M 1 =1 φ, 4 where φ = PrW R denotes the probability that the data is not correctly decoded up to the end of the - th round with W being the accuulated utual inforation AMI at the end of round. Also, the outage probability is given by PrOutage = φ M = PrW M R M. Thus, to analyze the throughput and outage probability, the key point is to deterine the probabilities φ, = 1,...,M. Then, having the probabilities, the considered perforance etrics are obtained. In -FSO systes, it was deonstrated by, e.g., [5], [9] and the references therein, that the link experiences very slow variations and the coherence tie of the link is in the order of ties larger than the coherence tie of the FSO link. For this reason, we consider the setup as illustrated in Fig. where the link reains constant in the retransissions quasi-static channel [1], [11] while in each retransission round of HARQ N different channel realizations are experienced in the FSO link. In this way, considering 3 and Fig., we can use the results of [3, Chapter 7] to find the probability φ, = 1,...,M, as φ = Pr Y r,,n. = ψ 1+ 1 ϑ j=1 i=1 ǫp cons P ϑg +Y r,,n R M N 1+c r P FSO G FSO,1+j 1i. Here, ψ represents the relative sybol rates of the and FSO links which is a design paraeter selected by the network designer. Also, 5 is based on the fact that the achievable rate of an FSO link is given by 1 + c r x with x being the instantaneous received SNR and c r denoting a constant ter such that c r = 1 for heterodyne detection and c r = e π for 5, IM/DD [], [31], [3, Eq. 7.43], [33, Eq. 6]. Considering different values of N, there is no closed-for expression for 5. Thus, we use the central liit theore to approxiate Y r,,n by the Gaussian rando variable 1 Z Nµ,. Here, µ and are the ean and variance deterined based on the FSO link channel condition. Particularly, considering the Gaa-Gaa PDF 1 and denoting the expectation operator by E{ }, we have µ = ψe{1+c r P FSO G FSO } = ξ ψ rxγαγβ 1+c r P FSO xg 3, 1,3 and = ρ µ with x hαβ µ r 1 r ξ +1 ξ,α,β dx, 6 ρ = ψ E{1+c r P FSO G FSO ξ ψ } = rxγαγβ 1 x 1+c r P FSO x G 3, r ξ +1 1,3 hαβ dx 7 µ r ξ,α,β which can be found nuerically, because they are onediensional integrations. Having µ and, we find the probabilities φ,, as follows. Considering Rician fading conditions for the link, 5 is rephrased as d f x φ = x Y r,,n 1+ R 1 ϑ Pr d a = d b d = a f x x Q f u Q f uv τ,λ udu b f udu+ a ǫp cons P ϑx 1+ 1 ϑ ǫp cons x P ϑ dx = +µ R ǫp 1+ 1 ϑ cons P u +µ R ϑ 1 f u λ u τ du In [33], 1+cSNR is proved as a tight lower bound on the capacity in the cases with an average power constraint. Then, [], [31] show that the forula of the kind 1 + csnr is an asyptotically tight lower bound on the achievable rates for the cases with an average power constraint, a peak power constraint, as well as cobined peak and average power constraints. du dx

4 c 1 F a + +λ τ Fb F a λ b F b a F a b a F a +b. e R 1. d =,τ 1 ϑ ǫp cons = e R µ 1, P 1 ϑ ǫp cons ϑ P ϑ. e R µ e R µ λ = π. a =,τ 1 λ, 1 ϑ ǫp cons P,b ϑ,. = in τ + 1,d λ. Here, a is obtained by variable transfor u = x. Then, b coes fro the linear approxiation technique Q ǫp 1+ 1 ϑ cons P u +µ R ϑ 8 V τ,λ x with 1 x < a, 1 V τ,λ x = λ x τ a x b, x > b, where λ defined in 8 is obtained by taking the derivative of Q ǫp 1+ 1 ϑ cons P u +µ R ϑ 9 at point u = τ. Then, c is obtained by the first order Rieann integral approxiation x x 1 fxdx x x 1 f x1+x. Also, F x = 1 Q ν M ω, ω x is the CDF of the Rician variable with Q M, being the Marcu Q function. Finally, it is interesting to note that 1 N li N j=1 i=1 1+c rp FSO G FSO,1+j 1i = E{1+c r P FSO G FSO },. Intuitively, this eans that for asyptotically large values of N, i.e., significantly shorter coherence tie of the FSO link copared to the one in the link, the AMI of the FSO link converges to its ergodic capacity E{1 + c r P FSO G FSO }. Thus, in this case the -FSO link is apped to an equivalent wave-based link in which successful decoding of the rate equal to the ergodic capacity of the FSO link is always guaranteed. Also, as a second-order approxiation, the probabilities φ, = 1,...,M, are approxiated as 1+ 1 ϑ ǫp cons P R µ φ Pr ϑg = 1 Q M ν ω, e R µ 1. 1 ǫp ω 1 ϑ cons P ϑ Using 8-1, one can find the probabilities φ, = 1,...,M, and, consequently, the throughput and the outage probability of the -FSO syste. In Section IV, we verify the accuracy of our derived analytical results and investigate the effect of different paraeters such as the PAs efficiency, the FSO link pointing errors, different sybol rates/coherence ties of the and FSO links and different FSO-based data transission techniques on the throughput/outage probability of -FSO systes. IV. NUMERICAL RESULTS In all figures, we set α = , β =.5636 which correspond to Rytov variance 1 of the FSO link in the cases with no pointing error [14]. Also, the paraeters of Rician PDF in are set to ω =.736,ν =.995, leading to unit ean and variance of the channel gain distribution f G x. Finally, SNR is defined as 1 1 P with P = P FSO +P cons, and we set P FSO = P cons in all figures. Then, using 3, we can find the transission power of the link P for every given P cons. In Fig. 3, we consider an ideal PA, corresponding to ǫ = 1,ϑ =,P = in 3, while the effect of iperfect PAs is studied in Figs Particularly, Fig. 3 verifies the accuracy of the approxiation techniques 8 and 1, and investigates the outage probability in the cases without M = 1 and with HARQ M = 3. Here, the results are obtained for the heterodyne detection technique and we set R = 1 npcu,n = 1,ξ =.9,ψ =.3. In Fig. 4, we investigate the effect of iperfect PAs on the syste throughput 4. Particularly, considering heterodyne detection, R =.5 npcu,n = 1,ξ =.9, and ψ =.3, the figure copares the throughput in the cases with an ideal ǫ = 1,ϑ =,P = and non-ideal ǫ =.65,ϑ = = 18 db [4] PA. Then, Fig. 5 studies the effect of pointing error in the FSO link, and the outage probability is derived for different values of pointing error paraeter ξ. Here, the results are obtained for heterodyne detection technique and we set R = 3 npcu,n = 1,ψ =.5,ϑ =.5,P.5,ǫ =.65,P = 3 db. Finally, Fig. 6 evaluates the outage probability for different data transission techniques in the FSO link and coherence ties of the and FSO links. The results of the figure are presented for R = 1 npcu,m = 1,ψ =,ϑ =.5,ǫ =.65,P = 18 db,p = 18 db,ξ = 1., and the nubers of channel realizations N for which central liit theore provides accurate approxiation for the rando variable Y r,,n in 5. According to the results, the following conclusions can be drawn: 1 The analytical results of 8 and 1 accurately iic the exact nuerical results, and the difference between the approxiation-based and exact results is negligible for a broad range of SNRs/paraeter settings Fig. 3. Therefore, 8 and 1 can effectively be used to investigate the perforance of -FSO links analytically. Finally, note that in Figs. 4-6 the results are plotted based on exact evaluation of 8. However, we have checked the results with the ones obtained via approxiations 8 and 1, and in all cases the approxiation results are very tight. With different paraeter settings, the ipleentation of HARQ leads to significant outage probability and energy

5 efficiency iproveent Fig. 3. For instance, with the paraeter settings of Fig. 3 and the outage probability 1, the ipleentation of HARQ with a iu of M = 3 retransissions reduces the required power by alost 8 db, copared to the cases with openloop counication M = 1. On the other hand, in harony with the results on links [13], the HARQ ay decrease the throughput of the -FSO links Fig. 4. However, the throughput degradation is negligible for a broad range of paraeter settings. 4 The PAs inefficiency affects the perforance of - FSO systes significantly Fig. 4. For instance, with the paraeter settings of Fig. 4, M = 1 and P = 6 db, the inefficiency of the PA reduces the achievable throughput fro.4 npcu to.15 npcu, i.e., 15% throughput loss. However, the effect of iperfect PAs decreases with the SNR. This is intuitively because the effective efficiency ϑ of the PAs ǫ effective = ǫ P P increases with the SNR. 5 The outage probability of the -FSO syste is sensitive to severe pointing errors of the FSO link, i.e., sall values of ξ. However, the effect of pointing error is negligible for oderate/large values of ξ, i.e., when the pointing error is negligible Fig. 5. Also, with the paraeter settings of Fig. 5, the outage probability achieved with severe pointing errors ξ =.1 and M = HARQ-based retransission rounds is less than one in the open-loop setups M = 1 and no pointing error ξ. Thus, the HARQ can effectively be used to copensate the effect of pointing errors in -FSO links. 6 As expected, better syste perforance is achieved by the ipleentation of heterodyne technique, copared to IM/DD technique Fig. 6. Also, the outage probability decreases with increasing the nuber of channel realizations in the FSO link N Fig. 6. This is intuitively because ore tie diversity is exploited by the HARQ when the channel changes during the data transission. Finally, in harony with the intuitive understandings of 1, the syste perforance becoes insensitive to the nuber of channel realizations in the FSO link as N increases. V. CONCLUSION In this paper, we studied the data transission efficiency of wave-based -FSO links in the cases with and without HARQ feedback. Considering pointing errors in the FSO link and iperfect power aplifiers in the link, we derived closed-for expressions for the essage decoding probabilities, throughput and outage probability of the - FSO systes. The results show that, while the throughput is not necessarily increasing by HARQ, substantial outage probability reduction is achieved by the ipleentation of HARQ protocols. Moreover, the inefficiency of the power aplifiers deteriorates the perforance of -FSO systes considerably. Therefore, the properties of the power aplifiers should be carefully considered in the network design. Finally, Outage probability M=3 M=1 Exact result Approxiation result of 8 Approxiation result of 1 Heterodyne detection, ψ=.3, ξ=.9 R=1, N=1 8 db gain SNR, 1 P db 1 Figure 3. On the tightness of the approxiation results. Heterodyne detection technique, R = 1 npcu,n = 1,ξ =.9, and ψ =.3. Throughput npcu Ideal power aplifier Heterodyne detection, ξ=.9, ψ=.3, N=1 M=1 M= M=3 Iperfect power aplifier, ϑ=.5, ε=.65, P =18 db SNR 1 P db 1 Figure 4. Throughput for different types and power aplifiers and iu nubers of retransissions M. Heterodyne detection technique, R =.5 npcu,n = 1,ξ =.9, and ψ =.3. the HARQ can be effectively utilized to copensate the effect of pointing errors in the FSO link. REFERENCES [1] M. Usan, H. C. Yang, and M.-S. Alouini, Practical switchingbased hybrid FSO/ transission and its perforance analysis, IEEE Photon. J., vol. 6, no. 5, pp. 1 13, Oct. 14. [] H. Wu, B. Hazeh, and M. Kavehrad, Achieving carrier class availability of FSO link via a copleentary link, in Proc. IEEE Asiloar 4, California, USA, Nov. 4, pp [3] Y. Tang and M. Brandt-Pearce, Link allocation, routing and scheduling of FSO augented wireless esh networks, in Proc. IEEE ICC 1, Ottawa, Canada, June 1, pp [4] K. Kuar and D. K. Borah, Hybrid FSO/ sybol appings: Merging high speed FSO with low speed through BICM-ID, in Proc. IEEE GLOBECOM 1, California, USA, Dec. 1, pp [5] N. Letzepis, K. D. Nguyen, A. Guillen i Fabregas, and W. G. Cowley, Outage analysis of the hybrid free-space optical and radio-frequency channel, IEEE J. Sel. Areas Coun., vol. 7, no. 9, pp , Dec. 9. [6] S. Vangala and H. Pishro-Nik, A highly reliable FSO/ counication syste using efficient codes, in Proc. IEEE GLOBECOM 7, Washington, DC, USA, Nov. 7, pp

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