Outage Probability of Triple-Hop Mixed RF/FSO/RF Stratospheric Communication Systems

Transcription

1 SPACOMM 08 : The Tenth Interntion Conference on Advnces in Steite nd Sce Communictions Outge Probbiity of Trie-Ho Mixed RF/FSO/RF Strtosheric Communiction Systems Emmnoue T. Michiidis,, Nikoos Nomikos 3, Petros Biths,, Demosthenes Vouyiouks 3, nd Athnsios G. Knts Dertment of Digit Systems, University of Pireus, Pireus, Greece e-mi: {emichi, biths, knts}@unii.gr Dertment of Eectric nd Eectronics Engineering, University of West Attic, Cmus, Aigeo, Athens, Greece 3 Dertment of Informtion nd Communiction Systems Engineering, University of the Aegen, Krovssi, Smos, Greece emi: {nnomikos, dvouyiou}@egen.gr Abstrct This er rooses trie-ho mixed Rdio- Frequency/Free-Sce-Otic/Rdio-Frequency (RF/FSO/RF) communiction system, which intends to suort wireess ongrnge inks between two terrestri sttions vi two strtosheric reys. It is considered tht these terrestri sttions communicte with the reys over RF inks, wheres the reys communicte with ech other over FSO ink. The RF chnnes exerience Ricin fding due to the Line-of-Sight (LoS) nd Non-Line-of-Sight (NLoS) sign comonents. Besides, the otic chnne is ffected by tmosheric ttenution, tmosheric turbuence, nd ointing errors. Mthemtic exressions for the outge robbiity re derived, considering the bem wnder effect. The resuts demonstrte the theoretic derivtions. Keywords-Atmosheric turbuence; bem wnder; Free- Sce-Otic (FSO) communictions; High-Atitude Ptforms (HAPs); outge robbiity; ointing errors; Ricin chnnes. I. INTRODUCTION The deveoment of next-genertion wireess brodbnd communictions comrises the semess integrtion of terrestri nd erosce infrstructures over heterogeneous networks []. In recent yers, the use of mobie irborne services vi High-Atitude Ptforms (HAPs) fying in the strtoshere hs been suggested for civi nd miitry ictions []. To successfuy fufi the demnds of future wireess communiction services, shifting from the Rdio- Frequency (RF) domin to the otic domin is indisensbe [3] [4]. In Free-Sce-Otic (FSO) systems, the dt is trnsmitted t high dt rtes in the mutigigbit regime using coimted highy directed ser bems with comct equiment nd ow ower consumtion. The FSO technoogy ensures rivcy with ow robbiity of intercetion, immunity to eectromgnetic interference, nd exemtion from sectrum regutory restrictions. The strtoshere stnds for rogtion medium we suited for FSO connections. Hoefuy, the inter-hap crossink is bove ttenuting couds, fog or significnt erosos. Hence, inter-hap distnces of u to 900 km re ossibe with 00% vibiity [5]. Nevertheess, strtosheric FSO inks my exerience substnti fuctutions in both the intensity nd the hse of the received sign due to vritions of the Index of Refrction Turbuence (IRT) ong the rogtion th resuting by the inhomogeneities in temerture nd ressure fuctutions, eseciy for ink distnces of km nd bove [6]. Moreover, bem ointing error effects re highy ronounced on the erformnce of strtosheric network, which invoves rge distnces nd ossibe discement of the tforms due to the winds or ressure vritions of the strtoshere [7]. In ddition, both mechnic vibrtions nd eectronic noise my cuse the received sots from the ser bems to wnder on the detector nes. Hence, cquisition, ointing, nd trcking errors shoud so be mitigted to chieve high directivity of the trnsmitted bem. To extend the network rnge, nd effectivey combt the effect of turbuence, the use of rey-ided trnsmission schemes hs been suggested [8]. In [7], fu-fso system with mutie strtosheric reys nd fixed sttions on the ground ws roosed. However, FSO systems shoud oerte under ccurte ointing requirements. Hence, emoying FSO techniques is highy chenging nd insufficient s soon s the terrestri sttions re in motion. Motivted by these observtions, this er investigtes the use of two strtosheric reys cting s Decode-nd- Forwrd (DF) rey nodes, in order to fciitte chenging trie-ho ong-rnge wireess communiction between two terrestri mobie sttions. Athough the Amify-nd- Forwrd (AF) scheme is sime to imement, DF offers better erformnce nd is common ssumtion in mutiho networks. A mixed RF/FSO/RF irborne communiction scenrio is considered, where n RF trnsmission scheme is doted for the communiction between the terrestri sttions nd the strtosheric reys, wheres these reys re interconnected through n FSO ink. A strtosheric communiction chnne is exected to be Ricin in its gener form [9]. Hence, the Ricin distribution is doted to mode the chnnes for the RF inks. To investigte the effect of tmosheric turbuence on the FSO ink, Komogorov ower sectrum for refrctive-index fuctutions is considered nd the Gmm-Gmm (G-G) distribution is used, which mtched dt vues obtined from mesurements, under vriety of turbuence conditions [0]. Finy, the effects of ointing errors re described by the Ryeigh distribution [7]. Mthemtic exressions re Coyright (c) IARIA, 08. ISBN:

2 SPACOMM 08 : The Tenth Interntion Conference on Advnces in Steite nd Sce Communictions derived for the outge robbiity nd numeric resuts re rovided for different vues of the system rmeters. The rest of the er is orgnized s foows. Section II resents the system mode. In Section III, the RF nd FSO fding chnnes re modeed. In Section IV, the outge robbiity is mthemticy derived. Resuts re rovided in Section V. Finy, concusions re drwn in Section VI. II. SYSTEM MODEL This er considers mixed RF/FSO/RF irborne communiction system with sowy-vrying nd frequencyft-fding chnnes. As shown in Figure, the trnsmitted sign from source node rogtes through two seri DF strtosheric reys of simir size nd tye before rriving t destintion node. It is considered tht the direct ink between the source nd the destintion is obstructed due to high ttenution. To id our nysis, the subscrits S, D, nd R m, where m, re ffiited with the source, the destintion, nd the m-th rey, resectivey. In this system, the S R nd R D inks use RF technoogy, whie the R R ink is bsed on FSO technoogy. The communiction is ssumed to oerte in hf-duex mode nd to be conducted over three hses: S R, R R, nd R D. The source nd the destintion re equied with singe ntenns. Besides, the reys not ony incude ntenns, but so sers nd hoto-detectors. A. First RF Link The received sign t the strtosheric rey R cn be exressed s [] y P h x n () SR, S SR, SR,, R where P S is the trnsmit ower, h SR, is non-zero-men comex Gussin rndom vribe, x is the trnsmitted SR, SR, symbo from the source with E x, E is the sttistic execttion oertor, n R reresents the zero-men comex Gussin noise t R with N or, noise Power Sectr Density (PSD). Using (), the instntneous Signto-Noise Rtio (SNR) t R cn be written, resectivey, s P. () S SR, h SR, NoR, B. FSO Inter-HAP Link In the FSO ink, the cost-effective Intensity Modution Direct-Detection (IM/DD) is emoyed. The received RF sign t the R is decoded nd converted to otic sign by emoying the Subcrrier Intensity Modution (SIM) technique. In rticur, fter fitering by Bndss Fiter (BPF), Direct Current (DC) bis is dded to the fitered RF sign to ensure tht the otic sign is non-negtive. Then, the bised sign is sent to continuous wve ser driver. The retrnsmitted otic sign t R is written s [] R, ot ot S, R y P My, (3) where P ot denotes the verge trnsmitted otic ower nd it is reted to the rey eectric ower P R by the eectric-to-otic conversion efficiency η s Pot n PR, nd M denotes the modution index. The otic sign t R received from R cn be exressed s yr, R I P ot My S, R n, R (4) where I > 0 is the received fding gin (irrdince) between the ser of R nd the hotodetector of R through the otic chnne nd n R is the zero-men comex Gussin noise t R with N or, noise PSD. The DC comonent is fitered out t R nd n otic-toeectric conversion is erformed. Then, ssuming tht M =, the received sign cn be exressed s yr, R I P ee Poty S, R n, R (5) where Pee npot nnpr is the eectric ower received t R nd n is the otic-to-eectric conversion efficiency. The instntneous SNR t R cn be roximted s [] min,, (6) where nn P I R S, R R, R / N. R, R R o, R The erformnce of the FSO ink is imited by bckground rdition nd therm noise, which cn be modeed s indeendent nd identicy distributed (i.i.d.) AWGN, s n ccurte roximtion of the Poisson hotoncounting detection mode [3]. FSO S-R R -D On-Off Keyed Light Puses RF RF Source R R Destintion Figure. Sime reresenttion of the trie-ho mixed RF/FSO/RF strtosheric communiction system. Coyright (c) IARIA, 08. ISBN:

3 SPACOMM 08 : The Tenth Interntion Conference on Advnces in Steite nd Sce Communictions C. Second RF Link The FSO sign t the R is finy reconverted to n RF sign before being sent to the destintion over the second RF ink. The sign received t the destintion is written s y P h x n (7) D R R, S R, S D, where P R is the trnsmit ower, h RS is non-zero-men comex Gussin rndom vribe (eding to Ricin distributed mitude), x is the sign trnsmitted by the R with R, S R, S E x, nd n D is the zero-men comex Gussin noise t D with N od, noise PSD. Using (7), the SNR t the destintion cn be written s P. (8) R R, D hr, D NoD, The instntneous end-to-end SNR t the destintion cn be roximted s [] min,,. (9) D S, R R, R R, D III. STATISTICAL MODELING OF THE TRIPLE-HOP MIXED RF/FSO/RF CHANNEL In this er, the Ricin distribution is utiized to mode the chnnes for the RF inks. The Probbiity Density Function (PDF) of the instntneous SNR received t R, denoted s SR,, is given by [4] K SR, f SR, SR, ex K K SR, SR, SR, I0 KK, SR, (0) where K is the Ricin fctor of the first RF ink, i.e., the verge ower rtio of the Line-of-Sight (LoS) comonent to the Non-Line-of-Sight (NLoS) comonent, nd I0 is the modified Besse function of the first kind nd zero-th order. The Ricin fctor K strongy deends on the eevtion nge of the HAPs nd the oerting frequency [5]. The PDF, f of the Ricin distribution for the second R, D R D RF ink with Ricin fctor K cn be defined s in the first RF ink by recing the indices. For the FSO ink, comosite otic chnne mode is used [7]. In rticur, the chnne stte I modes the rndom ttenution of the rogtion chnne tht rises due to the th oss I, the tmosheric turbuence I, nd the ointing errors I. The combined otic chnne mode is defined s foows I II I. () Since the time sces of these fding rocesses re of the -3 - order of 0 s to 0 s [6], which re fr rger thn the -9 bit interv (» 0 s for muti-gbs systems ), I is constnt over rge number of trnsmitted bits [7]. A. Effects of Atmosheric Attenution The tmosheric ttenution is deterministic nd is defined by the exonenti Beers Lmbert Lw [8] where I I L ex L, () L is the tmosheric ttenution oss of the FSO ink over th of ength L, i.e., the distnce between the reys, nd σ is the wveength- nd wether-deendent ttenution coefficient. The ttenution I is considered fixed during ong eriod of time. B. Effects of Turbuence In this er, the effects of turbuence re modeed using the G-G distribution. Hence, the PDF of I is given by [9] b / b b b b f I I K bi, (3) I where Ku is the u-th order modified Besse function of the second kind. Note tht (3) cn be written in terms of the,0 Meijer s G-function s Ku x 0.5 G 0, x / 4 u/ u / [0]. The rmeters nd b re directy reted to the tmoshere nd cn be djusted to chieve good greement between f I I nd mesurement dt. These rmeters re determined by the Rytov scintition mode. However, for rge distnces, s those invoved in the roosed system, this mode is inrorite due to the hot sot discement of the bem cused by the bem wnder, i.e., the defection of the bem due to turbuence. By considering the bem wnder effect, nd b cn be modeed s [] 5/6 4.4R e e 0.49 B ex, /5 7/6 w LT 0.56 B (4) 0.5 B b ex, /5 5/ B 7/6 /6 (5) where R.3Ck n L is the Rytov vrince, C is the index of refrction structure rmeter, L/ kw, e n LT Coyright (c) IARIA, 08. ISBN:

4 SPACOMM 08 : The Tenth Interntion Conference on Advnces in Steite nd Sce Communictions k / is the wve number, is the crrier wveength, 5/6 R wlt w.33 is the ong-term sot rdius, w is the bem rdius t the receiver, L / kw, e is the vrince of ointing error cused by bem wnder ([],. 350), B is the Rytov vrince with bem wnder correction ([],. 35), 0 / 0 0, 0 L / F0, F 0 is the hse curvture rmeter of the Gussin bem t the trnsmitter, 0 L / kw0, nd w 0 is the trnsmitter bem rdius. Using [3, eq. (3)], one cn so obtin the Scintition Index (SI) I. The vue of C n reresents the turbuence condition of the tmoshere nd cn be estimted using the Hufnge-Vey mode, which is bsed on vrious emiric scintition dt of the tmoshere. This mode defines the index of refrction structure rmeter s function of the wind seed nd the titude of the HAPs bove the ground eve s ([],. 48) 5 0 h n ex u C h h h.7 0 ex ˆ h Aex, (6) where  is the nomin vue of the C n t the ground, u is wind seed in m/s, nd h is the titude of the HAPs in meters. As C n increses, the turbuence becomes stronger. For ictions invoving rogtion ong horizont th, it is customry to ssume tht C n remins constnt []. C. Effects of Pointing Errors To ensure tht the communiction scenrio is vibe, roer LoS ignment between the reys vi rorite ointing nd trcking mechnisms is required. In this er, mode tht incorortes geometric sreding in the ointing error PDF ([8],. 703) is used. Considering Gussin bem rofie of bem wist w z (t distnce z) nd modeing the rndom rdi discement of the bem t the detector s Ryeigh distributed, the PDF of the ointing error I incudes the rndom ttenution due to both geometric sreding nd ointing errors nd cn be exressed s [8] f I I, 0 I A I, A (7) where g w eq / s s, w erf / ex eq wz u u u is the equivent bem width t the receiver, u = ( r) ( wz) = /, s s is the jitter stndrd devition due to the ointing error t the detector determined by the degree of the misignment between the ertures, A= éerf ( u) ù ë û, nd r is the receiver erture rdius. Using (), (3), nd (7), the PDF of the comosite chnne in () cn be evuted by writing the Besse u function K in terms of the Meijer s G-function s [7] b 3,0 b fi I G,3 I. (8) AI b AI,, b Using (8), the PDF of the instntneous SNR received t R, denoted s cn be exressed s f R, R, R, R R, R b AI b G R, R R, R b, (9) AI,, b 3,0 R, R,3 R, R where is the verge SNR received t R. R, R IV. DERIVATION OF OUTAGE PROBABILITY The outge robbiity is defined s the robbiity tht the SNR t the destintion fs beow redetermined outge threshod out, i.e., Pout Pr D out, where Pr is the robbiity oertion. In this cse, the communiction system cnnot chieve dequte recetion. The outge robbiity cn be obtined from the Cumutive Distribution Function (CDF) of the end-to-end SNR s Pout F D out. This CDF cn be written in terms of the CDFs of the three hos SNRs s [4] F D out FS, R out FR, R out F R, D out, (0) where F F nd SR,, out R, R, out F re R, D the CDFs of the SNRs of the first, second, nd third ho, resectivey. One observes tht the system fs in outge roviding tht t est one of the three hos gets in outge or, equiventy, the SNR of one ho becomes ess thn out. The CDF of the instntneous SNR received t R cn be exressed s [5] where K F,,,,, SR SR Q K SR SR, out () Q is the first-order Mrcum Q-function. The CDF F R, D R, D of the Ricin distribution for the second RF ink cn be simiry defined by recing the indices. Coyright (c) IARIA, 08. ISBN:

5 SPACOMM 08 : The Tenth Interntion Conference on Advnces in Steite nd Sce Communictions The CDF of the instntneous SNR received t R cn be obtined s foows R, R RR R, R 0 R, R F f x dx. () Using (9) nd [6, eq. ( )], () becomes F R, R R, R b AI b G R, R R, R b 0,. (3) AI,, b, 3, R, R,4 R, R The exressions in () nd (3) cn be numericy evuted using we-known softwre ckges, e.g., Mthemtic nd MATLAB. V. RESULTS In this section, the erformnce of the roosed system is evuted in terms of the outge robbiity. Uness indicted otherwise, the vues of mode rmeters used re SR, R, D 0 db, R, R 50 db, 0 db, out K = K = K = 0 db, L = 400 km, h 0 km, 0.0 db/km (cer wether conditions), w w0 cm, Θ 0 = 0 (focus Gussin bem), nd s 0.5 m. Note tht ser erture dimeter of r = 0.3 m is ssumed. Then, wz.38 m [7]. A wveength λ = 550 nm is considered for the FSO ink since it is widey used for most irborne otic communiction scenrios. In ddition, two vues of the wind seed tht determine C n re considered; u 0 m/s (best cse) nd u 30 m/s (worst cse) [3]. 9 /3 For these vues, we obtin C nu,.7 0 m, 8 /3 C nu,.550 m, Ru, 0., Ru,.8, Iu, 0.08, nd Iu, Figure deicts the outge robbiity for different vues of the Ricin fctor K = K = K nd u = 0 m/s. It is obvious tht incresing the Ricin fctor imroves the erformnce of the system. Note tht certin outge foor exists t high vues of K due to the verge SNR over the FSO ink. Hence, curves tend to the sme sturtion foor. Figure 3 demonstrtes the outge robbiity for both the best nd worst cse of turbuence conditions nd different inter-hap distnce. As this distnce decreses, significnt erformnce imrovement cn be chieved. However, the vrition of the FSO rogtion distnce sighty ffects the outge robbiity when the worst cse of turbuence conditions is observed. Outge Probbiity Figure. The outge robbiity in terms of the RF verge SNR for different Ricin fctor of the RF inks. Figure 3. The outge robbiity in terms of the FSO verge SNR for different turbuence conditions nd different inter-hap distnce. Figure 4. The outge robbiity in terms of the FSO verge SNR for different normized jitter stndrd devition. Coyright (c) IARIA, 08. ISBN:

6 SPACOMM 08 : The Tenth Interntion Conference on Advnces in Steite nd Sce Communictions Finy, Figure 4 shows the effect of the normized jitter stndrd devition s s / r on the outge robbiity for u = 0 m/s. One observes tht the erformnce significnty degrdes nd the ointing errors hve dominnt effect on the system erformnce, s s / increses. s VI. CONCLUSION In this er, the erformnce of trie-ho mixed RF/FSO/RF strtosheric communiction system hs been investigted. The resuts hve deicted tht the Ricin fctor significnty infuences the system erformnce. These resuts hve so underined tht the erformnce degrdes, s the inter-hap distnce increses. However, for the worst turbuence cse, this distnce sighty ffects the outge robbiity. Finy, the resuts hve shown tht the misignment-induced fding hs severe effect on the system erformnce. Since there re no exeriment dt vibe in the iterture to fuy verify the theoretic resuts, future reserch efforts my be devoted to coecting mesured chnne dt in re-word rogtion conditions. ACKNOWLEDGMENT This reserch is imemented through Stte Schorshis Foundtion (IKY) nd co-finnced by the Euroen Union (Euroen Soci Fund ESF) nd Greek ntion funds through the ction entited Reinforcement of Postdoctor Reserchers in the frmework of the Oertion Progrmme Humn Resources Deveoment Progrm, Eduction nd Lifeong Lerning, with riority xis 6, 8, 9, of the Ntion Strtegic Reference Frmework (NSRF) REFERENCES [] R. Giuino, M. Lugio, nd F. Mzzeng, Interoerbiity between WiMAX nd brodbnd mobie sce networks, IEEE Commun. Mg., vo. 46, no. 3, , Mr [] A. Mohmmed, A. Mehmood, F. Pvidou, nd M. Mohorcic, The roe of high-titude tforms (HAPs) in the gob wireess connectivity, Proc. IEEE, vo. 99, no., , Nov. 0. [3] B. Moision et. Demonstrtion of free-sce otic communiction for ong-rnge dt inks between boons on Project Loon, in Proc. SPIE 0096, Feb. 07. [4] H. Kush nd G. Kddoum, Otic Communiction in Sce: Chenges nd Mitigtion Techniques, IEEE Comm. Surv. & Tutoris, vo. 9, no., , Firstqurter 07. [5] D. Giggenbch, R. Purvinskis, M. Werner, nd M. Hozbock, Strtosheric Otic Inter-Ptform Links for High Atitude Ptforms, in Proc. 0th AIAA ICSSC, Montre,. -, My 00. [6] L. Andrews, R. L. Phiis, nd C. Y. Hoen, Lser Bem Scintition With Aictions. SPIE Press, 00. [7] M. Shrm, D. Chdh, nd V. Chndr, High-titude tform for free-sce otic communiction: Performnce evution nd reibiity nysis, J. Ot. Commun. Netw., vo. 8, no. 8, , Aug. 06. [8] C. Dtsiks, K. P. Pes, N. C. Sgis, nd G. S. Tombrs, Seri free-sce otic reying communictions over gmm-gmm tmosheric turbuence chnnes, J. Ot. Commun. Netw., vo., , Ju. 00. r [9] A. Argón-Zv, J. L. Cuevs-Ruíz, nd J. A. Degdo- Penín, High Atitude Ptforms for Wireess Communictions, st ed. New York: Wiey, Dec [0] F. S. Veteino, C. Young, L. Andrews, nd J. Recoons, Aerture verging effects on the robbiity density of irrndince fuctutions in moderte-to-strong turbuence, Aied Otics, vo. 46, no., , Ar [] A. M. Shb, A New Scenrio of Trie-Ho Mixed RF/FSO/RF Rey Network with Generized Order User Scheduing nd Power Aoction, EURASIP Journ on Wireess Communictions nd Networking (06) 06:60. [] E. Lee, J. Prk, D. Hn, nd G. Yoon, Performnce nysis of the symmetric du-ho rey trnsmission with mixed RF/FSO inks, IEEE Photonic Tech. L., vo. 3, no., , 0. [3] S. M. Nvidour, M. Uys, nd M. Kvehrd, BER erformnce of free-sce otic trnsmission with sti diversity, IEEE Trns. Wire. Commun., vo. 6, no. 8, , Aug [4] M. K. Simon nd M.-S. Aouini, Digit Communiction over Fding Chnnes, nd ed. New York: Wiey, 005. [5] Iskndr nd S. Shimmoto, Chnne chrcteriztion nd erformnce evution of mobie communiction emoying strtosheric tforms, IEICE Trns. on Commun., vo. E- B, no. 3, , Mr [6] X. Zhu nd J. Khn, Free sce otic communiction through tmosheric turbuence chnnes, IEEE Trns. Commun., vo. 50, no. 8, , Aug. 00. [7] H. G. Sndidis, Coded free-sce otic inks over strong turbuence nd misignment fding chnnes, IEEE Trns. Commun., vo. 59, no. 3, , 0. [8] A. A. Frid, S. Member, nd S. Hrniovic, Outge ccity otimiztion for free-sce otic inks with ointing errors, J. Lightwve Techno., vo. 5, , Ju [9] M. A. A-Hbsh, Mthemtic mode for the irrdince robbiity density function of ser bem rogting through turbuent medi, J. Ot. Eng., vo. 40, no. 8, , Aug. 00. [0] V. S. Admchik nd O. I. Mrichev, The gorithm for ccuting integrs of hyergeometric tye functions nd its reiztion in REDUCE system, in Proc. Int. Conf. on Symbo. nd Ageb. Com., Tokyo, Jn,. -4, 990. [] Y. Ren, A. Dng, B. Luo, nd H. Guo, Ccities for ongdistnce free-sce otic inks under bem wnder effects, IEEE Photon. Techn. Lett., vo., no. 4, , Ju. 00. [] L. Andrews nd R. L. Phiis, Lser Bem Progtion Through Rndom Medi, nd ed. Beinghm, WA: SPIE, , 005. [3] S. Prthsrthy, D. Giggenbch, nd A. Kirstädter, Chnne modeing for free-sce otic inter-hap inks using dtive ARQ trnsmission, in Proc. SPIE 948, 9480Q,. -, Oct. 04. [4] S. S. Ikki nd S. Aiss, A study of otimiztion robem for mify-nd-forwrd reying over Weibu fding chnnes with mutie ntenns, IEEE Commun. Lett., vo. 5, no.,. 48-5, 0. [5] A. A. Abu-Dyy nd N. C. Beuieu, Switched diversity on microceur Ricen chnnes, IEEE Trns. Veh. Techno., vo. 43, no. 4, , 994. [6] The Wofrm Functions Site, 03. [Onine]. Avibe from: htt://functions.wofrm.com [retrieved: Mrch, 08]. [7] N. Vioouos, H. G. Sndidis, nd D. Vrouts, Using HAP network to trnsfer WiMAX OFDM signs: Outge robbiity nysis, J. Ot. Commun. Netw., vo. 5,. 7-7, Ju. 03. Coyright (c) IARIA, 08. ISBN: