Topology Design for Directional Range Extension Networks with Antenna Blockage

Transcription

1 Topology Desg for Drectoal Rage Exteso etworks wth Atea Blockage Thomas Shake MIT Lcol Laboratory Abstract Extedg the rage of local area surface etworks by usg small arcraft to relay traffc to geographcally dstat areas s a frequetly cosdered topc mltary etwork techology developmet. Ths paper cosders the use of a modular pod desg for corporatg hghly drectoal ateas ad assocated electrocs to small arcraft to perform such rage exteso. I partcular, the paper exames trade-offs etwork topology desg troduced by pod-based atea blockages. Usg certa modelg approxmatos, the paper presets a quattatve aalyss showg desg trade-offs amog several desg parameters, cludg the umber of atea beams supported by the pod desg, the umber of surface odes to be supported by each arcraft, ad the topology characterstcs of the aeral relay etwork. The aalyss suggests that low-degree ar topologes such as rgs ad strgs be used to maxmze the coecto avalablty of surface odes, ad to optmze a trade-off betwee coecto avalablty ad the total umber of surface odes that ca be coected to the backboe (ad hece to each other). The aalyss also results a optmzato crtero for the formato ad mateace of low-degree ar topologes. 1 A promsg method of corporatg electrocs ad ateas to a arbore relay platform s to eclose them a separate pod, whch ca be modularly desged ad attached to the bottom of the wgs or fuselage of a varety of arcraft types [1]. Fg. shows a geerc cocept for such a pod desg wth potetal atea placemets o each ed of the pod ad o the bottom. There s great advatage to makg these ateas hghly drectoal; ths eables both a much hgher data rate coecto betwee arcraft ad a hgher level of rejecto of local terferece the surface-ar coectos. Such drectoal ateas may be mplemeted by mechacally steered dsh ateas or by electrocally steered devces (e.g., phased arrays). However, usg hghly drectoal ateas also makes the desg, dscovery, ad mateace of the relay etwork topology sgfcatly more dffcult. Pod Moutg structure I. ITRODUCTIO Tactcal mltary etworks both o lad ad at sea ofte have restrcted trasmsso rages due to lmts o termal trasmsso power, geographc features that block le-ofsght, ad poor over-the-horzo sgal propagato. Lmtg commucatos to local tactcal areas ca strogly costra msso success, ad some form of rage exteso s ofte eeded for these tactcal etworks. Oe frequetly cosdered opto for rage exteso s the use of relatvely small umaed arcraft to serve as over-the-horzo relay platforms coectg geographcally separated local groups of surface odes. Fg. 1 llustrates a coceptual example of such a rageexteso scearo that cludes both martme ad lad-based etwork termals. Fg. 1. Coceptual example of etwork rage exteso va aeral platforms 1 Ths work s sposored by the Uted States Departmet of the avy uder Ar Force Cotract #FA C-000. Opos, terpretatos, recommedatos ad coclusos are those of the authors ad are ot ecessarly edorsed by the Uted States Govermet. Ateas Fg.. Geerc pod cocept for modular aeral electrocs Depedg o whch of the potetal atea placemets show Fg. s used for a gve desg, the le-of-sght (LOS) betwee two arcraft or betwee arcraft ad surface odes may udergo termttet blockages as arcraft fly patters that eable them to mata LOS to a local surface ode group. (The flghtpaths typcally cosdered for such rage exteso purposes are closed paths wth crcular or racetrack-shaped patters [1].) Ateas placed o the eds of the pod are especally vulerable to regular blockages, ad such blockages are a mportat factor affectg the desg ad maagemet of the etwork topology [][3]. I partcular, such blockages ca cause sgfcat perods of uavalablty of the rage exteso capablty as see by surface odes local groups. Ths paper cosders the stuato where the relay etwork ateas are placed o ether ed of the pod, but ot o the bottom. Ths may correspod to desg scearos where the pod physcal desg does ot allow placemet of drectoal ateas o the bottom, or to scearos where ateas o the pod bottom must be reserved for other uses

2 such as sesor sutes or other commucato systems. Ths paper derves mathematcal relatoshps amog varous desg parameters ad performace measures usg certa modelg approxmatos approprate to aeral relay etworks. These relatoshps are used to quatfy trade-offs amog relay etwork avalablty, the degree of ter-coectvty that ca be attaed amog surface odes separated local groups, the umber of surface odes per arcraft that ca be accommodated, ad the umber of drectoal atea beams that ca be corporated to a gve pod desg. The outle of the rest of the paper s as follows. Secto II surveys prevous work ths area. Secto III descrbes the rage exteso etwork model ad desg parameters. Secto IV develops quattatve relatoshps amog key desg elemets ad performace metrcs. Secto V cosders some mplcatos of the results Secto IV for rage exteso etwork topology desg ad for techology developmet. Secto VI summarzes the results ad offers some cocludg thoughts. II. PREVIOUS WORK Topology maagemet for wreless ad hoc ad sesor etworks s a area that has receved extesve atteto the research lterature. A extesve survey s cotaed [4]. However, the great majorty of ths work assumes ether statc odes, om-drectoal trasmssos, or both. There s also a sgfcat body of work o Medum Access Cotrol (MAC) for wreless ad hoc etworks wth drectoal ateas, whch s surveyed [5], ad whch ofte cotas materal o topology dscovery ad/or cotrol. Other work modelg topology maagemet wth drectoal arcraft ateas has bee preseted [6] ad [7] for rado frequecy trasmsso, ad [8]-[10] for optcal free-space etworks. oe of ths work, as far as the author s aware, deals wth atea blockages due to structural factors such as arcraft fuselage or pod structures. The cocept of pod-based atea blockage has bee brought up [1]-[3]. The frst of these papers exames the effects of platform dyamcs ad arcraft orbt shapes o coecto avalablty, but does ot geeralze the aalyss to arbtrary topologes or cosder more tha two ateas per pod. The secod ad thrd of these papers cocetrate o the effects of atea swtchg o specfc small-scale scearos. The curret work models pod-based atea blockages a way that allows geeralzato to arbtrary topologes wth arbtrary umbers of arcraft ad surface odes, ad presets ew closed-form aalytcal results for low-degree ar topologes. III. RAGE EXTESIO TOPOLOGY MODEL A. Modelg Parameters Ths paper explores trade-offs ad optmzatos topology desg for the types of rage exteso etworks descrbed qualtatvely above. To quatfy these trades ad optmzatos, the followg formal model s establshed. Fgs. 3 ad 4 llustrate the model of the pod desg ad rage exteso etwork topology cosdered here. Each relay arcraft s assumed to have oe pod whch has arrow atea beams, / of whch are placed o each ed of the pod. The relay etwork topology model cossts of arcraft, each of whch supports S surface odes. Each surface ode has exactly oe atea beam whch ca be poted at the earest arcraft for rage exteso. Arcraft odes do ot source or sk traffc, but smply relay etwork traffc amog surface odes. (Surface odes uder a sgle arcraft may or may ot have other meas of local commucato that do ot volve the arcraft relay.) The arcraft are assumed to be relatvely far away from each other (otherwse the rage exteso provded would be poor), ad to fly approxmately crcular flghtpaths wth rad that are small compared to the dstace betwee the arcraft. A represetatve ode lay-dow wth three example coecto topologes s llustrated Fg. 5. Ths fgure shows the cetrods of racetrack flghtpaths as lght crcles; the realstcally modeled racetrack flghtpaths are the gree les aroud the cetrods. The surface odes are show wth lear paths, ad the lght tragles represet specfc postos of the odes at a partcular pot tme. / drectoal beams Fg. 3. Pod atea model / drectoal beams Arcraft ode Surface ode Fg. 4. Abstract topology model for rage exteso etwork T1 T3 Fg. 5. Represetatve practcal rage exteso ode lay-dow wth alteratve topologes T

3 B. Key Modelg Approxmatos The atea blockage modelg ths paper s based o two key approxmatos: 1) Compass drectos from a gve ar ode to other odes are assumed to be approxmately costat as the arcraft moves. ) Atea Feld-of-Vew (FOV) blockages are modeled by fxed azmuth ad elevato lmts. These approxmatos eable a geeral mathematcal aalyss of a otherwse specfc ad complcated stuato. The frst approxmato s that the relatve compass drecto of both ar ad surface odes as see from ay ar ode chages oly eglgbly durg the tme t takes to complete oe crcut of the closed flghtpath. Ths should be approxmately true for other ar odes for most practcal rage exteso scearos. It should also be approxmately true for may surface ode dstrbutos, but wll ot be such a good approxmato for scearos where the surface odes are located close to the ar relay ode. The secod key approxmato s how atea feld of vew (FOV) o each pod s modeled. Sce all ar odes are lkely to fly at approxmately the same alttude, the requred elevato agle ( arcraft cetrc coordates) to other arcraft wll stay wth a arrow rage whch s mostly free of blockages caused by elevato agle restrctos. Due to lkely pod geometres, show geercally Fgs. ad 3, the ma cause of blockage the azmuth compoet wll be due to the pod body. Ths paper approxmates the FOV of the ateas o each ed of the pod as beg clear for a azmuthal agle of (180+ ) o aroud atea boresght, ad approxmates the elevato FOV as beg lmted to o past adr, as llustrated Fg. 6. Ths approxmato should be farly accurate for the type of pod desg cosdered ad for FOV the drectos of most ar ad surface ode locatos. Arcraft wg blockages partcular are eglected ths approxmato, but wg blockages geerally represet relatvely short perods of blockage for crcular ad racetrack flghtpaths, so ths approxmato should ot have a great deal of effect o the le-of-sght avalablty of lks averaged over the tme t takes a arcraft to complete oe crcut of ts flghtpath. Ths paper presets quattatve results for the case of 0 ad 0(represetg o overlap betwee the FOV of the ateas o opposte eds of the pod). A subsequet paper wll preset results the more complex case of >0 ad >0. Gve the approxmatos just descrbed, the coectos of a specfc ar ode to other odes (both ar ad surface) ca be modeled by the azmuth agle of the potg vector to each of the odes that are vsble ad wth trasmsso rage of the arcraft questo. Ths s llustrated Fg. 7, whch shows the potg vectors to hypothetcal ar ad surface odes the arcraft-cetrc azmuth of ar ode. Sce the flghtpath s approxmated by a crcle of essetally zero radus, as the arcraft fles aroud oe crcut of ts path (whch takes tme Azmuth Feld of Vew (FOV) γ o Elevato Feld of Vew (FOV) δ o Fg. 6. Approxmate atea feld-of-vew model T for the th ar ode) the drectos to the other odes smply rotate the azmuth plae of ar ode. Fg. 7 also defes agular drectos to the other ar odes j, k, l. Oe fal parameter of terest s the umber of coectos of ar ode to other ar odes (.e., the degree of ar ode wth respect to the ar-to-ar topology of the relay etwork), whch wll be deoted by d a. β l to ar ode l A. Desg Crtera to surface ode to surface ode to ar ode k β k to ar ode j β j Pod ose drecto at tme t ( orth ) Fg. 7. Azmuth plae vew of ar ode IV. TOPOLOGY DESIG TRADE-OFFS Ths paper focuses o maxmzg both the total umber of surface odes that ca be coected to the ar backboe (ad hece to each other) ad the avalablty of these coectos. The performace metrc for the umber of coectable surface odes wll be deoted by /, the average umber of surface odes per arcraft that ca be supported by the ar topology. The fgure of mert used here for the avalablty of these coectos wll be the average fractoal coecto avalablty of the etre esemble of surface odes the etwork, whch s gve by A f /( S). (Ths may be apportoed ether evely or uevely amog surface odes.) The metrc / depeds o several factors ths etwork model, cludg the umber of atea beams (presumably restrcted by hardware desg costrats ad possbly by processg costrats for phased-array ateas); the umber ad compass drecto of ar backboe odes (determed by the locatos of the arcraft ad by the ar topology desg); Other optmzatos were cosdered, such as maxmzg some form of all-to-all traffc, or optmzg the survvablty of the ar backboe. The frst s a complex problem volvg mult-commodty flow optmzato [11] ad faress ssues [1], ad the secod seems poorly suted to ths type of etwork sce the restrcto that each surface ode to a sgle atea sets the maxmum coectvty of surface-to-ar odes at 1.

4 ad the umber ad locatos of the surface odes relatve both to ther local arcraft ad to the compass drectos of the local arcraft s coectos to other arcraft. B. Geeral results Gve the problem formulato above wth 0 o, there are a few smple ad geeral results whch are readly apparet. There s a upper boud to the umber of surface odes per ar ode that ca be coected, whch s gve by umber of beams requred, x x d a 3, radom ode locatos d a, radom ode locatos d a 3, optmum ode locatos d a, optmum ode locatos U K 1 X ( d a) (1) 1 Ths s a straghtforward cosequece of the fact that atea beams that are used for the ar topology are ot avalable to be used to coect surface odes. The average umber of coected surface odes per ar ode, /, ca approach ths upper boud ether by the optmum choce of specfc fxed locatos for all surface odes or by smply creasg S, the umber of surface odes udereath each arcraft. Icreasg S, however, may lower the overall average fractoal ode coecto avalablty ad may prevet the upper boud (1) from beg attaable. If oe wshes to guaratee that all surface odes have 100% coecto avalablty (ha f 1), the followg crtera wll do that uder the approprate codtos. If surface ode locatos are arbtrary ad ukow, 100% average coecto avalablty ca be attaed oly whe S apple max(d a) () whch guaratees that the upper boud of (1) s ot attaed. If surface ode locatos are optmally placed fxed locatos, ha f 1ca be attaed oly whe S apple max(d a) (3) wth the upper boud K U / beg attaed whe equalty holds (3). Fg. 8 shows the relatoshp betwee the umber of surface odes, S, that ca be supported per arcraft ad the umber of atea beams per pod,, whle guarateeg ha f 1. The sold les the plot represet the relatoshp for radomly located surface odes, ad the dotted les represet the relatoshp for optmally located, fxed surface ode locatos. I addto, the relatoshp s plotted for two dfferet values of the maxmum degree of the ar odes the overall ar topology max (d a), the blue curves beg for max (d a) ad the red curves for max (d a)3. Fg. 9 shows the maxmum degree of the ar odes that ca be attaed whle stll matag ha f 1for S 1surface ode per arcraft as a fucto of the umber of atea beams per pod,. Ths plot dcates a trade-off betwee surface ode avalablty ad capacty ad/or survvablty for the case whe a sgle surface ode s to be supported uder each arcraft. Both the capacty ad survvablty of the ar backboe are related to the maxmum degree of the ar odes, though ot umber of surface odes per arcraft, S Fg. 8. Mmum umber of atea beams,, requred for ha f 1 straghtforward ways. Low ar ode degrees certaly lmt both ar backboe capacty ad survvablty, but hgher ode degrees do ot ecessarly guaratee ether hgher capacty or better survvablty. Stll, ths fgure does llustrate a geeral relatoshp betwee matag full surface ode avalablty ad a mmum capablty to provde ar backboe capacty ad survvablty. Maxmum ar ode degree, d a umber of atea beams, Fg. 9. Maxmum ar ode degree for S 1ad ha f 1 C. Rg ad Strg Ar Topologes The results Secto IV-B mply that the degree of the odes the ar topology should be lmted to maxmze the tercoectvty of surface odes ad ther coecto avalablty. Ths suggests that rg or strg topologes should strogly be cosdered for the ar backboe. I a rg topology, d a for all ar odes; for a strg, d a for all odes except the oes o the eds of the strg, where d a 1. Wth these restrctos, ad for the case of 0ad 0, the value of / ca be wrtte as a closed form equato. Ths equato ca be derved by cosderg each sgle ar ode solato. For a gve ode, defe tme t 0 such that oe of the eghbor ar odes (the oly oe the case of a strg ed ode) s postoed drectly at the ose of the pod, ad such that the other eghbor ode (f ay) s at a azmuth agle such that < 180 o, as llustrated Fg. 10. At tme t 0, surface odes may be located at azmuth agles that are ether kow ad specfed, or are ukow ad assumed radom. The case of radomly located surface odes s cosdered frst.

5 All rg odes, ad termedate strg odes 3, 4 Ed odes o strg ode β haf eghbor ar odes Fg. 10. ode locatos from ar ode for rg or strg topologes , 4 / KU 1) Radomly Located Surface odes: Ths aalyss as- sumes that surface odes of ukow locato are equally lkely to be o ether the orth (pod ose) or South (pod tal) sdes of the pod. I ths case, at t0 the surface odes are # of surface odes per arcraft, S # of surface odes per arcraft, S bomally dstrbuted, wth bomal parameters p 0.5 ad b S. The umber of surface odes that ca be supported at ha ha tme t0 ca the easly be calculated. Ths umber ca the be haff haff averaged over oe complete crcut of the arcraft s flghtpath (takg tme T for the th ar ode). Gve the approxmatos of Secto III, oe complete crcut of ode s flghtpath s # of surface odes per arcraft, S # of surface odes per arcraft, S equvalet to a 360o rotato of the pod s azmuth oretato. / / (a) (b) The average umber of coected surface odes per ar ode / / the etre topology s thus gve by Fg. 11. Expected coectvty ad avalablty for two smple examples ( " S X 1 S 1 X m[, (da 1 + j)] j0 S j surface odes ad ther average avalablty whe the locatos # " S of the surface odes are kow, assumg that these locatos X 1 S are ether fxed or approxmately fxed for the durato, T, +m[, (S j + 1)] + 1 S j 180 of oe flghtpath crcut. Let fj be defed as the fracto of j0 ) # tme T that j surface odes ca be coected. The expected m[, j] + m[, (S j + da )] da (4) umber of surface odes coected to ode s gve by S X ad the total average coecto avalablty of surface odes hkf j fj (6) the etwork s j0 haf (5) ad the expected total umber of coected surface odes per S ar ode s Fg. 11 shows some sample results of these calculatos for hkf 1 X two smple, regular ar topologes. The examples use 4 hk (7) 1 F atea beams per arcraft pod, wth two o each ed of the pod. The top plots each case show the total average umber The calculatos for fj are ot smple to wrte closed form of coected surface odes per ar ode as a fucto of the for most cases of terest, but ca be easly calculated by a umber of surface odes S uder each arcraft, wth the blue smple heurstc.3 The heurstc ca also corporate a mxture curve showg results for the strg topology ad the red curve of kow ad ukow (bomally dstrbuted) surface ode showg results for the rg topology. The upper bouds for locatos the computatos of expected coectvty ad each topology are show by the red ad blue dotted les. avalablty, ad accommodates dfferet umbers of surface The bottom plots each case show the average coecto odes uder each ar ode (.e., S 6 Sj ). avalablty for surface odes. The strg topologes outperform Some sample results for the three rage exteso topologes the rg topologes for both metrcs for ay gve value of S, of Fg. 5 are show Table I. The top left topology (T1) whch s expected sce the strg topologes have more total Fg. 5 s a strg topology, whle the top rght ad lower left ateas avalable to be used for surface coectos. ote topologes (T ad T3 respectvely) augmet ths topology by that there s a trade-off betwee maxmzg the total average addg oe ar-ar lk each case. Topology T3 represets a umber of coected surface odes ad the average avalablty rg (though t may be mpractcal the example llustrated of each surface ode s coecto to the ar backboe. Also, due to the log rage betwee the Southermost arcraft ad the case show these partcular examples, the average the Eastermost arcraft). The results Table I show the excoecto avalablty haf s ever 100% because there are pected average coectvty ad avalablty for each topology too few ateas to meet the crtera of (). ) Kow Surface ode Locatos: A smlar procedure 3 The heurstc s too log to be cluded ths paper but wll be descrbed ca be used to calculate the average umber of coected a subsequet paper metoed above cludg results for 0 < < 90o.

6 ha 0 1 fx X for two dfferet values of ad for two separate cases: a) fxed 1 locatos of all lad ad sea surface odes; ad b) fxed lad ode locatos ad radom sea ode locatos. ote that X 1, 6 for 4 atea beams, the ar topology augmetatos decrease both the expected surface ode coectvty ad the expected surface ode avalablty. If s creased to sx, however, the decrease both metrcs s mmal, ad lkely worth the trade-off to get extra coectvty the ar backboe haf haf haf / / haf / 4 atea beams T1 (strg) T T3 (rg) # of surface odes per arcraft, S haf haf 6 atea beams T1 (strg) T T3 (rg) Fxed lad ad shp ode locatos # of surface odes per arcraft, S Fg. 1. Expected coectvty ad avalablty wth a sample larger ar / topology TABLE I E XPECTED COECTIVITY AD AVAILABILITY FOR EXAMPLES I F IG. 5 V. D ESIG I MPLICATIOS A. Topology Algorthm Selecto The sample results prevous sectos dcate that formg ad matag rg or strg ar topologes yelds the best combato of surface ode coecto avalablty ad umber of surface ode coectos that ca be supported. Depedg o the desg costrats o the umber of atea beams that a pod ca support, a strg topology formato ad mateace algorthm may be the best desg choce for small scale aeral rage exteso etworks. As the umber of ar odes creases, the dffereces coectvty ad avalablty betwee rg ad strg topologes decrease (compare Fg. 1 wth Fg. 11), but may practcal rage exteso etworks may cota just a few ar odes. A careful examato of (4) reveals that the avalablty of surface P ode coectos s maxmzed by maxmzg the sum 1. Ths s due to the fact that for each ar ode, the sum (4) that s multpled by ( /180) s always greater tha or equal to the sum that s multpled by (1 /180). Fg. 13 llustrates ths crtero for topology optmzato for a set of sx arbtrarly placed odes. Ths maxmzato s a computatoally dffcult problem, however, though t may be practcal to solve ths for very small scale topologes. A more computatoally effcet approach would be to form ad mata a Mmum Weght Spag Tree (MST) topology [13] for the ar odes. However, for > 3 a mmum weght spag tree topology does ot always maxmze surface ode avalablty, ad wll sometmes clude odes of degree >. A degree costraed MST could be calculated, but ths s equvalet to the Hamltoa Path Problem, whch s P-hard. More work o computatoally effcet topology formato ad mateace algorthms for ths scearo s eeded. / B. Techology Developmet Cosderatos I the ear term, small values of may be practcal wth mechacally steered or phased array atea desgs. Sze, / Good β4 β Bad Fxed lad, radom shp ode locatos β β3 5 β β3 β4 β5 Fg. 13. Illustrato of the topology optmzato crtero of Secto V-A weght, ad power requremets are key cosderatos for a pod desg that must be mouted to a small arcraft, ad these factors are lkely to strogly costra the ear term. Small values of do place stroger costrats of the coectvty of the ar backboe (to keep surface ode avalablty hgh) ad also lmt the survvablty of the ar backboe. The ablty to crease practcal rage exteso etwork avalablty by performg make-before-break atea swtches o ar-ar lks s also costraed by havg small. Larger values of allow the support of greater umbers of surface odes for a gve level of ar backboe coectvty, ad may also allow smpler topology maagemet techques to be used for formg ad matag the ar topology. (Oe reaso for ths s that MST algorthms are lkely to result a smaller pealty surface ode coecto avalablty wth large.) Therefore, developg techologes that ca crease the potetal value of wth mmum sze, weght, ad power requremets should be a prorty for creasg the performace of aeral rage exteso etworks. Icreasg the umber of ateas avalable o the pod may result greater complexty other ways that have ot bee the focus of ths paper. For example, frequecy ad spectrum maagemet wll almost certaly be more complcated wth large sce more beams must be maaged, ad recever frot ed mplemetatos may have sgfcat levels of sgal crosstalk betwee processg chas for each beam, makg frequecy reuse more dffcult. Schedulg trasmssos ad receptos etworks wth large umbers of drectoal beams s also a potetal ssue. I the far term, dgtal beamformg approaches wth phased array ateas may offer a soluto to ths potetal problem [14], but the

7 ear term t may be problematc. C. Future Work The work ths paper ca be both geeralzed to reduce the specfcty of some of the assumptos ad approxmatos, for example extedg the calculatos to less restrctve feldof-vew assumptos. I partcular, further work s already progress to exted the calculatos to overlappg atea felds-of-vew from each ed of the pod (.e., 0 < apple 90 o ). The calculatos ca also be made more accurate for specfc effects, cludg corporato of wg blockages, o-zero swtchg tmes whe ateas must be swtched from oe destato ode to aother, ad effects of etwork layer effects such as routg reachablty o the avalablty of edto-ed coectos. VI. COCLUSIOS Ths paper has explored topology-related desg trade-offs for aeral rage exteso etworks usg hghly drectoal ateas o relay arcraft. The paper preseted a desg whch arcraft electrocs ad atea structures are modularly ecapsulated a pod attachg to the udersde of the arcraft, ad corporatg multple atea beams placed o each ed of the pod. The paper developed approxmate models of the effects of atea beam blockages resultg from represetatve pod geometres typcal rage exteso etwork topologes. The prmary fgures of mert cosdered ths paper are the average umber of surface odes that ca be coected to the aeral rage-exteso backboe, ad the average avalablty of the coectos from these surface odes to the backboe, ad hece to each other. Both of these factors are costraed by the atea blockage characterstcs of the pod-based desg; the paper quatfed how these factors may be traded agast oe aother as a fucto of the total umber of arcraft, the arcraft topology, the umber of surface odes supported per arcraft, ad the umber of atea beams suppled by the pod desg. The umber of atea beams that ca be desged to the arcraft electrocs pod s a prmary factor lmtg both the umber of surface odes that ca be coected ad ther coecto avalablty. For example, creasg ths umber from four to sx beams per arcraft allowed the average coecto avalablty of sx total surface odes a represetatve fourarcraft ar topology to be creased from 76% to 100% whle matag a -coected ar backboe. For small umbers of atea beams per pod (e.g., 4-6) the results of the aalyss suggest that low-degree ar topologes (ether a rg or strg) be the goal of ar topology formato ad mateace algorthms to maxmze the coecto avalablty of surface odes to the ar backboe. The paper has derved a crtero for ar topology formato based o the compass drectos of eghborg ar odes, ad recommeds further research to computatoally effcet algorthms that optmze ths crtero. ACKOWLEDGEMETS The author would lke to thak Terrace Gbbos of MIT Lcol Laboratory s Tactcal etworks Group for supplyg detals of the example four-arcraft scearos Fg. 5. REFERECES [1] D. Mehta, B. Gaguly, The Effect of Platform Dyamcs o Aeral Layer etwork Performace, IEEE Mlcom014, Oct. 014 [] J. Wag. P. Deutsch, A. Coyle, T. Shake, B- Cheg, A Implemetato of a Flexble Topology Maagemet System for Aeral Hgh Capacty Drectoal etworks, IEEE Mlcom015, Oct. 015 [3] J. Wag, T. Shake, P. Deutsch, A. Coyle, B- Cheg, Topology Maagemet Algorthms for Large-Scale Aeral Hgh Capacty Drectoal etworks, submtted to IEEE Mlcom016, ov. 016 [4] P. Sat, Topology Cotrol Wreless Ad Hoc ad Sesor etworks, ACM Computg Surveys, Vol. 37, o., Jue 005 [5] O. Baza, M. Jaseemudd, A Survey O MAC Protocols for Wreless Adhoc etworks wth Beamformg Ateas, textslieee Commucato Surveys ad Tutorals, Vol. 14, o., Secod Quarter 01 [6] D. Va Hook, M. Yeager, J. Lard, Automated Topology Cotrol for Wdebad Drectoal Lks Arbore Mltary etworks, IEEE Mlcom005, Oct. 005 [7] P. Wag, B. Hez, Atea Assgmet for JAL HCB, IEEE Mlcom015, Oct 015 [8] J. Zhuag, M. Casey, S. Mler, S. Gabrel, G. Baecher, Mult-Objectve Optmzato Techques Topology Cotrol of Free Space Optcal etworks IEEE Mlcom004. [9] A. Desa, S. Mler, Autoomous Recofgurato free-space Optcal Sesor etworks, textslieee Joural o Selected Areas Commucatos, Vol. 3, o. 8, Aug. 005 [10] A. Kashyap, K. Lee, M. Kalatar, S. Khuller, M. Shayma, Itegrated topology cotrol ad routg wreless optcal mesh etworks, Computer etworks, Vol 51, pp , 007 [11] T. Corme, C. Leserso, R. Rvest, ad C. Ste, Itroducto to Algorthms (3rd ed.). MIT Press, 009 [1] T. Boald, L. Massoulé, Impact of faress of Iteret performace, ACM SIGMETRICS 001 [13] D. Bertsekas, R. Gallager, Data etworks, d ed., Pretce Hall, 1987 [14] G. Kuperma, R. Margoles,. Joes, B. Proulx, A. arula-tam, Ucoordated MAC for Adaptve Mult-Beam Drectoal etworks: Aalyss ad Evaluato, submtted to ICCC 016