mobile FSO communication has not been realized, particularly for ad hoc networking and communication environments.

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1 Optimal Communication Coveage fo Fee-Space-Optical MANET Building Blocks Muat Yuksel, Jayasi Akella, Shivkuma Kalyanaaman, Patha Dutta ensselae Polytechnic Institute, ECSE Depatment, JEC th Steet, Toy, NY 1180, USA. Phone: +1 (518) , Fax: +1 (95) s: yuksem@ecse.pi.edu, akellj@pi.edu, shivkuma@ecse.pi.edu, duttap@pi.edu Abstact- Existence of line of sight (LOS) and alignment between the communicating antennas is one of the key equiements fo fee-space-optical (FSO) communication. To ensue uninteupted data flow, auto-aligning tansmitte and eceive modules ae necessay. We peviously poposed [1] a new FSO node design that uses spheical sufaces coveed with tansmitte and eceive modules fo maintaining optical links even when nodes ae in elative motion. In this pape, though theoetical modeling, we answe the question of how much coveage can be achieved by a -d cicula FSO node with the highest possible numbe of tansceives. The essence of ou analysis is to demonstate scalability of ou FSO node designs to longe distances as well as feasibility of dense packaging of tansceives on such nodes. Keywods- Fee Space Optical communication, Auto- Configuable, Angula Divesity. I. INTODUCTION Optical wieless, also known as fee space optics (FSO), is an effective high bandwidth communication technology seving commecial point-to-point links in teestial last mile applications and in infaed indoo LANs [6] [] []. FSO has seveal attactive chaacteistics like license-fee band of opeation, dense spatial euse, low powe usage pe tansmitted bit, and elatively high bandwidth. Howeve, one of the majo limitations of FSO is line of sight (LOS) maintenance fo continuous data flow. Cuent FSO equipment is tageted at point-to-point links using high-poweed lases and elatively expensive components used in fibe-optical tansmission. Mobile communication using FSO is consideed fo indoo envionments, within a single oom, using diffuse optics technology [7]. Due to limited powe of a single souce that is being diffused to spead in all diections, these techniques ae suitable fo small distances (typically s of metes), but not suitable fo longe distances. Fo outdoos, fixed FSO communication techniques to emedy small vibations [3], swaying of the buildings have been implemented using mechanical autotacking [4] o beam steeing [11], and intefeence [8] and noise [9]. Similaly, fo optical inteconnects, autoalignment o wavelength divesity techniques ae epoted to impove the misalignment toleances in -dimensional aays [5]. These techniques wok only ove small anges (e.g. 1µm 1 cm) and some of these ae cumbesome involving heavy mechanical tacking instuments. Moeove, they ae designed to impove the toleance to movement and vibation but not to handle mobility. Thus, mobile FSO communication has not been ealized, paticulaly fo ad hoc netwoking and communication envionments. Spheical Antenna (a) Tessellated sphee (b) Honeycombed aays of tansceives Figue 1: 3-d spheical FSO systems tessellated with LED+PD pais. In ode to enable FSO communication in mobile envionments, we intoduce the concept of spheical FSO node that povides angula divesity and hence LOS in all diections. Figue 1 shows the geneal concept of spheical sufaces being tessellated with FSO tansceives, i.e. a pai of optical tansmitte (e.g. Light Emitting Diode (LED)) and optical eceive (e.g. Photo- Detecto (PD)). Such spheical FSO nodes use multiple optical tansceives tessellated on the suface of a sphee. As shown in Figue 1-(b), tadeoffs between spatial euse and angula divesity can be obtained by constucting the FSO node as honeycombed aays of tansceives whee each aay is a cell on the honeycomb. We peviously illustated [1] feasibility of such spheical FSO nodes and demonstated mobile communication in a two-node pototype expeiment. In this pape, we show that these FSO node designs can allow vey dense packaging and scale to vey long communication anges as well as coveage (e.g. a 1cm adius FSO node with tansceives of adius 0.1cm and souce powe 3mWatts can cove a total of 7.68m in advese weathe and 5.97m in clea weathe). Ou modeling of the poposed spheical FSO node evealed that the souce powe at tansmittes and the visibility have little o no effect on the optimality of the numbe of LED Mico Mio PhotoDetecto Optical Tansmitte/eceive Unit

2 tansceives on such stuctues. athe, the geometic shape of the FSO node and the divegence angle play the majo ole, which means that adaptive tuning of the souce powe based on the actual visibility is possible without having to change the physical numbe of tansceives on these FSO nodes. This is an impotant esult since it means that optimum numbe of tansceives is fixed fo a paticula FSO node design. II. OPTIMUM COMMUNICATION COVEAGE In spheical FSO nodes tessellated with multiple optical tansceives, thee ae tadeoffs involving (i) intefeence (o cosstalk) between the neighboing tansceives, (ii) aggegate coveage aea achieved by the FSO node, (iii) packaging density of the optical tansceives, and (iv) communication ange. Theefoe, highe packaging density povides highe aggegate coveage but also inceases the intefeence of the neighboing tansceives. An impotant design question is to ask how dense the packaging should be so that highest (o optimal) possible aggegate coveage is achieved without causing intefeence. Anothe design tadeoff dimension is the communication ange that can be achieved with such densely-packaged FSO nodes. If highe powe is fed to the optical tansmittes on the node, communication ange inceases; howeve, intefeence also inceases at longe distances due to beam divegence. To investigate the above-mentioned tadeoffs, we pesent ou analysis of the scalability of the angula divesity and spatial euse povided by a cicula shaped FSO node. In paticula, we answe the question of how much coveage can be achieved by a -d cicula FSO node with the highest possible numbe of tansceives. To find the optimal numbe of tansceives imizing the total coveage of a -d cicula FSO node, we fist develop the model fo total coveage aea of such a node. Then, we devise an iteative algoithm to find the optimal numbe of tansceives that imize the total coveage. A. Coveage Model We define the coveage aea of an FSO node as the aea in which anothe FSO node can be aligned fo communication. Thus, the aea, points of which ae within the LOS of the FSO node, is called the coveage aea of the FSO node unde consideation. Fo a -d cicula FSO node, the total coveage is dependent on the effective coveage aea achieved by a single tansceive C, and the total numbe of tansceives n. The effective coveage aea of a single tansceive can be fomulated based on two diffeent possibilities as shown in Figue. Let be the adius of the cicula -d FSO node, ρ be the adius of a tansceive, and be the divegence angle of a tansceive. We appoximate an FSO tansceive s coveage aea (which is the vetical pojection of a lobe) as the combination of a tiangle and a half cicle. Let be the height of the tiangle, which means the adius of the half cicle is tan. Also, let be the length of the ac in between two neighboing tansceives on the -d cicula FSO node. Table 1: MATHEMATICAL NOTATIONS Symbol n ρ ϕ Meaning Numbe of tansceives on the FSO node adius of the FSO node (cm) adius of a tansmitte (cm) Ac length between neighbo tansceives (cm) Divegence angle of a tansceive (ad) Angula diffeence between neighbo tansceives (ad) L Coveage aea of a tansceive (cm ) C Effective coveage aea of a tansceive (cm ) I P S ς V q λ Intefeence aea of two neighbo tansceives (cm ) Height of the tiangle in the coveage aea of a tansceive (cm) Maximum ange eachable by the FSO node (cm) Tansmitte souce powe (dbm) Sensitivity of the photo-detecto eceive (dbm) (assumed -43dBm) adius of the eceive (cm) Visibility (km) Paticle distibution constant Optical signal wavelength (nm) q Paticle distibution constant x Side angle of the uppe isosceles tiangle within the intefeence aea (ad) k Length of the base side of the uppe isosceles tiangle (cm) y Vetex angle seeing the intesecting ac of the intefeence aea (ad) Assuming that n tansceives ae placed at equal distance gaps on the cicula FSO node, and since the diamete of a tansceive is ρ : π nρ π = = ρ n n Fom (1), the angula diffeence ϕ between two neighboing tansceives can be deived: ϕ = () π Let L be the coveage aea of a single tansceive, which can be deived as: 1 L + (1) = tan π ( tan ) (3)

3 (a) Case I: Coveage aeas of tansceives do not ovelap. Intefeence aea φ (b) Case II: Coveage aeas of tansceives ovelap. Figue : Coveage aea of a -d cicula FSO node. ρ Fo the effective coveage aea C of a single tansceive, two cases can happen based on the values of ϕ,,, and : Case I: Coveage aeas of the neighbo tansceives do not ovelap, i.e. tan ( + ) tan( ϕ / ). In this case, the effective coveage aea is equivalent to the coveage aea, i.e. C = L. Case II: Coveage aeas of the neighbo tansceives ovelap, i.e. tan > ( + ) tan( ϕ / ). In this case, the effective coveage aea is equivalent to the coveage aea excluding the aea that intefees with the neighbo tansceive. Let I be the intefeence aea that ovelaps with the neighbo tansceive s coveage, then C = L I. How to calculate the intefeence aea I? : As shown in Figue -(b), the intefeence aea I is composed of two isosceles tiangles and two leftove pies. To find Tansceive Not coveed aea Maximum possible ange Half lobe aea the aea I, we need to find the angles x and y, and the length k, as shown in Figue 3. Fom Figue 3-(a), we can wite the following elationships: 180 y x + ϕ = (4) k y = tan sin (5) cos x Fom (4) and (5), we find x and y, which means aea of the uppe isosceles tiangle can be found. Howeve, we still need to know the length k, which can be found by angles and lengths of the seveal tiangles in Figue 3-(b): ϕ ϕ k = sin sin (6) cos How to calculate the imum ange? : Anothe impotant unknown is the imum ange that can be eached by the -d FSO node. is dependent on the tansmitte s souce powe P dbm, the eceive s sensitivity S dbm, the adius of the tansmitte ρ cm, the adius of the eceive ς cm, the visibility V km, the optical signal wavelength λ nm, and the paticle distibution constant q. FSO popagation is affected by both the atmospheic attenuation A L and the geometic spead A G, which pactically necessitates the souce powe to be geate than the powe lost []. Thus, fo a conventional photo-detecto (PD) sensitivity of S = - 43dB, the following inequality must be satisfied fo the PD to detect the optical signal: ( P + 43) > A L + A G Substituting A L and A G leads us to inequality, minimum solution of which is []: P + 43 > log σ ( e ) 3.91 λ = V 550 whee σ. B. Optimal Coveage ς + log ρ + 50 q Fo given tansmitte souce powe P, divegence angle, and visibility V, optimal numbe of tansceives that should be placed on the -d cicula FSO node can diffe. We optimize the total effective coveage aea nc (7)

4 of the -d cicula FSO node, though othe metics can also be chosen. Since C is dependent on P,, V and n; fo given and ρ, the optimization poblem can be witten as:, P, V, n { nc(, P, V, n) } (8) such that 0.1mad, P 3mW, and V 0, 00m. In ou seach fo the best n, fo a paticula FSO node and tansceive size, we vaied P, and V based on cuent FSO technology and liteatue, as shown in Table. φ/ x Table : PAAMETES FO OPTIMIZATION Paamete y (a) Need the angles x and y. (b) Need the length k. Figue 3: A few key angles and lengths need to be found to find the intefeence aea. Unit Value(s) Min Max Step mad P mwatts V M 00 0,00,000 cm ρ cm 0.1 /8 0.1 C. Optimal Coveage esults By applying the appoach descibed in the pevious section, we obtained optimal numbe of tansceives on a -d cicula FSO node that imizes the coveage aea. Hee, we epot a subset of ou esults fo the FSO node adius values of 1cm and 5cm fo indoos, and 0cm fo outdoos. Similaly, to examine diffeent weathe conditions, we vaied the visibility V. We epot a subset φ/ - φ/ φ k of ou esults fo visibility of 0.km fo advese, 6.km fo nomal, and 0.km fo clea weathe. Figue 4 shows the optimal numbe of tansceives n fo thee FSO node designs (one fo indoos, and two fo outdoos) fo all weathe conditions. Note that the optimal n values epoted in Figue 4 ae valid fo all the thee weathe conditions. So, an inteesting obsevation is that the souce powe P and the visibility V have little o no effect on the optimality of n; athe, the geometic shape of the FSO node and the divegence angle plays the majo ole. This is a vey impotant esult since it means that optimum numbe of tansceives is fixed fo a paticula FSO node and tansceive size egadless of the visibility and the souce powe situation. This popety of cicula o spheical (the popety can be shown to be valid fo 3-d sphees) FSO nodes allows adaptive tuning of the souce powe based on the actual visibility. Futhemoe, as can be seen fom Figue 4, the elative size of the FSO node adius and the tansceive adius ρ detemines the shape of the optimal n as changes. Also, as expected, the optimal n educes as deceases, though with steps at specific values coesponding to significant changes in the atio of the intefeence aea with espect to the total coveage aea. D. Design ecommendations Value of the communication ange,, fo vaious FSO node designs is vey impotant as it shows scalability of ou cicula -d FSO node designs fo long distances. As it can be seen fom Table 3, the imum communication ange of the node depends solely on the aea of the tansceive fo fixed and P. Table 3: MAXIMUM COMMUNICATION ANGE IN METES FO OPTIMAL FSO NODE DESIGNS WITH =170.1mad AND P=3mWatts. Designs Weathe Possible ID, ρ Advese Nomal Clea Usage (cm) V=0.km V=6.km V=0.km 1 1, Indoo 5, Indoo 3 5, Outdoo 4, Indoo 5, Outdoo 6, Outdoo 7 15, Indoo 8 15, Outdoo 9 15, Outdoo 0, Indoo 11 0, Outdoo 1 0, Outdoo Table 3 povides the paticula designs we investigated. We ecommend some of these designs in fo

5 Numbe of Tansceives Numbe of Tansceives Numbe of Tansceives Souce Powe (mwatts) Divegence Angle -- Theta (mad) Souce Powe (mwatts) Divegence Angle -- Theta (mad) Souce Powe (mwatts) Divegence Angle -- Theta (mad) (a) = 1cm, ρ =0.1cm (b) = 0cm, ρ =1cm (c) = 0cm, ρ =.4cm 0 Figue 4: Optimal n fo thee diffeent FSO nodes at all weathe conditions: Souce powe and visibility have little o no effect on the optimality of n. The shape of the FSO node and the divegence angle detemine the optimality of the total coveage. indoo usage (i.e. designs #1, #, #4, #7, and #) and othe fo outdoo usage (i.e. designs #3, #5, #6, #8, #9, #11, and #1). Though each design can seve a paticula pupose based on the application, we maked the ones that we think fit best to indoo and outdoo usages. Fo example, designs #7 and # would be vey good at using as a cental hub attached to the ceiling of a cowded oom as it can have lots of tansceives on it (i.e. ρ =0.1cm) while communication ange can be maintained at the ode of 50m. Designs #1 and # would pefom vey well as a small device being attached to laptops o othe mobile indoo devices whee size of the system is not desied to be lage. Similaly, designs #9 and #1 can be used at mobile nodes needing long-ange (~00m) outdoo communication, such as ships and flying objects like helicoptes. Designs #6 and #8 seems best fo medium-ange (~0m) outdoo usage whee anothe communicating node can be found within few hunded metes, as in fo the cas o othe mobile vehicles in a city. Table 3 also shows that ou FSO node designs scale up to m as the communication ange fo outdoos. III. SUMMAY We modeled communication coveage and ange fo a peviously poposed scheme fo mobile fee space optical communications using spheical sufaces tessellated with optical tansceives to obtain spatial euse as well as angula divesity. We showed, though two-dimensional modeling, that this kind of fee-space-optical system designs allow vey dense packaging, and can scale to vey long communication anges as well as lage coveage. Futue wok includes issues like optimal tansceive packaging pattens fo desied coveage in theedimensions, and application-specific designs of such systems. ACKNOWLEDGMENT This wok is funded by NSF gant STI EFEENCES [1] J. Akella, M. Yuksel, and S. Kalyanaaman, Multi- Element Aay Antennas fo Fee-Space-Optical Communication, Poceedings of IFIP/IEEE Intenational Confeence on Wieless and Optical Communications Netwoks (WOCN), Dubai, United Aab Emiates, Mach 005. [] S. Acampoa and S. V. Kishnamuthy, A boadband wieless access netwok based on mesh-connected feespace optical links, IEEE Pesonal Communications (Octobe 1999), Volume 6, pp [3] S. Anon, S.. otman, and N. S. Kopeika, Pefomance limitations of fee-space optical communication satellite netwoks due to vibations: diect detection digital mode, SPIE Optical Engineeing (Novembe 1997), Volume 36, Issue 11, pp [4] E. Bisaillon, D. F. Bosseau, T. Yamamoto, M. Mony, E. Benie, D. Goodwill, D. V. Plant, and A. G. Kik, Fee-space optical link with spatial edundancy fo misalignment toleance, IEEE Photonics Technology Lettes (Febuay 00), Volume 14, pp [5] G. E. F. Faulkne, D. C. O'Bien, and D. J. Edwads, A cellula optical wieless system demonstato, IEEE Colloquium on Optical Wieless Communications, 1999, pp 1/1-1/6. [6] D. J. T. Heatley, D.. Wisely, I. Neild, and P. Cochane, Optical Wieless: The stoy so fa, IEEE Communications (Decembe 1998), Volume 36, pp [7] J. M. Kahn and J.. Bay, "Wieless Infaed Communications", Poceedings of the IEEE (Febuay 1997), Volume 85, pp [8] A. J. C. Moeia,. T. Valadas, and A. M. O. Duate, Optical intefeence poduced by atificial light, ACM/Kluwe Wieless Netwoks, Volume 3, pages , [9] H. Uno, K. Kumatani, H. Okuhata, I. Shikawa, and T. Chiba, ASK digital demodulation scheme fo noise immune infaed data communication, ACM/Kluwe Wieless Netwoks, Volume 3, pages 11-19, [] H. Willeband and B. S. Ghuman, Fee Space Optics (Sams Pubs, 1st edition, 001). [11] Y. E. Yenice and B. G. Evans, Adaptive beam-size contol scheme fo gound-to-satellite optical communications, SPIE Optical Engineeing (Novembe 1999), Volume 38, Issue 11, pp