Advances in Military Technology Vol. 7, No. 1, June Requirements for Control System of Mobile Free Space Optical Link

Transcription

1 AiMT Advances in Military Technology Vol. 7, No. 1, June 01 Requireents for Control Syste of Mobile Free Space Optical Link J. Čižár * and J. Něeček Departent of Aerospace Electrical Systes, University of Defence, Brno, Czech Republic The anuscript was received on 9 January 01 and was accepted after revision for publication on 3 February 01. Abstract: The paper deals with the influence of control syste of a obile free-space optical (FSO) link on the power budget of the link. Perissible fluctuations of the received power are taken into consideration. It is assued that these fluctuations are caused by oscillations of the optical bea across the receiver aperture. The design, operation and transfer functions of the control syste of the optical axes position are described. Keywords: Free space optical link, power budget, steady odel, control syste, global positioning syste, inertial reference unit, video caera, transfer function 1. Introduction Free space optical (FSO) links are an alternative of the radio frequency wireless links. The FSO links are inherently resistant to jaing and tapping because of the low optical bea divergence and the sall receiver field of view. However these syste paraeters are the reason of a high sensitivity of the link to spatial fluctuations of link stations. The fluctuations cause angular deflections of the bea which deteriorate the power budget. It results in the link fade, if the link argin is depleted. The entioned features are significantly iportant naely for the directional obile FSO links because they are naturally affected by optical beas oscillations around the deanded direction. For the chosen exaple, liit angular bea deflections are calculated. These deflections represent basic requireents which are iposed on the syste which controls the angular position of the FSO link. For the Gaussian bea, the dependence of the liit deflections on the link distance is derived. Influences of the atosphere, such as the turbulence of air and the absorption and the scattering of the optical radiation are not assessed in the article. * Corresponding author: Departent of Aerospace Electrical Systes, University of Defence, Kounicova 65, Brno, Czech Republic, phone: , E-ail: jan.cizar@unob.cz

2 70 J. Čižár and J. Něeček. Power Budget of FSO Link The power budget of the FSO link serves to the calculation of the radiant flux incident on the detector or the receiver aperture. If a span of desired values is defined, it can be judged whether the value of the radiant flux obtained fro the steady odel lies in the given span and what is the link argin on rando effects. Thus, the power budget provides basic inputs for assessing the link reliability. Transitter of Station 1 Receiver of Station R S SR TXA TW G RW RXA F TX TW RW A RXA P D F P SR P t P r P PD R Fig. 1 Arrangeent of one channel of the FSO link [1] In Fig. 1 [1], the schee of the atospheric part of the FSO link is shown, where: F is the filter, SR is the source of radiation, PD is the photodiode, RW is the receiver window, RXA is the receiver optical syste, TXA is the transitter optical syste, TW is the transitter window, R is the distance between stations, P SR is the optical power eitted by the source and detected by the photodiode respectively, P r is the power received by the station No., P t is the power transitted by the station No. 1, is the optical attenuation. On the basis of knowledge of the transittance of the FSO link eleents and losses arising fro iperfect relations between the corresponding eleents, the radiation attenuation caused by individual parts and then the total attenuation can be expressed. Fro the known transitted power and the total attenuation, the received power can be calculated. With the ai to assess the influence of the control syste on fluctuations of the received power, a reduced steady odel can be used. This odel expresses relationship between the output power P t [db] of the station 1 and the power P r [db] of radiation incident on a receiver window area of the receiver aperture size, see Fig. 1. Let us suppose the so-called ideal pointing of the link. The ideal pointing is such relative position of the opposite stations when the axes of the optical bea of the transitter and receiver field of view are identical. The reduced atheatical steady odel of a link gives the dependence of the received power on geoetric losses. Their origin consists in the propagation of optical radiation between the link stations. If additional gain of the receiver consequent upon a specific distribution of the optical intensity in the bea is ignored, this odel can be expressed by the forula [, 3]:

3 Requireents for Control Syste of Mobile Free Space Optical Link 71 DRXA Pr Pt G Pt 0log (1) D ΘR where D TXA [] is the diaeter of the transitter aperture, D RXA [] is the diaeter of the receiver aperture, P t is the transitted optical power, R [] is the distance between the stations, α G [db] is the geoetrical attenuation, [rad] is the angular width of the bea. The reduced steady odel of the link with ideal pointing ust eet the requireent [3]: S r TXA DRXA Pt 0log Prsat DTXA ΘR () where P rsat [db] is the axiu perissible received optical power, S r [db] is the receiver sensitivity. The difference between the axial perissible optical power P rsat and the receiver sensitivity S r is the dynaic range Δ [db]: Δ P rsat S r (3) The difference between the received optical power P r and the receiver sensitivity S r is the link argin M [db]: M P r S r (4) which is constant for stationary FSO links. For obile FSO links, it depends on the instantaneous distance between the stations. Fig. The reduced steady odel [4] Let the individual variables be: P t = db (30 W), D TXA = 3 c, D RXA = 0 c, S r = db ( W), Δ = db, = 17 rad ( 1 ) and required

4 7 J. Čižár and J. Něeček interval of the distance R 100, 000. Fro the forula (3), we receive: P rsat = db, (5 10 ) W. For the values of the individual variables entioned above, the graphical representation of the steady odel of the link is in Fig.. There is the link argin arked for the distance R = It is obvious that the link is usable approxiately fro the distance of 300 because the received power P r > P rsat for R < 300. The fact does not coply with the condition (3). If the link should be usable in the entire span of the distances R, the power budget ust be adjusted. Let us suppose that the bea divergence or the transitted optical power P t can be altered only. The fact that the deanded values of both the divergence and the power P t are achieved can be assessed according to the condition P r (R) = P rsat, where R = 100. If the divergence is altered and the other quantities are constant, the liit state is reached for = 5 rad. If the transitted power P t is adjusted only, the liit state occurs for P t = db (14.7 W). The iportant result of the power budget is the link argin M which plays a crucial role in the link reliability []. This quantity specifies the axiu allowable value of additional power losses of the real link which are caused by the atosphere, radiation background and aiing errors. If the syste should be sufficiently robust against these influences, the link argin ust be as big as possible for all required lengths. For the link with constant paraeters, it is obvious that this argin decreases as the distance between the stations increases. Thus, the length of the link affects its sensitivity to undesirable phenoena which are practically anifested with deterioration of transission characteristics and degradation of the link availability. In this situation, it is appropriate to ensure copliance with the condition () at a big value of the bea divergence. It is necessary for the receiver to have a big dynaic range Δ. This can ensure the sufficient link argin. 3. The Influence of Deflection on the Magnitude of Received Power Given that pointing errors occur for the real obile FSO link, the paraeters of the link or the paraeters of the control tracking syste have to be chosen in dependence on perissible fluctuations of the received power. These fluctuations are caused by changes of the linear and angle link station position. The changes are natural and peranent circustances of the operation. They affect the stations placed on an arbitrary platfor. Differences follow fro a character of a oveent of specific platfors. The entioned fluctuations depend on the platfor type and the perforance of the control syste which provides autoatic tracking of the opposite link stations. The pointing errors are: angular deflections of the receiver field of view fro the ideal position, angular deflections of the optical bea fro the ideal position. The angular deflections of the receiver induce rando displaceents of a radiation spot relative to the sensitive surface of the detector. If the surface is not large enough, the power losses can occur because only portion of radiation received by the optical syste is incident on the sensitive surface. This article does not deal with the pointing errors of the receiver, influence of the atosphere and influence of background radiation. It is focused only on the losses caused by the displaceent of the optical bea relative to the receiver aperture.

5 Requireents for Control Syste of Mobile Free Space Optical Link 73 The angular deflections of the optical bea ba [rad] result in rando linear bea deflections bl [] in the receiver aperture plane. The draft requireent placed on these deviations is to fulfil the inequality δ bl R DRXA wr (5) where w(r) is the bea waist at the distance R. For the bea with the sall divergence and for the tiny pointing deflections, it applies R w ΘR (6) R δbl δbar (7) Meeting of relation (5) ensures that the receiver aperture does not shift fro the optical bea. In general, even if the (5) is coplied we ust assue that M = 0 db for bl = bl = ba R, where bl, ba are the liit linear and angular bea deflection, respectively. However, we can also assue that received power is sufficient for deviation bl (R) > w(r) D RXA /. We have to take into consideration the fact that the optical intensity of the bea is dependent on the distance fro the bea axis. Let us suppose that the intensity distribution is Gaussian. For the Gaussian bea, we can write []: P t r I R, r exp (8) ΘR ΘR where r is the distance fro the centre of the bea spot in the plane of the receiver aperture. To assess the influence of the pointing errors on the link reliability, it is proper to deterine the liit angular deflection ba on the basis of the power incident on the receiver aperture which is out of the bea axis. y R Bea footprint A w( Receiver aperture C D RXA x R Fig. 3 Misalignent of the bea footprint [5] The shift of the bea spot relative to the receiver aperture in the receiver coordinate syste Cx RXA y RXA is depicted in Fig. 3 [5]. If the area of the receiver aperture A r is coparable with the area of the bea spot, the received power P r (R, bl ) has to be calculated on the basis of the general equation [5]

6 74 J. Čižár and J. Něeček R, Ir δ, Rdr P (9) r bl Ar where I(r bl, R) is the optical intensity in the receiver coordinate syste, r is the radial vector fro the bea centre. π If D RXA << R, the optical intensity on the receiver aperture can be considered constant and its value is a function of the distance between the receiver aperture centre C and the bea axis. For purposes of the deterination of the requireents for the control syste, the received power is expressed in the dependence on the angular deflection of the bea. When bl is substituted for r into (8) and then (7) is substituted for bl, the power incident on the receiver aperture of the area A r can be expressed as R, δ IR, δ bl Pt δba P A 0.185πD exp (10) r ba ba r RXA ΘR Θ Fig. 4 Course of the liit angular bea deflection

7 Requireents for Control Syste of Mobile Free Space Optical Link 75 The condition for the liit angular deflection of the bea ba is then given by P TXA δba.185πd RXA exp S 0 (11) Θ R Θ 0 r Fro the (11), the analytical expression of the ba can be derived as δ ba Sr ΘR 0.5Θ ln (1) 0.185πD P RXA In accordance with the chosen exaple, the graphs of the liit angular deflection ba are in Fig. 4 for two configurations of the obile FSO variables: P t = db (14.7 W), = rad, P t = db (30 W), = 0.05 rad. In line with expectation, it is obvious fro Fig. 4 that the link with the higher divergence is ore favourable fro the view of the sensitivity to the pointing errors. For the design of the link, it is iportant that the value of the ba decreases as the distance R increases. Thus, the tracking syste should be designed as adaptive, or the worst situation has to be taken into account when the distance R is axial. The corresponding liit angular bea deflections ba are 3.0 rad and 16.0 rad, for = 5.0 rad and = 17.0 rad, respectively. 4. Control of Position of the Optical Axis of the FSO Stations There are two possibilities of the position control of the optical axis of the FSO link station. The optical axis is the line which is parallel to both the optical bea axis and the receiver field of the view axis. The first variation is based on the control of position of the entire station, see Fig. 5. The entioned axes are separated. Movable parts are relatively assive and have a high oentu of inertia. This iplies the requireent for higher power of the actuator. The second variation lies in the usage of the syste of irrors. At least two irrors are needed. One of the is fixed and the second one is ovable, see Fig. 6. A saller power and sipler design of the actuator can be supposed. The axes of the bea and the receiver field of view are joined. TXA Fig. 5 Control of the position of the entire station Fig. 6 Control of the optical axis of the position of the FOS link by eans of an asseblage of irrors

8 76 J. Čižár and J. Něeček A design of the control syste of the FSO station otion is a icroprocessor syste (MPS). The ethod of the control of the optical axes of the link is designed as a twostep ethod. Each of both FSO stations is equipped with a receiver of the global positioning syste (GPS), an inertial reference unit (IRU) and a television caera (TVC), see Fig. 7. Fig. 7 Structure of the control syste of the FSO station otion The first step is based on the satellite navigation. Both of the FSO stations are equipped with receivers indicating their geographic co-ordinates, naely L s for the stationary station and L for the obile station. The structure of these co-ordinates (longitude λ s,, latitude s,, ellipsoid high h s, ) of the WGS-84 syste is as follows: L s λs, s, hs, L,, h (13) Fro the co-ordinates L s,, the MPS calculates the coponents of the distance between the stationary and obile stations in the South-North direction n s- and in the East-West direction e s- : e s n s R z s s Rzcos s (14) h s h where R z is the radius of the Earth. With regard to the relatively sall distance between the stations (approx. k; it represents the equatorial angle approx. 1.1), the Earth orb can be treated as a sphere and the local Earth radii in the points of both stations can be unified into one by eans of the arithetic average of the latitudes of both stations. The distance between both stations can be expressed by the forula: s h s s s R n e h (15) The aziuth of the optical-axis bea of the stationary station can be expressed in all of the individual quadrants by the forulas:

9 Requireents for Control Syste of Mobile Free Space Optical Link 77 ψ ψ s s n arctan e s s, e s 0, n s 0 ns ψ s π arctan, ns 0 (16) e s ns π arctan, es 0, ns e s The elevation angle of the optical-axis bea of the stationary station can be expressed by the forula: 0 h hs ξ (17) s Siilar forulas are valid also for the aziuth and elevation of the optical-axis bea of the obile FSO station. The forulas (14) to (17) have been derived for the local Earth co-ordinate syste (LECS), e.g. the beginning of the systes lies on the circuference of the Earth, the axes X and Y lie in the horizontal level the axis X points to the North and the axis Y to the East. The axis Z points to the centre of the Earth. The control signals for the aziuth and elevation servoechaniss of the FSO stations ust be calculated with regard to the body co-ordinate syste (BCS) of the respective station which in respect of the local Earth co-ordinate syste is in practice turned by the angles of the aziuth, turn and pitch (Euler angles). Therefore the control signals calculated fro the data of the GPS receivers ust be transfored fro the LECS to the BCS e.g. by eans of the direction cosine atrices or the rotation quaternions. The position angles BCS with regard to the LECS are easured with the IRU. It is a easuring central the ain sensors of which are three-axis systes of icroechanical (MEMS) gyros, acceleroeters and agnetoeters. This unit has been developed within the cooperation of our departent with the copany Oprox., s. r. o. [6]. Fig. 8 The block diagra of the servoechaniss of the FSO stations The second step of the otion control of the optical axis of the link station is based on the observation of the optical beacon by eans of a TV caera. Through the technology of the diagnosis of the picture, the deviations of the up-to-date position of the optical axis fro the ideal position (the centre of the caera field of view) are evaluated. With regard to the fact that the caera is steadily connected with the body of the FSO station and its optical axis is parallel to the optical axis of the link station, the evaluated signals are directly usable as a positional feed-back in the servoechaniss of the aziuth and elevation. To suppress the oscillation of the servoechaniss, also

10 78 J. Čižár and J. Něeček a speed feed-back ust be established. Signals of the speed feed-backs of both servoechaniss are created in the icroechanical sensors of angular speed (gyroscopes), which are parts of the IRU. The IRU are also steady parts of the both FSO stations and the sensitive axes of their sensors ust be orientated into the syetry axes of the bodies of the FSO stations. Therefore also the angular-speed signals are directly usable as signals of the speed feed-backs for the servoechaniss of the aziuth and elevation. The transfer function of the angle can be written as follows, see Fig. 8: 1 αt ( s) kp F α ( s) (18) αr ( s) I kr s s 1 Ak k k where α r is the required angle, α t is the true angle, A is the power aplification, k is the aplification of the servoechanis engine, I is the total oent of the inertia of the servoechanis obile part of the FSO station, k p is the aplification of the position feed-back, k r is the aplification of the speed feed-back, s is the Laplace operator. For the transfer function of the disturbing oent M i (M s is the oent of the servoechanis and M is the total oent applied to the body of the FSO station.), the forula is valid: p p 1 αt ( s) Akkp F M ( s) (19) Mi( s) IΣ kr s s 1 Ak k k Fro the transfer function, it can be seen that the steady deviation caused by the disturbing oent M i is: p p 1 αt ( s) Mi( s) (0) Ak k The greater the total aplification of the servoechanis, the lesser the influence of the disturbing oent. The tie constant T and the duping coefficient are described by the forulas: p 1 Ak T I Ak k, ξ kr (1) p IΣkp 5. Conclusion The individual construction coponents of the servoechaniss, as well as general syste paraeters ust be able to ensure the stabilization of the optical axis of the FSO station with sufficient accuracy so that the discontinued optical link does not cause link fades. It is its angular precision which is the fundaental requireent for the control syste. The real perissible deviations of the laser bea ust be lower than the liit

11 Requireents for Control Syste of Mobile Free Space Optical Link 79 angular bea deflections. These deflections depend on the transitted optical power, the bea divergence and the distance between link stations. The operational interval of the link distances plays the crucial role, see Fig. 4. To optiize the values of the individual construction paraeters, coputer siulations of various variants of the conditions of the FSO usage will be carried out. References [1] NĚMEČEK, J. Chosen Paraeters of the statistical odel of Free Space Optical Link (in Czech). In Trendy rozvoja vzdušných sil. Košice: Vojenský letecký technický a skúšobný ústav, p. [] KOLKA, Z. and WILFERT, O. Statistical Model of Free-Space Optical Data Link. In Proceedings of the International Syposiu on Optical Science and Technology. Denver: The International Society for Optical Engineering, 004, p. 03. DOI / [3] NĚMEČEK, J. and ČIŽMÁR, J. Control Syste for Positioning of a Transitter Optical Bea and a Receiver Field of View for a Mobile Free Space Optical Link. In Proceedings of 5th International Syposiu Advances in Mechatronics (AiM 010). Trenčín: Faculty of Mechatronics, Alexander Dubček University of Trenčín, 010, p ISBN [4] WILFERT, O. and NĚMEČEK, J. The availability of optical wireless links in chosen localities of the Czech Republic. In 1st International Scientific Conference on Technology. Bratislava: Special Technology 006, p ISBN [5] FARID, A.A. and HRANILOVIC, S. Outage Capacity Optiization for Free- Space Optical Links With Pointing Errors. Journal of Lightwave Technology [on line]. July 011, vol. 5, no. 7, p [cited ] Available fro: < [6] JALOVECKÝ, R., ČIŽMÁR, J. and ŠKVAREK, J. An Inertial Reference Unit developent and Testing. In Proceedings of the nd International Scientific Conference Special Technology. Bratislava, 008, p ISBN Acknowledgeent This research has been supported by the Research progra of the Czech Science Foundation No. 10/09/0550.