Approximate Performance Study of Non-Line-of- Sight Ultraviolet Communication Links in Noncoplanar Geometry

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1 01 7th International ICS Conference on Communications and Networking in China (CHINACOM) Approximate Performance Study of Non-Line-of- Sight Ultraviolet Communication Links in Noncoplanar Geometry Yong Zuo, Houfei Xiao, Wenbo Zhang, Haoran Xu, Jian Wu State Key Laboratory of Information Photonics and Optical Communications Beijing University of Posts and elecommunications Beijing, China Abstract his paper presents an approximate closed-form model of non-line-of-sight (NLOS) ultraviolet (UV) singlescatter propagation in noncoplanar geometry for tractable analysis. he path loss is given as a function of the transceiver geometry settings and the optical properties of the atmosphere. Numerical examples on path loss show that the approximate model is consistent with the integral-form noncoplanar propagation model. hen, the data rate and the channel capacity of a quantum-limited receiver are further investigated with different parameters, such as bit error rate (BE), communication range, and transmitter optical power and offaxis angle. Keywords-ultraviolet communication; non-line-of-sight; single-scatter I. INODUCION Optical wireless communication systems can be arranged in a number of configurations depending on the specific requirements [1]. he line-of-sight (LOS) optical wireless communication system, in which the transmitter (x) and the receiver (x) are in direct view without any object obstructing the path between them, is constrained by difficult alignment of the x and the x. he non-line-of-sight (NLOS) ultraviolet (UV) communication, on the other hand, is proposed as a new type of atmospheric optical communication technology with some important and potential advantages, and can be considered an effective supplement to conventional communications. In recent years, some NLOS UV communication link models have been developed. A NLOS single-scatter propagation model based on the prolate-spheroidal coordinate system was developed by eilly et al. [,3], and some approximate channel models in [4-6] extended it by means of closed-from expressions for tractable analysis. Based on extensive measurements at the 60 nm wavelength, an empirical channel path loss model was presented in [7]. All the above models considered the same case where the x beam and the x field-of-view (FOV) have coplanar axes. In recent literature [8,9], the models for noncoplanar geometries were investigated. eference [8] considered the special case of vertical x and arbitrary x orientation. he work in [9] proposed a propagation model to describe the path loss, where the x and x cone axes can be pointed in arbitrary directions. Some papers already analyzed the performance of NLOS UV links in terms of signal-to-noise ratio (SN) and bit error rate (BE) of the x for noncoplanar geometries [4,5,7,10,11]. In this paper, an approximate closed-form model is developed in noncoplanar geometry by considering the case of vertical x pointing and small scattering volume. his approximate model is compared with the integral-form model in [8] by numerical examples, which shows a good agreement. hen, the data rate and channel capacity performances for a quantum-limited x are derived to show trade-offs in BE, communication range, and x optical power and off-axis angle. Without integral computations, this model makes performance analysis of NLOS UV communication links much more convenient and can provide guidelines for field experiments. II. NLOS SINGLE-SCAE LINK he geometry sketch of NLOS UV single-scatter propagation is shown in Fig. 1. A x at point has the beam angle, the apex angle, and the off-axis angle which equals the angle between the transceiver baseline and the projection of the x beam axis onto the ground. A x with FOV is located at point. he x apex angle is 90º. An emitted ray C intersects the FOV boundary twice by the entrance point B and the departure point A. Figure 1. Sketch of NLOS UV single-scatter communication /1/$ IEEE

2 Following the propagation theory in [], the energy per unit area scattered from the differential volume V and received by the x can be calculated by E Pk cos( )exp[ k ( rr)] P( ) V, s e 1 S 4 rr 1 where [1 cos( / )] is the x solid cone angle, is the angle between the x FOV axis and the direction from the x to the scattering volume V, E is the beam energy, S is the angle between the forward direction of C and the scattering direction, P( S ) is the single-scatter phase function, ks and k e are the atmospheric scattering coefficient and extinction coefficient, r 1 and r are the distances of the differential volume V to the x and the x, respectively. In Fig. 1, denote the length of A as l. By applying the cosine rule and laws of trigonometry to some triangles, we have [cos sin tan ( / )] l rlcoscos r 0. (1) () Its two roots are cos cos sin tan ( / ) cos sin min,max r cos sin tan ( / ) l, where l max A and l min B correspond to the + and terms, respectively. For a small LED beam width, the common volume of the x beam and the x FOV can be well approximated by a cylinder with volume V D h, where h lmax lmin and D ( lmax lmin ) /4 are the height and the underside radius of the cylinder, respectively. When the scattering volume V is small, we can assume approximates zero, such that r 1 ( l max l min )/. eferring to [8], we obtain r r[ r l l sin ( ) / cos ( / )] ( r / l 1) r, 1 1 min min 1 min s arccos[( r r1 r ) / ( rr 1 )]. herefore, the total energy received by the x with detection area A is E E A k rr P( ) sin tan ( / ) cos sin. 16 [1 cos( / )][cos sin tan ( / )]exp[ ( )] s S ke r1 r (3) his closed-form expression can give well approximate results, which will be verified in the following. So it is useful for analyzing link performances and designing UV communication systems. III. NUMEICAL EXAMPLES We first characterize the path loss with different system geometric parameters, and then further study the data rate and the channel capacity Path Loss(dB) Standard model: Analytical model: Standard model: Analytical model: Standard model: =8 o Analytical model: =8 o A. Path loss he analytical model is validated by the integral-form single-scatter path loss model [8] (called standard model in this paper) in noncoplanar geometry regardless of turbulence. he model parameters are chosen as in [8], and the fixed geometric parameters are set as (,, ) (90, 30,10 ). he simulation results of (3) are shown in Fig. -4, demonstrating that this analytical model is fairly consistent with the standard model. he path loss (defined by E E ) gradually increases along with the range r varying from 1m to 0m or the increase of. hese results indicate that the proposed approximate model can make a good prediction about link performances for the cases of the short baseline range and the small scattering volume. Path Loss(dB) Figure. Path loss (per cm) ( 30). Standard model: Analytical model: Standard model: Analytical model: Standard model: Analytical model: Standard model: Analytical model: Figure 3. Path loss (per cm) ( 45). 97

3 Path Loss(dB) Standard model: Analytical model: Standard model: =16 o Analytical model: =16 o Standard model: =5 o Analytical model: =5 o relatively little. When is larger than 10º, the data rate starts to decrease fast. he effect of P on the data rate are presented in Fig. 7 while 0 and BE is While P increases by a factor of ten, the data rate increases by the same factor B. Data rate Figure 4. Path loss (per cm) ( 60 ). Each photon carries energy hc /, where c is the speed of light, is the wavelength, and h is the Planck s constant. So the average number of emitted photons generated by the signal per pulse is N P /( hc), where P is the x emission power and is the data rate. hen, the average number of photons delivered to the x per pulse is N P / ( Lhc), where L N / N is the path loss. Assume the x is a solar blind filter in series with a photomultiplier tube (PM), f is the filter transmission, r and M are the PM quantum efficiency and gain, respectively. hen the average number of detected signal photoelectrons per bit is expressed by NS M frp/( Lhc). For direct detection by a quantumlimited on-off keying (OOK) modulation system, the BE is given by [1,13] PM fr BE exp. (4) L( hc / ) For Hamamastu PM 6834, the diameter of effective sensing window is 5mm, resulting in an active detection area of 4.9cm. he PM quantum efficiency is given by r ( S ) / %, where S is the radiant sensitivity 3 in A/W at the given wavelength. For 6834, S 810 A/W, so the quantum efficiency approximated 13.7% at 54nm. he 5 gain of 6834 is M We assume 0.1. Fig. 5 demonstrates the data rate-range-be performance while P 1 mw and 0. For the BE requirements of 10-3 (voice service) and 10-6 (data service), the corresponding data rates can approach Mbit/s and 40Mbit/s for the range of 10m, and drop to 6Mbit/s and 3Mbit/s for m, respectively. Fig. 6 shows the effect of on the data rate while 6 P 1mW and the BE = 10. It can be seen that due to the reduced scattering volume, the data rate decreases as increases. he data rate decreases slowly along with varying from 0º to 10º, since the scattering volume changes f BE=10-3 BE=10-4 BE=10-5 BE=10-6 Figure 5. Data rate, range, and BE trade-offs Figure 6. Data rate, range, and 0 trade-offs. P =0.5 mw P =5 mw P =50 mw Figure 7. Data rate, range, and x power trade-offs. C. Channel capacity he nature of the UV channel is governed by the properties of atmospheric gases, resulting in the variety of the channel capacity. We assume the atmospheric channel is an additive white Gaussian noise (AWGN) channel. he channel capacity can be defined as the maximum amount of information. Based 98

4 on Shannon theory [14], the capacity ( bit/s ) of the AWGN channel with the channel bandwidth B and SN is: C Blog (1 SN), (5) where the quantum-limited SN [13] can be described by SN P / ( hcbl). (6) f r After some algebraic manipulations, we can have P hcbl P C log (1 ) hcl P hcl. (7) f r f r f r When the bandwidth B approaches infinite, we can find frp hcbl frp lim C lim log (1 ) B hcl B f rp hcl (8) f rp f rp log e hcl hcl Assume that the data rate equals the bandwidth B. hen, the channel capacity will not increases to infinite but tends to a certain value while the data rate approaches infinite, as shown in Fig. 8. his figure demonstrates the channel capacity-rangedata rate performance for P 1 mw and 0. In the short-range NLOS UV communication, the increasing rate of the channel capacity will decline as the data rate increases. he channel capacity always deceases as the range becomes longer Data rate=10 (bit/s) Data rate= (bit/s) Data rate= (bit/s) Data rate=infinite Figure 8. Channel capacity, range, and data rate trade-offs. Fig. 9 shows the effect of on the channel capacity while P 1mW and the data rate is bit/s. It can be seen that due to the reduced scattering volume, the channel capacity deceases as increases. he channel capacity decreases slowly along with varying from 0º to 10º, and then decreases fast when becomes larger. he effect of P on the channel capacity is presented in Fig. 10 while 0 and the data rate is bit/s. It can be seen that the channel capacity is sensitive to P. As P increases, more energy is received, and the channel capacity increases. At present, the radiated optical power levels of a deep UV LED is in the mw ranges [15]. In order to further increase the total emission power, an array of UV LEDs [5,7,10] were used to achieve better performances, such as the data rate and the channel capacity Figure 9. Channel capacity, range, and 10 P =0.5 mw trade-offs P =5 mw P =50 mw Figure 10. Channel capacity, range, and x power trade-offs. IV. CONCLUSIONS In this paper, an approximate closed-form model of NLOS single-scatter propagation is presented for noncoplanar geometry, which is tractable for path loss analysis. Numerical examples show that the approximate model agrees with the integral-form model in [8]. he data rate and the channel capacity are also studied for various system parameters. Our numerical results indicate that these performances are affected by the x emission power, the transceiver geometry parameters, and the properties of the x (e.g., quantum efficiency, gain and detection area). Without integral computations, this model makes performance evaluations much more convenient. Our future work will apply this model to UV mobile ad hoc network simulations and provide guidelines for UV communication system design. ACKNOWLEDGMEN his work was supported by the Fundamental esearch Funds for the Central Universities 01. EFEENCES [1].. Iniguez, S. M. Idrus, Z. Sun, Optical wireless communications: I for wireless connectivity, CC Press, 008, pp

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