Receiver Design for Underwater Wireless Optical Communication Link based on APD

Transcription

1 1 7th International ICST Conference on Communications and Networking in China (CHINACOM) Receiver Design for Underwater Wireless Optical Communication Link based on APD Shijian Tang, Yuhan Dong, Xuedan Zhang Tsinghua University, Department of Electronic Engineering, P. R. China {dongyuhan, Abstract In this paper, we present a gain control scheme of receiver based on avalanche photodiodes (APDs) for underwater wireless optical communication links. We first derive the approximate expression of optimal gain of APD. Then based on beam-spread function, a closed-form expression of relationship of optimal gain of APD, link range and receiver offset distance is derived. Then a self-adaptive gain control scheme is designed to keep the gain of receiver as optimal gain when the receiver deviates unpredictably. We also evaluate the dynamic range of receiver gain. Our results are beneficial for receiver design and link reliability improvement. Index Terms underwater wireless optical communication, gain control, link misalignment, avalanche photodiode I. INTRODUCTION Underwater wireless optical communications provide an alternate method to traditional acoustic communications, which utilize blue/green region of visible spectrum as this wavelength suffers lowest absorption. The acoustic communication links 1] ] has widely used as the long propagation distance of sound. But, acoustic links have several disadvantages such as bandwidth restriction, multipath reflections, high latency and low security. Compared with acoustic links, this new technology has a main advantage of high data rates up to 1 Gbps 4] in the relative short distance and also avoids the other shortcomings of the acoustic links mentioned above. Most previous studies of underwater wireless optical communications have assumed ideally aligned optical links between the transmitters and receivers (see 5], 6] and references therein), which is hard to implement in the realistic links due to the unpredictable offset distance caused by fluctuations of the seawater and relative motion between source and receiver. To keep the link reliability for the misaligned link, we present a gain control scheme for APD receiver for given transmit power. In this paper, we derived a closed-form expression to describe the relationship of optimal gain of APD, link range and receiver offset distance. Then a self-adaptive gain control scheme is designed to keep the gain of APD as optimal gain, i.e., the symbol-error-rate (SER) remains minimum. Furthermore, numerical results suggest that, for specific transmit power and link ranges, the dynamic range of APD gain can be calculated for given permitted offset distance of receiver, which is beneficial for receiver design. Our scheme will enhance link reliability and release the pointing reuirement of underwater wireless optical links /11/$6. c 11 IEEE A. Receiver Model II. SYSTEM MODEL The optical detector used in this paper is avalanche photodiode (APD). Compared with photomultiplier (PMT), APD has a more compact size, and can be easily mounted into underwater devices. While the gain of APD is lower than PMT, the larger uantum efficiency of APD in visible spectrum than PMT is as compensation. Instead of the ideal photon counting model, the noise distribution of APD is closer to the realistic devices. Here we give a brief introduction of the noise distribution of APD. Details of this model can be found in 7], 8]. The number of detected photoelectrons is determined by a modulated Poisson point process based on the semi-classical theory of photodetection. We designate incident power of the active area of detector as P (t). The number of generated photoelectrons in the duration of T follows a Poisson distribution with the parameter K which is also the mean number of generated photoelectrons. We can obtain K from K = η T P (t)dt hν where η is the uantum efficiency, h = J s is the Planck s constant, and ν is the center optical freuency of the source. The second process of the optical detection is the avalanche multiplication of photoelectrons. As the result, the secondary electrons will generate through this process. The number of secondary electrons is described by a complex distribution derived by Webb, Mclntyre, and Conradi 9]. However, under the condition that the background radiation and dark current is not negligible as well as the contribution of additive thermal noise of the receiver electronics is considered, a Gaussian distribution can be used to describe the received signal approximately with parameters as σ x = µ x = GK x + I st s G F K x + I st s + κt T s R L (1) () ] BT s () where µ x is the mean of the received signal in a slot, and σ x is the variance. We use subscript x = 1 and to represent the slots with and without pulse, respectively. K and K 1, /1/$1. 1 IEEE

2 therefore, are the mean numbers of the detected photons in empty and pulse slots, respectively. K and K 1 take the forms K = K b + I bt s K 1 = K s + K b + I bt s where K b = ηp b T s /hν and K s = ηp av T s /hν, describing the mean number of photoelectrons generated by the background noise and source, respectively, with T s as the duration of a slot, P av as the average received power of the pulse slots of signal, and P b as the background noise power including the background ambient light from refracted surface solar estimated by (6) and the blackbody radiation by (8). I b is the bulk leakage current which can be multiplied by APD, and therefore, I b can be treated as an euivalent background radiation. I s is the surface leakage current which cannot be multiplied by APD and can be treated as the direct-current. Note that the dark current I d is the sum of multiplied bulk leakage current and surface leakage current, i.e., I d = GI b +I s. G is the gain of APD, and F is the excess noise factor can be computed by F = Gk eff + ( 1/G)(1 k eff ) with k eff as the effective ratio of the hole and electron ionization coefficients. T is the euivalent noise temperature, and B is the euivalent noise bandwidth of the receiver. κ = J/K is the Boltzmann s constant, and = C is the electron charge. R L is the load resistance. B. Background Radiation Estimation The background noise power including ambient light and blackbody radiation can be estimated using the methods in 1], 11]. The ambient light from the sunlight can be estimated by P ba = π a (F OV ) λl sol 16 where P ba is the average power of the ambient light, a is the diameter of the receiver aperture, F OV is the field of view of the receiver in units of radian, and λ is the receiver bandpass of the wavelength. Parameter L sol can be obtained by L sol = ERL f ac exp( cd) π where L sol is the downwelling radiance from the sunlight, E is the downwelling irradiance, R is the reflectance of downwelling irradiance, L fac is a parameter to represent the directional characteristic of the radiance, and D is the depth of the link. The blackbody radiance can be estimated by P bb = hv απ (F OV ) a λ exp( cd) λ 5 (exp(hc /λκt ) 1) where c is the speed of the light in the seawater, α is the radiant absorption factor, and other symbols remain the same meaning in this paper. (4) (5) (6) (7) (8) The background noise power P b is the sum of ambient light power and blackbody radiation, i.e., P b = P b a + P b b. The value of parameters above in our estimations are summarized here. E = 144 watts/m, corresponding to the 5 nm light. R = 1.5%, and the depth of our link is 1 m. L fac is.9 in horizonal direction. α =.5, and c = m/s. We also set the wavelength bandpass as 1% with the center wavelength as 5 nm. Other values of parameters will be presented in IV. C. Channel Model The channel model utilized in our paper is the BSF model 1]. The irradiance (incident power per unit area) distribution of receiver plane can be derived from volume scattering function (VSF) in this model. This model is defined based on three assumptions. First, it is assumed that the receiver is located in a plane, i.e., the receiver plane, perpendicular to the beam axis. The second assumption is that the light field is symmetric about the beam axis due to the homogenous and isotropic medium. The final one is that the directions of the scattered light strongly concentrate on small forward angles which also named as small angle scattering approximation. Based on these assumptions, the closed-form expression of this model is B(r, L) = E(r, L) exp ( cl) + 1 E(v, L) exp ( cl) π ( ) ] L ( ) exp bs v(l l) dl 1 J (vr)vdv (9) where B(r, L) is the irradiance distribution of the receiver plane. E(r, L) and E(v, L) are the irradiance distribution of Gaussian source in coordinate and freuency domain, respectively. J ( ) is the zero-order first class Bessel function. v is the spatial freuency. L is the link range, namely, the distance between the source and the receiver plane. r is the offset distance of the receiver, which is the distance between the center of the receiver aperture and the light field of the receiver plane. It is obvious that the zero offset distance means the precise alignment between the source and the receiver. b and c are the attenuation and scattering coefficients of the channel, respectively. s(v) is scattering phase function in spatial freuency domain, which can be derived from VSF by s(v) = 1 π s(β)j (vβ)βdβ (1) where β is the angle, and s(β) is the scattering phase function which can be derived from VSF by normalizing the VSF by scattering coefficient b. A. Signal Detection III. SYSTEM ANALYSIS The Pulse-Position-Modulation (PPM) is the modulation scheme in our paper as the wide usage of this modulation in optical communications. The PPM signal is detected by the maximum likelihood (ML) decision. The basic rules of this decision are summarized here: to the QPPM signal, log Q bits

3 are transmitted by Q slots with only one pulse slot and Q-1 empty slots. So we define the Q adjacent slots as a symbol. The received signal is detected in the unit of a symbol. For each symbol, we choose the slot which has the largest observed value as the pulse slot. If any ties occur, the ties are broken arbitrarily. Errors, therefore, may occur when the observed values of any empty slots larger than pulse slot or any ties happen. We designate Y i as the ith received slot and X i as the ith transmitted slot (i = 1,,..., Q) of a symbol. Then we assume that the pulse slot appears eually in each position of Q slots. The SER is SER = 1 P (Y 1 = max (Y 1, Y,..., Y Q ) X 1 = 1) (11) If we ignore the case of ties occur which has a little contribution to SER, we obtain an upper-bound of SER with a more simple expression. Q SER 1 P Y 1 < Y j X 1 = 1. (1) j= With the assumption that the signal of each slot is independent, we have SER 1 (P ( Y 1 < Y X 1 = 1 )) Q 1 (1) By substituting the distribution of the received signal in () and () to (1), SER becomes: SER 1 (1 1 ( erfc µ 1 µ ) ) Q 1 (σ + σ1 ) (14) where the right side of (14) is the upper-bound of SER which can be easily computed. Note that the SER in the following sections refers to the upper-bound of SER. Then we define a new variable ε, where ε = (µ 1 µ )/ (σ + σ 1 ). Using the upper-bound in (14), we have ε = erfc 1 ( (1 SER) 1 Q 1 B. Optimal Gain of APD ) (15) The results in earlier works 1], 14] have shown that the optimal gain of APD exists. The receiver reaches the lowest SER when the gain of the APD is the optimal gain. Notice that, the optimal gain of APD is not euivalent to the maximum gain. This is because the noise will also be multiplied as the gain increases, which will have a negative impact on the SER performance. Considering () (5) and (14) again, we find that the optimal gain of APD depends on the received power. Here, we will present the relationship between the optimal gain and K s. From () (5 and the definition of ε, we yield ε = GK s 4BTs G F (K + K s ) + C] (16) where C = I s T s / + κt T s / R L. Note that G is the argument and ε is the dependent variable with other parameters fixed. The optimal gain comes as the ε obtained the maximum value, i.e., Solving (17), we have G opt = 1 k eff ( G opt = arg max ε (17) B ) 1 ( + B + ) 1 (18) with B = 6k eff C/(K + K s ) and = B + 1k eff (1 k eff ). With the assumption that the optical signal penalties heavily in the seawater, i.e., the received power is weak, B is much greater than 1k eff (1 k eff ). Hence, (18) becomes G opt = 4C k eff (K + K s ) ] 1 (19) where G opt is the optimal gain. Euation (19) suggests that the optimal gain is the function of K s under given APD parameters and channel coefficients. Then by substituting G opt to (16) and combining with (15), the minimum SER is obtained. Then we derive a closed-form expression to describe the relationship of optimal gain, link range and receiver offset distance. Combining (19) with (9), we have G opt = 4C k eff (K + K s (r)) ] 1. () With the assumption that the aperture of receiver is narrow, K s (r) = πa ηb(r, L)T s /4hν with a as the aperture of receiver. Optimal gain for given link range and receiver offset distance can be calculated by (). IV. SIMULATION RESULTS First, we design a self-adaptive gain control scheme for APD based on (19). Then we calculate optimal gain for various link ranges and offset distance and evaluate the dynamic range of gain. Furthermore, we evaluate SER performance for the link with the gain control scheme. Using VSF as well as corresponding scattering and attenuation coefficients of coastal and harbor waters in 15] as channel coefficients, we set up two channels. A well collimated 5 nm laser source with a narrow divergence angle as.1 transmits 8 PPM signal with 1 MHz slots freuency. Then a compactsize receiver based on APD is assumed by setting the aperture as 1 cm (diameter) and the field of view as 18 (wide open FOV). The surface leakage current I s and bulk leakage current I b are 1 na and 1 pa, respectively. The euivalent noise temperature is 96 K and the uantum efficiency is.8. Finally, the load resistance is 1 Ω. The background noise power estimated is dbm and dbm in coastal and harbor, respectively.

4 Symbol Error Rate (SER) Analytical Results Simulation Results offset distance = 1.5m offset distance = 1m Optimal Gain db] L=6m L=8m L=1m L=15m 1 8 offset distance =.5m Gain of APD Offset Distance r m] Fig. 1. SER versus the gain of APD with varying offset distance for the link range of m and transmit power of W in coastal water Fig.. Optimal gain for various link ranges and offset distance in harbor water with transmit power as 5 W A. Self-adaptive Gain Control Scheme Fig. 1 depicts that the optimal gain of APD varies for different offset distance with a fixed transmit power, and the corresponding minimum SER also varies. The numerical results of the optimal gains and minimum SER calculated by (14) and (15) fit well with the values predicted by (19). Similar results can be obtained in other link ranges and water type. Therefore, a self-adaptive gain control scheme based on (19) will adjust gain automatically by receive power. Note that the gain of APD can be controlled by bias voltage. This scheme will keep the gain of APD as the optimal gain when the transmit power changes or the receiver deviates unpredictably. B. Optimal Gain for various Offset Distance Considering () again, we compute optimal gain for various L and r in both coastal and harbor waters. The transmit power is W and 5 W in coastal and harbor, respectively. Fig. and Fig. suggest that optimal gain increases as offset distance increases for given link range. This can be interpreted as the dynamic range of receiver gain is enlarged when the receiver is permitted with larger offset region. These results are instructive for designing the dynamic range of receiver gain. C. SER Performance Our study shifts to evaluate SER performance. Using (14), (16) and (), the minimum SER correspond to optimal gain is calculated for various offset distance. Fig. 4 shows SER decreases as the increase of transmit power. The increase of transmit power, therefore, is beneficial for releasing the pointing reuirement for links. The relationship between minimum SER correspond to optimal gain and 44 1 Optimal Gain db] L=m L=m L=4m L=5m Minimum Symbol Error Rate (SER) P = 1W P = W P =.5W P = W Offset Distance r m] Offset Distance r m] Fig.. Optimal gain for various link ranges and offset distance in coastal water with transmit power as W Fig. 4. Minimum SER performance versus offset distance for various transmit power of the 1 m link in harbor 4

5 transmit power for different offset distance is out of our scope of this paper. V. CONCLUSION In this paper, we have investigated the receiver design for underwater wireless optical communication link with APD as receiver. We have presented a gain control scheme to improve the link reliability. Then a closed-form expression is derived to evaluate the dynamic range of gain for specific link range and offset distance. Our results are beneficial for receiver design and link reliability enhancement. Our future work is building up the experiment platform to realize the self-adaptive gain control scheme mentioned in this paper. REFERENCES 1] T. J. Hayward and T. C. Yang, Underwater acoustic communication channel capacity: a simulation study, AIP Conference Proceedings, La Jolla, CA, USA, pp , 4. ] L. Freitag, M. Johnson, and D. Frye, High-rate acoustic communications of ocean observatories-performance testing over a m vertical path, in Proc. OCEANS Conf, Sep., vol., pp. 144C1448. ] H. Ochi, Y. Watanabe, and T. Shimura, Experiments of underwater acoustic communication using 16-QAM, 8th International Congress on Acoustics, Kyoto, Japan, 4. 4] F. Hanson and S. Radic, High bandwidth underwater optical communication, Appl. Opt., vol. 47, pp. 77C8, 8. 5] C. Gabriel, M. Khaligi, S. Bourennane, P. Leon, and V. Rigaud, Channel modeling for underwater optical communication, in IEEE nd Workshop on Opt. Wireless Commun., pp. 8-87, Dec ] W. Hou, A simple underwater imaging model, Opt. Lett., vol. 4, no. 17, pp , Sep. 9. 7] J. B. Abshire, Performance of OOK and low-order PPM modulations in optical communication when using APD-based receivers, IEEE Trans. Commun., vol., no. 1, pp , Oct ] F. M. Davidson and X. Sun, Gaussian approximation versus nearly exact performance analysis of optical communication systems with PPM signaling and APD receivers, IEEE Trans. Commun., vol. 6, no. 11, pp , Nov ] P. P. Webb, R. J. Mclntyre, and J. Conradi, Properties of avalanche photodiodes, RCA Review, vol. 5, pp. 4-78, Jun ] J. W. Giles and I. N. Bankman, Underwater optical communications systems. Part : basic design considerations, IEEE Military Communications Conference, Atlantic City, NJ, USA, pp. 17-5, 5. 11] S. Jaruwatanadilok, Underwater wireless optical communication channel modeling and performance evaluation using vector radiative transfer theory, IEEE J. Sel. Areas Commun., vol. 6, no. 9, pp , Dec. 8. 1] B. M. Cochenour, L. J. Mullen, and A. E. Laux, Characterization of the beam-spread function for underwater optical communications links, IEEE J. Ocean. Eng., vol., no. 4, pp , Oct. 8. 1] N. Cvijetic, S. G. Wilson, and M. B. Pearce, Receiver optimization in turbulent Free-Space Optical MIMO channels with APDs and Q- ary PPM, IEEE Photon. Technol. Lett., vol. 19, no., pp Jan ] K. Kiasaleh, Performance of APD-based, PPM Free-Space Optical communication systems in atmospheric turbulence, IEEE Trans. Commun., vo. 5, no. 9, pp , Sep ] C. D. Mobley, Light and Water. San Diego, CA: Academic Press/ Elsevier Science,