Ghassemlooy, Zabih

Lee, Chung Ghiu

Popoola, Wasiu Oyewole

Tang, Xuan

Xu, Zhengyuan

English

Northumbria University Research Portal

Citation:  Tang,  Xuan,  Xu,  Zhengyuan,  Ghassemlooy,  Zabih,  Popoola,  Wasiu  Oyewole and  Lee, Chung  Ghiu  (2012) Coherent  binary  polarization  shift  keying  in  free space optical  turbulence channel.  In:  Optics  and  Photonics Taiwan  International  Coference (OPTIC) 2012, 6-8 December 2012, Taipei, Taiwan.Published by: UNSPECIFIEDURL: This  version  was  downloaded  from  Northumbria  Research  Link:  http://nrl.northumbria.ac.uk/11502/Northumbria  University  has  developed Northumbria  Research  Link  (NRL)  to  enable users to access the University’s research output.  Copyright  © and moral  rights  for  items on NRL  are retained by the individual  author(s) and/or other  copyright  owners.  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To read and/or cite from the  published  version  of the  research,  please visit  the  publisher’s  website  (a subscription  may be required.)Coherent Binary Polarization Shift Keying in Free Space Optical Turbulence Channel 1Xuan Tang, 1Zhengyuan Xu, 2Zabih Ghassemlooy, 3Wasiu O. Popoola and 4C.G. Lee 1Department of Electronic Engineering, Tsinghua University, P. R. China 2Optical Communications Research Group, Faculty of Engineering and Environment, Northumbria University, Newcastle, UK 3School of Engineering and Built Environment, Glasgow Caledonian University, UK  4Department of Electronic Engineering, Chosun University, Gwangju, Republic of Korea   Abstract—In this paper the performance of a binary polarization shift keying (BPOLSK) modulated free space optical (FSO) link employing coherent detection in the presence of the atmospheric turbulence is investigated. First, a closed-form expression for the bit error rate (BER) of a BPOLSK-FSO system is presented taking into account the atmospheric turbulence-induced fading and noise. The BER performance of BPOLSK and on-off keying (OOK) with fixed and adaptive threshold schemes in the atmospheric turbulence channel is also shown.  Index Terms—FSO, coherent detection, polarization modulation, BER and outage probability. I. INTRODUCTION  The FSO technology has attracted much attention as a means to deal with the rise in bandwidth demand in core networks and multi-user access systems [1]. It is best suited for the point-to-point, high-capacity (multi-Gb/s) links spanning up to a few kilometers – in “last-mile” access network applications. However, FSO links are sensitive to atmospheric turbulence which is caused due to the air temperature inhomogeneities [2]. Light signal propagating through the turbulence channel will experience random fluctuation of phase and amplitude, which is referred to as the scintillation. It causes received power degradation, thus significantly limiting the transmission speed and the link range. Various models describing the probability density function (PDF) of the irradiance fluctuation have been developed. Lognormal distribution is the simplest turbulence model valid only for weak turbulence regime and is derived based on Rytov approximation [3]. Beyond the weak regime, where multiple scatterings exist, Rytov approximation is no longer valid [4, 5]. Therefore, the gamma-gamma and negative exponential models corresponding to the weak-to-strong and saturation regimes, respectively, have been widely used [6, 7].  Several approaches have been proposed to circumvent the atmospheric turbulence [8-10]. However, for optical beams propagating through a turbulent channel, the states of polarization are the most stable properties compared to the amplitude, phase and frequency, which can be maintained over a long propagation link [11, 12]. In this work we analyze BPOLSK with the coherent heterodyne detection for the FSO link under the atmosphere turbulence. Through comparison with OOK, the performance advantage of the BPOLSK-FSO system is outlined. The performance analysis will be based on the lognormal and negative exponential channel models. Since the FSO link under consideration is LOS, the ISI due to the multipath propagation is not considered here. The noise (the background radiation, thermal noise and shot noise) is modeled as an additive white Gaussian noise (AWGN) process.  The rest of the paper is organized as follows: the BPOLSK-FSO system structure is showed in Section II. The BER of BPOLSK system under the atmospheric turbulence channel has been analyzed in Section III. The results discussion is in Section IV. Finally, the conclusion is presented in Section V.    II. BPOLSK-FSO SYSTEM The system configuration of BPOLSK-FSO using the coherent detection is shown in Fig. 1. The optical carrier 𝐸 0 𝑡  from a laser source is linearly polarized along 𝜋 4  with respect to the reference axis of the PBS. 𝐸 0 𝑡  is split equally into two equal components ─ 𝑥  and 𝑦  polarizations. Only the 𝑥 -component is phase-modulated between 0 and 𝜋 depending on the input data stream, which leads to either 𝜋 4  or 3𝜋 4  polarization state of the optical carrier, respectively. The transmitted optical signal 𝐸 𝑠 𝑡  is expressed as: 𝐸 𝑠 𝑡 =  0.5𝑃𝑡𝑒𝑖 𝜔𝑡 +𝜑 𝑡   𝑒𝑖𝛽𝑥 (𝑡) ∙ 𝑥  + 𝑦  ,                        1  where 𝑃𝑡 , 𝜔, and 𝜑 𝑡  are the power, the angular frequency and the phase noise of the optical carrier, respectively. 𝛽𝑥 𝑡 =  0,𝜋  is the phase difference between the two field components 𝑥  and 𝑦 .  At the receiver an optical bandpass filter (OBPF) with a well defined field of view and bandwidth of ~ 1 nm is located at the front end in order to reduce the impact of the background light interference. The bandwidth of OBPF depends on the linewidth (LW) of the laser source, which has a narrow LW typically < 1 nm. The received signal 𝐸 𝑟(𝑡) can be viewed in both cases as two orthogonal amplitude modulated signals, related to the orthogonal components of 𝐸 𝑠 𝑡 . The local oscillator (LO) laser linearly polarized at 𝜋 4  is identical to the transmitter laser. The AFC module, of which the control signal derived from the IF signal, is a  (a)  (b) Fig. 1. Coherent BPOLSK-FSO transceiver: (a) the transmitter, and (b) the receiver. TL (transmitting laser), PM (phase modulation), PBS (polarization beam splitter), PBC (polarization beam combiner),  AFC (automatic frequency control circuit), BPF (electric bandpass filter). closed-loop circuit acting on the bias current. Its working principle is for system synchronisation and for compensating the slow-frequency fluctuations in LO [13]. The received optical signal 𝐸 𝑟 𝑡  and the LO signal 𝐸 𝑙𝑜  𝑡  are given as:    𝐸 𝑟 𝑡 =  0.5𝑃𝑟𝑒𝑖 𝜔𝑡 +𝜑𝑟 𝑡   𝑒𝑖𝛽𝑥 (𝑡) ∙ 𝑥 + 𝑦   .                      2  𝐸 𝑙𝑜  𝑡 = 0.5 𝑃𝑙𝑜𝑒𝑖 𝜔 𝑙𝑜 𝑡+𝜑𝑙𝑜  𝑡   𝑥 + 𝑦  .                               3  Both 𝑃𝑟  and 𝜑𝑟 𝑡  are time-variant quantities due to the turbulence fluctuation. 𝑃𝑙𝑜 , 𝜔𝑙𝑜  and 𝜑𝑙𝑜  𝑡  represent the power, angular frequency and the phase noise of the LO, respectively. 𝐸 𝑟 𝑡  is split by the PBS and mixed with the corresponding components of 𝐸 𝑙𝑜  𝑡  before being applied to two identical PDs with a unit area. PDs outputs are passed through ideal electric BPFs with a bandwidth and a center frequency of 𝐵𝑏𝑝  =  2(𝑅𝑠 + 𝑘𝐹𝐵𝐿)  and 𝜔𝐼𝐹 , respectively. Rs and BL are the symbol rate and LW of laser sources, respectively. It is assumed that BPFs are ideal which only pass the signal without any distortion, thus the filter outputs are expressed by: 𝑐𝑥𝑏  𝑡 = ℜ 𝑃𝑟𝑃𝑙𝑜 2 cos 𝜔𝐼𝐹𝑡 + 𝛽𝑥 (𝑡) + 𝜑𝐼𝐹 𝑡  + 𝑛𝑥 𝑡 ,                                                   4a  𝑐𝑦𝑏  𝑡 = ℜ 𝑃𝑟𝑃𝑙𝑜 2 cos 𝜔𝐼𝐹 𝑡 + 𝜑𝐼𝐹 𝑡  + 𝑛𝑦 𝑡 .      4b  where ℜ is the photodiode responsivity, 𝜔𝐼𝐹 = 𝜔 − 𝜔𝑙𝑜  and 𝜑𝐼𝐹  𝑡 = 𝜑𝑟 𝑡 − 𝜑𝑙𝑜  𝑡  are the frequency and phase noise of the intermediate signal (IF), respectively. The noise terms 𝑛𝑥 ,𝑦 𝑡 ~𝑁 0, 𝜎𝑛2  are assumed to be statistically independent AWGN with variance 𝜎𝑛2  comprising of the thermal noise (𝜎𝑇2) and the background radiation shot noise (𝜎𝐵2), i.e., 𝜎𝑛2 = 𝜎𝑇2 + 𝜎𝐵2. Both noise terms are uncorrelated such that 𝑛𝑥 𝑡 ∙ 𝑛𝑦 𝑡                 = 0. The noise signals 𝑛𝑥 ,𝑦 𝑡  in (4) can be expressed as [14, 15]:  𝑛 𝑡 = 𝑛𝐼 𝑡 cos 𝜔𝐼𝐹𝑡 + 𝜑𝐼𝐹  𝑡                             − 𝑛𝑄 𝑡 sin 𝜔𝐼𝐹𝑡 + 𝜑𝐼𝐹 𝑡  ,                 (5) where 𝑛𝐼 𝑡  and 𝑛𝑄 𝑡  are the in-phase and quadrature components of the noise 𝑛 𝑡 ~𝑁 0,𝜎𝑛2 , respectively. The electric currents 𝑐𝑥𝑏  𝑡  and 𝑐𝑦𝑏  𝑡  are processed by the mixer to generate 𝑐 𝑡 , which is then fed into the matched filter (MF). The output of the MF is passed through a sampler and a threshold detector.  The output of the MF 𝑉𝑗  is passed through a sampler and a threshold detector. A binary „0‟ is assumed to be received if 𝑉𝑗  is above the threshold level of zero and „1‟ otherwise. Assuming independent and identically distributed (i.i.d.) data transmission, the electric signal 𝑉𝑗  is expressed as:  𝑉𝑗 = 0.5𝑧 0.5ℜ2𝑃𝑟𝑃𝑙𝑜                                                           6  where 𝑧 =  0.5ℜ2𝑃𝑟𝑃𝑙𝑜 + 𝑛𝑥𝐼  𝑡 + 𝑛𝑦𝐼  𝑡 whose PDF is 𝑓 𝑧  and denoted as 𝑧~𝑁 0.5ℜ2𝑃𝑟𝑃𝑙𝑜 ,𝜎𝑛2 . Under the assumption of ideal channel, the conditional BER 𝑃𝑒𝑐  is derived as:    𝑃𝑒𝑐 = Q   ℜ2𝑃𝑟𝑃𝑙𝑜/2𝜎𝑛2 = Q  𝛾                                     7  where the electrical SNR per bit is given by 𝛾 =ℜ2𝑃𝑟𝑃𝑙𝑜 2𝜎𝑛2 .  III. LINK PERFORMANCE OF BPOLSK-FSO Adopting the approach given in [16], the unconditional probabilities 𝑃𝑒  in the weak and saturation regime are obtained by averaging (7) over the lognormal and negative exponential distribution PDFs: 𝑃𝑒𝐿𝑂𝐺 =  Q   𝛾 𝑃𝑟  1𝑃𝑟 2𝜋𝜎𝑙exp  − ln 𝑃𝑟 𝑃0  + 0.5𝜎𝑙2 22𝜎𝑙2  ∞0𝑑𝑃𝑟 .          8  𝑃𝑒𝑁𝐸𝐺 =  Q   𝛾 𝑃𝑟  1𝑃0exp  −𝑃𝑟𝑃0 ∞0𝑑𝑃𝑟 .                  9  No closed form solutions for (8) and (9) exist that could result in truncating its upper limit by using the numerical integration. Furthermore, the presence of the argument of the Q-function always causes analytical problems at the lower limit of the Q-function integral [17]. By combining an alternative form of the Q-function with the Gauss-Hermite quadrature integration approximation [16], the analytical difficulty in solving (8) and (9) can be overcome. By invoking variable change as 𝑦 =  ln 𝑃𝑟 𝑃0  + 0.5𝜎𝑙2  2𝜎𝑙  in (8), the unconditional BER can be reduced to the following form: 𝑃𝑒𝐿𝑂𝐺 =1 𝜋 𝑤𝑖Q   (ℜ2𝑃𝑙𝑜/2𝜎𝑛2)𝑃0  exp  2𝜎𝑙𝑥𝑖𝑛𝑖=1− 0.5𝜎𝑙2  .                                             10  where  𝑤𝑖 𝑖=1𝑛  and  𝑥𝑖 𝑖=1𝑛  are the weight factors and the zeros of an nth order Hermite polynomial, Hen(x) [18]. The degree of accuracy of (10) depends on the order n of Hen(x). By using the alternative representation of Q(.), the unconditional BER in the saturation regime and beyond is derived by averaging the conditional BER over the fully developed speckle PDF:  𝑃𝑒𝑁𝐸𝐺 =1𝜋𝑃0  exp  −ℜ2𝑃𝑟𝑃𝑙𝑜4𝜎𝑛2sin 2 𝜃 −𝑃𝑟𝑃0 𝑑𝑃𝑟𝑑𝜃∞0𝜋 2 0.      (11) Equation 3.322.2 in [19] is used to solve the multiple integration involved in (11). The BER is thus reduced to the following form: 𝑃𝑒𝑁𝐸𝐺 =2𝜋  𝜋𝒦0 𝜃 exp 𝒦0 𝜃  Q  2𝒦0 𝜃  𝑑𝜃𝜋 2 0. (12)  Fig. 2: Comparisons of BER performances of BPOLSK and OOK schemes against the normalized electric SNR 𝐸 ℜ𝑃𝑟𝑃𝑙𝑜  = 1  in the presence of turbulence.   where 𝒦0 𝜃 = 𝜎𝑛2sin2 𝜃 ℜ2𝑃𝑙𝑜 . The integral in (12) can be minimized with the substitution of = 𝜋 2  in its integrant, leading to the upper bound below 𝑃𝑒𝑁𝐸𝐺 ≤  𝜋𝒦0exp 𝒦0 Q  2𝒦0 .                                    13  where 𝒦0 = 𝜎𝑛2 ℜ2𝑃𝑙𝑜 .  IV. RESULTS DISCUSSION Figure 2 depicts the error probability against the normalized electrical SNR for BPOLSK and OOK with fixed and adaptive threshold schemes in the atmospheric turbulence channel. To achieve a BER of 10-9, the SNR requirements for BPOLSK is ~3 dB more than OOK with no turbulence. To achieve a fixed BER, the SNR requirement increases with the turbulence level irrespective of the modulation schemes and it is higher for lower values of BER at the same turbulence level. For example, to achieve a BER of 10-9 at 𝜎𝑙2 = 0.1 in a weak turbulence regime, the SNR requirements for BPOLSK and OOK with adaptive threshold detection are ~ 24.5 dB and ~ 33.5 dB, respectively. When the BER increases to 10-6, the corresponding SNR values drop to ~ 20 dB and ~ 28.5 dB, respectively. OOK with a fixed threshold suffers higher BER floor levels in the turbulence channel.   V. CONCLUSION The performance of coherent BPOLSK-FSO system in the presence of atmospheric turbulence has been investigated. The closed-form expression for the unconditional BER of the BPOLSK-FSO operating in weak and saturation turbulence channels have also been presented. BER of BPOLSK and OOK with fixed and adaptive threshold schemes in the atmospheric turbulence channel has been shown. For example, to achieve a BER of 10-9 at 𝜎𝑙2 = 0.1 in a weak turbulence regime, SNR requirements for BPOLSK and OOK with the adaptive threshold detection are ~ 24.5 dB and ~ 33.5 dB, respectively. OOK with a fixed thresholding scheme suffers a higher BER floor levels in the turbulence channel.  ACKNOWLEDGMENT This work was supported by National Natural Science Foundation of China (61171066) and the EU COST ACTIONS (IC0802 and IC1101). REFERENCES [1] N. Cvijetic, Dayou Qian, Jianjun Yu, Yue-Kai Huang, and Ting Wang, "Polarization multiplexed optical wireless transmission with coherent detection," Journal of Lightwave Technology, vol. 28, pp. 1218-1227, 2010. [2] W.K. Pratt, Laser communication systems. New York: John Wiley & Sons, Inc., 1969. [3] A.O. Aladeloba, A.J. Phillips, and M.S. Woolfson, "Improved bit error rate evaluation for optically pre-amplified free-space optical communication systems in turbulent atmosphere," IET Optoelectronics, vol. 6, pp. 26-33, 2012. [4] S. Karp, R.M. Gagliardi, S.E. Moran, and L.B. Stotts, Optical Channels: Fibers, Clouds, Water and the Atmosphere. New York: Plenum Press, 1988. [5] G.R. 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Ghafouri-Shiraz, "Transceiver architecture for incoherent optical CDMA network based on polarization modulation," Journal of Lightwave Technology, vol. 26, pp. 3820-3828, December 2008. [12] X. Tang, Z. Ghassemlooy, S. Rajbhandari, W. O. Popoola, and C. G. Lee," Coherent polarization shift keying modulated free space optical links over a gamma-gamma turbulence channel," American Journal of Engineering and Applied Sciences, vol. 4, pp. 520-530, January 2012. [13] K. Kikuchi, Coherent Optical Communication Systems: Elsevier Inc., 2008. [14] L.Y. L. Andy, Y.K. Chan, S.F. Chien, A.H. You, and T.S. Guan, "40 Gbit/s polarization modulation in ultra-long haul transmission systems by using optical phase conjugators," EICE Electronics Express, vol. 1, pp. 386-391, 2006. [15] J. G. Proakis, Digital Communications 4th ed. New York: McGraw-Hill Series in Electrical and Computer Engineering, 2001. [16] W.O. Popoola, "Subcarrier intensity modulated free-space optical communication systems," Doctor of Philosophy, School of Computing, Engineering and Information Sciences, University of Northumbria, Newcastle, September 2009. [17] M. K. Simon and M.-S. Alouini, Digital Communication over Fading Channels 2nd edition: Wiley, 2005. [18] M. Abramowitz and I.S. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover, 1977. [19] I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. London: Academic Press, Inc., 1994.   

40 Gbit/s polarization modulation in ultra-long haul transmission systems by using optical phase conjugators,&quot;

A novel polarizationmultiplexing system for free-space optical links,&quot;

Circle polarization shift keying with direct detection for free-space optical communication,&quot;

Coherent Optical Communication Systems:

Coherent polarization shift keying modulated free space optical links over a gamma-gamma turbulence channel,&quot;

Digital Communication over Fading Channels 2nd edition:

Diversity-multiplexing trade-off in coherent free-space optical systems with multiple receivers,&quot;

Improved bit error rate evaluation for optically pre-amplified free-space optical communication systems in turbulent atmosphere,&quot;

Laser Beam Propagation through Random Media.

Laser Beam Scintillation with Applications:

Laser communication systems.

Optical Channels: Fibers, Clouds, Water and the Atmosphere.

Optical Detection Theory for Laser Applications:

Polarization multiplexed optical wireless transmission with coherent detection,&quot;

Subcarrier intensity modulated free-space optical communication systems,&quot;

Transceiver architecture for incoherent optical CDMA network based on polarization modulation,&quot;

Coherent binary polarization shift keying in free space optical turbulence channel

Coherent binary polarization shift keying in free space optical turbulence channel

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