# Coherent Polarization Modulated Transmission through MIMO Atmospheric Optical Turbulence Channel

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<ul><li><p>JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 31, NO. 20, OCTOBER 15, 2013 3221</p><p>Coherent Polarization Modulated Transmissionthrough MIMO Atmospheric Optical</p><p>Turbulence ChannelXuan Tang, Zhengyuan Xu, Senior Member, IEEE, and Zabih Ghassemlooy, Senior Member, IEEE</p><p>AbstractAn optical signal suffers from irradiance and phasefluctuations when propagating through the free space optical (FSO)turbulence channel, thus resulting in the degradation of the biterror rate (BER) performance. The BER performance can be im-proved by adopting the multiple-input multiple-output (MIMO)scheme. In this paper, we propose a coherent binary polarizationshift keying (BPOLSK) modulation scheme with MIMO employ-ing maximum ratio combining and equal gain combining diversitytechniques to mitigate the turbulence effect. The gammagammastatistical channel model is adopted for all the turbulence regimes.The BER performance for the proposed BPOLSK-MIMO FSOlink is compared with the single-input single-output and ONOFF-keying systems by means of computer simulation. The op-tical power gain is investigated and demonstrated under differentturbulence regimes for a number of transmitters/receivers.</p><p>Index TermsAtmospheric turbulence, bit error rate (BER), bi-nary polarization shift keying (BPOLSK), free space optical (FSO),gammagamma (GG), multiple-input multiple-output (MIMO),single-input single-output (SISO).</p><p>I. INTRODUCTION</p><p>FREE space optical (FSO) communication, considered asa cost-effective and high bandwidth access technique, hasreceived increasing attention following its recent commercial-ization successes [1], [2]. It is an attractive solution for the lastmile access networks to bridge the bandwidth gap betweenthe end user and the fiber optic-based back-bone network al-ready in place. Its unique properties make it also appealing fora number of other applications, including fiber backup, enter-prise/local area network connectivity, metropolitan area networkextensions, redundant link, and back-haul for wireless cellularnetworks.</p><p>Manuscript received March 10, 2013; revised June 13, 2013 and July 29,2013; accepted September 4, 2013. Date of publication September 8, 2013; dateof current version September 23, 2013. This work was supported in part byNational 973 Program of China under Grant 2013CB329201, National NaturalScience Foundation of China under Grant 61171066, Tsinghua National Labo-ratory for Information Science and Technology under Grant 2011Z02289, andthe EU COST ACTIONS IC0802 and IC1101.</p><p>X. Tang and Z. Xu are with the Department of Electronic Engineering,Tsinghua University, Beijing 100084, China (e-mail: xtang2012@gmail.com;xuzy@tsinghua.edu.cn).</p><p>Z. Ghassemlooy is with the Optical Communications Research Group, Fac-ulty of Engineering and Environment, Northumbria University, Newcastle, NE18ST, U.K. (e-mail: z.ghassemlooy@northumbria.ac.uk).</p><p>Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.</p><p>Digital Object Identifier 10.1109/JLT.2013.2281216</p><p>However, the FSO link reliability and availability are sus-ceptible to the atmospheric conditions [1][3]. Apart from at-tenuation, the major impairment is the atmospheric turbulence,which is due to the variations in the refractive index as the resultof inhomogeneities in the pressure and temperature fluctuations.The atmospheric turbulence leads to signal fading, also known asscintillation, which severely degrades the link performance es-pecially for link length >1 km [4].The deep fading could last for1100 s, thus resulting in a loss of up to 105 consecutive bits for1 Gb/s data link [5]. The theoretical models for statistical distri-bution of the random fading irradiance signals have already beendeveloped, comprising the lognormal, gammagamma, and neg-ative exponential corresponding to weak, weak-to-strong, andsaturation regimes, respectively [1], [6].</p><p>There are a number of schemes to mitigate the turbulence in-duced fading in FSO links. The maximum-likelihood sequencedetection scheme is not feasible for most practical applicationsdue to the high complexity in determining the metric [7]. Thedeployment of large receiving aperture can improve the systemperformance by increasing the total received signal power. How-ever, incoherency of the received field caused by the atmosphericturbulence results in significant performance degradation partic-ularly for large apertures [8]. The spatial diversity (SD) utilizingthe multiple-input multiple-output (MIMO) technique createsa large aperture at the receiver by deploying multiple smallerapertures, which provides a striking approach to compensate forthe turbulence induced fading [1]. When the diameter of eachaperture becomes smaller, the received wavefront is more co-herent over each aperture compared to the system with a largeraperture. The outage probabilities of MIMO FSO systems overlognormal turbulence channels have been investigated in [9].In [10] and [11], the results for MIMO FSO systems employingpulse-position-modulation (PPM) and Q-ary PPM in lognormaland Rayleigh fading channels have been studied. The bit er-ror rate (BER) performance of MIMO FSO links for both theindependent and correlated lognormal atmospheric turbulencechannels have been fully covered in [12], whereas the coherentFSO with MIMO in Rician statistic channel has been reportedin [8]. The analysis for MIMO FSO systems in gammagamma(GG) channel is intractable due to the involvement of the modi-fied Bessel function of the second kind [3]. A limited number ofresearchers have published results of the distribution of the sumof independent GG variables. The pairwise error probabilities ofSISO and MIMO FSO systems with intensity modulation/directdetection (IM/DD) have been derived in [1], and the BER per-formance of IM/DD MIMO FSO systems over independent and</p><p>0733-8724 2013 IEEE</p></li><li><p>3222 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 31, NO. 20, OCTOBER 15, 2013</p><p>not necessarily identically distributed K atmospheric turbulencechannels have been reported in [2].</p><p>The simplest modulation technique widely used in the FSOsystems is the IM/DD ON-OFF-keying (OOK). However, OOKsuffers highly from the atmospheric turbulence, thus requir-ing the adaptive detection schemes at the receiver [13], [14].The adaptive threshold detection schemes have been developedwhere both the means and variances are precisely tracked us-ing a Kalman filter algorithm, which cannot be realized in thepractical FSO systems. Alternatively, the experimental resultshave shown that the polarization states of a propagating opticalbeam are the most stable parameters compared to the intensityand phase [15] and can be maintained over the entire FSO linkspan [16]. The FSO links employing polarization shift keyingare significantly insensitive to the phase noise of the laser localoscillator (LO) at the receiver, provided the intermediate fre-quency (IF) filter bandwidth is large enough [17]. The circlepolarization shift keying with DD offers a 3 dB lower signal-to-noise ratio (SNR) to achieve the same BER compared toOOK [15]. In [18], it was shown that polarization multiplexingtransmission with coherent detection in the lognormal fadingchannel offers a power gain of 514 dB along with the doubleof data rate compared to IM/DD links.</p><p>The main goal of this paper is to systematically investigatethe heterodyne binary polarization shift keying (BPOLSK)-FSOsystem by employing the MIMO technology over the GG tur-bulence channel. The system noise (the background radiation,thermal noise, and shot noise) is modeled as an additive whiteGaussian noise (AWGN) process. Maximum ratio combining(MRC) and equal gain combining (EGC) combining techniquesare considered to further improve the BER performance. Thedetailed unconditional BER analysis and the outage probabili-ties are also carried out. The error probabilities are compared toOOK to illustrate the advantages of the proposed scheme. TheSD gains for a range of transmitter/receiver configurations arealso demonstrated under different turbulence regimes.</p><p>The remainder of this paper is organized as follows: the GGstatistic channel model is introduced in Section II; the principlesof SISO BPOLSK-FSO system are outlined in Section III; thein-depth analytical and numerical results for MIMO BPOLSK-FSO are presented in Section IV. The results are discussed andcompared in Section V, and the conclusion is given in Section VI.</p><p>II. GAMMAGAMMA TURBULENCE CHANNELThe GG model is first proposed by Andrews et al. [6], [19].</p><p>This distribution is the product of two independent GG randomvariables. Both are statistically independent random processesand governed by GG distributions [6]. The PDF of a three-parameter GG random variable is derived as [3], [6]</p><p>f (;, , ) =()</p><p> + 2</p><p> () ()</p><p>(</p><p>) + 2 1</p><p>K(</p><p>2</p><p>)(1)</p><p>TABLE ITURBULENCE PARAMETERS FOR ALL TURBULENCE REGIMES</p><p>Fig. 1. Block diagram of the BPOLSK-FSO system: (a) the transmitter, and(b) the receiver.</p><p>where Kv () denotes the modified Bessel function of the secondkind (see [20, eq. (8.432.2)]) and () is the Gamma function(see [20, eq. (8.310.1)]). The electrical SNR and the averageSNR are defined as and = E [], respectively. Assumingspherical wave propagation, and can be directly related toatmospheric conditions [3], [6]</p><p> =</p><p>exp</p><p> 0.492l(</p><p>1 + 0.18d2 + 0.5612/5l)7/6</p><p> 1</p><p>1</p><p>, (2a)</p><p> =</p><p>exp</p><p> 0.51</p><p>2l</p><p>(1 + 0.6912/5l</p><p>)5/6(1 + 0.9d2 + 0.62d212/5l</p><p>)5/6 1</p><p>1</p><p>. (2b)</p><p>where Rytov variance 2l = 0.5C2nk7/6L11/6 , d = (kD2/4L)1/2 , L is the link span, k = 2/ is the wave number, is the wavelength, and D is the diameter of the receiver collect-ing lens aperture. The index of refraction structure parameterC2n varies from 1013 to 1017 m2/3 for the strong and weakturbulence regimes, respectively, with a typical average value of1015 m2/3 [21]. Values of the channel parameters are givenin Table I.</p><p>III. SYSTEM CONFIGURATION</p><p>A. BPOLSK-FSO System ModelFig. 1 shows the block diagram of the coherent BPOLSK-</p><p>FSO system. The transmitter consists of a transmitting laser(TL), a polarization beam splitter (PBS), and two external</p></li><li><p>TANG et al.: COHERENT POLARIZATION MODULATED TRANSMISSION THROUGH MIMO ATMOSPHERIC OPTICAL TURBULENCE CHANNEL 3223</p><p>LiNbO3-Mach-Zehnder Interferometers (MZIs) based ampli-tude modulators. The optical carrier E0 (t) is linearly polarizedalong /4 regarding the reference axis of PBS. E0 (t) is splitequally into two light beams with x and y polarizations, respec-tively, which are modulated by MZIs and then combined by apolarization beam combiner to form the BPOLSK signal. MZIsintroduce constructive and destructive interferences accordingto the bits 0and 1, respectively.</p><p>The transmitted optical signal viewed as a combination oftwo orthogonal amplitude modulated signals is given as [22]</p><p>Es (t) = a (t) {[1m (t)] x + m (t) y} (3)where a (t) = Aei(t+(t)) is the radio frequency (RF) carrier,A,, and (t) representing the amplitude, angular frequency,and the phase noise of the optical carrier, respectively.</p><p>BPOLSK-FSO using the heterodyne receiver is shown inFig. 1(b). The large-aperture lens can focus the incoming lightsignal and project it onto highly sensitive photo-detectors (PDs)located at its focal point. An optical bandpass filter (OBPF)(bandwidth typically 1 nm) can help reduce the potential im-pact of the background light interference on the FSO link per-formance. OBPFs bandwidth depends on the linewidth of thelaser, which is </p></li><li><p>3224 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 31, NO. 20, OCTOBER 15, 2013</p><p>Fig. 2. BER against the normalized electrical SNR across the whole turbulenceregimes using the BPOLSK and OOK with fixed (Fix) and adaptive (Adp)threshold.</p><p>adaptive detection shows performance relatively insensitive toSNR at the BER of 103 , and much worse than BPOLSK inweak to medium turbulence channels. It does require an accu-rate knowledge of both additive noise and fading levels, whichis not always practical [27]. OOK with a fixed threshold levelof 0.5 displays the worst system performance, and also createsthe BER floor, see Fig. 2 [27]. Another observation is that BERincreases drastically as the turbulence effect gets stronger forboth modulation schemes. This motivates the use of MIMOtechnology, as discussed later.</p><p>B. Outage ProbabilityThe outage probability Pout is an alternative performance</p><p>metric for quantifying the performance of communication sys-tems in the fading channels, which is defined as Pe > P e and P eis a predetermined BER threshold. The probability can be trans-lated into the probability of SNR falling below the specifiedthreshold . That is Pout = P (Pe > P e ) P (m < ),where the power margin m is the extra power needed to mitigateturbulence induced signal fading. By using (see [26, eq. (26)]),a closed-form solution for the outage probability is derived as</p><p>Pout = </p><p>m</p><p>0</p><p>() + </p><p>2</p><p> () ()</p><p>(1</p><p>) + 2 1</p><p>K(</p><p>2</p><p>1)</p><p>d</p><p>=()</p><p> + 2</p><p>2 () () (m) + </p><p>4</p><p> G2,11,3</p><p> m</p><p>1 + </p><p>4</p><p> 2</p><p>, </p><p>2, + </p><p>4</p><p> . (9)</p><p>IV. MULTIPLE-INPUT-MULTIPLE-OUTPUT BPOLSK-FSOBPOLSK-FSO with MIMO employing M-transmitter and</p><p>N -PD is depicted in Fig. 3. To avoid any correlation in thereceived irradiance, the spacing between detectors is assumedto be greater than the transverse correlation size 0 of the laserradiation in atmospheric turbulence channel, where 0 is inthe order of a few centimeters [27]. We have assumed thatthe propagation delay across the receiver array is negligible.Since the terrestrial FSO uses a line-of-sight with a negligibledelay spread, the intersymbol interference is not considered.The received optical power ij is assumed to be constant andtime invariant during one symbol duration T 0 , where thecoherence time 0 of the atmospheric fluctuation is in the orderof milliseconds [27].</p><p>The received signal from each branch is scaled by the gainfactor {Gi}Ni=1 . The output of the combiner is the sum of theweighted and cophased signals. Each receiver aperture sizeof N -PD is (1/N ) th of the aperture area of the single re-ceiver [2], [27]. Accordingly, the background noise varianceon each branch is proportional to the receiver aperture area,which is reduced by a factor of N , whereas the thermal noiseon each branch is not affected. Assuming the backgroundnoise being the dominant source, the system noise becomes2T </p><p>Ni=1 G</p><p>2i </p><p>2n/N , where i = 1, 2, 3, . . . ,N [2], [27]. The</p><p>electric currents are scaled by {Gi}Ni=1 before being cophasedand coherently combined. The total SNR is obtained as</p><p>T =(Alo)2M2N</p><p>(Ni=1 Gi</p><p>Mj=1 Arij</p><p>)2N</p><p>i=1 G2i </p><p>2n</p><p>(10)</p><p>where Arij denotes the received signal amplitude through theoptical turbulence channel between the ith transmitter and thejth receive aperture. M in the denominator ensures that a con-stant transmitted optical power is maintained to ensure a faircomparison. The unconditional BER for MIMO MRC is ob-tained by averaging the conditional error probability over thestatistics of GG distribution (1)</p><p>PMIMO = </p><p>0</p><p>12</p><p>exp(T</p><p>2</p><p>)f (;, , ) d. (11)</p><p>A. Maximum Ratio CombiningOn the receiver side using the MRC linear combiner scheme,</p><p>{Gi}Ni=1 is proportional to ij . As MRC...</p></li></ul>