Elsevier

Optics Communications

Volume 489, 15 June 2021, 126891
Optics Communications

Performance analysis of MRR FSO communication system under Gamma–Gamma​ turbulence channel with pointing error

https://doi.org/10.1016/j.optcom.2021.126891Get rights and content

Abstract

The performance of modulating retro-reflector (MRR) free space optical (FSO) communication system has been studied before for various atmospheric turbulence conditions. However, the effect of pointing error (PE) on the MRR FSO communication system has not been studied yet. In this work, we investigate the PE impact on the MRR FSO communication system. Specifically, we obtain the probability density function (PDF) of the system in closed form expression regarding Gamma–Gamma turbulence channel and Rayleigh PE. Using this PDF, we derive the statistical characteristics closed form expressions of the received optical signal-to-noise ratio (SNR) including PDF, cumulative distribution function (CDF), moments and moment generating function (MGF). Relying on the obtained analytical results, we derive the system average bit error rate (BER), outage probability, ergodic capacity (EC) and amount of fading (AF) performances in closed forms. The closed form expressions are given in terms of Meijer’s G-function with the exception of obtaining the moments of the received optical SNR and AF in terms of elementary functions. For the given weather, PE and system conditions, we optimize the beam divergence angle to minimize the system average BER. Based on this, we suggest controlling of the beam divergence angle with the transmission distance according to the optimum beam divergence angle to improve the system BER performance. Finally we demonstrate the system performances according to the optimum beam divergence angle.

Introduction

Free space optical (FSO) communication systems provide a lot of advantages that qualify them to be a promising upgrade to existing radio frequency (RF) systems. FSO communication systems provide secure communication, resilience to RF interference, free license spectrum, transmission of high data rates as well as being easily deployed with reduced maintenance cost [1].

Despite their advantages, FSO communication systems are affected by atmospheric turbulence which causes significant performance degradation. In addition to atmospheric turbulence, misalignment between transmitter and receiver which is known as pointing error (PE) may cause additional performance degradation. Hence, accurate pointing acquisition and tracking (PAT) systems have to be deployed in both transmitter and receiver [2].

However, asymmetric links, which have terminals subjected to different setup conditions and cannot equip with the same setup due to weight, size and power consumption limitations, cannot afford deploying PAT systems in both of terminals. In order to overcome these limitations, modulating retro-reflector (MRR) provides deploying PAT systems only in the interrogator unit which can afford their requirements [3].

MRR FSO communication systems have been used in many applications such as unmanned aerial vehicle (UAV) [4], optical wireless sensor networks [5], boat-to-shore [6], shore-to-shore [7] as well as inter and intra spacecraft communication [8].

MRR FSO communication systems can be divided into two groups, monostatic and bistatic. In monostatic MRR systems both transmitter and receivers are collocated [9], [10], [11]. On the other hand, the receiver in bistatic MRR systems is shifted from the on-axis component. Despite monostatic MRR systems receive much amount of power, the fading correlation between the forward and backward paths, since they have a common axis, is a major limitation [12], [13]. On the contrary, in bistatic MRR, off-axis components are detected. Therefore, as long as the transmitter and receiver are separated by the order of the Fresnel radius, independent fading can be obtained. However, bistatic MRR systems receive less power than monostatic MRR systems [14].

Bistatic MRR FSO communication systems have been studied previously regarding several aspects. Weak turbulence condition was studied in [15], [16] using lognormal (LN) distribution. Moderate to strong turbulence condition was studied in [16], [17] using Gamma–Gamma (GG) distribution. All turbulence regimes from weak to strong were studied in [18] using Malaga distribution for unbounded plane and spherical waves. However, as per authors’ best knowledge, PE effect at the MRR interrogator unit has not been previously studied in details in literature.

In this work we investigate the effects of PE on the MRR FSO communication system performances under moderate to strong turbulence for TEM00 Gaussian beam wave. The atmospheric turbulence is modeled using GG distribution while the PE is modeled using Rayleigh distribution. We present closed form expressions of the probability density function (PDF) for both the system and the received optical signal-to-noise ratio (SNR). In addition, we derive the cumulative distribution function (CDF), moment generating function (MGF) and moments of the received optical SNR. Using the obtained closed form expressions we derive closed form expressions for the system performances regarding bit-error-rate (BER), outage probability of the received optical SNR, the ergodic capacity (EC) as well as the amount of fading (AF). The closed form expressions are obtained in terms of Meijer’s G-function with the exception of obtaining the moments of the received optical SNR and AF in terms of elementary functions.

In order to enhance the system performance to overcome the PE impact, beam divergence angle control with transmission distance is suggested. For the studied system and weather conditions, the optimum beam divergence angle that minimizes the system average BER is obtained by means of exhaustive search. The system performances according to the optimum beam divergence angle are examined.

The rest of this paper is structured as follows; Section 2 concerns with the system and channel models. The system statistical characteristics are presented in Section 3. The MRR FSO communication system performances are derived in Section 4. Section 5 covers the simulation results and discussions. Finally conclusion is given in Section 6.

Section snippets

System and channel models

The bistatic MRR FSO communication system, as shown in Fig. 1, utilizes intensity modulation and direct detection (IM/DD) scheme with on–off keying (OOK) as the modulation format. The received data y at the interrogator can be expressed as y=Prhx+wwhere Pr is the received signal power, h is the channel fading coefficient of the MRR communication system, x is the OOK data and w is the additive white Gaussian noise (AWGN) with zero mean and variance σw2.

The channel fading coefficient h is a

Channel fading PDF

The PDF of the channel fading coefficient h can be obtained as fhh=0fh|h1h|h1fh1h1dh1Hence (17) can be represented as fhh=α1β1ε2α2β2α2+β22A0Γα1Γβ1Γα2Γβ2hα2+β221×0h1α2+β22G0,22,0α2β2hh1|α2β22,β2α22×G1,33,0α1β1h1A0|ε2ε21,α11,β11dh1 Using [19, Eq. 8.2.2.14] G0,22,0α2β2hh1|α2β22,β2α22 can be transformed into G2,00,2h1α2β2h|1α2β22,1β2α22, then using [19, Eq. 2.24.1.1] the above integration can be evaluated as fhh=α1α2β1β2ε2A0Γα1Γα2Γβ1Γβ2×G1,55,0α1α2β1β2A0h|ε2ε21,α11,β11,α21,β2

Average BER

The average BER can be obtained using the derived MGF in (26) as follows [24] Pb¯=1π0π2Mγgsin2θdθwhere, g=12 for OOK modulation.

The above integration can be evaluated using the transformation τ=sin2θ, then using [19, Eq. Eq. 2.24.2.2] the average BER can be obtained as Pe¯=2α1+α2+β1+β26ε2π2πΓα1Γα2Γβ1Γβ2G4,1110,2α1α2β1β2227γe¯A02|12,K1K2,0 As ε, for non-PE case, the average BER can be approximated as Pe¯=2α1+α2+β1+β25π2πΓα1Γα2Γβ1Γβ2G2,98,2α1α2β1β2227γe¯A02|K3K4 where K3=1,12, K4=α12,α1+12,α

Results and discussion

In this section, we verify the validity of the obtained theoretical results by means of Monte-Carlo simulation. Throughout the simulation, Cn2=1×1013m23,λ=1550nm, the MRR radius a1=1.25cm and the receiver radius a2=3.75cm. The separation between transmitter and receiver in the interrogator unit is set to d=10cm.

The average BER performance of MRR system with OOK modulated data using IM/DD under Gamma–Gamma turbulence and Rayleigh PE is presented in Fig. 2. In this figure, the average BER

Conclusion

In this work we demonstrated the effect of PE on the MRR FSO communication system performances. The considered system utilized IM/DD scheme with OOK as the modulation format. GG distribution is used to model the atmospheric turbulence channel fading where Rayleigh distribution is used to model the PE fading. We presented a closed form expressions for the system PDF in addition to the system received optical SNR PDF, CDF, MGF and moments. We also derived closed form expressions of the system

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References (24)

  • El SaghirB.M. et al.

    Performance analysis of modulating retro-reflector FSO communication systems over Málaga turbulence channels

    Opt. Commun.

    (2020)
  • FarooqE. et al.

    Survey on FSO communication system—Limitations and enhancement techniques

  • KaymakY. et al.

    A survey on acquisition tracking and pointing mechanisms for mobile free-space optical communications

    IEEE Commun. Surv. Tutor.

    (2018)
  • MajumdarA.K.

    Modulating retroreflector-based free-space optical (FSO) communications

  • GoetzP.G. et al.

    Modulating retro-reflector lasercom systems for small unmanned vehicles

    IEEE J. Sel. Areas Commun.

    (2012)
  • S. Teramoto, T. Ohtsuki, Optical wireless sensor network system using corner cube retroreflectors (CCRs), in: IEEE...
  • RabinovichW.S. et al.

    45 mbps cat’s eye modulating retro-reflector link over 7 km

  • PlettM.L. et al.

    Free-space optical communication link across 16 kilometers over the chesapeake bay to a modulated retroreflector array

    Opt. Eng.

    (2008)
  • GoetzP.G. et al.

    Multiple quantum well-based modulating retroreflectors for inter- and intra-spacecraft communication

  • YangG. et al.

    Performance analysis of full duplex modulating retro-reflector free-space optical communications over single and double gamma-gamma fading channels

    IEEE Trans. Commun.

    (2018)
  • YangG. et al.

    Wave-optics simulation of the double-pass beam propagation in modulating retro-reflector FSO systems using a corner cube reflector

    Appl. Opt.

    (2017)
  • YangG. et al.

    Channel modeling and performance analysis of modulating retroreflector FSO systems under weak turbulence conditions

    IEEE Photonics J.

    (2017)
  • View full text