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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 16 — Aug. 2, 2010
  • pp: 16618–16627
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Free space optical ultra-wideband communications over atmospheric turbulence channels

Kemal Davaslıoğlu, Erman Çağıral, and Mutlu Koca  »View Author Affiliations


Optics Express, Vol. 18, Issue 16, pp. 16618-16627 (2010)
http://dx.doi.org/10.1364/OE.18.016618


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Abstract

A hybrid impulse radio ultra-wideband (IR-UWB) communication system in which UWB pulses are transmitted over long distances through free space optical (FSO) links is proposed. FSO channels are characterized by random fluctuations in the received light intensity mainly due to the atmospheric turbulence. For this reason, theoretical detection error probability analysis is presented for the proposed system for a time-hopping pulse-position modulated (TH-PPM) UWB signal model under weak, moderate and strong turbulence conditions. For the optical system output distributed over radio frequency UWB channels, composite error analysis is also presented. The theoretical derivations are verified via simulation results, which indicate a computationally and spectrally efficient UWB-over-FSO system.

© 2010 OSA

1. Introduction

In this paper, we present a hybrid impulse radio ultra-wideband (IR-UWB) communication system employing optical pulse train signaling over free space optical (FSO) and radio-frequency (RF) links. UWB communication systems are able to provide high data rates over radio channels. However, low duty cycle and power requirement on UWB communication limits its use for only short-range (up to 10 m) applications such as those envisioned by the wireless personal area networks (WPANs). This short coverage distance implies that access network should provide efficient distribution over many small cells to extend the coverage of UWB radios. Recently, UWB-over-fiber transmission has emerged as a solution to this range problem where UWB signals are carried over long distances via fiber optical cables without the need for any conversion in the signal format [1

1. W. P. Lin and J. Y. Chen, “Implementation of a new ultra-wideband impulse system,” IEEE Photon. Technol. Lett. 17(11), 2418–2420 (2005). [CrossRef]

3

3. M. Jazayerifar, B. Cabon, and J. A. Salehi, “Transmision of multi-band OFDM and impulse radio ultra-wideband signals over single mode fiber,” J. Lightwave Technol. 26(15), 2594–2603 (2008). [CrossRef]

]. In order for these systems to be feasible, optical UWB pulses are designed satisfying the spectral mask requirements of the U.S. Federal Communications Commission (F.C.C.) as presented in [1

1. W. P. Lin and J. Y. Chen, “Implementation of a new ultra-wideband impulse system,” IEEE Photon. Technol. Lett. 17(11), 2418–2420 (2005). [CrossRef]

,2

2. F. Zeng and J. Yao, “An approach to ultra-wideband pulse generation and distribution over optical fiber,” IEEE Photon. Technol. Lett. 18(7), 823–825 (2006). [CrossRef]

,4

4. F. Zeng and J. Yao, “Ultra-wideband impulse radio signal generation using a high-speed electrooptic phase modulator and a fiber-bragg-grating-based frequency discriminator,” IEEE Photon. Technol. Lett. 18(19), 2062–2064 (2006). [CrossRef]

,5

5. P. C. Peng, W. R. Peng, J. H. Lin, W. P. Lin, and S. Chi, “Generation of wavelength- tunable optical pulses using EDFA as external-injection light source and amplifier for Fabry-Pérot laser diode,” IEEE Photon. Technol. Lett. 16(11), 2553–2555 (2004). [CrossRef]

]. Despite their advantages, UWB-over-fiber systems suffer from the drawback of large installation cost and time. On the other hand, free-space optical (FSO) communication systems (such as those proposed in [6

6. X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002). [CrossRef]

,7

7. S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wirel. Comm. 6(8), 2813–2819 (2007). [CrossRef]

]) have the potential of overcoming this drawback while still achieving significantly high data rates. Motivated by this potential, we propose a FSO transceiver architecture for the transmission of UWB signals over distances much longer than a few meters without the need to deploy fiber optic cables.

The organization of the rest of the paper is as follows: In Section 2, the system model is presented. Then in Section 3, the detection error probability analysis of the FSO and RF sections of the system is provided, together with the overall error probability analysis. Simulation results are presented in Section 4 followed by the conclusive remarks in Section 5.

2. Proposed system model

The generated optical TH-PPM signal can be represented as
xFSO(t)=Epn=1j=0Ns1p(tnTdjTfcjTcdnTp),
(1)
where Ep denotes the pulse energy amplified by EDPA, p(t) denotes the Gaussian pulse, dn and {cj} are the binary information and pseudo-random code sequences for time hopping, respectively. Td, Tf, Tc and Tp represent the symbol, bit, chip and pulse durations, respectively and bits are repeated Ns times in a symbol period.

The photo-detector receives the photon flux incident on the detector area and produces a current that is proportional to the received photons, providing the optical to electrical conversion of the received signal. The conversion coefficient η(0<η1) indicates the efficiency of the photodetector. After the removal of the background radiation bias ηIb, the resulting signal can be represented as
rFSO(t)=(ηI)xFSO(t)+n(t)=(ηI)Epn=1j=0Ns1p(tnTdjTfcjTcdnTp)+n(t),
(2)
where n(t) represents the combined effects of both the thermal noise and the shot noise, which can jointly be modeled as an additive white Gaussian noise (AWGN) with zero mean and variance N0/2. Assuming perfect synchronization, the received signal is passed through the matched filter xr(t) which can be written as
xr(t)=1Nsn=1j=0Ns1p(tcjTc)p(tcjTcTp),
(3)
resulting in the sampled output
yFSO(kTd)=(k1)TdkTdrFSO(t)xr(t)dt=±ηINsEp+νk,
(4)
where the noise term νk=(k1)TdkTdn(t)xr(t)dt is also AWGN with zero mean and variance N0/2. Zero-threshold detection is employed at the matched filter output. Notice that the decision output of the FSO subsystem can be used directly or can be to the users over an UWB channel. In this case, u^k’s or the decision on the signals transmitted over the FSO channel are modulated by an UWB transmitter where the modulated signal is expressed as
xRF(t)=EFn=1j=0Ns1q(tnTdjTfcjTcdnTp),
(5)
where EF denotes the energy pulse, q(t) denotes the Gaussian monocycle pulse train. The UWB channel can be modeled as
hRF(t)=κj=1Nk=1K(j)αjkδ(tTjτjk),
(6)
where κ denotes the RF log-normal fading random variable, N and K(j) denotes the number of observed clusters and multipaths within each cluster, respectively. Tj is the delay of the j th cluster. αjk denotes the channel coefficient of the j th cluster and the k th multipath and can be expressed as αjk = pjkβjk, where pjk is a Bernoulli random variable taking values of ± 1 and βjk is the log-normal distributed channel coefficient. To normalize each channel realization to unity requires that

j=1Nk=1K(j)βjk2=1.
(7)

Assuming the FCC compliant Gaussian monocycle pulse train defined in Eq. (5) is transmitted, the received signal at the UWB receiver can be expressed as

rRF(t) = xRF(t)hRF(t)+n(t)          = κEFn=1j=0Ns1k=1Nj=1K(j)q(tnTdjTfcjTcdnTpTjτjk)+n(t).
(9)

3. Detection error probability analysis

The overall error probability for the complete hybrid system can be found as
Pe(γFSO,γRF)=PFSO(γFSO)[1PRF(γRF)]+[1PFSO(γFSO)]PRF(γRF),
(10)
wherePFSO(γFSO), PRF(γRF)and γFSO, γRF are the error probabilities and symbol signal-to-noise ratios (SNRs) of the FSO and RF systems, respectively. Notice that, the scope of this paper is to analyze the FSO system performance for different channel regimes. Thus, the performance analysis of the RF channel is described briefly in this section and a detailed analysis of the FSO system error performance is given in the following subsections.

Assuming normalized channel coefficients, i.e., Eq. (7) holds, the received SNR at UWB receiver can be expressed as γRF = (κ2 Ns γp) where γp = EF/N0 denotes the pulse SNR and results in error probability of
PRF(γRF,κ)=12erfc(γRFκ22),
(11)
where erfc(⋅) is the complementary error function. After averaging out the probability density function (PDF) over κ

PRF(γRF)=012erfc(γRFκ22)20κln102πσg2exp((20log10κg0)22σg2)dκ.
(12)

This can be solved by Gauss-Hermite expansion given by
g(y)ey2dyi=1nωig(yi),
(13)
where yi and ωi, i = 1,…,n, are the ith root (abscissa) and associated weight, respectively [8

8. M. Abramowitz, and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

]. After the change of variables such that y=(20log10κg0)/(2σg2),

PRF(γRF)=12πi=1Nωierfc(γRF10(yi2σg2+g0)/102).
(14)

As for the FSO link, assuming perfect channel state information (CSI) is available at the FSO receiver, the DEP for the binary TH-PPM signal model over FSO channel can be expressed as
PFSO(γFSO,I)=0.5erfc(γFSO(ηI)2/2),
(15)
where γFSO = Nsγp and γp = Ep/(N0/2) are the symbol and pulse SNRs, respectively. Notice that due to the random fluctuations in its amplitude, the light intensity is modeled as a random variable whose distribution is dependent on the turbulence region. Therefore, in order to find the average DEP of the FSO link, one needs to evaluate the expectation over the distribution of the light intensity such that

PFSO(γFSO)=EI[Pe(γFSO,I)]=0Pe(γFSO,I)fI(I)dI.
(16)

Notice that the system proposed in Fig. 1 can also be implemented with a channel encoder-decoder pair to protect the information bits transmitted over the FSO channel against channel effects. If a convolutional encoder is employed together with the Viterbi decoding on the receiver side, the coded bit eror probability PFSOcoded(γFSO) in terms of the uncoded error probability PFSO(γFSO) is expressed approximately as ([9

9. S. Lin, and D. J. Costello, Error Control Coding, 2nd ed. (Pearson Prentice Hall, 2004).

] , pp. 531)
PFSOcoded(γFSO)Nb[4PFSO(γFSO)(1PFSO(γFSO))]dfree2,
(17)
where dfree is the minimum free distance of the convolutional code, and Nb is the sum of the Hamming weight of all the input sequences whose associated convolutional codeword have a Hamming weight of dfree .

3.1 Error performance of FSO system in weak turbulence

fI(I)=12I2πσX2exp((ln(I/I0))28σX2),I0.
(18)

The scintillation index is the normalized variance of fading intensity and it is defined as

σSI2=E[I2]/E[I]21=exp(σX2)1.
(19)

For instance, the log-normal distribution for the light intensity in Eq. (18) represents the condition where the amplitude fluctuations are weak and single scatters dominate the channel, which is valid for the 0σSI20.75.

The average DEP can be computed by the expectation in Eq. (16) over the log-normal intensity distribution given in Eq. (18) assuming zero mean such as
PFSO(γFSO)=012erfc(γFSO(ηI)2/2)12I2πσX2exp((ln(I/I0))28σX2)dI,
(20)
which can be rewritten by the change of parameters as
PFSO(γFSO)=12πerfc(γFSO(ηI0ey8σX2)2/2)ey2dy,
(21)
where y=ln(I/I0)/8σX2., we can approximate Eq. (21) using the expansion in Eq. (13)

PFSO(γFSO)=12πi=1nωierfc(γFSO(ηI0eyi8σx2)22).
(22)

As shown in the simulation results, the Gauss-Hermite expansion up to 20th order whose parameters are given in [8

8. M. Abramowitz, and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

] provides a close approximation to the actual integral in Eq. (20).

3.2 Error performance of FSO system in moderate turbulence

The average DEP can be computed by the expectation in Eq. (16) over the Gamma-Gamma intensity distribution given in Eq. (23) such as

PFSO(γFSO)=012erfc(γ(ηI)FSO2/2)2(αβ)(α+β)/2Γ(α)Γ(β)I(α+β)21Kαβ(2αβI)dI.
(25)

Using the formulation in [11

11. The Wolfram Function Site, (2004), http://functions.wolfram.com/.

] the integrands erfc(⋅) and Kn(⋅) in Eq. (25) can be expressed in terms of Meijer's G-function as
PFSO(γFSO)=2(αβ)(α+β)/2Γ(α)Γ(β)0I(α+β)/2112πG1,22,0[γFSO(ηI)22|10,0.5]12G0,22,0[αβI|(αβ)2,(βα)2]dI
(26)
which, using Eq. (07).34.21.0011.01 of [11

11. The Wolfram Function Site, (2004), http://functions.wolfram.com/.

], results in a closed-form expression such that

PFSO(γFSO)=2α+β3π3Γ(α)Γ(β)G5,22,4[8η2γFSO(αβ)2|1α2,2α2,1β2,2β2,10,12].
(27)

3.3 Error performance of FSO system in strong turbulence

Finally, the strong turbulence conditions are modelled as one-sided negative exponential distribution given by
fI(I)=1I¯exp(II¯),
(28)
where I¯=E[I] denotes the mean light intensity [12

12. S. G. Wilson, M. B. Pearce, Q. Cao, and M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Comm. 23(9), 1901–1910 (2005). [CrossRef]

]. This case represents the condition with many non-dominating scatterers and is usually valid for propagation over several kilometers. This saturation regime corresponds to scintillation index σSI21.

Using Eq. (16) and the distribution given in Eq. (28), the average DEP for strong turbulence conditions can be written as
PFSO(γFSO)=012erfc(γFSO(ηI)2/2)1I¯exp(II¯)dI=12[1erfc(1ηI¯2γFSO)exp(12(ηI¯)2γFSO)],
(29)
which again has a closed form expression.

4. Simulation results

In this section, we present the simulation results for the error performance of the proposed FSO-UWB system under weak, moderate and strong turbulence conditions and compare with the theoretical results derived in Section 3. The frame size, repetition rate and the efficiency of the photo-detector are chosen as N = 1000 symbols, Ns = 2 and η = 0.9, respectively. The channel parameters change at every 200 symbols, i.e., τc /(NTd) = 0.2 where τc is the channel coherence time and NTd is the total duration of a frame.

For strong turbulence, unit mean light intensity is considered E[I] = 1 and σSI2≅1. The analytical and the Monte-Carlo simulated results are also shown in Fig. 2 and as expected, the system exhibits the worst performance in this case due to the saturation characteristics in this regime.

Employing a simple convolutional encoder/Viterbi decoder pair within the FSO subsystem is considered so as to reduce the FSO errors and thus to improve the overall system performance. A rate ½ convolutional code with generator (27,31)8 and Nb = 2, dfree = 7 ([9

9. S. Lin, and D. J. Costello, Error Control Coding, 2nd ed. (Pearson Prentice Hall, 2004).

], pp. 540) is employed together with a Viterbi decoder. The coded system performance under each turbulence regime is shown in Fig. 4
Fig. 4 (27,31)8 convolutional coded FSO + RF UWB system performance over 2 km.
. Notice that the use of even a very simple code reduces the error floors significantly. For instance, error floors are decreased to the 9x10−20 at 32 dB and 4.8x10−43 at 42 dB for weak turbulence, 6.5x10−8 at 24 dB and 2.2x10−13 at 30 dB for moderate turbulence, 7.4x10−5 at 20 dB and 2x10−7 at 24 dB for strong turbulence. In Fig. 4, only the error floors under strong turbulence conditions are shown for comparison purposes with uncoded signaling scheme.

5. Conclusion

Acknowledgments

This work is supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under the contract number 105E077.

References and links

1.

W. P. Lin and J. Y. Chen, “Implementation of a new ultra-wideband impulse system,” IEEE Photon. Technol. Lett. 17(11), 2418–2420 (2005). [CrossRef]

2.

F. Zeng and J. Yao, “An approach to ultra-wideband pulse generation and distribution over optical fiber,” IEEE Photon. Technol. Lett. 18(7), 823–825 (2006). [CrossRef]

3.

M. Jazayerifar, B. Cabon, and J. A. Salehi, “Transmision of multi-band OFDM and impulse radio ultra-wideband signals over single mode fiber,” J. Lightwave Technol. 26(15), 2594–2603 (2008). [CrossRef]

4.

F. Zeng and J. Yao, “Ultra-wideband impulse radio signal generation using a high-speed electrooptic phase modulator and a fiber-bragg-grating-based frequency discriminator,” IEEE Photon. Technol. Lett. 18(19), 2062–2064 (2006). [CrossRef]

5.

P. C. Peng, W. R. Peng, J. H. Lin, W. P. Lin, and S. Chi, “Generation of wavelength- tunable optical pulses using EDFA as external-injection light source and amplifier for Fabry-Pérot laser diode,” IEEE Photon. Technol. Lett. 16(11), 2553–2555 (2004). [CrossRef]

6.

X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002). [CrossRef]

7.

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wirel. Comm. 6(8), 2813–2819 (2007). [CrossRef]

8.

M. Abramowitz, and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

9.

S. Lin, and D. J. Costello, Error Control Coding, 2nd ed. (Pearson Prentice Hall, 2004).

10.

E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of free-space optical systems in Gamma-Gamma fading,” in Global Telecommunications Conference 2008. GLOBECOM `08 (IEEE, 2008), 1–6.

11.

The Wolfram Function Site, (2004), http://functions.wolfram.com/.

12.

S. G. Wilson, M. B. Pearce, Q. Cao, and M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Comm. 23(9), 1901–1910 (2005). [CrossRef]

13.

S. S. Ghassemzadeh, L. J. Greenstein, A. Kavcic, T. Sveinsson, and V. Tarokh, “An empirical indoor path loss model for ultra-wideband channels,” J. Commun. Network 5, 303–308 (2003).

OCIS Codes
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(060.4510) Fiber optics and optical communications : Optical communications
(060.2605) Fiber optics and optical communications : Free-space optical communication

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: February 22, 2010
Revised Manuscript: May 3, 2010
Manuscript Accepted: July 1, 2010
Published: July 23, 2010

Citation
Kemal Davaslıoğlu, Erman Çağıral, and Mutlu Koca, "Free space optical ultra-wideband communications over atmospheric turbulence channels," Opt. Express 18, 16618-16627 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-16-16618


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References

  1. W. P. Lin and J. Y. Chen, “Implementation of a new ultra-wideband impulse system,” IEEE Photon. Technol. Lett. 17(11), 2418–2420 (2005). [CrossRef]
  2. F. Zeng and J. Yao, “An approach to ultra-wideband pulse generation and distribution over optical fiber,” IEEE Photon. Technol. Lett. 18(7), 823–825 (2006). [CrossRef]
  3. M. Jazayerifar, B. Cabon, and J. A. Salehi, “Transmision of multi-band OFDM and impulse radio ultra-wideband signals over single mode fiber,” J. Lightwave Technol. 26(15), 2594–2603 (2008). [CrossRef]
  4. F. Zeng and J. Yao, “Ultra-wideband impulse radio signal generation using a high-speed electrooptic phase modulator and a fiber-bragg-grating-based frequency discriminator,” IEEE Photon. Technol. Lett. 18(19), 2062–2064 (2006). [CrossRef]
  5. P. C. Peng, W. R. Peng, J. H. Lin, W. P. Lin, and S. Chi, “Generation of wavelength- tunable optical pulses using EDFA as external-injection light source and amplifier for Fabry-Pérot laser diode,” IEEE Photon. Technol. Lett. 16(11), 2553–2555 (2004). [CrossRef]
  6. X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002). [CrossRef]
  7. S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wirel. Comm. 6(8), 2813–2819 (2007). [CrossRef]
  8. M. Abramowitz, and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).
  9. S. Lin, and D. J. Costello, Error Control Coding, 2nd ed. (Pearson Prentice Hall, 2004).
  10. E. Bayaki, R. Schober, and R. K. Mallik, “Performance analysis of free-space optical systems in Gamma-Gamma fading,” in Global Telecommunications Conference 2008. GLOBECOM `08 (IEEE, 2008), 1–6.
  11. The Wolfram Function Site, (2004), http://functions.wolfram.com/ .
  12. S. G. Wilson, M. B. Pearce, Q. Cao, and M. Baedke, “Optical repetition MIMO transmission with multipulse PPM,” IEEE J. Sel. Areas Comm. 23(9), 1901–1910 (2005). [CrossRef]
  13. S. S. Ghassemzadeh, L. J. Greenstein, A. Kavcic, T. Sveinsson, and V. Tarokh, “An empirical indoor path loss model for ultra-wideband channels,” J. Commun. Network 5, 303–308 (2003).

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