Free space optical ultra-wideband communications over atmospheric turbulence channels

doi:10.1364/OE.18.016618

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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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▸ Article Outline
– Abstract
1. Introduction
2. Proposed system model
3. Detection error probability analysis
4. Simulation results
5. Conclusion
– References and links

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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.

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

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

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

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]

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]

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]

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

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

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 proposed system is able to generate an optical UWB signal or convert an RF UWB signal into an optical one through a simple electo-optical conversion. The optical UWB pulses transmitted over the FSO channels are received by the detector that either uses the bit decisions as end information or delivers them to the UWB end-users through the RF UWB channels. Optical UWB pulses are not only easy to generate but also known to reduce the interference between electrical devices. In addition, pulsed transmission over FSO channels is not impaired by multipath fading as in the case of radio frequency UWB systems. Moreover, producing optical UWB pulse trains is more cost efficient than on-off keying (OOK) that is frequently used in most FSO communication systems (e.g., [6

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

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]

]). For these reasons, the proposed FSO-UWB system is a feasible alternative not only to the UWB-over-fiber architectures over the links where direct line of sight (LOS) is available but also to the conventional FSO systems employing OOK. Hence, with the proposed system architecture, two attractive technologies UWB and FSO are converged to provide high data rates with less installation time and cost.

On the other hand, inhomogeneities induced by the temperature and atmospheric pressure in the FSO links cause fluctuations both in the amplitude and phase of the received optical signal intensity [6

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

]. Because the optical UWB signals are transmitted over FSO channels, they are impaired by these atmospheric effects, the most important of which is the turbulence induced fading. That is why, we evaluate the performance of the proposed FSO-UWB system under weak, moderate and strong turbulence regimes, each described by precise statistical models. In each case, we provide an exact or closely approximated theoretical error analysis and verify the derivations via the simulation results. We also provide the error analysis of the transmission over the UWB links and present the error performance of the composite FSO + UWB system. Both the theoretical and numerical results indicate the feasibility of the proposed hybrid FSO + UWB transceiver architecture for high data rate UWB transmission over long distances.

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

We consider the system model shown in Fig. 1 and particularly adopt the approach in [3

] and [4

] that employs gain-switched Fabry-Pérot laser diode (FPLD), a tunable-filter (TF) and an erbium-dope fiber amplifier (EDFA) to generate wavelength-tunable optical pulses and is primarily developed for UWB-over-fiber communication links. In our system model, the binary source outputs {u_k}’s are TH PPM modulated via Gaussian pulse train and passed through a bias-tee circuit to drive the FPLD into gain-switched operation. The 1550-nm FPLD operates with a threshold current of 18 mA at 25° C with 0.8 nm mode spacing and in this configuration, it is biased at 16 mA and gain-switched at 4 GHz. The generated optical signal is fed to the EDFA which serves both as an external-injection source and an amplifier for the FPLD output and it consists of a 980-nm pump laser diode that pumps 50 mW output power to couple an erbium-doped fiber via 980/1550-nm wavelength division multiplexer (WDM) and an isolator to reduce back reflections. The output of EDFA is passed through TF which operates in the range of 1527 to 1562 nm. The central wavelength of the TF is chosen to be close to that of FPLD output so that the system has a single wavelength output before it is sent to FSO channel.

Fig. 1 System model of the proposed communication link over FSO.

The generated optical TH-PPM signal can be represented as

x_{FSO} (t) ​ = \sqrt{E_{p}} \sum_{n = 1}^{\infty} \sum_{j = 0}^{N s - 1} p (t - n T_{d} - j T_{f} - c_{j} T_{c} - d_{n} T_{p}),

(1)

where E_p denotes the pulse energy amplified by EDPA, p(t) denotes the Gaussian pulse, d_n and {c_j } are the binary information and pseudo-random code sequences for time hopping, respectively. T_d , T_f , T_c and T_p represent the symbol, bit, chip and pulse durations, respectively and bits are repeated N_s times in a symbol period.

The FSO channel is described by the unit impulse response h(t) = I(t) + I_b where I(t) and I_b are the instantaneous light intensity and the background radiation whose effects are removed at the receiver as in [6

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

], respectively. Also, experiments show that the coherence time of the FSO links is large enough to approximate the intensity as a constant during the transmission of a frame, i.e.,

I (t) \approx I .

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 < η \leq 1

) indicates the efficiency of the photodetector. After the removal of the background radiation bias

η I_{b}

, the resulting signal can be represented as

r_{F S O} (t) ​ = (η I) x_{F S O} (t) + n (t) = (η I) \sqrt{E_{p}} \sum_{n = 1}^{\infty} \sum_{j = 0}^{N s - 1} p (t - n T_{d} - j T_{f} - c_{j} T_{c} - d_{n} T_{p}) + 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 x_r(t) which can be written as

x_{r} (t) = \frac{1}{\sqrt{N_{s}}} \sum_{n = 1}^{\infty} \sum_{j = 0}^{N_{s} - 1} p (t - c_{j} T_{c}) - p (t - c_{j} T_{c} - T_{p}),

(3)

resulting in the sampled output

y_{FSO} (k T d) = \int_{(k - 1) T_{d}}^{k T_{d}} r_{FSO} (t) x_{r} (t) d t = \pm η I \sqrt{N_{s} E_{p}} + ν_{k},

(4)

where the noise term

ν_{k} = \int_{(k - 1) T_{d}}^{k T_{d}} n (t) x_{r} (t) d t

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,

{\hat{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

x_{RF} (t) ​ = \sqrt{E_{F}} \sum_{n = 1}^{\infty} \sum_{j = 0}^{N s - 1} q (t - n T_{d} - j T_{f} - c_{j} T_{c} - d_{n} T_{p}),

(5)

where E_F denotes the energy pulse, q(t) denotes the Gaussian monocycle pulse train. The UWB channel can be modeled as

h_{RF} (t) = κ \sum_{j = 1}^{N} \sum_{k = 1}^{K (j)} α_{j k} δ (t - T_{j} - τ_{j k}),

(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. T_j is the delay of the j ^th cluster. α_jk denotes the channel coefficient of the j ^th cluster and the k ^th multipath and can be expressed as α_jk = p_jkβ_jk , where p_jk is a Bernoulli random variable taking values of ± 1 and β_jk is the log-normal distributed channel coefficient. To normalize each channel realization to unity requires that

\sum_{j = 1}^{N} \sum_{k = 1}^{K (j)} β_{j k}^{2} = 1.

(7)

The amplitude gain κ is also assumed to be a log-normal random variable with the relation

κ {= 10}^{g/20}

, where g is a normal random variable with mean g₀ and variance

σ_{g}^{2}

. The mean g₀ depends on the average total multi-path gain G and expressed as

g_{0} = \frac{10 \ln G}{\ln 10} - \frac{σ_{g}^{2} \ln 10}{20},

(8)

where ln(⋅) is the natural logarithm. G is dependent on average attenuation exponent Λ by G = G₀/D^Λ , and G₀ is the reference power gain evaluated at D = 1 m. A₀ = 10 log₁₀ (E_TX /E_RX ) denoting the path loss at a reference distance D₀ = 1 m in dB is related to G₀ by G₀ = 10 ^–A ₀ ^/10.

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

\begin{array}{l} r_{RF} (t) = x_{RF} (t) * h_{RF} (t) + n (t) \\ = κ \sqrt{E_{F}} \sum_{n = 1}^{\infty} \sum_{j = 0}^{N_{s} - 1} \sum_{k = 1}^{N} \sum_{j = 1}^{K (j)} q (t - n T_{d} - j T_{f} - c_{j} T_{c} - d_{n} T_{p} - T_{j} - τ_{j k}) + n (t) . \end{array}

(9)

Using an UWB receiver, estimates of the signal passed through RF,

{{\tilde{u}}_{k}}

are obtained. We present the average detection error probability (DEP) analysis for the hybrid system performance over the FSO and RF links below in Section 3.

3. Detection error probability analysis

The overall error probability for the complete hybrid system can be found as

P_{e} (γ_{F S O}, γ_{R F}) = P_{F S O} (γ_{F S O}) [1 - P_{R F} (γ_{R F})] + [1 - P_{F S O} (γ_{F S O})] P_{R F} (γ_{R F}),

(10)

where

P_{F S O} (γ_{F S O})

P_{R F} (γ_{R F})

and

γ_{F S O}

γ_{R F}

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 γ_RF = (κ² N_s γ_p) where γ_p = E_F/N₀ denotes the pulse SNR and results in error probability of

P_{R F} (γ_{R F}, κ) = \frac{1}{2} erfc (\sqrt{\frac{γ_{R F} κ^{_{2}}}{2}}),

(11)

where erfc(⋅) is the complementary error function. After averaging out the probability density function (PDF) over κ

P_{R F} (γ_{R F}) = \int_{0}^{\infty} \frac{1}{2} erfc (\sqrt{\frac{γ_{R F} κ^{_{2}}}{2}}) \frac{20}{κ \ln 10 \sqrt{2 π σ_{g}^{2}}} \exp (- \frac{{(20 \log_{10} κ - g_{0})}^{2}}{2 σ_{g}^{2}}) d κ .

(12)

This can be solved by Gauss-Hermite expansion given by

\int_{- \infty}^{\infty} g (y) e^{- y^{2}} d y \approx \sum_{i = 1}^{n} ω_{i} g (y_{i}),

(13)

where y_i and ω_i , i = 1,…,n, are the i^th root (abscissa) and associated weight, respectively [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 = (20 \log_{10} κ - g_{0}) / (\sqrt{2 σ_{g}^{2}})

P_{R F} (γ_{R F}) = \frac{1}{2 \sqrt{π}} \sum_{i = 1}^{N} ω_{i} erfc (\sqrt{\frac{γ_{R F} 10^{(y_{i} \sqrt{2 σ_{g}^{2}} + g_{0}) / 10}}{2}}) .

(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

P_{F S O} (γ_{F S O}, I) = 0.5 erfc (\sqrt{γ_{F S O} {(η I)}^{2} / 2}),

(15)

where γ_FSO = N_sγ_p and γ_p = E_p/(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

P_{F S O} (γ_{F S O}) = E_{I} [P_{e} (γ_{F S O}, I)] = \int_{0}^{\infty} P_{e} (γ_{F S O}, I) f_{I} (I) d I .

(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

P_{F S O}^{c o d e d} (γ_{F S O})

in terms of the uncoded error probability

P_{F S O} (γ_{F S O})

is expressed approximately as ([9

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

] , pp. 531)

P_{F S O}^{c o d e d} (γ_{F S O}) \approx N_{b} {[4 P_{F S O} (γ_{F S O}) (1 - P_{F S O} (γ_{F S O}))]}^{\frac{d_{f r e e}}{2}},

(17)

where d_free is the minimum free distance of the convolutional code, and N_b is the sum of the Hamming weight of all the input sequences whose associated convolutional codeword have a Hamming weight of d_free _.

In FSO channels, the light intensity is closely related to the strength of the atmospheric turbulence that is generally divided into three different regimes: weak, moderate and strong turbulence regimes. All three regimes are characterized by accurate statistical models, which can be used to compute the average error probability term in Eq. (16) as presented in the following.

3.1 Error performance of FSO system in weak turbulence

For weak turbulence regime, the received signal intensity at the photodetector is related to the amplitude fluctuations by

I = I_{0} exp (2 X - 2 μ_{X})

where I₀ represents the light intensity without turbulence and X denotes the random fluctuations in amplitude which has Gaussian distribution with mean μ_x and variance

σ_{X}^{2}

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

]. The variance of log-amplitude fluctuations is closely related to atmospheric conditions and link distance and for a plane wave, it is given by

σ_{X}^{2} = 0.307 C_{n}^{2} k^{7 / 6} L^{11 / 6}

, where

C_{n}^{2}

is an altitude-dependent parameter and in literature often referred as refractive-index structure parameter, k = 2π/λ is the optical wave number, where λ is the wavelength of the transmitted pulse and L is the link distance [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]

]. For this case, the PDF of the log-normal distributed received intensity is given by

f_{I} (I) = \frac{1}{2 I \sqrt{2 π σ_{X}^{2}}} \exp (- \frac{{(\ln (I / I_{0}))}^{2}}{8 σ_{X}^{2}}), I \geq 0.

(18)

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

σ_{S I}^{2} = E [I^{2}] / E {[I]}^{2} - 1 = \exp (σ_{X}^{2}) - 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

0 \leq σ_{S I}^{2} \leq 0.75

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

P_{F S O} (γ_{F S O}) = \int_{0}^{\infty} \frac{1}{2} e r f c (\sqrt{γ_{F S O} {(η I)}^{2} / 2}) \frac{1}{2 I \sqrt{2 π σ_{X}^{2}}} \exp (- \frac{{(\ln (I / I_{0}))}^{2}}{8 σ_{X}^{2}}) d I,

(20)

which can be rewritten by the change of parameters as

P_{F S O} (γ_{F S O}) = \frac{1}{2 \sqrt{π}} \int_{- \infty}^{\infty} e r f c (\sqrt{γ_{F S O} {(η I_{0} e^{y \sqrt{8 σ_{X}^{2}}})}^{2} / 2}) e^{- y^{2}} d y,

(21)

where

y = \ln (I / I_{0}) / \sqrt{8 σ_{X}^{2}}

., we can approximate Eq. (21) using the expansion in Eq. (13)

P_{F S O} (γ_{F S O}) = \frac{1}{2 \sqrt{π}} \sum_{i = 1}^{n} ω_{i} e r f c (\sqrt{\frac{γ_{F S O} {(η I_{0} e^{y_{i} \sqrt{8 σ_{x}^{2}}})}^{2}}{2}}) .

(22)

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

Under moderate turbulence conditions, both the small and large scatterers are effective and the intensity fluctuations are modeled by the Gamma-Gamma distribution described by the PDF

f_{I} (I; α, β) = \frac{2 {(α β)}^{(α + β) / 2}}{Γ (α) Γ (β)} I^{(α + β) / 2 - 1} K_{α - β} (2 \sqrt{α β I}),

(23)

where Γ(⋅) and K _n (⋅) are the Gamma function and the n ^th order modified Bessel function of the second kind, respectively [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]

,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.

]. In Eq. (23), small and large scale scattering effects that are represented by α and β, respectively, are related to the atmospheric conditions by

α = {[\exp (\frac{0.49 χ^{2}}{{(1 + 1.11 χ^{12 / 5})}^{7 / 6}}) - 1]}^{- 1}, β = {[\exp (\frac{0.51 χ^{2}}{{(1 + 0.69 χ^{12 / 5})}^{5 / 6}}) - 1]}^{- 1},

(24)

where

χ^{2} = 1.23 C_{n}^{2} k^{7 / 6} L^{11 / 6}

is the Rytov variance for a plane wave and the parameters

C_{n}^{2}

, k and L are given as above. These α and β parameters are related to the scintillation index by

σ_{S I}^{2} = α^{- 1} + β^{- 1} + {(α β)}^{- 1}

. Also, moderate turbulence regime is often characterized as the one with

0.75 \leq σ_{S I}^{2} < 1

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

P_{F S O} (γ_{F S O}) = \int_{0}^{\infty} \frac{1}{2} e r f c (\sqrt{γ {}_{F S O}{(η I)}^{2} / 2}) \frac{2 {(α β)}^{(α + β) / 2}}{Γ (α) Γ (β)} I^{\frac{(α + β)}{2} - 1} K_{α - β} (2 \sqrt{α β I}) d I .

(25)

Using the formulation in [11

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

] the integrands erfc(⋅) and K_n(⋅) in Eq. (25) can be expressed in terms of Meijer's G-function as

P_{F S O} (γ_{F S O}) = \frac{2 {(α β)}^{(α + β) / 2}}{Γ (α) Γ (β)} \int_{0}^{\infty} I^{(α + β) / 2 - 1} \frac{1}{2 \sqrt{π}} G_{1, 2}^{2, 0} [\frac{γ_{F S O} {(η I)}^{2}}{2} | \begin{matrix} 1 \\ 0, 0.5 \end{matrix}] \frac{1}{2} G_{0, 2}^{2, 0} [α β I | \begin{matrix} - \\ \frac{(α - β)}{2}, \frac{(β - α)}{2} \end{matrix}] d I

(26)

which, using Eq. (07).34.21.0011.01 of [11

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

], results in a closed-form expression such that

P_{F S O} (γ_{F S O}) = \frac{2^{α + β - 3}}{\sqrt{π^{3}}} Γ (α) Γ (β) G_{5, 2}^{2, 4} [\frac{8 η^{2} γ_{F S O}}{{(α β)}^{2}} | \begin{matrix} \frac{1 - α}{2}, \frac{2 - α}{2}, \frac{1 - β}{2}, \frac{2 - β}{2}, 1 \\ 0, \frac{1}{2} \end{matrix}] .

(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

f_{I} (I) ​ = \frac{1}{\bar{I}} \exp (- \frac{I}{\bar{I}}),

(28)

where

\bar{I} = E [I]

denotes the mean light intensity [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

σ_{S I}^{2} \geq 1

Using Eq. (16) and the distribution given in Eq. (28), the average DEP for strong turbulence conditions can be written as

P_{F S O} (γ_{F S O}) = \int_{0}^{\infty} \frac{1}{2} e r f c (\sqrt{γ_{F S O} {(η I)}^{2} / 2}) \frac{1}{\bar{I}} \exp (- \frac{I}{\bar{I}}) d I = \frac{1}{2} [1 - e r f c (\frac{1}{η \bar{I} \sqrt{2 γ_{F S O}}}) \exp (\frac{1}{2 {(η \bar{I})}^{2} γ_{F S O}})],

(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, N_s = 2 and η = 0.9, respectively. The channel parameters change at every 200 symbols, i.e., τ_c /(NT_d ) = 0.2 where τ_c is the channel coherence time and NT_d is the total duration of a frame.

For each turbulence condition, a constant

C_{n}^{2}

is assumed through the horizontal path that is taken as 5.1x10⁻¹⁵ for weak turbulence. For link distances over 2, 2.5, 3 and 4 km, the corresponding channel parameters are μ_x = 0 and σ_X = 0.3, 0.37, 0.44 and 0.57. From Eq. (19), these values correspond to

σ_{S I}^{2}

= 0.095, 0.15, 0.209 and 0.380, respectively. The comparison between the analytical approximation derived in Eq. (22) and the Monte-Carlo simulations for these values of

σ_{S I}^{2}

is shown in the group of first 4 BER curves in Fig. 2 . As seen in the figure, the theoretical derivations, represented with dashed-lines show a good correspondence to the simulated performances, depicted in solid lines.

Fig. 2 Comparison of the simulated and theoretical DEP’s for weak, moderate and strong turbulence fading conditions.

For moderate turbulence condition, we assume

C_{n}^{2}

= 1.76x10⁻¹⁴ and consider link distances over 2, 2.5 and 3 km. Using the formulation in Eq. (24), the (α,β) parameter pairs are (4.16,2.21), (4.00,1.75) and (4.05,1.51). These values correspond to the following scintillation index values

σ_{S I}^{2}

= {0.8, 0.96, 1.07}, respectively. The simulation results in Fig. 2 for all three cases are in full accordance with the exact closed form expressions given in terms of the Meijer functions.

For strong turbulence, unit mean light intensity is considered E[I] = 1 and

σ_{S I}^{2}

≅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.

For the transmission of the received signals over FSO through UWB environment, we consider the channel model 1 (CM1) in [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).

] with the suggested values for A₀ and Λ in LOS environment chosen as 47 dB and 1.7, respectively. The two cases where the UWB signals are transmitted over a FSO link of 2 km length at 30 and 45 dB, respectively, are considered. For weak and moderate conditions, we assume constant

C_{n}^{2}

values as 5.1x10⁻¹⁵ and 1.76x10⁻¹⁴ and the corresponding channel parameters are σ_X = 0.3 and (α,β) = (4.16,2.21), respectively. The RF UWB simulations adopt CM1 conditions and assume a link distance of D = 2 meters and σ_g is taken as 3 dB. The results are shown in Fig. 3 . The error performance of the UWB transmission over CM1 channels without any FSO link errors is included as a reference curve. Our results show that for weak turbulence conditions, FSO channel does not introduce additional performance degradation up to 10⁻⁶ BER limit at 30 dB. On the other hand, for moderate and strong turbulence conditions, error floors appear at relatively high BER levels due to the high error rates carried from the FSO subsystem.

Fig. 3 FSO + RF UWB system performance of a link distance of 2 km. For weak, moderate and strong FSO turbulences, channel parameters are taken as σ_X = 0.3, (α,β) = (4.16,2.21) and E[I] = 1, respectively. For RF environment, CM1 is assumed.

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 N_b = 2, d_free = 7 ([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 . 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.

Fig. 4 (27,31)₈ convolutional coded FSO + RF UWB system performance over 2 km.

5. Conclusion

A novel FSO communication system based on optical UWB signaling is presented. The proposed approach increases the range of conventional RF UWB signaling as the optical pulses are not subject to multipath interference. The drawback of the proposed system is that FSO channel introduces atmospheric turbulence fading which degrades the link performance whereas in fiber optical systems, the channel only suffers from AWGN. The error probability analyses of IR-UWB systems over the FSO system under low, moderate and strong turbulence induced fading conditions are presented and verified by simulation results.

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

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]
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]
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]
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]
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]
X. Zhu and J. M. Kahn, “Free-space optical communication through atmospheric turbulence channels,” IEEE Trans. Commun. 50(8), 1293–1300 (2002). [CrossRef]
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]
M. Abramowitz, and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).
S. Lin, and D. J. Costello, Error Control Coding, 2nd ed. (Pearson Prentice Hall, 2004).
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.
The Wolfram Function Site, (2004), http://functions.wolfram.com/ .
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]
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).

Baedke, M.
Cabon, B.
Cao, Q.
Chen, J. Y.
Chi, S.
Ghassemzadeh, S. S.
Greenstein, L. J.
Jazayerifar, M.
Kahn, J. M.
Kavcic, A.
Kavehrad, M.
Lin, J. H.
Lin, W. P.
Navidpour, S. M.
Pearce, M. B.
Peng, P. C.
Peng, W. R.
Salehi, J. A.
Sveinsson, T.
Tarokh, V.
Uysal, M.
Wilson, S. G.
Yao, J.
Zeng, F.
Zhu, X.

IEEE J. Sel. Areas Comm.

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]

IEEE Photon. Technol. Lett.

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]
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]
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]
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]

IEEE Trans. Commun.

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

IEEE Trans. Wirel. Comm.

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]

J. Commun. Network

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).

J. Lightwave Technol.

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]

Other

M. Abramowitz, and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).
S. Lin, and D. J. Costello, Error Control Coding, 2nd ed. (Pearson Prentice Hall, 2004).
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.
The Wolfram Function Site, (2004), http://functions.wolfram.com/ .

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