## 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 [1–3]. 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 [1,2,4,5]. 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 [6,7]) 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., [6,7]). 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]. 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.

The generated optical TH-PPM signal can be represented as

*E*denotes the pulse energy amplified by EDPA,

_{p}*p(t)*denotes the Gaussian pulse,

*d*and {

_{n}*c*} are the binary information and pseudo-random code sequences for time hopping, respectively.

_{j}*T*,

_{d}*T*,

_{f}*T*and

_{c}*T*represent the symbol, bit, chip and pulse durations, respectively and bits are repeated

_{p}*N*times in a symbol period.

_{s}The FSO channel is described by the unit impulse response *h(t) = I(t) + I _{b}* where

*I(t)*and

*I*are the instantaneous light intensity and the background radiation whose effects are removed at the receiver as in [6], 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., $I(t)\approx I.$

_{b}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*($0<\eta \le 1$) indicates the efficiency of the photodetector. After the removal of the background radiation bias $\eta {I}_{b}$, the resulting signal can be represented as

*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

*N*. Assuming perfect synchronization, the received signal is passed through the matched filter

_{0}/2*x*which can be written as

_{r}(t)*N*. 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, ${\widehat{u}}_{k}$’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

_{0}/2*E*denotes the energy pulse,

_{F}*q(t)*denotes the Gaussian monocycle pulse train. The UWB channel can be modeled as

*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*is the delay of the

_{j}*j*

^{th}cluster.

*α*denotes the channel coefficient of the

_{jk}*j*

^{th}cluster and the

*k*

^{th}multipath and can be expressed as

*α*, where

_{jk}= p_{jk}β_{jk}*p*is a Bernoulli random variable taking values of ± 1 and

_{jk}*β*is the log-normal distributed channel coefficient. To normalize each channel realization to unity requires that

_{jk}The amplitude gain *κ* is also assumed to be a log-normal random variable with the relation $\kappa {\text{=10}}^{\text{g/20}}$, where *g* is a normal random variable with mean *g _{0}* and variance ${\sigma}_{g}^{2}$. The mean

*g*depends on the average total multi-path gain

_{0}*G*and expressed as

*G*is dependent on average attenuation exponent

*Λ*by

*G = G*, and

_{0}/D^{Λ}*G*is the reference power gain evaluated at

_{0}*D*= 1 m.

*A*= 10 log

_{0}_{10}(

*E*) denoting the path loss at a reference distance

_{TX}/E_{RX}*D*= 1 m in dB is related to

_{0}*G*by

_{0}*G*10

_{0}=

^{–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

Using an UWB receiver, estimates of the signal passed through RF, $\left\{{\tilde{u}}_{k}\right\}$ 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

Assuming normalized channel coefficients, i.e., Eq. (7) holds, the received SNR at UWB receiver can be expressed as *γ _{RF} = (κ^{2} N_{s} γ_{p})* where

*γ*denotes the pulse SNR and results in error probability of

_{p}= E_{F}/N_{0}*κ*

This can be solved by Gauss-Hermite expansion given by

*y*and

_{i}*ω*,

_{i}*i*= 1,…,

*n*, are the

*i*root (abscissa) and associated weight, respectively [8]. After the change of variables such that $y=(20{\mathrm{log}}_{10}\kappa -{g}_{0})/(\sqrt{2{\sigma}_{g}^{2}})$,

^{th}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

where*γ*and

_{FSO}= N_{s}γ_{p}*γ*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}= E_{p}/(N_{0}/2)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 ${P}_{FSO}^{coded}({\gamma}_{FSO})$ in terms of the uncoded error probability ${P}_{FSO}({\gamma}_{FSO})$ is expressed approximately as ([9] , pp. 531)

*d*is the minimum free distance of the convolutional code, and

_{free}*N*is the sum of the Hamming weight of all the input sequences whose associated convolutional codeword have a Hamming weight of

_{b}*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 $I={I}_{0}\text{exp}(2X-2{\mu}_{X})$ where *I _{0}* represents the light intensity without turbulence and

*X*denotes the random fluctuations in amplitude which has Gaussian distribution with mean

*μ*and variance ${\sigma}_{X}^{2}$ [6]. The variance of log-amplitude fluctuations is closely related to atmospheric conditions and link distance and for a plane wave, it is given by ${\sigma}_{X}^{2}=0.307{C}_{n}^{2}{k}^{7/6}{L}^{11/6}$, where ${C}_{n}^{2}$is an altitude-dependent parameter and in literature often referred as refractive-index structure parameter,

_{x}*k*=

*2π/λ*is the optical wave number, where

*λ*is the wavelength of the transmitted pulse and

*L*is the link distance [7]. For this case, the PDF of the log-normal distributed received intensity is given by

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

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 $0\le {\sigma}_{SI}^{2}\le 0.75$.

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

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

*(⋅) are the Gamma function and the*

_{n}*n*

^{th}order modified Bessel function of the second kind, respectively [7,10]. In Eq. (23), small and large scale scattering effects that are represented by

*α*and

*β*, respectively, are related to the atmospheric conditions by

*k*and

*L*are given as above. These

*α*and

*β*parameters are related to the scintillation index by ${\sigma}_{SI}^{2}={\alpha}^{-1}+{\beta}^{-1}+{(\alpha \beta )}^{-1}$. Also, moderate turbulence regime is often characterized as the one with $0.75\le {\sigma}_{SI}^{2}<1$.

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

Using the formulation in [11] the integrands erfc(⋅) and K_{n}(⋅) in Eq. (25) can be expressed in terms of Meijer's G-function as

#### 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

where $\overline{I}=E[I]$ denotes the mean light intensity [12]. 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 ${\sigma}_{SI}^{2}\ge 1$.Using Eq. (16) and the distribution given in Eq. (28), the average DEP for strong turbulence conditions can be written as

## 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*) = 0.2 where

_{d}*τ*is the channel coherence time and

_{c}*NT*is the total duration of a frame.

_{d}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*= 0.3, 0.37, 0.44 and 0.57. From Eq. (19), these values correspond to ${\sigma}_{SI}^{2}$ = 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 ${\sigma}_{SI}^{2}$ 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.

_{X}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 ${\sigma}_{SI}^{2}$ = {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 ${\sigma}_{SI}^{2}$≅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] with the suggested values for *A _{0}* 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*= 0.3 and (

_{X}*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*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

_{g}^{−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.

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*= 7 ([9], 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

_{free}^{−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

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.

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