International Journal of Wireless Information Networks

, Volume 14, Issue 1, pp 33–45

Availability Evaluation of Ground-to-Air Hybrid FSO/RF Links

Authors

  • Haiping Wu
    • Center for Information and Communications Technology Research, Electrical Engineering DepartmentThe Pennsylvania State University
    • Center for Information and Communications Technology Research, Electrical Engineering DepartmentThe Pennsylvania State University
Article

DOI: 10.1007/s10776-006-0042-1

Cite this article as:
Wu, H. & Kavehrad, M. Int J Wireless Inf Networks (2007) 14: 33. doi:10.1007/s10776-006-0042-1

Abstract

Recently, a hybrid architecture that utilizes the complementary nature of free-space optics (FSO) and radio frequency (RF) links with respect to their individual weather sensitivities was proposed to significantly increase availability for terrestrial broadband links. Based on this architecture, we developed a channel model integrating both the RF and FSO channels. Using the model and cloud distribution data obtained from the International Satellite Cloud Climatology Project, availability of an airborne hybrid FSO/RF link is evaluated. From the results, we conclude that if the FSO link alone is used, availability is greatly hampered by clouds due to attenuation and temporal dispersion. Contrarily, the RF signals are relatively immune to cloud influence, thus improving the hybrid link availability significantly. Furthermore, because of the significant temporal dispersion caused by multiple scattering of cloud particles, availability of FSO links can be improved by using frequency division schemes, though far from compensating for losses incurred by clouds.

Index Terms

availabilitydispersive channelmultiple scattering

Introduction

Due to the increasing demand for broadband data communications, free space optical (FSO) links are gaining more attention for their high-bandwidth and inherent security over long distances. Recent advances in optical devices showed that such pointing communication links could even be used to interconnect very fast moving units such as airplanes [1].

However, FSO links are also well known for their susceptibility to adverse weather conditions such as cloud and fog, which pose a great challenge on link availability. For terrestrial FSO links, backup RF links have been proposed to ensure continuous availability during FSO downtimes such as when there is dense fog [1]. Because of the distinct weather sensitivities of RF waves and light waves, FSO links can also serve as a backup when RF links are severely attenuated, which typically happens when there is heavy rain. Due to the close resemblance of cloud and fog, the same method can be applied to ground-to-air FSO links to overcome communication interruptions caused by failure of FSO links. Though in this case, the complementary property of the two sub-links no longer holds due to the fact that rain and thick clouds often occur concurrently. However, a backup RF link still increases the overall system availability by enabling communications through clouds when no heavy rain is present.

In order to quantitatively analyze availability of an airborne hybrid link, we utilize cloud data obtained from the International Satellite Cloud Climatology Project (ISCCP) database. Based on the cloud statistical information and the channel model we developed for this application, we evaluated availability of stand-alone RF and FSO links. Due to the temporal dispersion caused by thick clouds, capacity is used as the measure to indicate availability instead of attenuation. Availability of hybrid links is evaluated and compared to the stand-alone cases to demonstrate advantages.

CHANNEL MODELS

We consider a hybrid wireless network shown in Figure 1. As illustrated in the figure, there are two types of links in this scenario: ground-to-air links, e.g. the link between ground station A and airplane C, and air-to-air links, e.g. the link between airplanes C and D. Typically, the airborne vehicles operate at an altitude of around 2000 m, while the density of airborne units is highly variable, depending on local weather conditions. If the ground stations are far apart, one or two more tiers of airborne vehicles may be present. Thus, communication packets can be relayed to the topmost tier (typically 10,000 m in altitude), and then transferred over long distance hops (200 km per hop), where no cloud blockage occurs. In this paper, we focus on the ground-to-air links, where each single link consists of two line-of-sight sub-links: an RF (15 GHz frequency) and an FSO (1550 nm wavelength) sub-link. Due to the fact that the two sub-links operate on very distinct frequencies, the overall channel can be modeled by combining channel models of the two subsystems. The RF channel model is based on an integrated set of three link attenuation models that estimate margin losses due to rain, cloud, and atmospheric (water vapor and oxygen) attenuation and multipath effects. The FSO channel model considers mainly attenuation and dispersion caused by cloud and rain. Due to the fact that the FSO link wavelength is 1550 nm, gaseous attenuation can be neglected.
https://static-content.springer.com/image/art%3A10.1007%2Fs10776-006-0042-1/MediaObjects/10776_2006_42_Fig1_HTML.gif
Fig. 1.

The hybrid broadband communication scenario.

However, scintillation has to be taken into account as a fading factor for the FSO link.

The Optical Channel Model

Laser propagation through atmosphere is mainly affected by absorption and scattering. Absorption by atmospheric gases, due to its quantum nature, is frequency dependent, and can be described by the so-called “atmospheric windows”. The 1550 nm wavelength falls within the 1520–1600 nm window, making the absorption negligible. Particles in atmosphere also scatter incident beam of light in all directions. As the name implies, scattering only redistributes energy of the incident light rather than absorbing it. Different sizes of particles cause different types of scattering. Based on the size of particles, scattering can be divided into the following three regimes. Rayleigh scattering occurs when particle size is much smaller than wavelength, such as gas molecules. It is inversely proportional to the fourth power of wavelength, and therefore is negligible for wavelengths such as 1550 nm. Mie scattering applies to particles that have comparable size to wavelength, such as water droplets in cloud and fog. Non-selective scattering can be used for particle sizes much greater than wavelength, such as raindrops. Mie theory still can be used to evaluate attenuation.

Cloud Scattering

Cloud is the primary factor that causes an FSO link outage. As mentioned earlier, cloud consists of water/ice droplets that are comparable in size to wavelength. Therefore, attenuation by clouds can be evaluated using Mie theory. Traditionally, attenuation is estimated through computing the extinction coefficient Qext, i.e., the amount of energy removed from the incident beam by scattering elements. This extinction coefficient is proportional to the extinction cross section Sext, which is the sum of absorption and scatter cross sections [2]:
$$ S_{\rm ext} =S_{\rm abs} +S_{\rm sca}.$$
(1)
If the scattering particle size distribution is known, the total scattering or attenuation coefficient can be calculated by summing the contributions from all particles:
$$ k_{\rm s} =\sum\limits_{i} n_{i} S_{\rm sca} (r_i),$$
(2)
where ni and ri are the number and radius of the i-th particle. Using the Beer-Lambert Law [4], the attenuation of laser power through atmosphere can be expressed as
$$ \beta_{\rm s} (L)= \hbox{exp}(-k_{\rm s} L),$$
(3)
where L is the distance between transmitter and receiver. The product, ksL is usually referred to as optical thickness and is denoted by τ.

However, the underlying assumption of this method is that light scattered by particles never reaches the receiver, which is valid for low optical thickness values. But for the cases of medium or high optical thicknesses, especially when the particle size is comparable to the wavelength (this causes most of the scattered energy to be concentrated in the forward direction), this approximation is no longer valid.

If scattered light is to be taken into account, then, similar to multipath in RF propagation, light arriving from different paths introduces time delay, and thereby broadens the impulse response of the channel. An analysis of this effect is usually accomplished through Monte Carlo simulations [37].

Figure 2 shows the simulation scheme. It assumes that a homogenous cloud lies within a cylinder (details of cloud model will be specified in the next section). The light is monochromatic with the wavelength being 1550 nm. Photon emission is assumed to be a delta function both spatially and temporally along the optical axis. When a photon collides with a particle, whose size is determined by the cloud particle size distribution, if it does not escape or is absorbed or received, is derived from three random variables: the rotation angle ρ, the polar angle θ and the distance to the next collision r.
https://static-content.springer.com/image/art%3A10.1007%2Fs10776-006-0042-1/MediaObjects/10776_2006_42_Fig2_HTML.gif
Fig. 2.

An illustration of the Monte Carlo simulation for the multiple scattering effect.

These three random variables are independent for each scatter, each with its own probability density function (PDF). The rotation angle is uniform between 0 and 2π; the polar angle PDF can be determined through Mie theory based on the size of the scattering particle; the distance r is exponential with the mean value D being the mean free path:
$$ D=\frac{\rm physical\;thickness}{\tau}.$$
(4)
When a photon reaches the receiver, it is counted as a received photon along with its travel distance within the cloud. If the amount of received photons is sufficient, an estimation of temporal dispersion can be made based on the photon travel distances.

Rain Attenuation

Raindrops are much greater in size than the optical wavelength. Hence, it is more appropriate to use geometric optics to simulate the scattering effects. However, Mie theory is still approximately valid. Additionally, because raindrops are relatively sparse compared to cloud particles, temporal dispersion is negligible, thus making Eq. (2) valid for attenuation evaluation. Yet in order to apply (2), raindrop size distribution is necessary. Here, we adopt the Weibull distribution by Assouline and Mualem [8]:
$$ M_g \left(\frac{D}{D_0}\right)=\frac{M_{gt}}{D_0}\varphi n\left(\frac{D}{D_{0}}\right)^{n-1} e^{-\varphi \left(\frac{D}{D_0}\right)^{n}},$$
(5)
where D0 = aRbecR, ϕ = Γ n(1 + 1/n).

Physically, D0 represents the mean drop size. Parameters a, b, c and n are constants derived from theoretical and measurement results. Mg is the number of particles of size D, Mgt is the total number of particles and R represents rain rate.

Scintillations

Apart from absorption and scattering, air turbulence also plays an important role in temporal fluctuation of the received signal. When a beam of light passes through air, the randomly fluctuating air temperature produces small refractive index non-homogeneities that distorts the light beam phase front, changes beam direction (beam wander) and causes intensity fluctuations (scintillation) [4].

The cause of all the above distortions is termed as atmospheric turbulence and occurs when air parcels of different temperature are mixed by wind and convection. Atmospheric turbulence is physically described by Kolmogorov theory; in which fluctuations of the signal log-amplitude induced by air turbulence are found to be Gaussian with a covariance given by [9]:
$$ \sigma_x^2 \vert_{\rm plane} =0.56\left({\frac{2\pi }{\lambda }} \right)^{7/6}\int_0^L C_n^2 (x)(L-x)^{5/6}{\rm d}x,$$
(6)
where L is the propagation path length for the beam. Cn2 is the wave-number structure parameter that is characterized by the Hufnagel-Valley model [10].
Denoting the log-amplitude using a random variable x, the light intensity is related to the log-amplitude by:
$$ I=I_{\rm o} \exp(2x-2E(x)),$$
(7)
where E(x) is the ensemble average of x. Thus, at a single point in space, at a single instant of time, the light intensity fading induced by turbulence is [9]:
$$ f_I (I)=\frac{1}{2I}\frac{1}{\sqrt {2\pi \sigma_x^2 } }\exp\left({-\frac{\left[ {\ln(I)-\ln(I_{\rm o})} \right]^2}{8\sigma_x^2 }} \right).$$
(8)

The RF Channel Model

Propagation of radio waves through atmosphere above 10 GHz involves a number of factors; the formula to calculate total transmission loss is given by [11]:
$$ {\rm Attenuation} ({\rm dB})=92.45+20\hbox{log}f_{\rm GHz} +20\hbox{log}D_{\rm km} +{\rm Excess}\;{\rm Attenuation},$$
(9)
where f is frequency in gigahertz and D is the distance between transmitter and receiver in kilometers. Excess attenuation generally includes absorption losses due to atmospheric gases, attenuation due to fog and cloud, attenuation due to rainfall and multipath effects. Due to the fact that the communication links are line-of-sight and far away from ground reflectors, multipath effects are negligible. Because airplanes are fast moving, Doppler effects cannot be neglected. But since multipath is negligible, Doppler only causes random frequency shifts [12], and hence is not included in our analysis of attenuation, though it should be included when constructing channel model for simulations. In summary, cloud, rain and atmospheric gaseous attenuation are the dominant excess attenuation factors, which we discuss in detail.

Gaseous Attenuation

The atmosphere contains a number of gaseous constituents that attenuate microwave radiation through molecular absorption that results from quantum level changes occurring only at a specific resonance frequency or narrow band of frequencies. In atmosphere, only oxygen and water vapor have observable resonance in the radio-wave band. Specific attenuation of oxygen and water vapor as a function of frequency can be found in [13]. Assuming a temperature of 20 °C and a water vapor concentration of 7.5 g/m3 (relative humidity 42% at 20 °C), the oxygen and water vapor attenuation for 15 GHz is found to be γo = 0.0077 dB/km and γw = 0.0182 dB/km.

Cloud Attenuation

Clouds are generally categorized into ice and water clouds. Attenuation caused by ice clouds is negligible [14]. However, scattering by very small liquid water droplets that make up water clouds can produce significant attenuation at high frequencies. Water cloud attenuation at frequencies lower than 10 GHz is negligible [15]. For frequencies higher than 10 GHz, water droplets in clouds are still much smaller compared to wavelength, making Rayleigh approximation valid for frequencies below 200 GHz. The specific attenuation in terms of the total water content per unit volume is [15]:
$$ \gamma_{\rm c} =K_{\rm l} W,$$
(10)
where γc is attenuation in dB/km, Kl is the attenuation coefficient and W is liquid water density in cloud, as listed in Table I. Kl is evaluated using a mathematical model based on Rayleigh scattering [15]. At 20 °C, the specific attenuation coefficient is found to be Kl = 0.1203 dB/km g/m3 at 15 GHz. Along with the liquid water content that is listed in Table I, cloud attenuation can be evaluated.
Table I.

Parameters of low-level water and ice clouds

Altitude

Base altitude (m)

Maximum physical thickness (m)

Constituent

N (cm−3)

W (g m−3)

Sext (km−1)

Low

100

3100

ice

18.65

N/A

122.14

water

247.76

0.7472

Rain Attenuation

Rain attenuation for radio-waves is similar to fog attenuation for optical links. Because raindrop size is comparable to millimeter radio wavelength, Mie scattering is appropriate to quantify the attenuation. But traditionally, specific point rain attenuation (dB/Km) is also expressed as:
$$ \alpha =aR^b,$$
(11)
where R is the rain rate in mm/h, and a and b are frequency and temperature dependent constants. In this equation, the constant a and b represent the complex behavior of the complete representation of specific attenuation of Mie scattering. This relatively simple expression was used by early investigators in measurements, and later justified by an analytical approach.

Because rain generally displays significant spatial and temporal variation along a horizontal path, statistical procedures are required to estimate the instantaneous rain rate profile along the path. Several models such as the “Crane” model and the ITU model are available to fulfill this function. In our analysis, we chose the Global Crane model for rain rate statistics estimation and attenuation prediction.

Detailed procedure of rain attenuation estimation involves the following steps [16]:
  • Find rain attenuation coefficients a and b that are tabulated in [17], if the frequency is not found, use logarithmic interpolation for a and linear interpolation for b. For 15 GHz, a = 3.57  ×  10−2 and b = 1.160.

  • Use the Crane model to find rain rate statistics. As shown in [16], the state of Pennsylvania lies in the D2 climate zone. Based on this, the cumulative probability function of rain rate is computed and shown in Figure 3. As the graph indicates, in this area, rain occurs approximately 10% of the time.

  • Compute the path loss due to rain attenuation using equations based on the Crane model.

https://static-content.springer.com/image/art%3A10.1007%2Fs10776-006-0042-1/MediaObjects/10776_2006_42_Fig3_HTML.gif
Fig. 3.

Predicted rain rate CDF for climate zone D2.

Note that for the ground-to-air links, path length affected by rain is related to the rain height, which can be determined by looking up the height of the 0 °C isotherm [18]. For the area of Pennsylvania, it is found that the yearly mean rain height is approximately 3.36 km.

CAPACITY

Generally, availability is assessed by using a binary variable as indicator. If data can be received at a given rate while meeting a certain quality requirement such as BER, the link is available; otherwise, there is an outage. In case of flat fading, because the channel is memory-less, an evaluation of power loss (attenuation) is sufficient for finding the maximal data rate, and thereby link availability with different range, locations, etc.

For links of long distance and high probability of severe scattering, temporal dispersion can no longer be neglected. In order to include this effect, [19] evaluates bandwidth of impulse response through clouds to give a more practical estimation of availability. Nevertheless, implicit in it is that the transmitter laser power can be adjusted to an arbitrary level such that the receiver can always capture sufficient number of photons for signal detection, which is inadequate when real application is considered. In order to overcome this inadequacy, we evaluate channel capacity as a function of transmit power, such that attenuation is also taken into account. To proceed with capacity evaluation, an appropriate channel model is required. Oftentimes, direct detection optical channels are mathematically modeled as a Poisson channel because of the underlying photon detection mechanism. Typically, the channel is memory-less, regardless of the data rate. When the scattering effects are less significant, this assumption is valid. However, if the scattering causes temporal spread that exceeds the channel coherence bandwidth, this model is no longer appropriate for capacity evaluation. Furthermore, to reach the Poisson channel capacity, receiver needs to have the sensitivity to detect one single photon, which is impractical for real systems. Therefore, we take the conventional approach of modeling the channel as a Gaussian channel.

The reason that a direct detection optical channel can be modeled as a Gaussian channel lies in the nature of optical noise. More specifically, noise is a combination of several factors: when no signal is transmitted, the background radiation, dark current induced noise and thermal (Johnson) noise are the major contributors; when the detector is receiving an optical signal, two additional terms, laser’s relative intensity noise and shot-noise need to be added. The dominant sources in most cases of optical wireless channels are background and thermal noises, both of which can be modeled as Gaussian variables [6].

As shown in [5], impulse response of light through clouds can also be approximated by a double Gamma function:
$$ h(t)=k_1t \exp(-k_2 t)+k_3 t \exp(-k_4 t),$$
(12)
where k1, k2, k3 and k4 are constants. If the receiver aperture size is small, due to the fact that only a small fraction of photons will reach the receiver after being scattered, another component that accounts for light arriving at the receiver without being scattered needs to be taken into account, even for medium optical thicknesses. Thus, the impulse response is more appropriately expressed as:
$$ h(t)=k_1 t \exp(-k_2 t)+k_3 t \exp(-k_4 t)+k_5 \delta (t),$$
(13)
The corresponding frequency response is
$$ H(f)=\frac{k_1 }{\left({k_2 +j2\pi f} \right)^2}+\frac{k_3 }{\left({k_4 +j2\pi f} \right)^2}+k_5.$$
(14)
As an example, Figure 4 shows the frequency response of the optical wireless channel when a FSO link is blocked by 100 m of low altitude water cloud. The aperture diameter size is 20 cm in diameter and receiver field-of-view (FOV) angle is π/2. As this figure shows, bandwidth of the channel is in the MHz range when there is only 100 m of cloud (the thickest cloud in our model can be as thick as 3100 m).
https://static-content.springer.com/image/art%3A10.1007%2Fs10776-006-0042-1/MediaObjects/10776_2006_42_Fig4_HTML.gif
Fig. 4.

Frequency response of 1550 nm light wave through 150 m clouds.

Note that with our target data rate for the FSO subsystem being 2.5 Gbps; such a severe dispersion is disastrous, even if attenuation can somehow be compensated for. Hence, based on the fact that at around the same carrier frequency (within the range of several GHz), the impulse response remains unchanged, one would naturally conclude that if some kind of multiplexing scheme is employed, the overall capacity can be improved. One solution to this is to use a multiple-input multiple-output (MIMO) scheme to transmit multiple symbols through a pixilated image, simultaneously [20]. If the image size is sufficiently large, very high data rate can be achieved with very low frame rate. But if dispersion and beam divergence is significant, the task of wave-front correction in this scheme will be difficult. Alternatively, one can also assign orthogonal frequency carriers to each sub-channel, as in the OFDM scheme presented in [21]. Thus, if the number of sub-channels is sufficient, reliable communication is possible without resorting to complex equalizers or phase front correction devices.

Unlike conventional electrical channels, optical intensity-modulated direct-detection (IM/DD) channels are based on intensity, and therefore, have one important constraint when modeled as a Gaussian channel; the input of the channel must be non-negative. With this extra constraint, a general solution for channel capacity cannot be found. But for some specific modulation schemes, closed form expressions for capacity are available. For an on-off keying (OOK) single carrier FSO system, channel capacity has been evaluated in [22, 23], where the channel is modeled as a discrete-time channel with stationary and ergodic time-varying gain and additive white Gaussian noise. However, as the underlying channel being memoryless, it is only applicable to single carrier OOK when the channel bandwidth is greater than the signal bandwidth.

If multiple sub-carrier modulation is considered, each sub-channel still needs to be free of intersymbol interference (ISI) in order to maintain operational. But as the designated data rate for each sub-channel is much smaller than that of the single carrier scenario, system is much more robust against channel dispersion. Nevertheless, like the single carrier case, a bias is still required to maintain the non-negativity. It has been shown that average power efficiency can be improved by a variable bias, but generally for implementation considerations, the DC bias is often fixed. Based on a fixed bias, depending on the modulation being PAM or QAM, channel capacity is upper bounded by [21]:
$$ C_{\rm PAM}^k \leqslant \frac{1}{T}\left({\log_2 \left[ {2^k\prod\limits_{i=1}^k {\left({\frac{2i}{2i+1}} \right)^{k-i}} } \right]+\frac{k}{2}\log_2 \left[ {\frac{\rm SNR}{\pi e}} \right]} \right) $$
(15)
$$ C_{\rm QAM}^k \leqslant \frac{1}{T}\left({\log_2 \left[ {\frac{2^k\pi ^kk!}{(2k)!}} \right]+k\log_2 \left[ {\frac{\rm SNR}{\pi e}} \right]} \right)$$
(16)
where k in both formulas are the number of sub-carriers and SNR is the signal-to-noise ratio of one sub-carrier.
As to the RF channel, because the Rayleigh scattering caused by cloud particles introduces little temporal dispersion, we modeled clouds only as a factor of signal power attenuation. In addition, because the channel is LOS with negligible multipath effects, directly applying the Shannon capacity formula
$$ C=B\hbox{log}_2 (1+{\rm SNR})$$
(17)
generates a valid approximation to the RF channel capacity.

CLOUD CHARACTERIZATION

Now armed with the channel model and capacity evaluation methods, we still need information about clouds to be able to evaluate availability of a hybrid link. Though seemingly simple, clouds are in fact very complex to characterize.

Essentially, clouds are not very different from fog, which is composed of water/ice droplets. According to altitude, clouds are often categorized into low, middle and high-level clouds, each of which has a relatively constant characteristic particle size distribution. However, unlike fog, the spatial structure of cloud is far from uniform, making the spatial distribution information of cloud indispensable in availability evaluations, especially for links of long distances. Thus, to statistically characterize clouds, information on spatial distribution, particle size distribution and temporal distribution is required.

Because the hybrid link we consider operates only at low altitude, the only clouds that affect our communication channel are the low-level clouds. Normalized particle size distributions of water clouds are given as a gamma distribution [24]:
$$ n(r)=\left[{(r_{\rm eff} v_{\rm eff})^{1/v_{\rm eff} -2}\Gamma (1/v_{\rm eff} -2)} \right]^{-1}r^{1/v_{\rm eff} -3}\hbox{exp}(-r/(r_{\rm eff} v_{\rm eff}))$$
(18)
where reff = 10 μm is the effective radius (an average of 8 μm) and veff = 0.15 is the effective variance. For ice clouds, the particles are assumed to be random fractal crystals in shape with a “ −2” power law size distribution [24],
$$ n(r)=\left\{{{\begin{array}{*{20}c} {\frac{r_1 r_2 }{r_1 +r_2 }r^{-2}\quad \quad r_1 \leqslant r\leqslant r_2 } \hfill \\ {0\quad \quad \quad \quad \quad {\rm otherwise}} \hfill \\ \end{array} }} \right.$$
(19)

Here, r1 and r2 are given as 20 and 50 μm [24]. Note that these particle size distributions are normalized, i.e., the number of particles per unit volume is unity. To determine the actual particle density, we used a simple conversion based on the assumption that the maximal physical thickness corresponds to the maximal optical thickness [19]. Table I lists two different types of clouds that are used in our evaluations. The corresponding particle densities are listed under the variable N.

To complete the cloud modeling, we used data obtained from the International Satellite Cloud Climatology Project (ISCCP) D1 database. The ISCCP database contains global cloud information including percentage of spatial coverage and optical thickness. In this database, the globe is divided into 6596 equal size cells, each of which is approximately the area of 2.5° longitude  ×  2.5° latitude. Through satellite measurements, the cloud amount and optical thickness of each type of cloud in each cell are recorded at a sampling rate of once every 3 h. In our study, we only extracted detailed cloud data of one cell that covers most part of the state of Pennsylvania. The center of this cell is at longitude 281.67° and latitude 41.25° N. By examining this specific cell, we produced tools that evaluate statistical information about signal attenuation, fluctuation and temporal dispersion. With these tools, availability evaluation in other geographic locations can be performed by importing the data for the corresponding cells.

As discussed earlier, we are interested in the air-to-ground links. In order to evaluate availability, both cloud spatial distribution and thickness information is required. In the ISCCP database, cloud spatial distribution is measured in terms of number of pixels, i.e., the number of pixels that is covered by cloud type i is recorded as pi(t). Along with pi(t), the corresponding mean optical thickness of the cloud at the same time is given as τi(t). Denote the total number of pixels in a cell by p0, we interpret the probability of having cloud type i with its optical thickness less than τ0 as:
$$ P\{\tau \leqslant \tau_0 \vert {\rm cloud}\;{\rm type}\;i\}=\sum\limits_{\tau_i (t)\leqslant \tau_0 } {\frac{p_i (t)}{Mp_0}} $$
(20)

Here, M represents the number of snapshots processed. By setting the value of τ0 to the maximal optical thickness, probability of having a cloud of type i can be evaluated.

Results

In order to evaluate availability, the channel impulse responses are needed to find a reasonable number for sub-carriers. Because we are mainly interested in clouds of low and medium optical thicknesses, Monte Carlo simulations were used for the sake of better accuracy, though it takes much longer to simulate (approximately 200 h on a Sun Blade 800 server using MATLAB). In the simulation, we chose 1550 nm as the wavelength of the FSO subsystem. The impulse response was evaluated for both low-level water and ice clouds. For each type of cloud, five optical thicknesses were evaluated. Based on the simulation results, the impulse response is then sampled.

However, due to the limitation on computation power, spacing between samples must be relatively large. To overcome this resolution problem, the samples are fitted to the modified double Gamma function shown in (13). Based on the fitted curve, the impulse response can be obtained with an arbitrary sampling rate. As to the curve fitting, we used non-linear least-square as the fitting criterion. Through some simple transformation, the object function can be reduced to a double exponential function [25, 26], which can be optimally fitted using classical algorithms such as the Levenberg–Marquardt algorithm. In Table II, the resulting coefficients are listed. Some of the simulated impulse responses and the fitted curves are also presented in Figures 5 and 6.
Table II.

Coefficients obtained through curve fitting of the Monte Carlo simulation results

Optical thickness

Cloud type

k1

k2

k3

k4

k5

100

Water

43.0

3.43 ×  107

0.0797

6.48 ×  106

5.03 ×  10−6

Ice

57.4

3.63 ×  107

2.12 ×  10−9

6.57 × 106

5.03 ×  10−6

125

Water

19.5

2.65 ×  107

0.068

2.59 × 107

4.38 ×  10−7

Ice

25.4

2.9 ×  107

17.4

2.9 ×  108

4.38 ×  10−7

150

Water

10.0

2.18 ×  107

0.0223

2.14 ×  107

1.13 ×  10−8

Ice

8.14

2.42 ×  107

5.321

2.42 ×  107

1.13 ×  10−8

175

Water

5.49

1.78 ×  107

6.93 ×  10−4

1.63 ×  107

5.34 ×  10−10

Ice

6.28

1.93 ×  107

1.18

1.93 ×  107

5.34 ×  10−10

200

Water

1.72

1.46 ×  107

1.27

1.46 ×  107

2.53 ×  10−11

Ice

2.76

1.82 ×  107

2.675

1.82 ×  107

2.53 ×  10−11

https://static-content.springer.com/image/art%3A10.1007%2Fs10776-006-0042-1/MediaObjects/10776_2006_42_Fig5_HTML.gif
Fig. 5.

Impulse response through water cloud through simulation and curve fitting.

https://static-content.springer.com/image/art%3A10.1007%2Fs10776-006-0042-1/MediaObjects/10776_2006_42_Fig6_HTML.gif
Fig. 6.

Impulse response through ice cloud through simulation and curve fitting.

With the impulse responses available, we continue to define the pulse-width by an interval over which 90% of signal power is included [19]. For 200 m of water and ice clouds, the corresponding pulse-width values are 0.263 and 0.214 μs. Given the overall data rate being 2.5 Gbps, the number of sub-channels is thus chosen as 1024 to withstand the effect of temporal dispersion. As to the attenuation, a 30 dB laser power margin is added to the optical subsystem to compensate the energy loss induced by clouds. Setting the SNR without power margin to 40 dB, in clear weather conditions, the overall SNR is 100 dB. If the channel is blocked by more than 200 m of clouds, not only the SNR will become extremely low, but also the channel bandwidth will fall below the signal bandwidth. This creates an outage for our system. The RF link carrier frequency is selected to be 15 GHz. Under clear weather condition, we assume the SNR to be 20 dB. Because of the flat fading approximation, unit bandwidth capacity loss can be evaluated from attenuation. With the bandwidth set, total capacity can be obtained by scaling the capacity per unit bandwidth result.

Applying the formulas in Section 3, capacity of the FSO channel through both water and ice clouds are shown in Figure 7, when QAM modulation is used. Because of the severe cloud scattering, attenuation and dispersion caused by even a very small piece of cloud is significant. Under clear weather condition, the channel capacity is around 40 Gbits/s; but when there is only a 100 m of cloud, capacity is drastically reduced to approximately 3 Gbits/s. Though some adaptive schemes can be applied to modulation/coding, if the capacity is below 500 Mbps, an outage is assumed. Because of the difference in particle distribution, capacity loss caused by ice cloud is less than that by water cloud, but still very significant. Note that the impulse response is dependent on a number of variables, such as the cloud position, aperture size and the receiver FOV half-angle. In order to simplify the simulations, we only produced results corresponding to a best-case scenario; i.e., the receiver is at the cloud exit plane and the FOV half-angle is π/2. Examining our simulation results, it is found that when receiver is only a short distance away from the cloud exit plane, received power by a 20 cm receiver is almost zero, even for low optical thickness clouds. When the receiver is at the cloud exit plane, temporal dispersion is independent of the FOV angle, thereby making the FOV angle only a factor of attenuation [27]. Thus, maximizing the FOV angle provides an upper bound, which is consistent with the idea of capacity evaluation.
https://static-content.springer.com/image/art%3A10.1007%2Fs10776-006-0042-1/MediaObjects/10776_2006_42_Fig7_HTML.gif
Fig. 7.

Channel capacity through cloud with multiplexing.

On the contrary, RF signals experience little attenuation. As shown in Figure 8, even when there is 6 mm/h rain rate that happens with a probability less than 0.5%, capacity loss is only less than 6%. Here, capacity through rain is normalized to the capacity under clear weather conditions.
https://static-content.springer.com/image/art%3A10.1007%2Fs10776-006-0042-1/MediaObjects/10776_2006_42_Fig8_HTML.gif
Fig. 8.

RF channel capacity loss.

To investigate availability, the air-to-ground links can be viewed under two categories: uplink cases and downlink cases. As discussed in Section 2, rain and clouds are the main variable factors that attenuate RF signals. Due to the non-dispersive nature of both factors, uplink and downlink cases experience the same attenuation, regardless of the relative position of rain and clouds. However, FSO signals are distorted asymmetrically, mainly due to the difference in cloud position with respect to transmitter and receiver. This requires us to evaluate each case for the FSO subsystem, separately. To simplify the simulations, we assume planes fly right above clouds, with the transceivers right at the cloud exit plane.

In previous sections, we discussed various signal attenuation and distortion factors for both RF and FSO links. Based on the statistical information of cloud and rain, a CDF for each of the factors can be generated. However, in order to correctly evaluate signal degradations brought by different weather conditions, a joint PDF of the dominant factors is necessary. For example, for the ground-to-air links, because both rain and cloud play an important role, the relation between rain rate and cloud thickness is essential in availability evaluation of both RF and FSO links. However, since such information is not available to us, we are only able to study the two extremes that present bounds on the composite availability.

The two extremes are commonly referred to as perfect dependence and perfect independence [28]. Assumption of perfect dependence implies that as one effect increases in severity, all effects increase in severity. Under certain conditions, this assumption is reasonable, because heavy rains are generally accompanied by thick clouds. However, also implicit in this assumption is that the thickness of cloud determines the rain rate, which is rather questionable. In contrast, the perfect independence assumption implies that different factors are perfectly uncorrelated. In other words, it assumes that when it rains heavily, the chance of having any form of cloud is the same as when it does not. Though this may not seem a realistic assumption, it does provide us with another bound that confines the outage probability.

Figure 9 shows the joint Cumulative Distribution Functions for both uplink and downlink cases. Figure 9a and c correspond to the perfect dependence assumption, while Figure 9b and d correspond to the perfect independence assumption. As these figures indicate, due to the severe scattering caused by clouds, FSO subsystems in both cases offer a very low availability.
https://static-content.springer.com/image/art%3A10.1007%2Fs10776-006-0042-1/MediaObjects/10776_2006_42_Fig9_HTML.gif
Fig. 9.

(a) Availability CDF of the hybrid uplink under perfect dependence. (b) Availability CDF of the hybrid uplink under perfect independence. (c) Availability CDF for the FSO downlink under perfect dependence case (RF link is always un-attenuated). (d) Availability CDF for the hybrid downlink under perfect dependence.

In contrast, RF capacity shows little degradation, due to the fact that heavy rain occurs only with a very small probability. In the uplink case, because a significant portion of the scattered photons still can reach the receiver, capacity degrades relatively slowly as optical thickness increases. But in the downlink case, attenuation increases near exponentially with optical thickness, causing the capacity to decrease much faster as the optical thickness increases. If perfect correlation exists between cloud and rain, the probability of FSO outage is even greater than the rain probability. In other words, FSO will always be out when it rains. Furthermore, comparing the two extremes, it can be found that the perfect dependence case shows a higher outage probability than the perfect independence case. This can intuitively be explained through diversity. When the two subsystems are perfectly independent, full diversity gain can be explored. Yet if the two sub-channels are identical, the overall system is no different than systems with just two parallel identical channels. Therefore, this scenario results in a rather worse availability.

CONCLUSIONS

In this paper, we focused on examining availability of an airborne hybrid RF/FSO links. A channel model is established, incorporating factors such as scattering, absorption, scintillation, etc. Based on the channel model, along with the cloud information acquired from the ISCCP database, we produced the probability distribution of capacity for both the RF and FSO channels. From the results, it is shown that FSO-alone can only achieve a very small availability, due to its strong sensitivity to cloud blockage. But with a backup RF link, availability can be significantly increased due to the immunity of RF signals to cloud attenuation. However, if a backup RF link is used during FSO down time, capacity is still significantly reduced due to bandwidth limitations on the RF channel. For relatively thin clouds, multiplexing schemes can be used to significantly improve FSO channel capacity, and thus enhance the FSO subsystem availability.

Haiping Wu

received his B.Eng. degree from Tsinghua University, Beijing, China, in 1998 and M.S. degree from University of Utah, UT in 2001, both in Electrical Engineering. He is completing his Ph.D. degree in Electrical Engineering at The Pennsylvania State University, University Park. His current research interests include MIMO wireless communications systems and FSO communication systems.

Mohsen Kavehrad

(S’75–M’78–SM’86–F’92) received the Ph.D. degree in electrical engineering from Polytechnic University (Brooklyn Polytechnic), Brooklyn, NY, in 1977.

He was with the Space Communications Division, Fairchild Industries, and Satellite Corporation and Laboratories, GTE, 1978–1981. In December 1981, he joined Bell Laboratories and in March 1989, he joined the Department of Electrical Engineering, University of Ottawa, Ottawa, ON, Canada, as a Full Professor, while he also was Director of Broadband Communications Research Laboratory, Director of Photonic Networks and Systems Thrust, Project Leader in Communications and Information Technology Ontario (CITO), and Director of Ottawa–Carleton Communications Center for Research (OCCCR). He was an Academic Visitor (Senior Consultant) at NTT Laboratories, Yokosuka, Japan, in summer 1991. He spent a six-month sabbatical term as an Academic Visitor (Senior Consultant) with Nortel, Ottawa, ON, Canada, in 1996. In January 1997, he joined the Department of Electrical Engineering, The Pennsylvania State University, State College, as the AMERITECH (W. L. Weiss) Professor of Electrical Engineering and Director of Communications Engineering and, later, in August 1997, he was appointed as Founding Director of the Center for Information and Communications Technology Research (CICTR). From 1997 to 1998, he also was Chief Technology Officer and Vice President with Tele-Beam Inc., State College, PA. He visited, as an Academic Visitor (Senior Consultant), Lucent Technologies (Bell Laboratories), Holmdel, NJ, in summer 1999. He spent a six-month sabbatical term as an Academic Visitor (Senior Technical Consultant) at AT&T Shannon Research Laboratories, Florham Park, NJ, in 2004. He has also served as a Consultant to a score of major corporations and government agencies. He has published over 300 refereed journal and conference papers, several book chapters, and books and holds several key issued patents in these areas. His research interests are in the areas of technologies, systems, and network architectures that enable the vision of the information age, e.g., broadband wireless communications systems and networks and optical fiber communications systems and networks.

Dr. Kavehrad received three Exceptional Technical Contributions Awards while he was with Bell Laboratories for his work on wireless communications systems, the 1990 TRIO Feedback Award for his patent on a “Passive Optical Interconnect” and the 2001 IEEE Vehicular Technology Society Neal Shepherd Best Propagation Paper Award, three IEEE Lasers and Electro-Optics Society Best Paper Awards, and a Canada National Science and Engineering Research Council (NSERC) Ph.D. dissertation Gold medal award, jointly with his former graduate students, for their work on wireless and optical systems. He has lectured worldwide as an IEEE distinguished Lecturer and as Plenary and Keynote Speaker at leading conferences.

Acknowledgments

A DARPA Grant sponsored by the U.S. Air Force Research Laboratory/Wright-Patterson AFB Contract-FA8650-04-C-7114 and The Pennsylvania State University CICTR has supported this research.

Copyright information

© Springer Science+Business Media, Inc. 2006