Outage Probability of Triple-Hop Mixed RF/FSO/RF Stratospheric Communication Systems

Abstract

This paper proposes a triple-hop mixed radio-frequency/free-space optical/radio-frequency (RF/FSO/RF) communication system, which intends to support wireless long-range links between two terrestrial stations via two stratospheric relays. It is considered that these terrestrial stations communicate with the relays over RF links, whereas the relays communicate with each other over a FSO link. The RF channel experiences Rician fading due to the line-of-sight (LoS) and non-line-of-sight (NLoS) signal components. Besides, the optical channel is affected by atmospheric attenuation, atmospheric turbulence, and pointing errors. Mathematical expressions for the outage probability are derived, considering the beam wander effect. The results demonstrate the theoretical derivations and investigate the performance of this system.

Full text

Outage Probability of Triple-Hop Mixed RF/FSO/RF Stratospheric
Communication Systems
Emmanouel T. Michailidis1,2, Nikolaos Nomikos3, Petros Bithas1,2, Demosthenes Vouyioukas3,
and Athanasios G. Kanatas1
1Department of Digital Systems, University of Piraeus, Piraeus, Greece
e-mail: {emichail, pbithas, kanatas}@unipi.gr
2Department of Electrical and Electronics Engineering, University of West Attica, Campus 2, Aigaleo, Athens, Greece
3Department of Information and Communication Systems Engineering, University of the Aegean, Karlovassi, Samos, Greece
email: {nnomikos, dvouyiou}@aegean.gr
Abstract—This paper proposes a triple-hop mixed Radio-
Frequency/Free-Space-Optical/Radio-Frequency (RF/FSO/RF)
communication system, which intends to support wireless long-
range links between two terrestrial stations via two
stratospheric relays. It is considered that these terrestrial
stations communicate with the relays over RF links, whereas
the relays communicate with each other over a FSO link. The
RF channels experience Rician fading due to the Line-of-Sight
(LoS) and Non-Line-of-Sight (NLoS) signal components.
Besides, the optical channel is affected by atmospheric
attenuation, atmospheric turbulence, and pointing errors.
Mathematical expressions for the outage probability are
derived, considering the beam wander effect. The results
demonstrate the theoretical derivations.
Keywords-Atmospheric turbulence; beam wander; Free-
Space-Optical (FSO) communications; High-Altitude Platforms
(HAPs); outage probability; pointing errors; Rician channels.
I. INTRODUCTION
The development of next-generation wireless broadband
communications comprises the seamless integration of
terrestrial and aerospace infrastructures over heterogeneous
networks [1]. In recent years, the use of mobile airborne
services via High-Altitude Platforms (HAPs) flying in the
stratosphere has been suggested for civil and military
applications [2]. To successfully fulfill the demands of future
wireless communication services, shifting from the Radio-
Frequency (RF) domain to the optical domain is
indispensable [3] [4]. In Free-Space-Optical (FSO) systems,
the data is transmitted at high data rates in the multigigabit
regime using collimated highly directed laser beams with
compact equipment and low power consumption. The FSO
technology ensures privacy with low probability of
interception, immunity to electromagnetic interference, and
exemption from spectrum regulatory restrictions.
The stratosphere stands for a propagation medium well
suited for FSO connections. Hopefully, the inter-HAP
crosslink is above attenuating clouds, fog or significant
aerosols. Hence, inter-HAP distances of up to 900 km are
possible with 100% availability [5]. Nevertheless,
stratospheric FSO links may experience substantial
fluctuations in both the intensity and the phase of the
received signal due to variations of the Index of Refraction
Turbulence (IRT) along the propagation path resulting by the
inhomogeneities in temperature and pressure fluctuations,
especially for link distances of 1 km and above [6].
Moreover, beam pointing error effects are highly pronounced
on the performance of a stratospheric network, which
involves large distances and possible displacement of the
platforms due to the winds or pressure variations of the
stratosphere [7]. In addition, both mechanical vibrations and
electronic noise may cause the received spots from the laser
beams to wander on the detector planes. Hence, acquisition,
pointing, and tracking errors should also be mitigated to
achieve high directivity of the transmitted beam. To extend
the network range, and effectively combat the effect of
turbulence, the use of relay-aided transmission schemes has
been suggested [8]. In [7], a full-FSO system with multiple
stratospheric relays and fixed stations on the ground was
proposed. However, FSO systems should operate under
accurate pointing requirements. Hence, employing FSO
techniques is highly challenging and insufficient as soon as
the terrestrial stations are in motion.
Motivated by these observations, this paper investigates
the use of two stratospheric relays acting as Decode-and-
Forward (DF) relay nodes, in order to facilitate challenging
triple-hop long-range wireless communication between two
terrestrial mobile stations. Although the Amplify-and-
Forward (AF) scheme is simple to implement, DF offers
better performance and is a common assumption in multi-
hop networks. A mixed RF/FSO/RF airborne communication
scenario is considered, where an RF transmission scheme is
adopted for the communication between the terrestrial
stations and the stratospheric relays, whereas these relays are
interconnected through an FSO link. A stratospheric
communication channel is expected to be Rician in its
general form [9]. Hence, the Rician distribution is adopted to
model the channels for the RF links. To investigate the effect
of atmospheric turbulence on the FSO link, a Kolmogorov
power spectrum for refractive-index fluctuations is
considered and the Gamma-Gamma (G-G) distribution is
used, which matched data values obtained from
measurements, under a variety of turbulence conditions [10].
Finally, the effects of pointing errors are described by the
Rayleigh distribution [7]. Mathematical expressions are

derived for the outage probability and numerical results are
provided for different values of the system parameters.
The rest of the paper is organized as follows. Section II
presents the system model. In Section III, the RF and FSO
fading channels are modeled. In Section IV, the outage
probability is mathematically derived. Results are provided
in Section V. Finally, conclusions are drawn in Section VI.
II. SYSTEM MODEL
This paper considers a mixed RF/FSO/RF airborne
communication system with slowly-varying and frequency-
flat-fading channels. As shown in Figure 1, the transmitted
signal from a source node propagates through two serial DF
stratospheric relays of similar size and type before arriving at
a destination node. It is considered that the direct link
between the source and the destination is obstructed due to
high attenuation. To aid our analysis, the subscripts S, D, and
,
m
R
where 12,m are affiliated with the source, the
destination, and the m-th relay, respectively. In this system,
the S–R1 and R2–D links use RF technology, while the R1–R2
link is based on FSO technology. The communication is
assumed to operate in a half-duplex mode and to be
conducted over three phases: S → R1, R1 → R2, and R2 → D.
The source and the destination are equipped with single
antennas. Besides, the relays not only include antennas, but
also lasers and photo-detectors.
A. First RF Link
The received signal at the stratospheric relay R1 can be
expressed as [11]
1111
,,,
,
SR S SR SR R
yPhxn
(1)
where S
P is the transmit power, 1
,SR
h is a non-zero-mean
complex Gaussian random variable, 1
,SR
x
is the transmitted
symbol from the source with


1
2
,
E1,
SR
x


E

is the
statistical expectation operator, 1
R
n represents the zero-mean
complex Gaussian noise at R1 with 1
,oR
N noise Power
Spectral Density (PSD). Using (1), the instantaneous Signal-
to-Noise Ratio (SNR) at R1 can be written, respectively, as
11
1
2
,,
,
.
S
SR SR
oR
Ph
N

 (2)
B. FSO Inter-HAP Link
In the FSO link, the cost-effective Intensity Modulation
Direct-Detection (IM/DD) is employed. The received RF
signal at the R1 is decoded and converted to optical signal by
employing the Subcarrier Intensity Modulation (SIM)
technique. In particular, after filtering by a Bandpass Filter
(BPF), a Direct Current (DC) bias is added to the filtered RF
signal to ensure that the optical signal is non-negative. Then,
the biased signal is sent to a continuous wave laser driver.
The retransmitted optical signal at R1 is written as [12]


11
,,
1,
Ropt opt SR
yPMy (3)
where opt
P denotes the average transmitted optical power
and it is related to the relay electrical power 1
R
P by the
electrical-to-optical conversion efficiency η1 as
1
1,
opt R
PnP

and M denotes the modulation index.
The optical signal at R2 received from R1 can be
expressed as


12 1 2
,,
1,
RR opt SR R
yIPMy n



(4)
where 0I> is the received fading gain (irradiance) between
the laser of R1 and the photodetector of R2 through the
optical channel and 2
R
n is the zero-mean complex Gaussian
noise at R2 with 2
,oR
N noise PSD.
The DC component is filtered out at R2 and an optical-to-
electrical conversion is performed. Then, assuming that
M = 1, the received signal can be expressed as
12 1 2
,,
,
RR ele opt SR R
yIPPyn



(5)
where 1
212ele opt R
PnP nnP

 is the electrical power
received at R2 and 2
n is the optical-to-electrical conversion
efficiency.
The instantaneous SNR at R2 can be approximated as
[11]


2112
,,
min , ,
RSRRR

 (6)
where


12 1 2
2
,12 ,
/.
RR R oR
nn P I N


The performance of the FSO link is limited by
background radiation and thermal noise, which can be
modeled as independent and identically distributed (i.i.d.)
AWGN, as an accurate approximation of the Poisson photon-
counting detection model [13].
Source
Destination
1
S-R
2
R-D
1
R
2
R
RF
RF
FSO
On-Off Keyed
Light Pulses
Figure 1. Simple representation of the triple-hop mixed RF/FSO/RF
stratospheric communication system.

C. Second RF Link
The FSO signal at the R2 is finally reconverted to an RF
signal before being sent to the destination over the second
RF link. The signal received at the destination is written as
22 2
,, ,
D
RRSRS D
yPhxn (7)
where 2
R
P is the transmit power, 2
RS
h is a non-zero-mean
complex Gaussian random variable (leading to a Rician
distributed amplitude), 2,RS
x is the signal transmitted by the
R2 with


2
2
,
E1,
RS
x and D
n is the zero-mean complex
Gaussian noise at D with ,oD
N noise PSD. Using (7), the
SNR at the destination can be written as
2
22
2
,,
,
.
R
RD RD
oD
Ph
N

 (8)
The instantaneous end-to-end SNR at the destination can be
approximated as [11]


112 2
,, ,
min , , .
DSRRRRD

 (9)
III. STATISTICAL MODELING OF THE TRIPLE-HOP MIXED
RF/FSO/RF CHANNEL
In this paper, the Rician distribution is utilized to model
the channels for the RF links. The Probability Density
Function (PDF) of the instantaneous SNR received at R1,
denoted as 1
,,
SR

is given by [14]


1
,1
1
11
,
1
,11
,,
1exp 1
SR
SR
SR
SR SR
K
f
KK










1
1
,
011
,
21,
SR
SR
IKK







(10)
where 1
K is the Rician factor of the first RF link, i.e., the
average power ratio of the Line-of-Sight (LoS) component to
the Non-Line-of-Sight (NLoS) component, and


0
I

is the
modified Bessel function of the first kind and zero-th order.
The Rician factor 1
K strongly depends on the elevation
angle of the HAPs and the operating frequency [15]. The
PDF


,2
2,
RD RD
f


of the Rician distribution for the second
RF link with Rician factor K2 can be defined as in the first
RF link by replacing the indices.
For the FSO link, a composite optical channel model is
used [7]. In particular, the channel state
I
models the
random attenuation of the propagation channel that arises
due to the path loss ,
l
I
the atmospheric turbulence ,
a
I
and
the pointing errors .
p
I
The combined optical channel model
is defined as follows
.
lap
I
II I (11)
Since the time scales of these fading processes are of the
order of 32
10 s to 10 s [16]
--
, which are far larger than the
bit interval
(
)
9
10 s for multi-Gbps systems ,
-
»
I
is constant
over a large number of transmitted bits [17].
A. Effects of Atmospheric Attenuation
The atmospheric attenuation is deterministic and is
defined by the exponential Beers–Lambert Law [18]




exp ,
l
I
LL

 (12)
where


l
I
L is the atmospheric attenuation loss of the FSO
link over a path of length L, i.e., the distance between the
relays, and σ is the wavelength- and weather-dependent
attenuation coefficient. The attenuation l
I
is considered
fixed during a long period of time.
B. Effects of Turbulence
In this paper, the effects of turbulence are modeled using
the G-G distribution. Hence, the PDF of a
I
is given by [19]




 




/2 1
2
22,
a
ab ab
aa a
ab
I
ab
f
I I K abI
ab



 (13)
where


u
K

is the u-th order modified Bessel function of
the second kind. Note that (13) can be written in terms of the
Meijer’s G-function as

2,0 2
0,2
0.5 / 4 / 2 / 2
u
Kx G x u u



[20]. The parameters a and b are directly related to the
atmosphere and can be adjusted to achieve a good agreement
between


a
a
I
f
I and measurement data. These parameters
are determined by the Rytov scintillation model. However,
for large distances, as those involved in the proposed system,
this model is inappropriate due to the hot spot displacement
of the beam caused by the beam wander, i.e., the deflection
of the beam due to turbulence. By considering the beam
wander effect, a and b can be modeled as [21]


1
25/62 2
27/6
12/ 5
4.42 0.49
exp 1 ,
10.561
Re pe B
LT B
aw
 









 










(14)

1
2
5/6
12/ 5
0.51
exp 1 ,
10.69
B
B
b




















(15)
where 227/611/6
1.23
Rn
Ck L

 is the Rytov variance, 2
n
C is
the index of refraction structure parameter, 2
2/ ,
eLT
Lkw

2/k


 is the wave number,

is the carrier wavelength,
25/6
11.33
LT R
ww

 
is the long-term spot radius, w is
the beam radius at the receiver, 2
2/ ,
L
kw 2
pe

is the
variance of pointing error caused by beam wander ([22], p.
350), 2
B

is the Rytov variance with beam wander correction
([22], p. 351),


22
000
/,   00
1/,
L
F 0
F is
the phase curvature parameter of the Gaussian beam at the
transmitter, 2
00
2/ ,
L
kw and 0
w is the transmitter beam
radius. Using [23, eq. (3)], one can also obtain the
Scintillation Index (SI) 2.
I

The value of 2
n
C represents the
turbulence condition of the atmosphere and can be estimated
using the Hufnagel-Valley model, which is based on various
empirical scintillation data of the atmosphere. This model
defines the index of refraction structure parameter as a
function of the wind speed and the altitude of the HAPs
above the ground level as ([22], p. 481)


210
25
0.00594 10 exp
27 1000
n
uh
Ch h

  

  
  
16 ˆ
2.7 10 exp exp ,
1500 100
hh
A
 
   
 
 
(16)
where ˆ
A is the nominal value of the


20
n
C at the ground, u
is wind speed in m/s, and h is the altitude of the HAPs in
meters. As 2
n
C increases, the turbulence becomes stronger.
For applications involving propagation along a horizontal
path, it is customary to assume that 2
n
C remains constant
[22].
C. Effects of Pointing Errors
To ensure that the communication scenario is viable,
proper LoS alignment between the relays via appropriate
pointing and tracking mechanisms is required. In this paper,
a model that incorporates geometric spreading in the pointing
error PDF ([18], p. 1703) is used. Considering a Gaussian
beam profile of beam waist wz (at a distance z) and modeling
the random radial displacement of the beam at the detector as
Rayleigh distributed, the PDF of the pointing error p
I
includes the random attenuation due to both geometric
spreading and pointing errors and can be expressed as [18]



2
2
21, 0 ,





p
ppp
I
f
IIIA
A
(17)
where /2 ,
eq s
wgs=



22 2
erf / 2 exp
eq z
ww u u u


 

is the equivalent beam width at the receiver, u=
(
)
(
)
/2 ,
rz
awp
s
s is the jitter standard deviation due to
the pointing error at the detector determined by the degree of
the misalignment between the apertures,
()
2
erf ,Au
éù
=ëû
and
r
a is the receiver aperture radius.
Using (12), (13), and (17), the PDF of the composite
channel in (11) can be evaluated by writing the Bessel
function


u
K

in terms of the Meijer’s G-function as [7]
  
2
2
3,0
1,3 2.
1, 1, 1
Ill
ab ab
fI G I
AI a b AI ab





 


(18)
Using (18), the PDF of the instantaneous SNR received at R2,
denoted as 12
,,
RR

can be expressed as

 
12
1, 2
12 12
2
,
,,
1
2
RR RR lRR RR
ab
fAI a b




12
12
2
,
3,0
1,3 2
,
,
1, 1, 1
RR
lRR
ab
GAI ab












(19)
where 12
,RR

is the average SNR received at R2.
IV. DERIVATION OF OUTAGE PROBABILITY
The outage probability is defined as the probability that
the SNR at the destination falls below a predetermined
outage threshold ,
out

i.e.,


Pr ,
out D out
P

 where


Pr

is the probability operation. In this case, the
communication system cannot achieve adequate reception.
The outage probability can be obtained from the Cumulative
Distribution Function (CDF) of the end-to-end SNR as


.
out D out
PF


 This CDF can be written in terms of the
CDFs of the three hops’ SNRs as [24]


Dout
F












1121
,, ,
11 1 1 ,
S R out R R out R D out
FF F
 



  


(20)
where


1
,,
SR out
F




12
,,
R R out
F


and


1,RD out
F


are
the CDFs of the SNRs of the first, second, and third hop,
respectively. One observes that the system falls in outage
providing that at least one of the three hops gets in outage or,
equivalently, the SNR of one hop becomes less than .
out

The CDF of the instantaneous SNR received at R1 can be
expressed as [25]


,1 1
1
1
1
,11 ,
,
21
12, ,
SR SR SR
SR
K
FQK













(21)
where


1
Q

is the first-order Marcum Q-function. The CDF


,2
2,
RD RD
F


of the Rician distribution for the second RF
link can be similarly defined by replacing the indices.

The CDF of the instantaneous SNR received at R2 can be
obtained as follows


,
12
12 ,
12 1 2
,
0
.
RR
RR R R
RR
Ffxdx



 (22)
Using (19) and [26, eq. (07.34.21.0003.01)], (22) becomes

 
12
,12
12
12
2,
,
,
RR
RR
RR lRR
ab
FAI a b





12
12
2
,
3,1
2,4 2
,
0, .
1, 1, 1, 1
RR
lRR
ab
GAI ab







(23)
The expressions in (21) and (23) can be numerically
evaluated using well-known software packages, e.g.,
Mathematica and MATLAB.
V. RESULTS
In this section, the performance of the proposed system is
evaluated in terms of the outage probability. Unless indicated
otherwise, the values of model parameters used are
12
,,
20 dB,
SR R D


 12
,50 dB,
RR

 0 dB,
out

 K1 =
K2 = K = 10 dB, L = 400 km, 20 km,h

0.01 dB/km


(clear weather conditions), 02 cm,ww

 Θ0 = 0 (focus
Gaussian beam), and 0.15 m.
s

 Note that a laser
aperture diameter of 20.3 m
r
a= is assumed. Then,
1.38 m
z
w [27]. A wavelength λ = 1550 nm is considered
for the FSO link since it is widely used for most airborne
optical communication scenarios. In addition, two values of
the wind speed that determine 2
n
C are considered;
110 m/su (best case) and 230 m/su

(worst case) [23].
For these values, we obtain 1
2192/3
,1.72 10 m ,
nu
C

2
2182/3
,1.55 10 m ,
nu
C
 1
2
,0.2,
Ru

2
2
,1.82,
Ru

1
2
,Iu


0.08, and 2
2
,0.67.
Iu


Figure 2 depicts the outage probability for different
values of the Rician factor K1 = K2 = K and u = 10 m/s. It is
obvious that increasing the Rician factor improves the
performance of the system. Note that a certain outage floor
exists at high values of K due to the average SNR over the
FSO link. Hence, all curves tend to the same saturation
floor.
Figure 3 demonstrates the outage probability for both the
best and worst case of turbulence conditions and different
inter-HAP distance. As this distance decreases, a significant
performance improvement can be achieved. However, the
variation of the FSO propagation distance slightly affects the
outage probability when the worst case of turbulence
conditions is observed.
Outage Probability
Figure 2. The outage probability in terms of the RF average SNR for
different Rician factor of the RF links.
Figure 3. The outage probability in terms of the FSO average SNR for
different turbulence conditions and different inter-HAP distance.
Figure 4. The outage probability in terms of the FSO average SNR for
different normalized jitter standard deviation.

Finally, Figure 4 shows the effect of the normalized jitter
standard deviation /
s
r
as on the outage probability for
u = 10 m/s. One observes that the performance significantly
degrades and the pointing errors have a dominant effect on
the system performance, as /
s
r
as increases.
VI. CONCLUSION
In this paper, the performance of a triple-hop mixed
RF/FSO/RF stratospheric communication system has been
investigated. The results have depicted that the Rician factor
significantly influences the system performance. These
results have also underlined that the performance degrades,
as the inter-HAP distance increases. However, for the worst
turbulence case, this distance slightly affects the outage
probability. Finally, the results have shown that the
misalignment-induced fading has a severe effect on the
system performance. Since there are no experimental data
available in the literature to fully verify the theoretical
results, future research efforts may be devoted to collecting
measured channel data in real-world propagation conditions.
ACKNOWLEDGMENT
This research is implemented through State Scholarships
Foundation (IKY) and co-financed by the European Union
(European Social Fund – ESF) and Greek national funds
through the action entitled “Reinforcement of Postdoctoral
Researchers” in the framework of the Operational
Programme “Human Resources Development Program,
Education and Lifelong Learning”, with priority axis 6, 8, 9,
of the National Strategic Reference Framework (NSRF)
2014-2020.
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