� Abstract—Broadband Satellite Communication links have been

proposed as an effective solution for backhaul links in access

networks. Moreover, the ever increasing demand for high data

rates has led to the use of frequencies above 10GHz. At these

frequency bands, rain attenuation is the dominant fading

mechanism and the only atmospheric phenomenon exhibiting

significant spatial inhomogeneity. The cooperation of hybrid

satellite-terrestrial systems and the Multiple-Input Multiple-

Output (MIMO) techniques have been proposed in order to

support high throughput and overcome the fading effects. In this

work, the performance of a hybrid satellite-terrestrial MIMO

system is studied and the outage capacity is analytically

calculated. The antenna gains are adjusted to the different path

losses of the satellite and terrestrial links resulting in a balanced

MIMO system in terms of the Equivalent Isotropically Radiated

Power (EIRP). Extended numerical results illustrate the

performance gain of the spatial multiplexing techniques

compared to a single satellite (SISO) system.

Index Terms—Multiple-Input Multiple-Output (MIMO),

satellite communications, hybrid satellite-terrestrial system,

outage capacity

I. INTRODUCTION

HE demand for high capacity and broadband access is

ever increasing with various applications in science,

business, education and entertainment. Satellite

communication systems will play a significant role in

broadband networks as an integral backhaul part of the

network of the future that will support Future Internet services.

However, the frequency resources have become scarce due to

the spectrum segmentation and the dedicated frequency

allocation of the standardized terrestrial wireless systems, thus

higher frequency bands, such as Ku, Ka and Q/V, are

employed in modern satellite systems [1-3]. Therefore, it

becomes crucial to investigate the new capabilities of the

future hybrid satellite-terrestrial network architectures [4]

This work was supported by the Research Project Thales NTUA-

MIMOSA – MIMO Techniques for Satellite and Stratospheric

Communication Systems, funded by EU and Greece.

The authors are with the Mobile Radio Communications Laboratory,

Division of Information Transmission Systems and Materials Technology,

School of Electrical and Computer Engineering, National Technical

University of Athens, 9 Iroon Polytechniou Street, GR 157 80, Zografou,

Athens, Greece (e-mail: bsakarel@mail.ntua.gr, harkour@mail.ntua.gr,

thpanag@ece.ntua.gr).

which will have the ability to support higher system throughput

with energy efficiency, while providing large-scale coverage

[1].

On the other hand, Multiple-Input Multiple-Output (MIMO)

technology has recently emerged as one of the most significant

technical breakthroughs in modern digital communications due

to its promise for very high data rates at no cost of extra

spectrum and transmitted power [3]. The application of MIMO

technology in Satellite Communication Systems (fixed and

mobile) is under investigation by the Research community [3].

Broadband Satellite communication can be benefited from

MIMO [5-6] signaling in two different ways: spatial

multiplexing and diversity. In the spatial multiplexing concept,

independent data are transmitted by separate antennas in order

to maximize throughput (i.e., linear capacity growth can be

achieved by increasing the number of antennas). In the

diversity configurations, the same signal is transmitted along

multiple fading paths with low correlation in order to improve

the robustness of the link in terms of each user BER

performance. These advantages have already led to the success

of MIMO both as a research topic and as a commercially

viable technology in terrestrial communications, while they

offer a promising perspective for satellite communications.

In this paper we investigate the applicability of multiple

antenna technology to broadband hybrid satellite-terrestrial

communication configurations for backhaul applications

operating at frequencies above 10GHz. In order to calculate

the capacity enhancement, we propose to see that the diversity

sources form a multiple-input multiple-output matrix channel

between satellite and terrestrial broadband links. More

specifically, the capacity improvement achieved by MIMO

spatial multiplexing is studied and the outage capacity is

analytically calculated. A physical hybrid MIMO channel

model at these frequencies is assumed taking into account the

propagation phenomena related to the frequencies of interest,

such as clear line-of-sight operation, high antenna directivity,

the effect of rain fading.

More particularly, we focus on a dual MIMO hybrid

satellite-terrestrial backhaul scenario offering fixed satellite

services and operating at Ku band and above, considering that

multipath propagation is insignificant at these frequencies.

However, by virtue of satellite diversity, MIMO can be

considered to effectively exploit the rainfall spatial

Hybrid Satellite-Terrestrial Broadband Backhaul

Links: Capacity Enhancement through Spatial

Multiplexing

Vasileios K. Sakarellos, Charilaos I. Kourogiorgas, Athanasios D. Panagopoulos

T

978-1-4673-4688-7/12/$31.00 ©2012 IEEE

inhomogeneity instead. The model is flexible and can be

applied on a global scale since it has physical inputs obtained

by regression fitting analysis on the ITU-R rainmaps [7] and is

based on general assumptions concerning the rain process.

Moreover, the different path losses of the satellite and

terrestrial links are compensated by the different antenna gains

resulting in a balanced MIMO channel in terms of the

Equivalent Isotropically Radiated Power (EIRP). It should be

noted that this selection of antenna gains correspond to

practical scenarios where large antenna gains are used in

satellite communications in contrast to the small antenna gains

of terrestrial links.

A potential drawback of this system is the different

propagation delay offset of the satellite and terrestrial links.

Nevertheless, this delay offset is assumed to be properly taken

into account at both transmitters that communicate with each

other. A possible practical solution of this problem might be

the one implemented in [8] where matched filters are applied

to the received signals for the detection of the propagation

delay offset, which is then fed to a timing aligner.

Subsequently, the proposed timing aligner eliminates the delay

offset by adjusting the timing of a parallel-to-serial signal

converter. The study of more efficient solutions of the

asynchronism problem associated with satellite diversity,

although rather challenging, is out of the scope of this paper

and will be the subject of a future work.

II. MIMO CHANNEL MODEL

The geometrical configuration of a hybrid satellite-

terrestrial MIMO system is shown in Figure 1. The final

destination D receives two independent data streams: one

transmitted by the satellite S and another transmitted by the

Earth terminal T. The elevation angle of the satellite S is

denoted as 1� (degrees). The effective length of the satellite

link SD, corresponding to the part of the slant path SD from

the Earth destination D to the isotherm of 0° C, is denoted as

1(km)L and its projection on Earth is denoted as

1 1 1(km) cosL L �� � , while the length of the terrestrial link TD

is denoted as 2 (km)L . The terrestrial link TD and the

projection of Earth of the satellite link SD subtend an angle

� (degrees).

Both satellite and terrestrial links satisfy the Line-Of-Sight

(LOS) conditions (since we are referring to Fixed Satellite

Service and Fixed Service links). Since the satellite link is

larger than the terrestrial one, it suffers from greater free space

path losses. Nevertheless, the antenna gains of the transmitter

� �, dBij trG and the receiver � �, dBij recG of both links

� �1,2j j � are chosen so as to compensate for the free space

path losses � �dBj

PL :

, ,j tr j rec jG G PL� � . (1)

This choice results in a balanced MIMO channel in terms of

the Equivalent Isotropically Radiated Power (EIRP).

Therefore, the total transmit power � �TP W can be equally

allocated to the satellite and terrestrial links assuming perfect

knowledge of the channel at the receiver and no channel

knowledge at both the satellite and the terrestrial transmitters.

It should be noted that this selection of antenna gains

correspond to practical scenarios where large antenna gains are

used in satellite communications in contrast to the smaller

antenna gains of terrestrial links.

S

1L

2LD

Cofisotherm�

0

1��

T

1L�

Figure 1: Geometrical configuration of a hybrid satellite-terrestrial MIMO

system.

The system operates at frequencies above 10GHz and

suffers from rain attenuation. The rain attenuations induced in

the satellite and terrestrial paths are denoted as

� �dB , 1,2j

A j � respectively. The vertical structure of the

rainfall medium is described by the Crane’s assumption [9]

and the rain attenuation of the projection of the effective

length of the satellite link on Earth which has length 1L� is

given by (in dB):

1 1 1cosA A �� � . (2)

The rain attenuations 1 2,A A� are assumed to be correlated

random variables that follow the unconditional joint lognormal

distribution [10]. The term unconditional is meant to include

both raining and non-raining time. The statistical parameters of

the random variables 1 2,A A� are denoted as � �, 1, 2

mj ajA S j �

and can be found in [10]. These parameters depend on the path

lengths 1 2,L L� respectively, the constants of the specific rain

attenuation ,a b [11] and the statistical parameters of the point

rainfall rate ,m r

R S . The latter parameters can be calculated

through regression fitting analysis on local rainfall data or on

ITU-R rainmaps [7] for any location of the world, while the

constants ,a b depend on frequency, incident polarization,

temperature and raindrop size distribution.

The correlation coefficient between the normal random

variables 1 2

ln , lnA A� can be calculated by [10]:

� �� � � �� � � �2 21 2 1 2ln 1 exp 1 exp 1n a a a aS S S S �

� � � � �� �

. (3)

In (3), is the correlation coefficient between 1 2,A A�

which depends on the path lengths 1 2,L L� and the angular

separation � taking into account the horizontal rainfall

medium spatial inhomogeneity and can be found in [10].

Spatial multiplexing is achieved using highly directive

antennas and selecting an angle � as large as possible. The

large angular separation results in a relatively low correlation

coefficient and thus, the MIMO channel can be assumed to be

(ideally) decorrelated [5].

Taking into account the above assumptions and the

expressions (1) and (2), a parallel MIMO channel depending

only on rain attenuation can be considered with channel matrix

H given by:

� �1

2 2

1110c11

os

12 0

12

21 2

10 0

0 10

A i

A i

h h e

h he

� �

�

��

�

� �� � � �� �� � � �� � � �

H (4).

In (4), � �1,2j j� � are assumed to be uniformly distributed

over � �0,2� .

III. OUTAGE CAPACITY ANALYSIS

The outage probability of the capacity of a hybrid satellite-

terrestrial MIMO system is defined as the fraction where the

total MIMO capacity � �bps/HzC does not exceed a specified

threshold thC :

� �out thP P C C� � . (5)

Assuming equal power allocation of the total transmit power

TP between the satellite and terrestrial paths as described in

Section II, the MIMO capacity in (5) is given by the well-

known formula of standard MIMO theory [12, 13]:

2 2 2

2

10 0

log det log 12 2

HT

j

Tj

P PC

N N�

�

� �� � � � � �

� � � ��I HH , (6)

where 2I is the 2 2� identity matrix, 0N is the noise spectral

density at the receiver, � �1,2j j� � are the positive

eigenvalues of the matrix HHH and the superscript H stands

for conjugate transposition.

Taking into account the channel model of (4) and defining

as � �dBcsSNR the Signal-to-Noise Ratio (SNR) under clear

sky conditions which corresponds to the total MIMO transmit

power TP , the capacity of (6) can be calculated by:

1 1 2cos

102

12

01 1

log 1 10 log 1 102 2

cs csSNR A SNR A

C

��� � � � � �� � � � � �� � � �

. (7)

The joint lognormal distribution of 1 2,A A� can be

constructed by the joint normal distribution using the

methodology of [14, Section 7.1] through the transformations:

� �� �

1 1 1 1

2 2 2 2

ln ln /

ln ln /

m a

m a

U A A S

U A A S

�� � ��

� ��!. (8)

The outage probability of (5) can be calculated using the

methodology described in [15] for a similar problem of orbital

satellite diversity. Integrating the joint lognormal distribution

over the outage event defined by (5) and (7), using the

transformation of (8) and after employing the Bayes’ theorem

[14, Section 6.6], the outage probability can be calculated by:

� �� �1

10

20 11 1

2

1erfc

2 2 1

nout U

nu

u uP f u du

�" �

� �� �

� �� �

# . (9)

In (9), � �erfc $ is the complementary error function,

� �1 1Uf u is the normal distribution [14], while the limits

� �0 1, 2ju j � can be calculated by:

� �0 0ln ln /j j mj aju A A S� � , (10)

where:

� �1010 1 1

110cos log 10 10cos log 2 1

2cs thSNR C

A � � �� � � �� �

, (11)

1 1

1 1

cos

10

cos

1

1020

0

1 110log 10 10log 1 10

2 2

110log 2 1 10 .

2

cs

cs

cs

th

SNR A

SN

SN

C

R A

RA

�

�

��

��

� � �� � � � �� � � �

� �� � � �� �

(12)

IV. NUMERICAL RESULTS AND DISCUSSION

In this Section, numerical results are presented for a

hypothetical hybrid broadband satellite-terrestrial

configuration that is located in Athens, Greece (37.58° N,

23.43° E) and operates at 20GHz. The satellite elevation angle

is taken 1 43.46� � � (satellite slant path with Hellas Sat 2). The

following numerical results are compared with a single

satellite system (Single-Input Single-Output – SISO) which

transmits with power equal to the total transmit power of the

MIMO system TP . Moreover, the corresponding performance

curves of a hybrid satellite-terrestrial diversity system are also

given for comparison. In this system, the same information

signal is transmitted in both the satellite and terrestrial links

and the final destination combines the multiple versions of the

received signal using the Maximal Ratio Combining (MRC)

technique. The assumptions of the MIMO system described in

Section II concerning the total transmit power and the antenna

gains are also applied in the MRC system. The outage

probability of this system is calculated using the methodology

of [15] in the geometrical configuration of Figure 1. A similar

approach has been presented in [16] for gamma fading

channels.

In Figure 2, the outage capacity is plotted versus the

capacity threshold thC for different values of angular

separation � . The corresponding curves of a SISO system and

a MRC system for 30� � � are also plotted. Similar curves can

be plotted for other values of angular separation, not shown in

this Figure for the MRC case. The clear sky SNR is

25dBcsSNR � for all systems and the terrestrial path length is

considered 2 2kmL � . Longer paths can be used and

implemented using radio relays [17]. As can be seen by this

Figure, the spatial multiplexing MIMO system outperforms

both the SISO and the MRC systems, especially for high and

medium values of outage probability. On the other hand, the

MRC technique has the same performance as the

corresponding MIMO system for very low values of outage

probability. Moreover, as the angular separation increases, the

performance of the MIMO system improves, since the two

links become more uncorrelated. Nevertheless, the

performance gain, i.e. the difference in the capacity threshold

for the same value of outage probability, is reducing with

increasing angular separation.

In Figure 3, the performance of a hybrid MIMO system is

plotted for different values of the terrestrial path length. The

SISO performance is also plotted, as well as the MRC

performance for 2 2kmL � , while similar curves can be

derived for other values of 2L . The clear sky SNR is

25dBcsSNR � for all systems and the angular separation is

30� � � . The system performance deteriorates as the terrestrial

path length increases, but the level of this degradation is

decreasing with increasing path length especially for low

values of outage probability, reaching up to a limit which is

shown for 2 10kmL � . Nevertheless, the MIMO system still

outperforms both the SISO and the corresponding MRC

systems, which is not shown for 2 10kmL � , but its

performance is relative to the case of 2 2kmL � . Similar

results are for greater paths.

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Capacity threshold (bps/Hz)

Ou

tag

e C

ap

acit

y

MIMO, �=30 (deg)

MIMO, �=90 (deg)

MIMO,�=180 (deg)

Single Satellite

MRC, �=30 (deg)

Figure 2: Outage Capacity for different values of angular separation.

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Capacity threshold (bps/Hz)O

uta

ge C

ap

acit

y

MIMO, L2=2km

MIMO, L2=4km

MIMO,L2=10km

Single Satellite

MRC, L2=2km

Figure 3: Outage Capacity for different values of the terrestrial path length.

In Figure 4, the outage capacity threshold is plotted versus

the clear-sky SNR for a MIMO, a SISO and a MRC system for

outage probability 410outP �� . The values of system

parameters are 2 2kmL � and 30� � � . As can be seen by this

Figure, the MIMO system outperforms both the MRC and the

SISO systems. As the value of the clear-sky SNR increases, the

MIMO performance gain, i.e. the difference in the outage

capacity threshold for a given value of SNR, also increases

compared to both the MRC and the SISO systems. On the

contrary, the performance gain of MRC over the single

satellite system remains constant for SNR values larger than

10dB, since the two curves are parallel for these specific

values of SNR.

Pout=10-4

0

2

4

6

8

10

12

14

16

0 5 10 15 20 25 30SNRcs (dB)

Ou

tag

e C

ap

acit

y t

hre

sh

old

(bp

s/H

z)

2x2 MIMO

Single Satellite

MRC

Figure 4: Outage Capacity threshold versus clear-sky SNR.

V. CONCLUSIONS

In this work, the performance of a hybrid backhaul satellite-

terrestrial MIMO system operating at frequencies above

10GHz and suffering from rain attenuation has been

investigated. The application scenario of such a system is in

emergency communications and critical infrastructures

systems. Spatial multiplexing is used in order to enhance the

system performance and achieve high data rates. The outage

capacity of this system is analytically calculated using standard

MIMO theory and lognormal fading channels. Extended

numerical results show the relative performance of a MIMO, a

SISO and a MRC diversity system. The MIMO hybrid system

outperforms both these systems, while the numerical results

highlight the values of the system parameters where the MIMO

performance gain is significant.

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