Telecommunication Systems
https://doi.org/10.1007/s11235-018-0466-9
Multiple-high altitude platforms aided system architecture for
achieving maximum last mile capacity in satellite communication
P. G. Sudheesh1 · Maurizio Magarini2 · P. Muthuchidambaranathan1
© Springer Science+Business Media, LLC, part of Springer Nature 2018
Abstract
Satellite communication provides services to users over wide area. However, the propagation delay and the link budget
associated with the long path make the communication difficult. Better link budget and smaller user antennas make highaltitude platform (HAP) based communication one of the favourite choice to last mile users over satellite connectivity. HAPs
with overlapped service area form an interference limited system. To this end, interference alignment is proposed as promising
solution to maximize capacity between multiple HAPs and ground stations. In this context, explicit expressions for system’s
sum-rate and bit error rate (BER) are derived. The sum-rate and BER performance of the proposed scheme are studied
for different Rician factors representing different geographical locations. Monte Carlo simulations are used to validate the
analytical expressions.
Keywords High altitude platform · Interference alignment · Degrees of freedom
1 Introduction
Demand for high data rate is increasing day by day. In addition to data rate, users demand reliability, no matter where
the user is located. Present day terrestrial communication
technologies like massive multiple-input multiple-output
(MIMO), Heterogeneous network architecture, millimeter
wave communication etc., offer high data rate and reliable
service. A well known scheme to provide quality of service
to all users regardless of their location is satellite based communication. Though satellites have wider coverage area and
extend their services to the remote users, received narrow
beam signal at ground station makes it difficult for every
ground user to access signal from satellite [1]. It is almost
B
P. G. Sudheesh
pgsudheesh@gmail.com
Maurizio Magarini
maurizio.magarini@polimi.it
P. Muthuchidambaranathan
muthuc@nitt.edu
1
Department of Electronics and Communication Engineering,
National Institute of Technology, Tiruchirappalli 620015,
India
2
Dipartimento di Elettronica, Informazione e Bioingegneria,
Politecnico di Milano, 20133 Milan, Italy
impossible for every ground user to possess specific antennas to receive spot beams from satellite. Also, it is indeed a
necessity of the present day communication industry to have
miniaturized user equipments (UEs). A possible solution for
this is to use a platform between ground station and satellite
to provide last mile/first mile access to users [2,3]. Highaltitude platforms (HAPs) address this issue by operating as
either airships or planes in the stratosphere, 17-22 km above
the ground. This unique position offers a significant link budget advantage compared to satellites and thereby reducing the
antenna size in the end user equipment [4].
In other words, HAPs operate as a global sink that collects
information from several ground sensors [5]. Such a network
architecture assists in deploying the network in shorter span
and minimizes the cost of deployment [2]. In [6], the effect
of HAP based transmission in cellular system is considered,
where a single HAP serves multiple ground stations located
in different cells. In addition, associating aerial platforms
with centralized networks data rate further [6,7].
Recently, researchers have suggested networking multiple
HAPs to provide higher data rate. Such an interconnection
between several HAPs are carried out by Interplatform Link
(IPL). Networked configurations of several HAPs via IPLs
can be considered as a virtual MIMO (V-MIMO) [8,9] and by
doing so, it is possible to exploit the advantages of distributed
antenna techniques. It is worth noting that the antenna spac-
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P. G. Sudheesh et al.
ing in V-MIMO should be so high to provide good correlation
properties. However, having IPL between HAPs are an extra
burden and a V-MIMO restricts each HAPs to transmit same
information. This is not the case in real scenario, where
each HAP would be having separate data streams or any
other information. The overall capacity of the system can
be maximized if each of the transmitters transmits separate
information. Such an architecture, where each transmitter has
data for separate receiver is called as a wireless X-network.
Unlike [8,9], where authors have considered V-MIMO,
studies in [10,11] suggest that multiple HAPs can serve a
common coverage area without an IPL between each other.
Such an HAP configuration would lead to formation of interference limited X-network system.
Interference alignment (IA) was proposed as a practical
solution to achieve multiplexing gain or Degrees of Freedom (DoF) in a MIMO X-network [12]. A restriction to the
number of users in X-network IA was found out in [13].
For realizing IA in spatial domain, it is mandatory to limit
the number of transmitters or receivers to two [13]. Hence,
the possible solution is to realize either 2 × N or M × 2 X
networks. Hence, with the proposed technique, it is possible
to extend our method to M HAP transmitters. However the
number of the receiver stations remains as 2.
Unlike terrestrial channel modeling, Air-to-Ground (Ato-G) should consider four propagation mechanisms, which
includes free-space propagation, reflection, diffraction, and
scattering. Parameters such as rain attenuation, gaseous
absorption and scintillation affect the propagation in A-to-G
channel [14]. As a result, A-to-G channel is modeled using
line-of-sight (LOS) and non-line-of-sight (NLOS) components at millimeter frequency band. An important condition
to achieve IA [15–17] is that channel state information (CSI)
is globally available at each transmitting node. After acquiring CSI, IA can be implemented to improve the sumrate of
multiple HAP based communication in [18]. A geometrical
channel model was used in [19] to analyze the effect of position of HAPs or GSs in the system’s performance.
In this paper, we extend our work [18,19], where the analysis were based on Monte-Carlo simulations and, we derive
analytical expressions for sum-rate and error performance for
IA based HAP communication. On the contrary to V-MIMO
configuration involving multiple HAPs, our technique aims
at transmitting separate data from each HAP by avoiding
IPLs between individual HAP. A common practice is to use
directional antennas at HAPs to maximize capacity through
non interfering cell structure [4], but the cost incurred for
developing this cell like configuration is high. Our proposed
technique does not require precise beamforming and reduces
the hardware requirements and cost of the system considerably.
The organization of the paper is described as follows. The
system model and channel modeling is provided in Sect. 2.
123
Section 3 presents an IA scheme for 2 user overlapping
A-to-G channel. While Sect. 4 presents numerical results,
conclusions are drawn in Sect. 5.
2 System and channel models
We consider two receiver ground stations served by two
HAPs with overlapping coverage areas, aiming to maximize
the capacity in HAP to GS communication, The reference
network architecture, which is investigated in this paper,
is depicted in Fig. 1. Each receiver gets separate signals
from each HAP forming an X-network. Each transmitter and
receiver is equipped with 3 antennas to facilitate IA [16]. The
transmitters are assumed to be transmitting equal amount of
power. It is also assumed that the transmitters and receivers
transmit at a frequency band which do not posses interference
from other terrestrial or aerial communication.
2.1 Channel modeling
The satellite-to-HAP communication separation is very
large, therefore, we assume that the propogation is due to
the LoS nature of the channel. As a result, we assume
that the satellite-to-HAP channel possesses similar characteristics, therefore we neglect the effect of propagation in
satellite-to-HAP channel [20]. On the other hand, in terrestrial communication, the channel is modeled as Rayleigh
in urban and Rician in suburban area. This is not the same
for A-to-G channel [14,21]. Under urban conditions, A-toG channel experiences Rician fading due to the presence of
LOS path. In suburban areas a Rayleigh fading is experienced
due to the presence of stronger reflected signals which are
stronger than LOS.
A generalized approach to model HAP-ground station
channel is to follow Rician distribution where both LOS
and NLOS paths are considered [14]. Therefore, the channel
model can be represented as
H=
κ
HLOS +
1+κ
1
HNLOS ,
1+κ
(1)
where HLOS represents shadowed free space propagation
loss and HNLOS represents only the NLOS path. Hence H is
the A × A matrix having complex fading coefficients. With
σ L2 O S and σ N2 L O S being the power of LOS components and
NLOS components respectively, the Rician factor κ is given
by [22]
κ=
σ L2 O S
σ N2 L O S
(2)
Multiple-high altitude platforms aided system architecture for achieving maximum last mile…
Fig. 1 Multiple HAP with overlapping coverage area
In our work, we consider multiple antennas at both transmitter and receiver. The MIMO channel is considered to be
static and hence the LOS MIMO channel is defined as in
[22]
⎡
HLOS
⎢
⎢
=⎢
⎢
⎣
e j2π
e j2π
dR
λ
dR
λ
1
e
j2π
e j2π
dT
λ
dT
λ
⎥
⎥
⎥
⎥
⎦
sin(Ao A R )
..
.
(M−1)
⎡
⎢
⎢
.⎢
⎢
⎣
⎤
1
sin(Ao A R )
⎤T
sin(AoDT )
..
.
(N −1)
⎥
⎥
⎥
⎥
⎦
3 Role of interference alignment for HAP
based transmission
In our work, we consider two HAPs serving a common area.
This kind of system is applicable where a service area has
huge data traffic, which is generated by mobile users. To
analyze the role of IA in HAP-GS based communication, we
perform our analysis by considering two system architectures. In the first, we model our system as two-user MIMO
X channel and in second, the number of GS is increased to
three within the fixed service area.
3.1 Communication with two ground stations
(3)
sin(AoDT )
where, d R and dT represents the antenna spacing in the
receiver and transmitter, Ao A R and AoDT represent the
Angle-of-Arrival at the receiver and the Angle-of-Departure
at the transmitter and λ is the wavelength of signal. Since
the HNLOS represents only the NLOS path, resultant NLOS
MIMO channel follows Rayleigh distribution.
A two-user MIMO X channel is shown in Fig. 1. Each transmitting and receiving node is equipped with three antennas.
With signals from both the transmitters, the received signal
will be:
y1 = H11 x1 + H12 x2 + n1
(4)
and
y2 = H21 x1 + H22 x2 + n2 ,
(5)
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P. G. Sudheesh et al.
respectively, where xi is the signal vector transmitted by the
i-th user, H ji is a channel matrix between transmitter i and
receiver j, with i, j ∈ {1, 2}, where H ji is obtained using
(1), and n j ∼ N (0, σn2 ) . Each transmitter has independent
messages to each receivers. The two transmitted vectors are:
x1 = b11 x11 + b21 x21 ,
(6)
x2 = b12 x12 + b22 x22 ,
(7)
where x ji is the message to be transmitted from transmitter
i to receiver j and b ji is the beamforming vector associated
with x ji . By replacing (6) and (7) in (4) and (5), respectively,
we have
y1 = H11 b11 x11 + H11 b21 x21
+H12 b12 x12 + H12 b22 x22 + n1
(8)
and
y2 = H21 b11 x11 + H21 b21 x21
+H22 b12 x12 + H22 b22 x22 + n2 .
(9)
To achieve IA, the interferer’s signals should lie in the null
space of the desired signal. That is, in order to satisfy the IA
condition the interfering signals must span the same subspace
[16]
S P AN {H12 b22 } = S P AN {H11 b21 } ,
(10)
S P AN {H22 b12 } = S P AN {H21 b11 } .
(11)
A possible choice of beamforming vectors is
−1
b22 = H12
H11 b21
(12)
and
−1
b12 = H22
H21 b11 .
(13)
Equations (12) and (13) define the original IA solution, here
termed “conventional IA”, proposed in [16].
3.2 Improving system capacity by cellular concept
For the system architecture in Fig. 1, IA provides an ideal way
of providing maximized system capacity. With two receivers
and two HAPs, the communication has been described in
previous subsection. Now, we investigate the effect of adding
additional nodes on system capacity. There are two possible
ways by which additional units can be added to the system.
1. By increasing the number of HAPs to more than two,
keeping the ground stations as 2, i.e, M > 2 and N = 2
123
2. Fixing the number of HAPs to 2, increase the number of
ground stations, i.e, M = 2 and N > 2
Both the methods has identical effect on sum-rate In other
words, one is the reciprocal of the other. While the first
method has N = 2, the second assigns M = 2. However,
we consider second method for increasing sum-rate of end
user at ground. In this section, we analyze the system by
considering three ground stations ie N = 3 as in Fig. 2.
3.3 Capacity of Rician X network
The sum-rate of a network in high signal-to-noise-ratio, SNR
regime can be expressed as [13,15,16]:
C = d · log(γ ) + O(log(γ )),
(14)
where γ is the SNR value at a given receiver.
The DoF for an X network with M transmitters and N
MN A
receivers each with A antennas, is equal to d = M+N
−1 .
From (14), to find C, we need to compute the SNR for the
Rician X channel. Now, to find the behavior of the system
for different κ values, we derive the SNR expression for a
Rician X channel, for IA. In order to find capacity, we first
calculate SNR of first stream and proceed further by finding elements of (H ZHF H Z F )−1 . Clearly, the SNR of the k th
parallel channel, γk , is given by [9]:
γk =
Γ
[W −1 ]
,
(15)
k,k
where Γ is the transmit power per symbol, and W =
H ZHF H Z F with H Z F being the zero forcing matrix of the
first receiver. In this context, we derive the SNR for a system
consisting of two HAPs, one tethered balloon and two GSs,
since an explicit expression for finding the elements of W −1
cannot be derived when the number of rows or columns of
W −1 exceeds 2. Hence, by limiting number of HAPs,GSs
and the number of antennas to 2, a tractable and an explicit
expression for SNR can be derived,
Theorem 1 The capacity of a two-antenna, Rician X-Channel
is given by:
2
8
C=
3
log2 (1 + γk ),
(16)
k=1
where γ1 is given by:
γ1 =
Es Bb1
σ2
2
Ab1 × Bb1
2
,
(17)
Multiple-high altitude platforms aided system architecture for achieving maximum last mile…
Fig. 2 Multiple HAP with
multiple GS inside coverage
area
−1
γ
where A = H 11 H −1
21 , B = H 12 H 22 . Similarly, 2 is:
γ2 =
Es Ab1
σ2
H ZHF H Z F
2
Ab1 × Bb1
.
−1
H Z F = H 11 H −1
21 b1 : H 12 H 22 b1 ,
(18)
(19)
where H i j is the channel between transmitter j and receiver
i and bi is the beamforming vector associated with xi j . In
order to compute γk , we begin by finding γ1 and, then, γ2
can be derived in similar way. The SNR at the first stream of
receiver 1 given by:
Es
σ 2 NT
H ZHF H Z F
1,1
=
2
Proof First we define ZF matrix for a 2 × 2 X channel IA
system as in [13]:
γ1 =
−1
,
−1
(20)
1,1
where NETs is the transmitted energy per symbol, and σ 2 is
the noise power. Since there is no explicit formula to find
(H ZHF H Z F )−1 1,1 for matrices of dimension above [2 × 2],
we consider a 2-antenna system and find (H ZHF H Z F )−1 1,1 .
Given that H Z F is a square matrix, we proceed to find
[W −1 ]1,1 as follows:
Bb1
2
2
det H ZHF H Z F
2
Bb1 2
=
H
det H Z F det H Z F
=
Bb1
2
2
Ab1 × Bb1
2
(21)
,
where Ab1 × Bb1 denotes the cross product of vectors Ab1
and Bb1 , whose output is another vector. Finally, considering
MN A
M = N = A = 2 in d = M+N
−1 and, then, using (20) and
(21) this theorem is proved.
Using Theorem 1, it is possible to analyze the relation
between κ and the capacity of the Rician X-channel in the
HAP drones wireless system. Though we considered Rician
X-channel to find the relationship between κ and system
capacity, the theorem can be used to find relation between
the system capacity and any other parameter that affects the
channel.
Remark 1 At high S N R, the system fails to achieve higher
sum-rate. This is because, at higher κ, columns of H Z F will
be correlated. Hence, IA will fail to achieve maximum capacity in higher κ channels.
123
P. G. Sudheesh et al.
22
3.4 Error performance of Rician X network
Rician factor, K= −10 dB
Rician factor, K= 0dB
Rician factor, K= 10 dB
Rayleigh
20
Here we discuss the effect of IA in error performance. The
average symbol error rate (SER) can be calculated using [23],
14
12
10
8
6
4
2
0
(23)
3
where g Q AM = 2(M−1)
and γ̄ is the average SNR and individual SNR’s are calculated as discussed in Eq. (1). After
acquiring SER, computation of BER is straightforward. That
is, for a given modulation scheme, apart from the order of
modulation, the only factor to reflect in S E Ravg is γ̄ at the
receiver.
4 Numerical results
The analysis is done in two phases. In the first phase, the
error performance is evaluated for the IA based system as
well as non interference system under Rician channel. The
second phase describes the capacity improvement with IA
under Rician channel.
A quadrature phase-shift keying (QPSK) modulation
scheme is considered in the work. We assume exact CSI
knowledge at HAPs and each HAP and ground station is
equipped with three antennas. We also assume full rank channel matrix in all the cases, which can be obtained by carefully
considering inter-antenna spacing.
In the first phase, we consider the sum-rate analysis of
the HAPs-GSs communication system. First, the sum-rate
is plotted against SNR for different κ to analyze the effect
of LOS components in sum-rate performance. Second, the
sum-rate is plotted against SNR for IA and non-interference
(mentioned as non-IA) systems. Third, the analytical expression for sum-rate is plotted along with the Monte-Carlo
simulation based one. Finally, the impact of number of
receivers in the system sum-rate is shown.
Figure 3 shows the Sum-rate as a function of SNR for a
MIMO system with QPSK modulation. For this simulation 3
antennas at transmitter and receiver is considered. With this
a single user MIMO system is formed and effect of Rician
factor (κ) on MIMO channel is studied. It can be seen from
Fig. 3 that, in general, sum-rate increases with SNR, which
is in agreement with [9]. But unlike in [9] where increasing Rician component has adverse effect on sum-rate, our
scheme shows an improvement in sum-rate. It can also be
123
bps/Hz
(22)
16
5
10
15
20
SNR[dB]
Fig. 3 Sum-rate versus SNR for MIMO with various Rician factors
25
With IA, = -20 dB
With IA, = 20 dB
Without IA , = -20 dB
Without IA , = 20 dB
20
sum-rate (bps/Hz)
S E Ravg
g Q AM γ̄
1
=2 1− √
1−
1 + g Q AM γ̄
M
2
4
g Q AM γ̄
1
+ 1− √
π 1 + g Q AM γ̄
M
1 + g Q AM γ̄
−1
−1 ,
tan
g Q AM γ̄
18
15
10
5
0
0
5
10
15
20
25
30
SNR (dB)
Fig. 4 Sum-rate versus SNR for IA and non-IA systems
noted that the Rayleigh component behaves like a lower
bound, since there is no direct component in received signal. With κ = −10 dB, the proportion of direct component
in received signal is slightly increased, and as a result, a
slight improvement in capacity can be observed. Furthermore, κ = 0 and 10 dB introduces more direct component
into the received signal, leading to significant improvement
in sum-rate. However, the inter-antenna spacing in HAP must
be sufficient to provide full-rank channel matrix, which may
not be practically feasible.
Figure 4 reports the effect of IA on the sum-rate performance of the system. Here, we consider an interference
limited system where the DoF is 43 for a 2 × 2 X network and
a interference limited system whose DoF is 1 for the same
system architecture. The sum-rate of non-IA system is lesser
compared to the IA systems because, for non IA systems
like time division multiple access (TDMA), DoF falls to 1
for same architecture. As a result, the interferece free system
shows better sum-rate. Another interesting feature is that,
when the antennas are not optimally spaced, the sum-rate
drops at higher κ due to the presence of correlation between
Multiple-high altitude platforms aided system architecture for achieving maximum last mile…
25
100
With IA (analytical),
With IA (analytical),
With IA, = -20 dB
With IA, = 20 dB
10-1
15
BER
sum-rate (bps/Hz)
20
= -20 dB
= 20 dB
10
10-2
With IA, = 0 dB
With IA, = 10 dB
Without interference, = 0 dB
Without interference, = -10 dB
5
10-3
0
0
5
10
15
20
25
30
0
2
4
6
SNR (dB)
40
14
16
18
14
16
18
simulated, =-10 dB
analyical, =-10 dB
10-1
25
BER
bps / Hz
12
100
Rician factor, K= −10dB (3 receivers)
Rician factor, K= 0dB (3 receivers)
Rician factor, K= 10dB (3 receivers)
Rician factor, K= −10dB (2 receivers)
Rician factor, K= 0dB (2 receivers)
Rician factor, K= 10dB (2 receivers)
30
10
Fig. 7 BER versus SNR for IA and non IA system
Fig. 5 Sum-rate versus SNR using derivation
35
8
SNR (dB)
20
15
10-2
10
5
0
0
2
4
6
8
10
12
14
16
18
SNR (dB)
10-3
0
2
4
6
8
10
12
SNR (dB)
Fig. 6 Sum-rate of HAP based communication with 2 and 3 ground
stations
Fig. 8 BER versus SNR using derivation
columns in the MIMO channel. This is a practical situation,
as the HAP may not be possible to provide enough spacing
for antennas, due to the hardware limitations [24]. In Fig. 5,
the analytical and Monte-Carlo simulation based results are
plotted. It is clear that the analytical derivation in 16 matches
with the Monte-Carlo simulation.
Figure 6 illustrates the sum-rate offered by two HAPs to
a fixed service area with three ground stations as depicted in
Fig. 2. It can be seen that sum-rate increases as the number of
ground stations are increased. The reason for such a behavior is the improvement in DoF and a successive improvement
in sum-rate. Another observation is that the improvement in
capacity in channel with higher κ value is more comparing
to lower κ values. This is because the system offers spatial multiplexing, under the assumption that the antennas are
optimally placed.
In the second phase, Monte Carlo simulations and analytical expressions are presented to evaluate the bit error
rate (BER) of the proposed IA scheme. Also, the BER performance is plotted both for IA and for a scenario without
interference. Figure 7 reports the BER performance for IA
and no interference HAPs-GSs communication system. It
is clear that an increase in SNR result in improved BER
performance. This is common for systems with and without
interference. However, IA system offer better performance
compared to interference less systems. It can also be noted
that a system in higher κ shows improved error performance.
This behaviour pertains for IA as well as non interference
based systems. In Fig. 8, error performance is plotted for
both analytical and Monte-Carlo simulation based results.
The analytical error performance is plotted using (22) and the
analytically obtained results matches with the Monte-Carlo
simulation
In fact, with the reciprocity property, the same sum-rate
will be obtained, if the number of HAPs are increased to three
and fixing ground stations to 2. Number of ground station is
limited to 2, to the inherent property of IA. Hence, to achieve
maximum sum-rate, it is suggested to use multiple ground
stations, if the coverage area spanned by ground station is
larger.
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P. G. Sudheesh et al.
5 Conclusion
An interference alignment based communication has been
proposed for an HAP assisted satellite-to-ground communication system involving one satellite, 2 HAPs and multiple
ground stations. With the overlapped service area, the IA
based communication shows significant improvement in
error performance as well as in capacity, when the antennas
are optimally placed in transmitter and receiver. Analytical expressions for sum-rate and BER are derived for the
proposed model. The IA based HAP communication system provides an additional advantage of having less traffic
between inter-platform links, which in turn saves precious
hardware of HAP. With the assumption of overlapped service area, our system avoids the necessity of using highly
directive beamformers in HAPs.
From the results, it is concluded that multiple ground stations or multiple HAPs increases the sum-rate However, a
channel with higher rician factor (κ) provides higher sum-rate
compared to lower ones, only when antennas are optimally
spaced. Though our proposed technique suggest a solution
to maximize sum-rate in ground stations with interfering signals from multiple HAPs, the inherent limitation due to IA
limits the number either HAPs or ground station nodes to 2.
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Multiple-high altitude platforms aided system architecture for achieving maximum last mile…
P. G. Sudheesh received his
B.Tech Degree in Electronics and
Communication Engineering from
Mahatma Gandhi University, Kottayam, India, in 2010, the M.E.
Degree in Communication Systems, from Anna University Chennai (Guindy campus), Chennai,
India, in 2012. He is pursuing
Ph.D. degree in from the National
Institute of Technology (NIT),
Tiruchirappalli, India from 2014.
He worked as Assistant Professor
at RSET, Cochin, during 20122014. His research interests
include MIMO communication, channel modelling.
Maurizio Magarini was born in
Milano, Italy, in 1969. He received
the Master and Ph.D. degrees in
electronic engineering from the
Politecnico di Milano, Milano,
Italy, in 1994 and 1999, respectively. In 1994, he was granted
the TELECOM Italia scholarship
award for his Master thesis. From
1999 to 2001 he was a Research
Associate in the Dipartimento di
Elettronica e Informazione at the
Politecnico di Milano where, he
has been an Assistant Professor
since 2001 and Associate Professor from 2017. From August 2008 to January 2009 he spent a sabbatical leave at Bell Labs, Alcatel-Lucent, Holmdel, NJ. He has authored
and coauthored more than 40 journal and conference papers. His
research interests are in the broad area of communication theory. Topics include synchronization, channel estimation, equalization, coding
and reduced complexity detection schemes for multi-antenna systems.
P. Muthuchidambaranathan received his B.Eng. Degree in Electronics and Communication Engineering from Government College
of Technology, Coimbatore, India,
in 1992, the M.Eng. Degree in
Microwave and Optical Engineering, from A.C. College of Engineering
and
Technology,
Karaikudi, India, in 1994. He
obtained his Ph.D. degree in optical communication from the
National Institute of Technology
(NIT), Tiruchirappalli, India in
2009. He is currently working as
an Associate Professor in the Department of Electronics and Communication Engineering, National Institute of Technology (NIT), Tiruchirappalli, India. His research interests include wireless communications, and optical communications. He published his research papers
in refereed international journals, and international and national conferences. He is an author of the textbook “Wireless Communications”
(published by Prentice Hall of India).
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