In this paper we address the potential gain of using compact MIMO antenna array configurations in conjunction with High Altitude Platforms (HAPs) diversity techniques in order to increase the capacity in HAP communication systems. For this purpose, we also propose a novel compact MIMO antenna which we denote as the “MIMOOctahedron” and compare its performance with the vector element antenna. Simulation results show that the MIMO-Octahedron antenna provides superior performance to the vector element antenna and the single HAP case.

1. ACEEE International Journal on Communication, Vol 1, No. 1, Jan 2010
Capacity Evaluation of a High Altitude Platform
Diversity System Equipped with Compact MIMO
Antennas
A. Mohammed1 and T. Hult2
1
Department of Signal Processing, Blekinge Institute of Technology, Ronneby, Sweden
Email: abbas.mohammed@bth.se
2
Department of Electro- and Information Technology, Lund University, Lund, Sweden
Email: tommy.hult@eit.lth.se
Abstract— In this paper we address the potential gain It has been widely recognized that the capacity in
of using compact MIMO antenna array wireless communication systems can be greatly increased
configurations in conjunction with High Altitude by exploiting environments with rich scattering such as
Platforms (HAPs) diversity techniques in order to urban areas or indoors [6-9]. Independent spatial or
increase the capacity in HAP communication systems. polarization channels can be accessed by means of
For this purpose, we also propose a novel compact multiple antennas at both the transmitter and the receiver
MIMO antenna which we denote as the “MIMO- and the technique is thus referred to as Multiple-Input
Octahedron” and compare its performance with the Multiple-Output (MIMO) system. For a fixed total power
vector element antenna. Simulation results show that and bandwidth, and with a matrix transfer function of
the MIMO-Octahedron antenna provides superior independent complex Gaussian random variables, the
performance to the vector element antenna and the MIMO wireless communication channel has an
single HAP case. information theoretic capacity that (initially) grows
linearly with the number of antenna elements [6-9].
Index Terms—High Altitude Platforms (HAPs), compact Constellations of multiple HAPs have been shown to
MIMO antennas, diversity techniques, 4G systems enhance broadband fixed wireless access capacity by
exploiting antenna user directionality, when using shared
spectrum in co-located coverage areas, where a
I. INTRODUCTION predominant LOS propagation is present for mm-
High Altitude Platforms (HAPs) are quasi-stationary wavebands (e.g., 47/48 GHz). In addition, HAPs have
aerial platforms operating in the stratosphere. This been also proposed for 3G and broadband applications
emerging technique is preserving many of the advantages where multipath propagation might be significant. The
of both satellite and terrestrial systems [1-5] and central idea in this paper is to create a virtual MIMO
presently started to attract more attention in Europe system by exploiting the diversity provided by multiple
through the European Community CAPANINA Project HAPs (see figure 1) in order to increase the capacity in
and the recently formed COST 297 Action, in which the HAP communication links. In addition, a number of
authors are the Swedish representatives in this Cost different compact antenna array configurations, (e.g., the
Action. Recently, the first author has led an international vector element antenna and our proposed novel MIMO-
editorial team for a HAP special issue at EURASIP Octahedron antenna) specifically designed for MIMO
Journal of Communications and Networking [1] to applications, in which the propagation environment is
promote this technology and the research activities of further utilized to achieve diversity in space and
Cost 297 to a wider audience. Cost 297 is the largest polarization. Thus, in this paper we also analyse the effect
gathering of research community with interest in HAPs of using these different compact MIMO antenna
and related technologies [1]. configurations and power control on the information
Using narrow bandwidth repeaters on HAP for high theoretic capacity of the total transmission channel of the
speed data traffic have several advantages compared to HAP system.
using satellites, especially when operating in a local The organization of the remainder of the paper will be
geographical area. One of the main advantages is that the as follows. In Section 2, we give a theoretical background
received signal from the HAP would be much stronger of the polarization and pattern of antennas. The MIMO-
than a received signal of equal transmitted power from a HAP diversity system and various used MIMO antennas
satellite. This allows for a much lower sufficient are presented in Section 3. The basic of MIMO-OFDM
transmitter power which would decrease the size and system and power control are presented in Section 4. In
weight of the repeater equipment carried by the HAP. Section 5, the simulations results of the different MIMO
Also the HAP provides for a much easier deployment so antenna array configurations and presented. Finally,
that a high-speed connection can be made on demand for Section 6 concludes the paper.
a specific geographical area [1].
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2. ACEEE International Journal on Communication, Vol 1, No. 1, Jan 2010
II. THE POLARIZATION CHANNEL that the OFDM format is useful for propagation scenarios
in 3G frequency band and is a promising candidate for
The polarization and antenna pattern of the
many 4G communication systems. Figure 1 shows the
electromagnetic field can be expressed as a multipole
diversity setup for the case of three HAPs separated by
expansion [10] of the field emanating from a virtual
sphere enveloping the antenna that is being analyzed. the angles θ a,b and θ a,c .
This series expansion consist of weighted orthogonal base
functions on the surface of the virtual sphere and allow
for a solution to Maxwell’s equations that can be written
as:
⎧ ⎡j ⎤
⎪E =
⎪ ⎣
∑
⎢ k a E (l , m)(∇ × fl (kr )) Xlm + aM (l , m) gl (kr ) Xlm ⎥
⎦
l,m
⎪ (1)
⎨
⎪
⎡ ⎤
⎪H = 1
∑
j
aE (l , m) f l ( kr ) Xlm − aM (l , m)(∇ × gl (kr ))Xlm ⎥
⎪ η l,m ⎢⎣ k ⎦
⎩
Figure 1: The MIMO-HAP diversity system with three HAPs and the
These base functions Xlm are orthogonal functions of
channel paths from the transmitter to the receiver.
the spherical field when the far-field of the antenna is
projected onto the virtual sphere. The functions gl and fl
in equation (1) are Hankel functions representing an Each transmit and receive antenna of the system
outgoing (transmitted) wave or an incoming (received) consists of a special compact MIMO antenna array. These
wave. The weights aE and aM are the corresponding compact antenna arrays can be of different complexity
coefficients and will give the gain of each orthogonal and design. In Fig. 2a we show the structure of a vector
function (mode) for a particular electromagnetic far-field element antenna consisting of three orthogonal electric
pattern, as shown by equation (2): dipoles forming an electric tripole together with a
magnetic tripole formed by three orthogonal magnetic
⎧ ⎡ d [r j l ( kr ) ] ⎤ dipoles (loop antennas) which will give a maximum of
⎪ ⎢cρ dr ⎥
⎪ μ 0 ck 2 ⎢ ⎥
⎪a E (l, m ) ≅ ∫Y
*
lm ⎢ + jk ( r ⋅ J ) j l ( kr ) ⎥ d
3
r six independent antenna ports.
⎪ j l (l + 1) ⎢ − jk ∇ ⋅ ( r × M ) j ( kr ) ⎥
⎪ ⎢ l ⎥ The second compact antenna we propose and
⎪ ⎣ ⎦ (2) investigate is a novel array configuration, which we
⎪
⎨
⎪ denote as the “MIMO-Octahedron”. This antenna consists
⎪ ⎡ ∇ ⋅ ( r × J ) j l ( kr ) ⎤
⎢ ⎥
⎢ + ∇ ⋅ M d [r j l ( kr ) ]⎥ d
⎪ μ 0 ck 2
of twelve electric dipoles positioned in double
(l, m ) ≅ ∫Y
* 3
⎪a r
⎪
M
j l (l + 1)
lm
⎢ dr ⎥
⎪ ⎢ ⎥ tetrahedron geometry, as can be seen in Fig. 2b. This
⎢ + k ( r ⋅ M ) j l ( kr ) ⎥
2
⎪ ⎣ ⎦
⎩ design is created by taking two MIMO-Tetrahedron
arrays and placing them with one tetrahedron vertex
Using equation (2) we can calculate which modes are facing a vertex of the other tetrahedron, and then rotating
active on any arbitrary antenna enveloped by a virtual one of the tetrahedrons 60 degrees around the axis going
sphere only by knowing the current distribution J, the through both vertices and finally displace one of the
charge distribution ρ and the intrinsic magnetization M of tetrahedron so that they both have the same central point.
the antenna. These modes are theoretically orthogonal to Theoretically this will give twelve independent ports.
each other and therefore represent independent ports of The three electric and three magnetic tripoles on their
the antenna. The transmitting channel Htx is then assumed own do not provide enough independent antenna ports to
as the linear transformation of the input signal x into the be able to utilize the HAP diversity feature which would
mode domain atx according to α tx = H tx x and for the require at least four independent channels. Thus, the
receiving channel we have a similar transformation from comparison of the capacity is done for the vector element
the mode domain arx into the output signal y of the antenna and the MIMO-Octahedron antenna only.
system following y = H rx α rx , where atx and arx are
vectors containing the mode gains for a specific antenna
type.
III. THE MIMO-HAP DIVERSITY SYSTEM MODEL
In this paper we are propose an application for high
data rate transmissions using a system employing
multiple HAPs. This system consists of virtually created
MIMO channels using HAP diversity in combination (a) (b)
with the polarization and pattern diversity of a special
type of MIMO antenna arrangements [11-13] and also Figure 2: The structure of the two compact MIMO antennas: (a) The
Vector element antenna, and (b) the MIMO-Octahedron antenna.
through using the OFDM modulation technique. Note
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3. ACEEE International Journal on Communication, Vol 1, No. 1, Jan 2010
The wave propagation channel Hch from the transmitter N DFT −1 r
mode vector atx to the receiver mode vector arx can be P= ∑ ∑σ
k = 0 m =1
2
xm
(k ) (10)
seen as a simple transformation that contain the distance
dependent decaying values of the signal being transmitted To maximize the total sum of capacities in all the sub-
2 channels we use the so called “water-filling” technique in
⎛ f ⎞
H mn (r, f ) = ⎜
⎜ 4πc r − r
⎟
⎟ (3)
which we allocate more power to the sub-channels with
high eigenvalues. The optimal “water-filling” solution [9]
⎝ m n ⎠ is then given by:
where rm − rn is the distance along the path between ⎧ 2 s2 s2
⎪ s xm (k ) = γ − 2 n , if γ − 2 n > 0
transmitter m and receiver n. There are no atmospheric ⎪ sm (k ) sm (k )
interferences and the noise in the system is modelled as ⎨ sn2
(11)
uncorrelated Gaussian noise. The total MIMO channel ⎪s xm (k ) = 0, if γ − 2
2
≤0
can then be assembled as: ⎪
⎩ sm (k )
H = H rx ⋅ H ch ⋅ H tx (4) where γ is a pre-defined threshold level of the signal-to-
noise ratio in the system.
where Hrx and Htx are the transmitter and receiver
antenna channels respectively.
V. SIMULATION RESULTS
IV. THE MIMO-OFDM SYSTEM MODEL In this section we compare the achieved capacity
using different types of compact MIMO antenna
Assuming that we have a MIMO antenna system with configurations. The type of antennas used here are the
N transmitting antennas and M receiving antennas, we vector element antenna and our proposed novel MIMO-
can then write the separate signals in the frequency Octahedron antenna. In these simulations we use a
domain between any pair of transmitting and receiving diversity system consisting of three or six HAPs,
antennas as: depending on whether we use the Vector element antenna
r (k ) = H (k )s(k ) + v(k ) (5) or the MIMO-Octahedron antenna. These results were
where r(k) and s(k) denotes the received and transmitted obtained for a system of HAPs operating at an altitude of
20 km and with a separation angle of 30 degrees, as
signals and H(k) is the frequency response of the channel
shown in Fig. 1.
between N transmitters and M receivers. The noise in the
The capacity achieved by the compact MIMO
system v(k) is assumed to be uncorrelated Gaussian noise.
antennas can be seen from Fig. 3 where the capacity is
By using singular value decomposition (SVD) plotted against the average signal-to-noise ratio of the
technique we can now write the channel matrix H(k) as: system. It is evident from this figure that the MIMO-HAP
H ( k ) = U ( k )Σ ( k ) V H ( k ) (6) diversity system provides superior performance as
compared to the single HAP or SISO (single-input single-
where ∑(k) is an N×N matrix containing the singular output) case, and the MIMO-Octahedron antenna
values that are larger than zero σ1(k) ≥ σ2(k) ≥ … ≥ provides a better capacity than the vector element antenna
σr(k) > 0, where U(k) and V(k) are matrices with the due to the higher number of acquired independent
corresponding vectors as columns. To obtain a channels. It is worth to mention that the electric and
diagonalized system we define: magnetic tripoles on their own did not provide enough
channels to make the HAP diversity work.
y ( k ) = Σ ( k ) x( k ) + n ( k ) (7)
with
y (k ) = U H (k )r (k )
s( k ) = V ( k ) x( k ) (8)
n( k ) = U H (k ) v ( k )
Since the channels in equation (6) are uncorrelated
and the correlation matrix of the noise n(k) is σ n ⋅ I then
2
we can write the theoretical information capacity [6-8] as:
N DFT −1 r
⎛ σ 2 (k ) ⎞
C= ∑ ∑ log
k =0 m =1
2 ⎜1 + σ xm (k ) m 2 ⎟
⎜
⎝
2
σn ⎟ ⎠
(9)
where σ (k ) is the variance of the separate uncorrelated
2
xm
input signals in x(k). The capacity in equation (9) is
constrained by the total radiated power from the Figure 3: The capacity versus the average SNR for a separation angle of
transmitting antennas, defined as: 30 degrees between HAPs.
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4. ACEEE International Journal on Communication, Vol 1, No. 1, Jan 2010
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