ACEEE International Journal on Communication, Vol 1, No. 1, Jan 2010Capacity Evaluation of a High Altitude PlatformDiversi...
ACEEE International Journal on Communication, Vol 1, No. 1, Jan 2010                             II.   THE POLARIZATION CH...
ACEEE International Journal on Communication, Vol 1, No. 1, Jan 2010  The wave propagation channel Hch from the transmitte...
ACEEE International Journal on Communication, Vol 1, No. 1, Jan 2010                       VI.   CONCLUSIONS              ...
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Capacity Evaluation of a High Altitude Platform Diversity System Equipped with Compact MIMO Antennas


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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.

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Capacity Evaluation of a High Altitude Platform Diversity System Equipped with Compact MIMO Antennas

  1. 1. ACEEE International Journal on Communication, Vol 1, No. 1, Jan 2010Capacity Evaluation of a High Altitude PlatformDiversity System Equipped with Compact MIMO Antennas A. Mohammed1 and T. Hult2 1 Department of Signal Processing, Blekinge Institute of Technology, Ronneby, Sweden Email: 2 Department of Electro- and Information Technology, Lund University, Lund, Sweden Email: tommy.hult@eit.lth.seAbstract— In this paper we address the potential gain It has been widely recognized that the capacity inof using compact MIMO antenna array wireless communication systems can be greatly increasedconfigurations in conjunction with High Altitude by exploiting environments with rich scattering such asPlatforms (HAPs) diversity techniques in order to urban areas or indoors [6-9]. Independent spatial orincrease the capacity in HAP communication systems. polarization channels can be accessed by means ofFor this purpose, we also propose a novel compact multiple antennas at both the transmitter and the receiverMIMO antenna which we denote as the “MIMO- and the technique is thus referred to as Multiple-InputOctahedron” and compare its performance with the Multiple-Output (MIMO) system. For a fixed total powervector element antenna. Simulation results show that and bandwidth, and with a matrix transfer function ofthe MIMO-Octahedron antenna provides superior independent complex Gaussian random variables, theperformance to the vector element antenna and the MIMO wireless communication channel has ansingle 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 toMIMO 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 haveaerial platforms operating in the stratosphere. This been also proposed for 3G and broadband applicationsemerging technique is preserving many of the advantages where multipath propagation might be significant. Theof both satellite and terrestrial systems [1-5] and central idea in this paper is to create a virtual MIMOpresently started to attract more attention in Europe system by exploiting the diversity provided by multiplethrough the European Community CAPANINA Project HAPs (see figure 1) in order to increase the capacity inand the recently formed COST 297 Action, in which the HAP communication links. In addition, a number ofauthors are the Swedish representatives in this Cost different compact antenna array configurations, (e.g., theAction. 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 MIMOJournal of Communications and Networking [1] to applications, in which the propagation environment ispromote this technology and the research activities of further utilized to achieve diversity in space andCost 297 to a wider audience. Cost 297 is the largest polarization. Thus, in this paper we also analyse the effectgathering of research community with interest in HAPs of using these different compact MIMO antennaand 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 thespeed 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 begeographical area. One of the main advantages is that the as follows. In Section 2, we give a theoretical backgroundreceived 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 antennassatellite. This allows for a much lower sufficient are presented in Section 3. The basic of MIMO-OFDMtransmitter power which would decrease the size and system and power control are presented in Section 4. Inweight of the repeater equipment carried by the HAP. Section 5, the simulations results of the different MIMOAlso 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]. 1© 2010 ACEEEDOI: 01.ijcom.01.01.01
  2. 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 theelectromagnetic field can be expressed as a multipole diversity setup for the case of three HAPs separated byexpansion [10] of the field emanating from a virtualsphere enveloping the antenna that is being analyzed. the angles θ a,b and θ a,c .This series expansion consist of weighted orthogonal basefunctions on the surface of the virtual sphere and allowfor a solution to Maxwell’s equations that can be writtenas: ⎧ ⎡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 isprojected onto the virtual sphere. The functions gl and flin equation (1) are Hankel functions representing an Each transmit and receive antenna of the systemoutgoing (transmitted) wave or an incoming (received) consists of a special compact MIMO antenna array. Thesewave. The weights aE and aM are the corresponding compact antenna arrays can be of different complexitycoefficients and will give the gain of each orthogonal and design. In Fig. 2a we show the structure of a vectorfunction (mode) for a particular electromagnetic far-field element antenna consisting of three orthogonal electricpattern, 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 rotatingactive on any arbitrary antenna enveloped by a virtual one of the tetrahedrons 60 degrees around the axis goingsphere only by knowing the current distribution J, the through both vertices and finally displace one of thecharge 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 theirthe antenna. The transmitting channel Htx is then assumed own do not provide enough independent antenna ports toas the linear transformation of the input signal x into the be able to utilize the HAP diversity feature which wouldmode domain atx according to α tx = H tx x and for the require at least four independent channels. Thus, thereceiving channel we have a similar transformation from comparison of the capacity is done for the vector elementthe 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 arevectors containing the mode gains for a specific antennatype. III. THE MIMO-HAP DIVERSITY SYSTEM MODEL In this paper we are propose an application for highdata rate transmissions using a system employingmultiple HAPs. This system consists of virtually createdMIMO channels using HAP diversity in combination (a) (b)with the polarization and pattern diversity of a specialtype 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 2© 2010 ACEEEDOI: 01.ijcom.01.01.01
  3. 3. ACEEE International Journal on Communication, Vol 1, No. 1, Jan 2010 The wave propagation channel Hch from the transmitter N DFT −1 rmode 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 distancedependent 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 > 0transmitter 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 ≤0can 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 receiverantenna 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 theN 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 adomain 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 werewhere 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, assignals 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 MIMOsystem 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 thetechnique 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 antennavalues that are larger than zero σ1(k) ≥ σ2(k) ≥ … ≥ provides a better capacity than the vector element antennaσr(k) > 0, where U(k) and V(k) are matrices with the due to the higher number of acquired independentcorresponding vectors as columns. To obtain a channels. It is worth to mention that the electric anddiagonalized 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 uncorrelatedand the correlation matrix of the noise n(k) is σ n ⋅ I then 2we 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 xminput signals in x(k). The capacity in equation (9) isconstrained by the total radiated power from the Figure 3: The capacity versus the average SNR for a separation angle oftransmitting antennas, defined as: 30 degrees between HAPs. 3© 2010 ACEEEDOI: 01.ijcom.01.01.01
  4. 4. ACEEE International Journal on Communication, Vol 1, No. 1, Jan 2010 VI. CONCLUSIONS [4] G. Aranti, A. Iera and A. Molinaro, “The role of HAPs in supporting multimedia broadcast and multicast services in In this paper we have studied the potential gain of terrestrial-satellite integrated systems”, special issue on "Highusing compact MIMO antennas and HAP diversity altitude platform (HAP) systems: technologies and applications", Wireless Personal Communications, 32, Springer, 2005.techniques in order to increase the capacity in HAPcommunication systems. Our results have shown that the [5] G. Chen, D. Grace and T. Tozer, “Performance of multiple high altitude platforms using directive HAP and user antennas”, specialcombined MIMO-HAP diversity system provide issue on "High altitude platform (HAP) systems: technologies andsignificant capacity enhancement compared to the single applications", Wireless Personal Communications, 32, Springer,HAP (SISO) system. Simulation results also show the 2005.performance of our proposed novel compact MIMO- [6] G. J. Foschini and M. J. Gans, “On limits of wirelessOctahedron antenna array is superior to the Vector communications in a fading environment when using multiple antennas”, Wireless Personal Communications, vol. 6, pp. 311-element antenna due to the higher number of acquired 335, 1998.independent channels. Using the vector element antenna [7] I. E. Telatar, “Capacity of multi-antenna Gaussian channels”,will give six independent channels and has also the European Transactions on Telecommunication, vol. 10, no. 6, pp.disadvantage that we have to feed both electric and 585-595, Nov 1999.magnetic dipoles which makes for a more complicated [8] M. Martone, “Multiantenna Digital Radio Transmission”, Artechinterface to the antenna. House Inc., 2002. [9] M. A. Khalighi, J. Brossier, G. Jourdain and M. Raoof, “Water filling capacity of Rayleigh MIMO channels”, 12th IEEE REFERENCES International Symposium on Personal, Indoor and Mobile Radio Communications, vol. 1, pp. 155-158, 1998.[1] A. Mohammed, S. Arnon, D. Grace, M. Mondin, and R. Miura, [10] G. Kristensson, “Spridningsteori med antenn-tillämpningar” "Advanced communications techniques and applications for high- Studentlitteratur, 1999. altitude platforms," Editorial for a Special Issue, EURASIP Journal on Wireless Commun. and Networking, vol. 2008, 2008. [11] S. Nordebo and A. Mohammed, “A semidefinite programming approach to spatial decorrelation of independently polarized signals”, Wileys International Journal of Wireless[2] A. Widiawan, R. Tafazolli, B. Evans, V. F. Milas, V and P. Communications and Mobile Computing (WCMC), vol. 7, Issue 1, Constantinou, “Coexistence of high altitude platform station, pp. 91-101, January 2007. satellite, and terrestrial systems for fixed and mobile services”, [12] M. R. Andrews, P. P. Mitra and R. deCarvalho, “Tripling the International Workshop on High Altitude Platform Systems - capacity of wireless communications using electromagnetic WHAPS 05, Athens, September 5, 2005. polarization”, Nature, vol. 409, pp. 316-318, Jan 2001.[3] V. F. Milas and P. Constantinou, “Interference environment [13] J. B. Andersen and B. N. Getu, “The MIMO Cube - A compact between high altitude platform networks (HAPN), geostationary MIMO antenna”, IEEE 5th International Symposium on Wireless (GEO) satellite and wireless terrestrial systems”, special issue on Personal Multimedia Communications, vol. 1, pp. 112-114, 2002. "High altitude platform (HAP) systems: technologies and applications", Wireless Personal Communications, 32, Springer, 2005. 4© 2010 ACEEEDOI: 01.ijcom.01.01.01