Satellite Communication

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(1)EURASIP Journal on Wireless Communications and Networking. Satellite Communications Guest Editors: Ray E. Sheriff, Anton Donner, and Alessandro Vanelli-Coralli.

(2) Satellite Communications.

(3) EURASIP Journal on Wireless Communications and Networking. Satellite Communications Guest Editors: Ray E. Sheriff, Anton Donner, and Alessandro Vanelli-Coralli.

(4) Copyright © 2007 Hindawi Publishing Corporation. All rights reserved. This is a special issue published in volume 2007 of “EURASIP Journal on Wireless Communications and Networking.” All articles are open access articles distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited..

(5) Editor-in-Chief Luc Vandendorpe, Université Catholique de Louvain, Belgium. Associate Editors Thushara Abhayapala, Australia Mohamed H. Ahmed, Canada Farid Ahmed, USA Alagan Anpalagan, Canada Anthony Boucouvalas, Greece Lin Cai, Canada Biao Chen, USA Yuh-Shyan Chen, Taiwan Pascal Chevalier, France Chia-Chin Chong, South Korea Huaiyu Dai, USA Soura Dasgupta, USA Ibrahim Develi, Turkey Petar M. Djurić, USA Mischa Dohler, France Abraham O. Fapojuwo, Canada Michael Gastpar, USA Alex Gershman, Germany Wolfgang Gerstacker, Germany. David Gesbert, France Fary Z. Ghassemlooy, UK Christian Hartmann, Germany Stefan Kaiser, Germany G. K. Karagiannidis, Greece Chi Chung Ko, Singapore Visa Koivunen, Finland Richard Kozick, USA Bhaskar Krishnamachari, USA S. Lambotharan, UK Vincent Lau, Hong Kong David I. Laurenson, UK Tho Le-Ngoc, Canada Wei Li, USA Yonghui Li, Australia Tongtong Li, USA Zhiqiang Liu, USA Stephen McLaughlin, Scotland Sudip Misra, Canada. Marc Moonen, Belgium Eric Moulines, France Sayandev Mukherjee, USA Kameswara Rao Namuduri, USA Amiya Nayak, Canada A. Pandharipande, The Netherlands Athina Petropulu, USA A. Lee Swindlehurst, USA Sergios Theodoridis, Greece George S. Tombras, Greece Lang Tong, USA Athanasios V. Vasilakos, Greece Weidong Xiang, USA Yang Xiao, USA Xueshi Yang, USA Lawrence Yeung, Hong Kong Dongmei Zhao, Canada Weihua Zhuang, Canada.

(6) Contents Satellite Communications, Ray E. Sheriff, Anton Donner, and Alessandro Vanelli-Coralli Volume 2007, Article ID 58964, 2 pages Multi-Satellite MIMO Communications at Ku-Band and Above: Investigations on Spatial Multiplexing for Capacity Improvement and Selection Diversity for Interference Mitigation, Konstantinos P. Liolis, Athanasios D. Panagopoulos, and Panayotis G. Cottis Volume 2007, Article ID 59608, 11 pages Investigations in Satellite MIMO Channel Modeling: Accent on Polarization, Péter Horváth, George K. Karagiannidis, Peter R. King, Stavros Stavrou, and István Frigyes Volume 2007, Article ID 98942, 10 pages Performance Analysis of SSC Diversity Receivers over Correlated Ricean Fading Satellite Channels, Petros S. Bithas and P. Takis Mathiopoulos Volume 2007, Article ID 25361, 9 pages Advanced Fade Countermeasures for DVB-S2 Systems in Railway Scenarios, Stefano Cioni, Cristina Párraga Niebla, Gonzalo Seco Granados, Sandro Scalise, Alessandro Vanelli-Coralli, and Mar´ıa Angeles Vázquez Castro Volume 2007, Article ID 49718, 17 pages Capacity Versus Bit Error Rate Trade-Off in the DVB-S2 Forward Link, Matteo Berioli, Christian Kissling, and Rémi Lapeyre Volume 2007, Article ID 14798, 10 pages Frequency Estimation in Iterative Interference Cancellation Applied to Multibeam Satellite Systems, J. P. Millerioux, M. L. Boucheret, C. Bazile, and A. Ducasse Volume 2007, Article ID 62310, 12 pages A QoS Architecture for DVB-RCS Next Generation Satellite Networks, Thierry Gayraud and Pascal Berthou Volume 2007, Article ID 58484, 9 pages Maximum Likelihood Timing and Carrier Synchronization in Burst-Mode Satellite Transmissions, Michele Morelli and Antonio A. D’Amico Volume 2007, Article ID 65058, 8 pages Burst Format Design for Optimum Joint Estimation of Doppler-Shift and Doppler-Rate in Packet Satellite Communications, Luca Giugno, Francesca Zanier, and Marco Luise Volume 2007, Article ID 29086, 12 pages TCP-Call Admission Control Interaction in Multiplatform Space Architectures, Georgios Theodoridis, Cesare Roseti, Niovi Pavlidou, and Michele Luglio Volume 2007, Article ID 23923, 8 pages Efficient Delay Tracking Methods with Sidelobes Cancellation for BOC-Modulated Signals, Adina Burian, Elena Simona Lohan, and Markku Kalevi Renfors Volume 2007, Article ID 72626, 20 pages.

(7) Analysis of Filter-Bank-Based Methods for Fast Serial Acquisition of BOC-Modulated Signals, Elena Simona Lohan Volume 2007, Article ID 25178, 12 pages.

(8) Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2007, Article ID 58964, 2 pages doi:10.1155/2007/58964. Editorial Satellite Communications Ray E. Sheriff,1 Anton Donner,2 and Alessandro Vanelli-Coralli3 1 Mobile. and Satellite Communications Research Centre, School of Engineering, Design and Technology, University of Bradford, Richmond Road Bradford BD7 1DP, UK 2 German Aerospace Center, Institute of Communications and Navigation, Oberpfaffenhofen, 82234 Wessling, Germany 3 ARCES, University of Bologna, Via Toffano 2, 40125 Bologna, Italy Received 28 November 2007; Accepted 9 December 2007 Copyright © 2007 Ray E. Sheriff et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.. We are delighted to bring to you this special issue on satellite communications, which we have prepared as part of the spreading of excellence remit of the satellite communications network of excellence (SatNEx). The SatNEx project, which began in 2004, is funded for five years under the European Union’s Sixth Framework Programme (FP6) Information Society Technologies (IST) Thematic Area. Led by the German Aerospace Center, SatNEx brings together a network of 24 partners, distributed throughout Europe, with membership drawn from ten countries. The philosophy underlying the SatNEx approach revolves around the selection of focused actions under Joint Programmes of Activities, which are carried out collectively by the partners and include research, integration, and dissemination activities. Training represents an important part of the SatNEx remit and is supported through a number of initiatives including the hosting of internship projects and an annual summer school. The call for papers resulted in a high number of submissions, from which we have been able to select 12 excellent papers dealing with the different aspects of satellite communications and navigation. Multiple-input multiple-output (MIMO) techniques are attracting a considerable amount of attention from within the terrestrial wireless community. The first paper of this special issue, “Multisatellite MIMO communications at Ku band and above: investigations on spatial multiplexing for capacity improvement and selection diversity for interference mitigation,” considers the application of such technology over a satellite platform operating in the Ku band and above. The paper considers how MIMO can be used to increase capacity by using a satellite spatial multiplexing system and how antenna selection can be used to mitigate interference. The next paper “Investigations in satellite MIMO channel model-. ing: accent on polarization” looks at MIMO systems from the polarization diversity point of view and dwells on the satellite cooperative communication concepts. Switch and stay combining (SSC) is a form of diversity technique used in digital receivers to compensate for fade events introduced by the mobile channel. The third paper “Performance analysis of SSC diversity receivers over correlated Ricean fading satellite channels” investigates the performance of dual-branch SSC receivers for different fading channel characteristics. The next four papers deal with the emerging scenario of mobile digital video broadcasting (DVB-S2 and RCS mobile). Alternative approaches to counteracting fading channels introduced when operating in a train environment receiving satellite DVB-S2 are presented in the paper “Advanced fade countermeasures for DVB-S2 systems in railway scenarios.” Here, as a result of simulation analysis, antenna diversity and packet-level forward error correction mechanisms are proposed and their impact is evaluated with respect to the receiver design and system complexity. The theme of DVB-S2 is continued with the paper “Capacity versus bit error rate trade-off in the DVB-S2 forward link,” which investigates how satellite capacity can be optimised for DVB-S2 transmissions. The DVB return channel via satellite (DVBRCS) is then addressed in “Frequency estimation in iterative interference cancellation applied to multibeam satellite systems,” which considers the application of interference cancellation on the reverse link of a multibeam satellite system, using DVB-RCS with convolutional coding as an example. The paper “A QoS architecture for DVB-RCS next-generation satellite networks” proceeds to design and emulate a qualityof-service (QoS) architecture that demonstrates using real multimedia applications how QoS can be supported over a DVB-RCS network..

(9) 2. EURASIP Journal on Wireless Communications and Networking. Synchronization aspects are dealt with in “Maximum likelihood timing and carrier synchronization in burst-mode satellite transmissions.” The paper addresses the problem of achieving synchronisation for a burst-mode satellite transmission over an AWGN channel. The subject of burst transmission continues with the paper “Burst format design for optimum joint estimation of Doppler-shift and Dopplerrate in packet satellite communications,” which considers optimising the burst-format of packet-oriented transmissions by proposing very-low-complexity algorithms for carrier Doppler-shift and Doppler-rate estimation. A network comprising satellite and high-altitude platforms is considered in the paper “TCP-call admission control interaction in multiplatform space architectures.” Crosslayer techniques are implemented by means of TCP feeding back into call admission control (CAC) procedures for the purpose of prevention of congestion and improvement in QoS. Finally, since navigation is an extremely important part of the satellite system family, we have included two papers. The first paper “Efficient delay tracking methods with sidelobes cancellation for BOC-modulated signals” deals with binary offset carrier (BOC) modulation, which is adopted in typical navigation systems. The paper considers how to improve the tracking of the main lobe of the BOC-modulated signal by using sidelobe suppression techniques. An alternative approach based on filter bank processing is presented in “Analysis of filter-bank-based methods for fast serial acquisition of BOC-modulated signals” to conclude the special issue. ACKNOWLEDGMENTS It has been a pleasure for us to have put together this special issue, which we hope you will find interesting. We would like to thank the editorial staff at Hindawi for their support and assistance during the preparation of this special issue. We would like to thank the contributing authors for the excellent quality of their submissions and our SatNEx colleagues for their valuable assistance in the reviewing of papers. SatNEx is partially funded by the European Commission under the Sixth Framework Programme. Further information on SatNEx can be found on the project web site: http://www.satnex.org/. Ray E. Sheriff Anton Donner Alessandro Vanelli-Coralli.

(10) Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2007, Article ID 59608, 11 pages doi:10.1155/2007/59608. Research Article Multi-Satellite MIMO Communications at Ku-Band and Above: Investigations on Spatial Multiplexing for Capacity Improvement and Selection Diversity for Interference Mitigation Konstantinos P. Liolis, Athanasios D. Panagopoulos, and Panayotis G. Cottis Wireless & Satellite Communications Group, School of Electrical and Computer Engineering, National Technical University of Athens (NTUA), 9 Iroon Polytechniou Street, Zografou, Athens 15780, Greece Received 28 August 2006; Revised 2 March 2007; Accepted 13 May 2007 Recommended by Alessandro Vanelli-Coralli This paper investigates the applicability of multiple-input multiple-output (MIMO) technology to satellite communications at the Ku-band and above. After introducing the possible diversity sources to form a MIMO matrix channel in a satellite environment, particular emphasis is put on satellite diversity. Two specific different topics from the field of MIMO technology applications to satellite communications at these frequencies are further analyzed: (i) capacity improvement achieved by MIMO spatial multiplexing systems and (ii) interference mitigation achieved by MIMO diversity systems employing receive antenna selection. In the first case, a single-user capacity analysis of a satellite 2 × 2 MIMO spatial multiplexing system is presented and a useful analytical closed form expression is derived for the outage capacity achieved. In the second case, a satellite 2 × 2 MIMO diversity system with receive antenna selection is considered, adjacent satellite cochannel interference on its forward link is studied and an analytical model predicting the interference mitigation achieved is presented. In both cases, an appropriate physical MIMO channel model is assumed which takes 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, and the slant path lengths difference. Useful numerical results obtained through the analytical expressions derived are presented to compare the performance of multi-satellite MIMO systems to relevant single-input single-output (SISO) ones. Copyright © 2007 Konstantinos P. Liolis et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.. 1.. INTRODUCTION. 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 of very high data rates at no cost of extra spectrum and transmit power [1, 2]. Wireless communication can be benefited from MIMO signaling in two different ways: spatial multiplexing and diversity. In the former case, independent data is transmitted from separate antennas, and aiming at maximizing throughput (i.e., linear capacity growth with the number of antennas can be achieved). In the latter case, the same signal is transmitted along multiple (ideally) independently fading paths aiming at improving the robustness of the link in terms of each user BER performance. These advantages have been largely responsible for the success of. MIMO both as a research topic and as a commercially viable technology in terrestrial communications [1, 2]. The appealing gains obtained by MIMO techniques in terrestrial networks generate a further interest in investigating the possibility of applying the same principle in satellite networks, as well. However, the underlying differences between the terrestrial and the satellite channels make such applicability a non straightforward matter and, therefore, a rather challenging subject. In this case, one of the fundamental problems is the difficulty of generating a completely independent fading profile over the space segment. In satellite communications, due to the huge free space losses along the earth-space link, line-of-sight (LOS) operation is usually deemed a practical necessity. However, this is not the typical case in terrestrial communications where rich scattering and non-LOS environments with multipath propagation.

(11) 2. EURASIP Journal on Wireless Communications and Networking. are encountered. Thus, placing multiple antennas on a single satellite does not seem a suitable choice in order to exploit the MIMO channel capabilities. In fact, the absence of scatterers in the vicinity of the satellite leads to an inherent rank deficiency of the MIMO channel matrix. Therefore, at a first glance, the applicability of MIMO technology to satellite channels does not seem well justified. The objective of this paper is in line with some other recent research efforts [4–8, 12–16] casting further light in this regard. These studies have been mainly concerned with the possible diversity sources that can be exploited in satellite communications to form a MIMO matrix channel. A categorization of these diversity sources follows. (i) Site diversity, where multiple cooperating terminal stations (TSs), sufficiently separated from each other, are in communication with a single satellite. So far, it has only been studied as an efficient rain fade mitigation technique at the Ku (12/14 GHz), Ka (20/30 GHz), and Q/V (40/50 GHz) frequency bands because of its very low achievable spatial correlation due to rain [3]. However, due to the enormous slant path lengths associated, the required separation distance between the multiple TSs to ensure ideally independent fading profile is of the order of several km, which rather hinders its practical interest in MIMO applications. (ii) Satellite (or orbital) diversity, where multiple satellites, sufficiently separated in orbit to provide (ideally) independently fading channels, communicate with a single TS equipped with either multiple antennas or even a single multiple-input antenna. So far, it has been studied mostly as an efficient rain fade mitigation technique in Ku-, Ka-, and Q/Vband satellite communications [3] and, also, recently, as a candidate to form satellite MIMO matrix channels at high (i.e., Ku, Ka, and Q/V) [4, 5] as well as at low frequency bands, such as L (1/2 GHz) and S (2/4 GHz) [6–8]. Also, it is worthwhile noting that it is already successfully employed in the continental US digital audio radio services (DARS), mobile systems, Sirius and XM satellite radio, operating at the S-band [9]. Satellite diversity provides a rather practical solution of reasonable complexity since the multiple received signals at the single TS can easily be combined due to the colocation of the antennas. However, an inherent problem of this scheme, apart from the costly utilization of multiple satellites, is the asynchronism of the multiple transmitted signals at the TS receiver, which comes as a result of the propagation delay difference due to the wide separation between the satellites. A similar problem is dealt with and solutions are proposed in several papers mainly concerning distributed sensor networks, such as in [10]. To the authors’ knowledge, for the more complicated satellite case—due to the much larger and variable delay difference—the only relevant solution proposed so far is reported in [5]. (iii) Polarization diversity, where a single dual-orthogonal polarized satellite communicates with a single TS equipped with a dual-orthogonal polarized antenna. Its principle is based on the polarization sensitivity of the reflection and diffraction processes, which causes random signal fading at the TS receiver. It represents a solution of rather practical interest due to the recent developments in MIMO compact. antennas (see, e.g., [11]) which allow for compact MIMO setups. It has already been examined as a promising solution to shape MIMO channels in S-band land mobile satellite communications [7, 12–16]. Its main advantage over satellite diversity is the elimination of any additional cost associated with the utilization of multiple satellites. It also bypasses the asynchronism problem associated with the distributed nature of satellite diversity. However, it can be disadvantageous to satellite diversity especially in satellite networks operating at high-frequency bands (i.e., Ku, Ka, and Q/V), which are affected by the highly correlated rainfall medium and, also, in case of large blockages resulting in hard system failures (i.e., on/off channel phenomena). Moreover, as concluded in [13], polarization diversity can only increase the transmission rate of a satellite communication system by a factor of two, whereas in multi-satellite systems, satellite diversity can result in m-fold capacity increase, where m is the number of satellites occupied. This paper focuses particularly on dual-satellite MIMO communication systems employing satellite diversity. Moreover, emphasis is put on the less congested high-frequency bands, such as Ku and above. At these frequencies, multipath propagation is insignificant. However, by virtue of satellite diversity, MIMO can be considered to effectively exploit the rainfall spatial inhomogeneity instead. A physical 2 × 2 MIMO satellite channel model is assumed taking into account the relevant propagation phenomena, such as clear LOS operation, high antenna directivity, rain fading, and rainfall spatial inhomogeneity [3, 17]. This 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 [18] and is based on general assumptions about the rain process [17]. Moreover, it incorporates the general case of an ordered MIMO satellite channel (due to the slant path lengths difference). To this end, the resulting propagation delay offset is assumed to be properly taken into account at the TS receiver. A possible practical solution to this problem might be the one implemented in [5] according to which matched filters are first 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 signal parallel-to-serial converter. The study of more efficient solutions to 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. In the first part of this work, emphasis is put on a satellite 2 × 2 MIMO spatial multiplexing system and on its possible capacity improvement with respect to the relevant SISO system. The term “spatial multiplexing” refers to the transmission of independent data streams from the multiple separate satellites [1, 2]. Well-known results obtained from the MIMO literature [19, 20] are applied here for the capacity analysis of such a 2 × 2 MIMO system. The figure of merit used to characterize the resulting MIMO fading channel is the outage capacity [1], for which an analytical closed form expression is provided. Note that such analytical expressions are extremely hard to obtain even in the well-established field.

(12) Konstantinos P. Liolis et al.. 3. S1. S2. To S1. To S2. d2 , AR2. d1 , AR1. Δθ ϕ1 TS. ϕ2. TS. (a). (b). Figure 1: (a) Configuration of a dual-satellite 2 × 2 MIMO channel. Individual satellites S1 and S2 transmit either independent data streams (MIMO spatial multiplexing system, Section 3) or the same signal over the multiple (ideally) independently fading paths (MIMO diversity system, Section 4), (b) associated elevation angles.. of MIMO theory due to the intractability of the outage capacity distribution [2]. In the second part, a satellite 2 × 2 MIMO diversity system employing receive antenna selection is examined, and issues specifically related to cochannel interference (CCI) are addressed from a propagation point of view. The term “diversity” refers to the transmission of the same signal over the multiple (ideally) independently fading paths [1, 2]. Receive antenna selection is a low-cost, low-complexity approach to benefit from many of the advantages of MIMO technology while, at the same time, bypassing the multiple RF chains associated with multiple antennas at the receiver, which are costly in terms of size, power, and hardware [21]. The interference analysis presented here is quite different from conventional communication-oriented approaches followed in standard MIMO theory [1]. Attention is paid to the CCI problems arising on the forward link of such a 2 × 2 MIMO satellite system due to differential rain attenuation from an adjacent satellite [22]. To deal with the statistical behaviour of the signal-to-interference ratio (SIR) introduced by the rainfall spatial inhomogeneity, the concept of unacceptable interference probability1 [23, 24] is employed here. An analytical prediction model concerning the interference mitigation achieved by the proposed satellite 2 × 2 MIMO diversity system is provided. The rest of the paper is organized as follows. Section 2 presents the channel model adopted for MIMO satellite communications at the Ku-band and above. Section 3 provides a communication-based capacity analysis for a satellite 2 × 2 MIMO spatial multiplexing system. A propagation-oriented. analysis for the possible interference mitigation achieved by a satellite 2 × 2 MIMO diversity system with receive antenna selection is presented in Section 4. Useful numerical results obtained for both the above satellite MIMO applications considered are provided in Section 5. Section 6 concludes the paper. 2.. MIMO SATELLITE CHANNEL MODEL. Figure 1 depicts the configuration of a dual-satellite MIMO communication channel at the Ku-band and above. The TS is equipped with two colocated highly directive antennas and communicates with two satellites, S1 and S2 , subtending an angle Δθ to the TS, large enough that the spatial correlation due to rain along the relevant slant paths is as low as possible. The normalized radiation pattern of each TS antenna, denoted by GR (·), is compatible with the ITU-R specifications [25] and is shown in Figure 2.2 The lengths of slant paths Si -TS are denoted by di (i = 1, 2) and the random variables (RVs) associated with the respective rain induced attenuations (in dB) are denoted by ARi (i = 1, 2). In general, the two slant paths Si -TS have different elevation angles denoted by φi (i = 1, 2), respectively. Assuming that clear LOS between the TS and each satellite Si exists, that each TS antenna is at boresight with the corresponding satellite Si (i = 1, 2) and that rain attenuation is the major fading mechanism, the path gain for each Si -TS link is modeled as . gi ∝ GR 0◦ · di−2 · 10−AR i /10 1. Note that the concept of the “unacceptable interference probability (UIP)” in this paper is exactly the same as that of the “acceptable interference probability (AIP)” employed in [23, 24]. Their only difference concerns their nomenclature.. 2. (i = 1, 2).. (1). Note that the analyses presented hereafter are quite general and, therefore, may incorporate other TS antenna radiation patterns, as well..

(13) 4. EURASIP Journal on Wireless Communications and Networking 1 Spatial correlation coefficient due to rain, ρ12. TS antenna normalized gain, GR (dB). 0 −5 −10 −15 −20 −25 −30 −35 −40 −100 −80 −60 −40 −20. 0 20 40 Off-axis angle (deg). 60. 80. 0.8 0.7 0.6 0.5 0.4 0.3. 100. Figure 2: Normalized radiation pattern of each TS antenna compatible with ITU-R specifications [25].. 0.9. 0. 20. 40. 60 80 100 120 140 Angular separation, Δθ (deg). 160. 180. Figure 3: Spatial correlation coefficient due to rain ρ12 versus angular separation Δθ for a dual-satellite MIMO channel operating in Atlanta, GA, at the Ka-band with satellite elevation angles φ1 = 45◦ and φ2 = 40◦ .. Hence, the total path loss along each Si -TS link (in dB) is Ai = FSLi + ARi. (i = 1, 2),. (2). where FSLi = 10 log10 (4πdi is the free space loss along each link, c the speed of light, and f the operating frequency. Note that the fundamental assumptions concerning the modeling of the rain attenuation RVs ARi (i = 1, 2) are the same as those analytically presented in [17]. The convective raincell model employing Crane’s assumptions is used for the description of the vertical variation of the rainfall structure [17]. Based on this assumption, if Δθ is sufficiently large, the spatial correlation coefficient between the RVs ARi is relatively low and, thus, an (ideally) decorrelated MIMO satellite channel is possible. To this end, an illustrative quantitative example is presented in Figure 3, which depicts the spatial correlation coefficient due to rain ρ12 versus Δθ for a dual-satellite MIMO channel operating in Atlanta, GA, USA at the Ka-band with satellite elevation angles φ1 = 45◦ and φ2 = 40◦ . Based on the above and, also, assuming frequency nonselective fading, the resulting MIMO channel matrix H is given by f /c)2. . h h H = 11 12 h21 h22 ⎡. √. 3.. SATELLITE MIMO SPATIAL MULTIPLEXING SYSTEM: CAPACITY ANALYSIS. In this Section, the two satellites Si (i = 1, 2) depicted in Figure 1 are assumed to transmit different and independent data streams (i.e., spatial multiplexing is investigated). The channel H is considered perfectly known to the TS receiver (via training and tracking), while at the transmit side, both satellites are assumed to have no channel knowledge. In the absence of channel state information (CSI) at the transmit side, equal power allocation to the two satellites is a reasonable and rather practical choice, due to the distributed nature of the system. Therefore, from the standard MIMO theory, the following well-known formula for the capacity (in bps/Hz) of MIMO channels is adopted [19, 20]:. . ⎢ g1 exp. =⎢ ⎣. (i = 1, 2). Finally, the assumption of independent identically distributed (i.i.d) elements of H, often made in conventional terrestrial MIMO systems, cannot be made here, since there is a relatively high spatial correlation due to rain.. j2πd1 f c. 0. ⎤. 0. √. g2 exp. j2πd2 f c. ⎥. ⎥ ⎦.. C = log2 det I2 + (3). The diagonal structure of H is due to the high directivity of the TS antennas and the large value of Δθ. In MIMO terminology, channels with diagonal H matrix are known as parallel MIMO channels. Further details about such channels can be found in [26]. Moreover, as opposed to standard MIMO theory [1, 2], H is not normalized here (i.e., ordered MIMO channel) due to the different slant path lengths di. PT P HHH = log2 1 + T λi , 2N0 2N 0 i=1 2. (4) where I2 is the 2 × 2 identity matrix, PT the total average power available at the transmit side,3 N0 the noise spectral 3. Note that PT is the sum transmit power of all transmitting satellites Si regardless of their number. This means that in both the dual-satellite MIMO case and the single satellite SISO case, the total available transmit power is constant and equal to PT . This is ensured employing the normalization factor “2” in (4), which allows for a fair comparison between the relevant MIMO and SISO cases..

(14) Konstantinos P. Liolis et al.. 5. density at the TS receiver input, and λi (i = 1, 2) the positive eigenvalues of the matrix HHH (the superscript H stands for conjugate transposition). Taking into account the channel modeling assumptions, (4) is written as 2 . C=. i=1. . . log2 1 + 0.5SNRCSi 10−ARi /10 ,. d2 . d1. (6). Equation (5) provides an expression for the instantaneous capacity of a deterministic 2 × 2 MIMO channel H. However, since the rainfall introduces slow fading and stochastic behaviour over the channel H, the appropriate statistic measure to characterize the resulting fading channel is the outage capacity defined by [1] . . P C ≤ Cout,q = q,. (7). where Cout,q is the information rate guaranteed for (1− q)100% of the channel realizations. Consider the RV transformation . ui =. . . . ln ARi − ln AmRi SaRi. . (i = 1, 2). (8). which relates the lognormal rain attenuation RVs ARi (i = 1, 2) to the normalized normal RVs ui (i = 1, 2). Substituting (5) into (7) and after some straightforward algebra, the following analytical closed form expression for the outage capacity is obtained: . P C ≤ Cout,q =. 1 2. . +∞ uA. . uB − ρn12 u1 du1 fU1 u1 erfc 2 2 1 − ρn12. = q,. (9) where erfc(·) is the complementary error function, fU1 (u1 ) the probability density function (pdf) of the normal distribution, ρn12 the logarithmic correlation coefficient between the normal RVs ui (i = 1, 2) [17] and uA , uB are analytically given by . . . . . uA = ln 10 log10 0.5SNRCS2 − 10 log10 2Cout,q − 1. . − ln AmR2 SaR2 ,. . . . uB = ln 10 log10 0.5SNRCS1 . . (10). . + 10 log10 1 + 0.5SNRCS2 10−AmR2 exp(u1 SaR2 )/10. . − 10 log10 2Cout,q − 1 − 0.5SNRCS2 10−AmR2 exp(u1 SaR2 )/10 SaR1 . − ln AmR1. (11). . Hi exp b2 S2r − 1 (i = 1, 2), L2Di 2 2 b Sr − S2aRi. = aRbm LDi exp (i = 1, 2), 2. S2aRi = ln 1 +. (5). where SNRCSi (i = 1, 2) are the nominal SNR values under clear sky conditions. Based on the path gain model given in (1), the SNRCSi values (in dB) are related through SNRCS1 − SNRCS2 = 20 log10. The quantities AmRi , SaRi (i = 1, 2), encountered in (8)–(11), are the statistical parameters of the lognormal RVs ARi (i = 1, 2) given by [17]. AmRi. (12). where LDi (i = 1, 2) are the projections of the effective path lengths Li (i = 1, 2) [17] on the earth surface, Hi (i = 1, 2) are spatial parameters related to each path of length LDi (i = 1, 2) which may be found in [17], and a, b are constants depending on the operating frequency f , the polarization tilt angle, the temperature, and the rainfall characteristics over the serviced area. Rm , Sr are the lognormal statistical parameters of the rainfall rate R (in mm/hr). A reliable database of rainfall statistics for any geographical location on earth is provided by ITU-R in [18] and is used throughout the present work as an input to the simulations performed in order to determine the values of Rm , Sr . 4.. SATELLITE MIMO DIVERSITY SYSTEM WITH RECEIVE ANTENNA SELECTION: INTERFERENCE ANALYSIS. In this section, the two satellites Si (i = 1, 2) depicted in Figure 1 are assumed to transmit the same signal over the (ideally) independently fading paths Si -TS (i = 1, 2) (i.e., diversity is investigated). To alleviate the high cost and complexity associated with multiple RF chains, the dual-antenna TS receiver is equipped with only one RF chain and performs antenna selection, that is, the 2 × 2 MIMO satellite system assumed employs receive selection diversity [21]. Therefore, the TS receiver detects the signal related to the path with the highest SNR. Under the constraint of only one RF chain at the receiver, in order to know all SNRs simultaneously for optimal selection, a training signal in a preamble to the transmitted data is assumed. During this preamble, the TS receiver scans the two antennas, finds that one with the highest SNR, and selects it for reception of the next data burst. Thus, only a few more training bits are required instead of additional RF chains. Particular emphasis is put on possible interference mitigation offered by the proposed satellite 2 × 2 MIMO diversity system. In this regard, a propagation-based analysis is performed which is quite different from conventional communication-oriented approaches followed in standard MIMO theory [1]. Specifically, the effect of rainfall on the interference analysis is taken into account and the differential rain attenuation related to an adjacent satellite is considered as the dominant cause of the SIR degradation [22]. Such an interference problem is further aggravated due to the spatial inhomogeneity of the rainfall medium. It constitutes a typical interference scenario, especially over congested urban areas, where the increased demand for link capacity and radio coverage imposes the coexistence of many satellite radio links over the same geographical and spectral area. In the following, an analytical prediction model is presented, which.

(15) 6. EURASIP Journal on Wireless Communications and Networking S1. S3. S2. To S3 To S2. To S1 d3 , AR3. d1 , AR1. d2 , AR2. Δψ Δθ ϕ1 TS. ϕ3 ϕ2. TS. (a). (b). Figure 4: (a) Configuration of the satellite 2 × 2 MIMO diversity system assumed and the interference scenario on its forward link, (b) associated elevation angles.. quantifies the adjacent satellite CCI mitigation achieved by the proposed 2 × 2 MIMO system with respect to the corresponding SISO one. Figure 4 depicts the configuration of the assumed interference scenario on the forward link of a satellite 2 × 2 MIMO diversity system operating at the Ku-band and above and employing receive antenna selection. The satellites S1 and S2 constitute the dual-satellite transmit part of the MIMO system also depicted in Figure 1. Another cochannel satellite (denoted by S3 ), which may belong to either the same or to another satellite network, is close in orbit to S1 . Thus, CCI problems may arise on the forward link of the 2 × 2 MIMO satellite system. S1 and S3 subtend an angle Δψ to TS. The length of the slant path S3 -TS is denoted by d3 , while its elevation angle is φ3 . The RV associated with the rain induced attenuation along the interfering path S3 -TS (in dB) is denoted by AR3 . Due to selection diversity at the TS receiver, the antenna with the maximum SNR is selected. In mathematical terms, the same statement is expressed as . . . . SNRout = max SNR1 , SNR2 ⇐⇒ Aout = min A1 , A2 , (13) where SNRi = SNRCSi − ARi (i = 1, 2) is the SNR at each TS antenna under rain fades and Ai (i = 1, 2) the total path loss along each Si -TS link (i = 1, 2). SNRout corresponds to Aout which determines the output of the selection combiner at every instant. The proposed scheme requires only the knowledge of the wanted signals’ channels at the receiver, whereas knowledge of the interferer’s channel is not necessary. Moreover, no CSI is required at the transmit side. If Md denotes the diversity system margin associated with the system availability pavail (see the appendix), the satellite MIMO diversity system is considered available when the probabilistic event . Ω = Aout < Md. . (14). is true. Assuming that . Ωi = Ai < Md , Ai < A j. . . . (i, j) = (1, 2), (2, 1). (15). denotes the event that “the TS is serviced by the corresponding satellite Si (i = 1, 2),” it becomes clear that, due to selection diversity, Ω = Ω1 ∪ Ω 2 , Ω1 ∩ Ω2 = ∅ .. (16). Therefore, the probability that the system is available (see the appendix) can be expressed as . . . . P(Ω) = P Ω1 + P Ω2 .. (17). While the satellite 2 × 2 MIMO diversity system is available (i.e., when either Ω1 or Ω2 are true), it might suffer from CCI originating from the adjacent satellite S3 . If SIRd and rd denote the SIR and the minimum acceptable SIR threshold of the MIMO diversity system, respectively (both measured at the output of the TS selection combiner), the probability of the event that “the system is interfered while being available” can be mathematically expressed based on the above considerations as . . UIPd = P SIRd < rd , Ω. = P SIRd1 < rd , Ω1 + P SIRd2 < rd , Ω2. (18). = P1 + P2 ,. where UIPd is the so-called unacceptable interference probability (UIP) [23, 24], and the quantities SIRdi (i = 1, 2) are expressed (in dB) as SIRd = SIRdi = SIRCSi − ARi + AR3. (i = 1, 2).. (19). In (19), SIRCSi (i = 1, 2) is the nominal SIR value under clear sky conditions. In propagation terminology, ARi − AR3.

(16) Konstantinos P. Liolis et al.. 7. (i = 1, 2) is known as the differential rain attenuation (DRA) [22]. Based on (19), when DRA becomes sufficiently large due to the spatial inhomogeneity of the rainfall medium, severe CCI problems may arise aggravating the SIRd distribution on the forward link of the proposed satellite 2 × 2 MIMO diversity system. To this end, UIPd is proposed as an efficient metric to deal with the statistical behaviour of the SIRd and, together with rd , they constitute a pair of design specifications concerning interference. Every user must comply with these specifications, given the QoS specified by the event Ω related to the system availability (see the appendix). The quantities SIRCSi (i = 1, 2) encountered in (19) are given by . SIRCSi = SIR∗i − GR θi. (i = 1, 2),. (20). where θi (i = 1, 2) are the off-axis angles formed by the interfering link S3 -TS and the wanted links Si -TS (i = 1, 2) in the radiation pattern of the TS antennas. From Figure 4, it follows that θ1 = Δψ and θ2 = Δθ − Δψ. Also, in (20), SIR∗i (i = 1, 2) are the relevant SIR values of the interfered links Si -TS (i = 1, 2) when θi = 1◦ , and correspond to the nominal CCI levels. Based on the channel model assumed, their interrelationship is defined through (6) by simply substituting the SNRCSi by SIR∗i . Extending the transformation given in (8) to include also the interfering link S3 -TS (i.e., for i = 1, 2, 3) and making the channel modeling assumptions, the probabilities Pi (i = 1, 2) encountered in (18) after some straightforward algebra are evaluated, that is, Pi =. +∞. uDi. du1. uCi. u1. . × 1−. . . du2 fU1 U2 u1 , u2. uEi − μ3/1,2 1 erfc √ 2 2σ3/1,2. . (21) (i = 1, 2),. where fU1 U2 (u1 , u2 ) is the pdf of the two-dimensional joint normal distribution. For i = 1, 2, the rest of the parameters encountered in (21) are . . . . ln xdi − ln AmRi uCi = SaRi ⎧ ⎪ ⎪ ⎨0, . . . xdi = ⎪ SIRCSi − rd cos φi , ⎪ ⎩M − FSL cos φ , d i i . uDi =. ln. . uEi = ln. . . , rd > SIRCSi , SIRCSi +FSLi − Md<rd ≤ SIRCSi , rd ≤ SIRCSi + FSLi − Md , . . Md − FSLi cos φi − ln AmRi SaRi. . . . . ,. exp ui SaRi AmRi − SIRCSi + rd cos φ3 cos φi. SaR3 . − ln AmR3. the other two normal RVs u1 , u2 and can be expressed in terms of the logarithmic correlation coefficients ρni j ((i, j) = (1, 2), (1, 3), (2, 3)) as [17, 27] μ3/1,2 = 2 σ3/1,2. 5.. ρn23 − ρn12 ρn13 ρn13 − ρn12 ρn23 u1 + u2 , 2 2 1 − ρn12 1 − ρn12. 2 2 2 1 − ρn12 − ρn13 − ρn23 + 2ρn12 ρn13 ρn23 = . 2 1 − ρn12. (23). NUMERICAL RESULTS AND DISCUSSION. The previous analyses have been applied for the prediction of possible capacity improvement and interference mitigation achieved by the proposed satellite 2 × 2 MIMO spatial multiplexing and diversity systems, respectively, and for comparison to the relevant SISO cases. To this end, the baseline configuration scenario considers a TS located in Atlanta, GA, and communicating with geostationary satellites S1 (φ1 = 45◦ ) and S2 (φ2 = 40◦ ). The angular separation assumed is Δθ =40◦ , which results in a spatial correlation coefficient of rain attenuation ρ12 = 0.6 (see Figure 3). Moreover, regarding the interference scenario, an adjacent geostationary satellite S3 (φ3 = 45◦ ), separated from S1 by Δψ =10◦ , is considered to cause CCI problems on the forward link of the satellite 2 × 2 MIMO diversity system. First, the validity of the proposed analytical model in (9), predicting the outage capacity achieved by a satellite 2 × 2 MIMO spatial multiplexing system, is numerically verified. The effect of various geometrical and operational system parameters on the outage capacity distribution is also examined. Figure 5 shows the dependence of the 1% outage capacity of the assumed 2 × 2 MIMO satellite system on the SNR.4 The baseline configuration scenario is adopted, whereas the operating frequency band assumed is Ka (i.e., f = 20 GHz). For the sake of comparison, the capacity of the relevant SISO system is also plotted. Together with the analytical results obtained from the analytical closed form expression in (9), Monte Carlo simulation results are also plotted for verification. The agreement observed between the analytical and the simulation results is very good over the whole SNR range. As can be seen, the difference between the relevant MIMO and SISO curves diminishes at very low SNR levels while it becomes significant as the SNR increases. As an illustration, for SNR = 10 dB, the spectral efficiency achieved by the MIMO system is 4.84 bps/Hz, whereas the one achieved by the SISO system is 3.23 bps/Hz. This constitutes, approximately, a 50% increase in user data rate obtained by MIMO spatial multiplexing. For SNR = 20 dB, the respective performance figures obtained are 10.95 bps/Hz and 6.41 bps/Hz corresponding to, approximately, a 71% increase in user data. (22) AmRi , SaRi (i = 1, 2, 3) are analytically given in (12). Furthermore, μ3/1,2 and σ3/1,2 are the statistical parameters of the conditional distribution of the normal RV u3 given. 4. Note that the clear sky SNR of strong eigenmode, SNRCS1 , has been particularly considered. However, due to the enormous slant path lengths associated, the resulting difference between SNR CSi (i = 1, 2) is minimum see (6) and, therefore, any of the two SNRCSi can be used as x-coordinates..

(17) 8. EURASIP Journal on Wireless Communications and Networking 18. 1% outage capacity (bps/Hz). 16 14 12 2 × 2 MIMO. 10 8. SISO. 6 4 2 0. 0. 5. 10. 15 SNR (dB). 20. 25. 30. Analytical expression (9) Monte Carlo simulation. Figure 5: 1% outage capacity versus SNR for a satellite 2 × 2 MIMO spatial multiplexing system. Relevant SISO case is also plotted for comparison. Verification of analytical closed form expression in (9) through Monte Carlo simulation. 18. Outage capacity achieved by 2 × 2 MIMO system (bps/Hz). 16 14 12 10 8 6 4 2 0. 0. 5. 10. 15. 20. 25. 30. SNR (dB) q = 1%, Δθ = 40◦ , Ka-band, Atlanta q = 0.1%, Δθ = 40◦ , Ka-band, Atlanta q = 1%, Δθ = 40◦ , Ku-band, Atlanta q = 1%, Δθ = 40◦ , Ka-band, Singapore q = 1%, Δθ = 60◦ , Ka-band, Atlanta. Figure 6: Outage capacity versus SNR for a satellite 2 × 2 MIMO spatial multiplexing system. Effect of capacity outage probability q, angular separation Δθ, operating frequency f , and climatic conditions over the serviced area.. rate. Therefore, the capacity gain obtained by the proposed satellite 2 × 2 MIMO spatial multiplexing system over the SISO system turns out to be significant for no additional transmit power or bandwidth expenditure. Figure 6 shows the dependence of the outage capacity achieved by a satellite 2 × 2 MIMO spatial multiplexing sys-. tem on the SNR, the angular separation Δθ, the operating frequency f , the capacity outage probability q, and the climatic conditions over the serviced area. All the results presented here have been obtained employing (9). The baseline configuration scenario is adopted. The rest of the relevant parameters assumed as well as the deviations from the baseline scenario are indicated on Figure 6. As can be seen, as either q decreases or f increases or as the rain conditions over the serviced area become heavier, the rain fading becomes more severe and, therefore, the outage capacity achieved by the 2 × 2 MIMO satellite system decreases. Moreover, as the angular separation Δθ increases (from 40◦ to 60◦ ), the spatial correlation coefficient due to rainfall medium ρ12 decreases correspondingly (from 0.6 to 0.5, see Figure 3), and the outage capacity achieved increases. In the following, the proposed analytical model in (21) predicting the interference mitigation achieved by a satellite 2 × 2 MIMO diversity system with receive antenna selection is numerically verified. The effect of various geometrical and operational system parameters on the forward link SIR distribution is also examined. Figure 7 shows the dependence of the UIP of the assumed 2 × 2 MIMO satellite system on the SIR, the system availability pavail , and the operating frequency band. Particularly, two different values of system availability, pavail = 99.9% and 99.99%, and two different operating frequencies, f = 12 GHz and 20 GHz, are assumed. For the sake of comparison, the UIP of the relevant SISO systems is also plotted. The baseline configuration scenario is adopted. The nominal CCI level assumed is SIR∗1 = 20 dB, whereas the rest of the parameters encountered in the interference analysis are indicated on Figure 7. It is obvious that, due to rain, an SIR degradation is observed for the same UIP level, which becomes more severe as either pavail or f increases. This further indicates that satellite systems operating at higher availabilities or at higher-frequency bands are more sensitive to interference. The SIR improvement achieved by the satellite 2 × 2 MIMO diversity system over the SISO one is significant, especially for high pavail and high f . As an illustration, for UIP = 0.001%, the interference mitigation obtained is 0.67 dB at the Ka-band and for a 99.9% availability, 1.60 dB at the Ku-band and for a 99.99% availability, and 3.52 dB at the Ka-band and for a 99.99% availability. Figure 8 quantifies the SIR improvement achieved by a satellite 2 × 2 MIMO diversity system employing receive antenna selection with respect to the relevant SISO one. Specifically, the difference (in dB) between the respective SIR thresholds achieved at the TS receiver input for UIP = 0.001% is plotted versus the angular separation Δθ. Two areas with different climatic conditions are considered, Atlanta, GA, and Athens, Greece. The operating frequency, system availability, and nominal CCI level assumed are 20 GHz, 99.99%, and SIR∗1 = 20 dB, respectively, while the rest of the parameters are the same as those of the baseline configuration scenario. As Δθ increases, the interference mitigation level achieved becomes higher. Moreover, it can easily be observed that the SIR improvement obtained in Atlanta,.

(18) Konstantinos P. Liolis et al.. 9 100 Unacceptable interference probability (UIP). Unacceptable interference probability (UIP). 100 10−1 10−2 Ka-band, pavail = 99.9%. 10−3 Ku-band, pavail = 99.99%. 10−4. Ka-band, pavail = 99.99%. 10−5 10−6. 2. 4. 6. 8. 10 12 SIR (dB). 14. 16. 18. SIR improvement achieved through MIMO diversity (dB). Δψ = 5◦. 10−4 10−5. 7. 9. 11. 13. 15. 17. 19 20. SISO 2 × 2 MIMO. 2.5 Atlanta, GA. 1.5. 1. 0.5 Athens, GR 30. Δψ = 4◦. 10−3. SIR (dB). Figure 7: UIP versus SIR for a satellite 2 × 2 MIMO diversity system employing receive antenna selection. Relevant SISO case is also plotted for comparison. Effect of system availability pavail , operating frequency f , and rain climatic conditions over the serviced area.. 0 20. 10−2. 10−6. 20. SISO 2 × 2 MIMO. 2. 10−1. 40 50 60 70 Angular separation, Δθ (deg). 80. 90. Figure 8: SIR improvement achieved by a satellite 2 × 2 MIMO diversity system with receive antenna selection over the relevant SISO system versus angular separation Δθ. Effect of rain climatic conditions over the serviced area.. GA, is much higher than that in Athens, Greece, due to the corresponding heavier rain conditions. For various obvious reasons, there is a tendency to place satellites in orbit close to each other. Due to the increased CCI, adjacent satellite networks cannot usually operate under certain SIR specifications. The proposed MIMO diversity system may overcome this problem by adequately increasing SIR in the presence of adjacent CCI. To demonstrate this, a satellite 2 × 2 MIMO diversity system together with its relevant SISO case are considered in Figure 9. The input parame-. Figure 9: UIP versus SIR for a satellite 2 × 2 MIMO diversity system employing receive antenna selection. Relevant SISO case is also plotted for comparison. Effect of angular separation ΔΨ.. ters assumed are the same as those in the baseline configuration scenario, with the exception of a different angular separation Δψ, that is, Δψ = 5◦ is now assumed. Operation of the system at the Ka-band and for a 99.99% availability is considered. To obtain the necessary QoS for UIP = 0.001%, suppose that an SIR threshold of 10 dB must be overcome. In the SISO case, when the angular separation between the wanted satellite S1 and the adjacent interfering one S3 is Δψ = 5◦ , an SIR level of 11.2 dB is obtained for UIP = 0.001%, thus satisfying the QoS requirement. If the interfering satellite S3 is closer in orbit to S1 , so that their angular separation is reduced to Δψ = 4◦ , the SIR level in the SISO case falls down to 9.8 dB, thus failing to satisfy the QoS requirement. Employing the proposed 2 × 2 MIMO satellite system, the SIR achieved when Δψ = 4◦ is 11.32 dB, thus remaining above the QoS threshold. This is another advantage of the proposed satellite MIMO diversity system, allowing the closer installation of satellites in orbit. 6.. CONCLUSIONS. In this paper, the applicability of MIMO technology to satellite communication systems operating at the Ku-band and above is investigated. Emphasis is put on satellite diversity as a potential candidate to form a MIMO matrix channel in the satellite environment. The relevant propagation phenomena at the frequencies of interest have been considered through an appropriate physical channel model, which takes into account clear LOS operation, high antenna directivity at the TS receiver, the effect of rain fading, and the slant path lengths difference. Also, as it may accept physical inputs from the ITU-R rainmaps, it is flexible and can be applied on a global scale..

(19) 10. EURASIP Journal on Wireless Communications and Networking. Useful analytical results are presented for two different applications of MIMO technology: (i) capacity improvement in a satellite 2 × 2 MIMO spatial multiplexing system, (ii) interference mitigation in a satellite 2 × 2 MIMO diversity system with receive antenna selection. In the first application, significant capacity gains of the MIMO system over the relevant SISO one are demonstrated, especially for moderate and high SNR levels. The practical case when no CSI is available at the transmitters of the two individual satellites is considered. A useful closed form expression for the outage capacity achieved by 2 × 2 MIMO satellite systems is provided and successfully verified through Monte Carlo simulations. Such an expression is extremely hard to obtain even in the well-established field of MIMO theory, is applicable over a large SNR range, and can incorporate the effect of various geometrical and operational system parameters on the outage capacity distribution. In the second application, the receive antenna selection scheme employed in the satellite MIMO system assumed is considered to counteract CCI problems over its forward link. SIR gain of several dB is demonstrated in the numerical results. An analytical propagation model for the calculation of the interference mitigation achieved is presented, which is flexible and can incorporate the influence of various geometrical and operational system parameters on the SIR distribution. APPENDIX CALCULATION OF SATELLITE 2 × 2 MIMO DIVERSITY SYSTEM MARGIN Md Every user in the assumed satellite 2 × 2 MIMO diversity system employing receive antenna selection must comply with a certain availability percentage pavail related to a diversity system margin Md : . pavail · 100% = P(Ω) = P Aout < Md. . = P min A1 , A2 < Md = 1 − P A1 > Md , A2 > Md = 1 − P AR1 > Md − FSL1 , AR2 > Md − FSL2 .. (.1) Considering the transformation given in (8), relating the lognormal rain attenuation RVs ARi (i = 1, 2) to the normalized normal RVs ui (i = 1, 2), and the channel modeling assumptions, pavail is expressed as pavail · 100% = 1 − where uFi =. . ln. . +∞. +∞ uF1. . du1. uF2. . . . du2 fU1 U2 u1 , u2 , . Md − FSLi cos φi − ln AmRi SaRi. (.2). . (i = 1, 2). (.3). After straightforward algebra, (.2) yields pavail · 100% = 1 − 0.5. +∞ uF1. . . uF2 − ρn12 u1 (.4) du1 fU1 u1 erfc . 2 2 1 − ρn12. 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(21) Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2007, Article ID 98942, 10 pages doi:10.1155/2007/98942. Research Article Investigations in Satellite MIMO Channel Modeling: Accent on Polarization ´ ´ 1 George K. Karagiannidis,2 Peter R. King,3 Stavros Stavrou,3 and Istvan ´ Frigyes1 Peter Horvath, 1 Department. of Broadband Infocommunications and Electromagnetic Theory, Budapest University of Technology and Economics, H-1111 Budapest, Hungary 2 Division of Telecommunications, Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece 3 Centre for Communication Systems Research, University of Surrey, Guildford, Surrey GU2 7XH, UK Received 30 September 2006; Accepted 19 March 2007 Recommended by Ray E. Sheriff Due to the much different environment in satellite and terrestrial links, possibilities in and design of MIMO systems are rather different as well. After pointing out these differences and problems arising from them, two MIMO designs are shown rather well adapted to satellite link characteristics. Cooperative diversity seems to be applicable; its concept is briefly presented without a detailed discussion, leaving solving particular satellite problems to later work. On the other hand, a detailed discussion of polarization time-coded diversity (PTC) is given. A physical-statistical model for dual-polarized satellite links is presented together with measuring results validating the model. The concept of 3D polarization is presented as well as briefly describing compact 3D-polarized antennas known from the literature and applicable in satellite links. A synthetic satellite-to-indoor link is constructed and its electromagnetic behavior is simulated via the FDTD (finite-difference time-domain) method. Previous result of the authors states that in 3D-PTC situations, MIMO capacity can be about two times higher than SIMO (single-input multiple-output) capacity while a diversity gain of nearly 2 × 3 is further verified via extensive FDTD computer simulation. Copyright © 2007 Péter Horváth et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.. 1.. INTRODUCTION. It is more or less a commonplace statement that in the wireless technology of recent years, systems applying multipletransmit and multiple-receive antennas (MIMO, multipleinput multiple-output) have become one of the few methods of real innovation. Space-time processing, in particular space-time coding (STC) techniques as applied to MIMO systems in a multipath environment, results in significant improvement both in transmission capacity and reliability. It turns out that there are significant differences between terrestrial and satellite multipath channels; these result in significant differences in MIMO applications as well. In this paper, we deal with some special problems raised by special characteristics of satellite links. In terrestrial applications of MIMO, the basic method to diversify channels is with the additional dimension of space, that is, antennas are displaced spatially from each other, resulting in space-time processing. In addition, multipath channels and relevant fading characteristics—Rayleigh, Rice, Suzuki, and so forth—are assumed. A similar situation. is present in satellite-to-mobile or satellite-to-indoor links. Among others, in [1] it is experimentally verified that the LEO satellite-to-indoor channel has nearly exactly Rayleigh character at any fixed indoor spot. More precise models are available (Loo, Corrazza, etc.) well describing the multipath behavior and not differing much from the terrestrial case. Consequently, similar-to-terrestrial results can be foreseen in satellite links of appropriate design. However, due to the very huge length of the radio path, transmit and/or receive antennas must be placed at significant distances from each other in order to ensure that the various paths are really diverse. To achieve this in principle generalization of satellite diversity and site diversity would be candidates in forming MIMO channels. (Note that in satellite diversity, there are two or more satellites transmitting/receiving the same signal; in site diversity there are two or more Earth stations.) These would make original space time processing possible: both ground and satellite terminals are in this case remote from each other and so are their antennas. Of course the original concept of site diversity can be excluded in the present—mostly handheld mobile/indoor—situations..

(22) 2. EURASIP Journal on Wireless Communications and Networking. In one class of cases, the ground terminals are located onboard large objects, such as trains, ships, or aircrafts. Largeantenna distances are possible then, realizing diverse routes. Multipath, on the other hand, is nonexistent or very sparse. Difference of LOS route lengths must be in such a case at least λ/16 · · · λ/4. Site diversity might be applicable then, if as a rough estimate, terminal antennas can be placed at a distance of b = 35 m from each other. (For that figure, an LEO satellite and 30 GHz carrier frequency were assumed; note that b is proportional to the square root of satellite distance × wavelength.) Satellite diversity for space-time processing would fulfill the requirement of uncorrelated channels and so it would be applicable. There is a few papers dealing with this topic; for example, [2] gives a physical-statistical model for satellite-tourban and satellite-to-highway channel and computes capacity of a 2 × 2 MIMO system. In [3], a satellite-diversity MIMO system and its system aspects are investigated. Further papers on satellite MIMO are, among others, [4, 5]. There exists, however, at least one problem not present in terrestrial systems, that is, that of synchronization. In terrestrial MIMO systems, both the group of transmit antennas and that of receive antennas are at distances from each other in the order of a wavelength. Consequently, the path lengths of the diversity routes are very closely identical, and thus signals arriving from the transmitter to the receiver are synchronous. This makes identification and decoding of the received signals rather easy. In the case of satellite diversity, the satellites serving as diversity terminals are very far from each other. Thus difference of path lengths and so delays between the satellites and the ground terminal can be very high and highly variable. (This variability is self-evidently existing in the case of LEO satellites but very likely also in the GEO case.) As a consequence, the arrival time of signals from two satellites (forming part of a single code word) can be shifted by tens or hundreds of symbol times relative to each other. Synchronization of the received signals is in this case rather complicated—both acquisition and tracking. Reference [2] or [3] or other satellite/MIMO papers known by the authors do not deal with this problem. General aspects of it are dealt with, for example, in [6–8], taking explicitly, however, shortrange, that is, terrestrial situations only into account. An alternative possible solution could be cooperative satellite diversity (CSD). In general, cooperative relaying systems have a source node (e.g., a terrestrial mobile terminal (TMT)) multicasting a message to a number of cooperative relays (satellites (SAT)), which in turn resend a processed version to the intended destination node (another TMT). The destination node combines the signal received from the relays, possibly also taking into account the source’s original signal. Recently, it has been shown that cooperative diversity systems provide an effective way of improving spectral and power efficiencies of the wireless networks without the additional complexity of multiple antennas [7–11]. However, a study on CSD systems, where the relays are satellites, to the best of the authors’ knowledge does not exist in the literature. A third possible method is to apply compact antennas, in which case the synchronization problem is nonexistent.. Compact antennas with low radiator spacing and dimensions as small as λ/20 or so are described, for example, in [12– 14]. These antennas were mainly developed for application in handheld terminals, in which the available space is very limited. In the case of onboard antennas, the whole antenna need not be small, however, the radiator elements need to be colocated, that is, their ports need to be very close to each other. Note that polarization, and in many cases the 3D character of it, has a significant role in each of the known compact antennas. In this paper, the concept of cooperative satellite diversity is briefly introduced, without, however, a detailed discussion; this is done in Section 2. Polarization diversity and the application of space-time coding concepts in polarization diversity are dealt with in Section 3. (In analogy to the name STC, we call that polarization time coding (PTC). Note that according to the authors’ understanding, the term STC is used to distinguish a transmit-and-receive-space-diversity situation from a simple receive diversity. The same understanding is applied in this paper; so we will call our topic PTC even if particular coding problems are not at all dealt with but coded signals are assumed.) Section 3.1 deals with dual-polarized MIMO channels, stating a physical-statistical model, presenting measuring results and validating the model; in this discussion conventional dual-polarized antennas are applied. In Section 3.2, PTC antennas of 3-dimensional polarization are dealt with, introducing the concept of 3D polarization, presenting a few compact MIMO antennas and showing the essential difference between terrestrial and satellite links from the point of view of 3D PTC. In Section 4, electromagnetic simulation results are given; in these it is verified that application of the FDTD method is suitable to investigate MIMO channel characteristics of very complex environments; capacity as well as diversity behavior are presented; these verify (at least for the present example) the statements of Section 3.2 and of the authors’ references [15, 16]. Conclusions are drawn in Section 5. 2.. A FEW WORDS ON COOPERATIVE SATELLITE DIVERSITY. In general, cooperative relaying systems have a source node (e.g., TMT) multicasting a message to a number of cooperative relays (SAT), which in turn resend a processed version to the intended destination node (another TMT). The destination node combines the signal received from the relays, possibly also taking into account the source’s original signal. An example of a CSD system with two satellite relays is shown in Figure 1. The idea of merging cooperation with space-time coding resulted in the so-called distributed or cooperative space-time coding (CSTC). Compared to the conventional space-time coding with collocated antennas, CSTC can be implemented when transmitter and relays share their antennas to create a virtual transmit array. A possible cooperation scenario is applied for the configuration of Figure 1, proposed in [9] as TMT1 communicates with SAT1 and SAT2 in a broadcasting mode during.

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