On the capacity of a SIMO land mobile satellite system at C-band: polarized and depolarized received field

Nektarios Moraitis 0 Pter Horvth 1 Philip Constantinou 0 Istvn Frigyes 1 0 Institute of Communications and Computer Systems, National Technical University of Athens , Athens, Greece 1 Department of Broadband Infocommunications and Electromagnetic Theory, Budapest University of Technology and Economics , Budapest, Hungary Land mobile satellite can exploit multiple input multiple output techniques to achieve high transmission rates. This article evaluates, theoretically, the capacity of the single input multiple output system utilizing uniform linear arrays at the receiver terminal for satellite applications. The theoretical study is performed at C-band and accounts for different shadowing conditions. Additionally, polarization effects are introduced and capacity results are presented that take into account the depolarization. For this investigation, a model for the scattering caused depolarization based on Stokes parameters is applied. Decrease of channel capacity is determined for some special cases both for Rayleigh fading and for the ULA with different number of receive antennas. - Introduction Multiple antenna wireless systems, and particularly multiple input multiple output (MIMO) systems, yield unprecedented possibilities of innovation in wireless communications. While in principle MIMO advantages are achievable both with free space channels (e.g. [1,2]) and multipath channels, practical reasons prefer the latter. As a consequence satellite links are not well suited for MIMO applications: the path-length is extremely long, propagation along most of the path is free space and antennas arenearly alwaysof very narrow beam. Furthermore, it is shown in the literature that the other forms of diversity (mainly satellite diversity, where two satellites orbiting far from each other serve as diversity terminals) cause severe intersymbol interference and raise synchronization issues [2]. The solution of these problems is not simple at all and details are not yet clear. Possibilities of polarization diversity, on the other hand, are more restricted than those of, e.g. space or frequency diversity. Having taken this into account, it seems reasonable to investigate what advantages (if any) of a true MIMO system can be achieved with architectures appropriate in satellite systems, these being more conservative than MIMO architecture, i.e. single input multiple output (SIMO) in the downlink. In particular, if channel capacity can significantly be increased by the application of multi-antenna satellite systems. The problem is related to MIMO studies as the question itself and concepts and methods applied have existed since the advent of MIMO in the mid 1990s. There are few articles dealing with the MIMO satellite topic. For example, King et al. [3] give a physical-statistical model and compute the capacity of a 2 2 MIMO system. Further articles involved with MIMO satellite measurements are [4-6], whereas [7] investigates the modelling of the satellite MIMO channel emphasizing on polarization. The aim of this article is to achieve a step on this path. A satellite downlink is investigated and our goal is to determine the channel capacity. The investigated system is SIMO, i.e. there is one transmit antenna onboard the satellite and a vertically polarized uniform linear array (ULA) receive antenna at the receiver terminal. Although it is known from theory that this structure yields only logarithmic increase of capacity versus the element number of the antenna, significant shift in signal-tonoise ratio (SNR) can be possible with appropriate environment and design. The number of applications using global navigation satellite system positioning is increasing steadily and currently the European Space Agency explores the possibility of satellite navigation signals operating in an already allocated frequency band for satellite radio navigation around 5 GHz [8]. For that reason, the study is performed at C-band (5.2 GHz), for a light and heavy shadowed environment. Depolarization can change channel characteristics, including capacity (usually neglected in single-polarized situations). Therefore, the second step is to examine the channel capacity introducing SIMO depolarization scenarios and compare the difference with the polarized state. The problem of depolarization is investigated in a more general framework. In that, usual channel modelsstatistical like Rayleigh, Rice, Corazza-Vatalaro, etc., or physical, like ray tracing, full-wave electromagnetic models (or that used in this article for polarized SIMO)are regarded as conditional models based on the loss due to polarization mismatch of the receive antenna. In order to determine statistics of the condition, a model described in [9], based on Stokes-parameters, is proposed. To give some general insight into the role of depolarization the model is also applied to various single input single output (SISO) and SIMO Rayleigh-fading situations. In several cases closed-form results were obtained and verified by simulation providing ergodic capacity results. The remainder of the article is organized as follows. In Section 2 we describe the propagation scenario and geometry, the channel model and the capacity calculation methodology. Section 3 presents the outage capacity results for the polarized state of the channel. In Section 4, unconditional statistics of representative channel models with representative depolarization models are determined, and, based on that, ergodic capacity of some SISO and SIMO situations is calculated. Finally, Section 5 is devoted to conclusions summarizing this study. Capacity evaluation methodology Propagation scenario The propagation scenario utilized to evaluate the channel capacity is illustrated in Figure 1. We assume that the direct component arrives at the mobile terminal having an angle-of-arrival (AoA), 0, in the vertical plane of propagation. The multipath components arrive at the receiver antenna elements according to the angular distribution of scatterers as depicted, three-dimensionally, in Figure 1. The mobile receiver is moving along the x-axis as indicated, heading away from the satellite. The multipath components are uniformly distributed within a sector with angular spread , where may vary between 0 and 2. This circle of scatterers has a radius of SR as shown in Figure 1. Since the receiver is moving away from the satellite, according to the proposed propagation scenario, the relationship between the angle of the direct component and the elevation angle of the satellite is Figure 1 SIMO satellite propagation scenario, and distribution of multipath. 0 = elev. Additionally, the number of the scatterers depends on the angular spread and it is given from L = 50a/, where is between 0 and 2. The time-varying (since we have a mobile terminal) received complex envelope can be described by the following relationship: where b~ is the time-varying angular-dependent complex envelope, 0 is the an (...truncated)