MIMO Dual Polarized Fixed Satellite Systems above 10GHz: Channel Modeling and Outage Capacity Evaluation Charilaos Kourogiorgas1, Athanasios D. Panagopoulos2, Pantelis-Daniel Arapoglou3, Stavros Stavrou4 1 2

School of Electrical and Computer Engineering, National Technical University of Athens, Greece, [email protected] School of Electrical and Computer Engineering, National Technical University of Athens, Greece, [email protected] 3 European Space Agency-ESTEC, The Netherlands, [email protected] 4 Open University of Cyprus, Nikosia, Cyprus, [email protected]

Abstract—In this paper, the performance of a dual polarized MIMO fixed satellite system under rain is investigated. Due to the increase of capacity that is observed from MIMO terrestrial communications, the later techniques are also tested and evaluated in satellite communications. In this paper, a dual polarization satellite system is considered operating at frequencies above 10 GHz (e.g. Ka-band). Using multi-dimensional Stochastic Differential Equations (SDEs), the outage capacity of spatial multiplexing technique is investigated and compared fairly to the single polarization system. A gain is observed from results especially in periods with low rain attenuation. Index Terms—Dual polarization, rain attenuation, spatial multiplexing, Satellite MIMO.

I.

INTRODUCTION

The use of higher frequency bands, i.e. Ka-band and above, for modern broadband Satellite Communication Systems has been gaining interest due to the availability of uncongested spectrum. Multi-beam High Throughput Satellite (HTS) systems with frequency re-use can reach a total throughput of Tb/sec [1]. In such HTS systems, the use of Ka-band at the end users and of Q/V band for the feeder links is considered. One way to further improve the spectral efficiency of satellite communication systems is the use of Multiple Input Multiple Output techniques [2]. Apart from the MIMO techniques defined in spatial domain, i.e. multiple antennas at the transmitter and/or receiver side, the polarization domain has been exploited as a resource for achieving multiplexing gain in highly correlated satellite channels [2]-[5]. In [3], [5] the dual polarization has been identified as a potential solution for the increase of throughput in mobile satellite system in L- or Sbands. In [6] a model is proposed for dual polarization Land Mobile Satellite channels. For the case of multi-beam satellite systems, the dual polarization can be used along with a more intense frequency re-use factor in order to increase the offered throughput. At high frequency bands, i.e. Ka-band and above, the channel is different than this at L- and S- bands. In particular the effects of the atmosphere play the most crucial role on the link performance as the directional antennas due not allow for multipath effects due to scattering. Specifically, rain causes the attenuation and depolarization of the signal [7] and its impact

can be given through the ITU-R recommendation [8]. Therefore, different physical factors form the channel matrix at Ka-band compared to the L- and S- bands. In [9], a review of the cross-polarization metrics and how these are connected to physical parameters is given. For the adoption of dual polarization MIMO spatial multiplexing (SM) for Ka band, the channel matrix must be defined. In this paper, the channel matrix is modeled for a Kaband dual polarization system with correlated channel elements. Moreover, a channel model for dual polarization satellite systems at Ka-band is introduced using the comprehensive tool of multi-dimensional Stochastic Differential Equations (SDEs) [10] for generating rain attenuation samples correlated values in the polarization domain. The system performance is examined through outage capacity statistics for a MIMO dual-polarized fixed satellite systems above 10GHz using SM. From this performance assessment, important conclusions are drawn. II.

SYSTEM MODEL

The system under investigation in this paper is composed by a single satellite operating at frequency above 10GHz, e.g. Kaband and transmitting into two orthogonal polarizations. On the ground, a fixed user is located and is able of receiving concurrently both polarizations with the help of a dual feed antenna, as shown in Fig. 1. Considering a single time slot for SM the symbols S=[s1 s2]T are sent and the received signal vector Y=[y1 y2]T is given by:

Y = H⋅S + n

(1)

with H being the 2x2 channel matrix and n the 2x1 white Gaussian noise vector. In such system, we denote the complex channel matrix as: h H =  11  h21

h12  h22 

(2)

where h11 is the co-polar component at one polarization, h22 is the co-polar component at the second polarization and the h12 and h21 are the cross-polar components. The cross-polar components depend not only on the cross-polar discrimination (XPD) due to the propagation effects (here only rain attenuation

is considered), but also on the satellite/ground station antenna XPD. On the satellite side, we make the assumption that the antenna XPD is infinite [6].

In the system under investigation, we further assume that there is no channel state information at the transmitter and therefore the power used for transmission at the two polarizations is equally divided [2]. Considering the above system for a spatial multiplexing system the Shannon Capacity is defined as:  P   (8) C = log 2  det  I + T HH H   2N    with H the symbol for the conjugate transpose of the matrix, I the 2x2 identity matrix, PT the total transmitted power and N the noise power without taking into account the effect of rain on noise temperature. In this paper, the metric of interest is the outage capacity, i.e. the probability that the capacity of the system is lower than a certain threshold: Pout = P ( C ≤ Cth ) (9) III.

Fig. 1. System Configuration

Considering a similar formulation as in [6], the complex elements of the channel matrix above are calculated through: − Ai

hii = 10 20 (1 − β ant )(1 − γ i ) e − jθ , i = 1, 2

hij

− Ai = 10 20

β ant γ i e − jθ , i ≠ j

(3) (4)

where θ is uniformly distributed in [0,2π) and Ai (dB) is the rain attenuation induced at the polarization 1 or 2 at the receiver. The parameter βant is used to take into account the receiver’s antenna XPD and it holds that:  1 − β ant  XPDant = 20 log    β ant 

(5)

Moreover, the parameter γ is to encounter the rain attenuation cross-polarization effects and it is given through: 1− γi  XPDrain ,i = 20 log    γi 

CHANNEL MODEL

For the channel model, rain attenuation is considered, since it is the dominant fading mechanism at frequencies higher than 10 GHz. For the single link induced rain attenuation, the Maseng-Bakken model is considered. Therefore, rain attenuation for a single link is modeled as a Markov process and described by the following SDE [11]:   a  dAt = At β A σ A2 − ln  t   dt + At 2 β A σ A dWt (10)   Am   where βΑ is the dynamic parameter of rain attenuation, Am and σΑ the statistical parameters of lognormal distribution of rain attenuation and dWt, the Brownian increments. The rain attenuation used in (3)-(4) is induced in the link for the two orthogonal polarizations and their values are correlated. Therefore, in our case since we need rain attenuation induced on two links with the same radiopath but on two different polarization angles, the two random processes of rain attenuation will be highly correlated. Therefore, the extension of the MB model on the two dimensional case will be considered for this study. The model proposed in [10] extends the MB model for rain attenuation correlated in space. In this paper we extend this model by assuming the correlation in polarization, with which we arrive to the following system of equations is used:

(6)

The XPDrain ,i (dB) is calculated in terms of rain attenuation Ai taking ITU-R P. 618-11 model [8]. More particularly, the general expression for the value of XPD not exceeded for p% time percentage is: XPDrain = U − V log Ap (7) with U and V parameters which depend on tilt angle, frequency and elevation angle and Ap rain attenuation exceeded for the p% time percentage.

 kii2 + kij2  A (t)  − βi ln  i  dt + Ai (t)kii dWti + Ai (t)kij dWt j , dAi (t) = Ai (t)   Ami   2 {i = 1,2, j = 2,1,respectively} (11) where the subscript i refers to polarization 1 and polarization 2. The coefficients kii and kij refer to the elements of the matrix K which is obtained through Cholesky decomposition of the matrix G whose elements are given by: Gij = − ( β i + β j ) Cij (12)

with Cij the correlation coefficient of rain attenuation between polarizations 1 and 2 and βi is the dynamic parameter of rain attenuation for the two polarizations. So, the resulting time series of rain attenuation correlated in the polarization domain can be generated as shown in Fig. 2. The considered polarizations are linear horizontal and vertical. For the time series at this latter figure, the ground stations are considered in Athens for 20GHz operating frequency. The correlation coefficient is considered equal to 0.9, using a high value of correlation coefficient. Experimental campaigns should be conducted in order to accurately evaluate the correlation coefficients under rain fades.

year period. It can be observed from the figure that the capacity is highly increased in the high probabilities, since in clear-sky or in case that rain attenuation is low, the channel matrix can be considered as diagonal due to the high receive antenna XPD. As the probability decreases, i.e. higher values of rain attenuation are appearing and the gain is getting lower. The same is observed for an operating frequency of 40 GHz.

(a)

Fig. 2. Correlated on polarization domain rain attenuation time series for a correlation coefficient equal to 0.9

IV.

NUMERICAL RESULTS

For the generation of the channel matrix, the rain attenuation time series are derived in order to reproduce the long-term expression in (11) and are used as inputs at the expression for XPD calculation of the recommendation of ITU-R. P. 618 [10] (given in general form at (7)), the XPD at each polarization can be calculated and then proceed to the formulation of the channel matrix in (2) through (3)-(6). In Fig. 3a, the time series of rain attenuation induced on the two links of two orthogonal polarizations are shown and in Fig. 3b, the received power at co-polar components is shown while in Fig. 3c at the cross-polar components for the same time instances. The Signal-to-Noise ratio (SNR) in clear sky conditions is set equal to 28.3 dB. The XPD of the antenna is equal to 35 dB, frequency of the link equal to 20 GHz and the ground station is considered in Athens, Greece. The elevation angle of the link is 44.58o. From these Figs., it can be observed that as rain attenuation increases the received power at co-polar components are decreased, while in the cross-polar components is increased. For the same parameters as in Fig. 3, the outage capacity has been calculated and it is shown in Fig. 4. In the same Figure the outage capacity for the corresponding single polarization (SISO, single input single output) system is shown. For a fair comparison, the SNR in clear sky conditions for the single polarization case is 3 dB higher. Moreover, the antenna XPD in case of single polarization is equal to infinity, while the XPD due to rain through the parameter γ of (2) and (6) was also considered to take into account the depolarization for the single polarization system. The outage capacity was evaluated for 10-

(b)

(c) Fig. 3. a) Time series of rain attenuation at the two different polarizations, b) Received power at co-polar components, c) received power at cross-polar components

In Fig. 5, the outage capacity is shown for different values of clear sky SNR. As it shall be expected with the decrease of the SNR in clear sky conditions the outage probability is

increased and the capacity thresholds for different probability values are decreased. Moreover, it shall be noted that the lines are not in parallel due to the high effect of rain attenuation on the capacity.

Finally, in Fig. 7, the outage capacity is calculated for a single polarization link, for dual polarization MIMO SM (which implies joint receiver processing) as well as dual polarization 2xSISO (which implies independent receiver processing of the two polarizations) [12].. For the simulation, the used parameters are the same as in Fig. 6 for the city of Athens. It is observed that the MIMO dual polarization capacity is close to the 2xSISO capacity. This occurs because, unlike spatial MIMO, the capacity improvement emanates mainly from the use of additional bandwidth (second polarization) and less from the multiplexing gain of the channel.

Fig. 4. Outage capacity for spatial multiplexing system and with single polarization for 20 GHz and 40 GHz

Fig. 7. Outage capacity for a SISO system, dual polarization system and a double SISO system

V. Fig. 5. Outage capacity for spatial multiplexing systems for different values of SNR in clear sky conditions

Moreover, in Fig. 6, the outage capacity is shown for two different cities. The first city is Athens and the second one is Bucharest. The frequency of the links is 20 GHz, and the SNR in clear sky conditions equal to 28.3 dB. Both links have the same elevation angle equal to 44.58o.

CONCLUSIONS

In this paper, the performance in terms of outage capacity for a dual polarization MIMO satellite system operating at Kaband was evaluated. Firstly, a system model was proposed for applying SM and a channel matrix was formed taking into account the rain attenuation and the antenna XPD. Then using the multi-dimensional synthesizer for generating correlated rain attenuation over polarization domain, channel matrix time series were generated and the outage capacity was calculated. Experimental campaigns are necessary in order to calculate some parameters of the channel matrix. The main observation of this paper is that the capacity is increased with the use of dual polarization MIMO compared to a single polarization system. The improvement is almost two-fold for most of time percentages due to the use of double bandwidth (second polarization) with respect to SISO. That is why, the MIMO capacity is very similar when using two single polarization SISO (2xSISO). ACKNOWLEDGMENT

Fig. 6. Outage capacity of dual polarization system for a ground station in Athens and in Bucharest

In Bucharest rain attenuation takes higher values at low exceedance probabilities than a link in Athens. Therefore, the outage capacity for Athens is higher than in Bucharest.

This work has been co-financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) - Research Funding Program: THALES-NTUA MIMOSA: Reinforcement of the interdisciplinary and/or interinstitutional research and innovation.

REFERENCES [1]

[2]

[3]

[4]

[5]

[6]

P. Thompson, B. Evans, L. Castanet, M. Bousquer, T. Mathiopoulos, “Concepts and Technologies for a Terabit/s Satellite, SPACOMM 2011, Budapest, Hungary. P.-D. Arapoglou, K. Liolis, M. Bertinelli, A. Panagopoulos, P. Cottis, R. De Gaudenzi, “MIMO over Satellite: A Review”, IEEE Communications Surveys and Tutorials, vol. 13, no. 1, pp. 27-51, 1st Quarter 2011. P. D. M. Arapoglou, P. Burzigotti, M. Bertinelli, A. B. Alamanac, R. De Gaudenzi, “To MIMO or Not To MIMO in Mobile Satellite Broadcasting Systems”, IEEE Transactions on Wireless Communications, vol. 10, no. 9, pp. 2807-2811, Sept. 2011 C. Oestges, B. Clerckx, M. Guillaud, M. Debbah, “Dual Polarized Wireless Communications: From Propagation Models to System Performance Evaluation”, IEEE Transactions on Wireless Communications, vol. 7, no. 10, pp. 4019-, Oct. 2008. P. R. King, S. Stavrou, “Capacity Improvement for a Land Mobile Single Satellite MIMO System”, IEEE Antennas and Wireless Propagation Letters, vol. 5, pp. 98-100, 2006 K. P. Liolis, J. Gomez-Vilarbedo, E. Casini, A. I. Perez-Neira, “Statistical modeling of dual-polarized MIMO land mobile satellite channels”, IEEE Transactions on Communications, vol. 58, no. 11, pp. 3077-3083, Nov. 2010.

[7]

A. D. Panagopoulos, P.-D. M. Arapoglou, P. G. Cottis, “Satellite Communications at Ku, Ka and V Bands: Propagation Impairments and Mitigation Techniques”, IEEE Communication Surveys and Tutorials, 2004. [8] ITU-R. P. 618-11, “Propagation Data and Prediction Methods Required for the Design of Earth-space Telecommunication Systems”, Geneva, 2013. [9] A. Paraboni, A. Martellucci, C. Capsoni, C. Riva, "The Physical Basis of Atmospheric Depolarization in Slant Paths in the V Band: Theory, Italsat Experiment and Models," Antennas and Propagation, IEEE Transactions on , vol.59, no.11, pp.4301,4314, Nov. 2011 [10] G. Karagiannis, A. D. Panagopoulos, J. D. Kanellopoulos, “MultiDimensional Rain Attenuation Stochastic Modelling: Application to Earth-Space Diversity Systems’, IEEE Transactions on Antennas and Propagation, October 2012. [11] T. Maseng, P. Bakken, “A Stochastic Dynamic Model of Rain Attenuation”, IEEE Transactions on Communications, vol. COM- 29, no. 5, pp. 660-669, 1981. [12] P.-D. Arapoglou, M. Zamkotsian, P.G. Cottis, “Dual polarization MIMO in LMS broadcasting systems: Possible benefits and challenges,” International Journal of Satellite Communications & Networking, vol. 29, no. 4, pp. 349-366, 2011.