Estimation of capabilities of cooperative CubeSat systems based on Alamouti transmission scheme

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1 Estimation of capabilities of cooperative CubeSat systems based on Alamouti transmission scheme Z.S. Gibalina Kazan National Research Technical University named after A. N. Tupolev- KAI Kazan, Russia V. A. Fadeev Kazan National Research Technical University named after A. N. Tupolev- KAI Kazan, Russia K. A. Korsukova Kazan National Research Technical University named after A. N. Tupolev- KAI Kazan, Russia M Hennhöfer Technische Universitat Ilmenau Ilmenau, Germany M. Haardt Technische Universitat Ilmenau Ilmenau, Germany Abstract Due to the size constraints of the CubeSat satellites and hence the limited capabilities in terms of battery power and solar panel s area, highly energy efficient transmission schemes are required. However, we can consider CubeSat satellites as a prospective tool for communication. In this case the effective transmission channels between CubeSats and a ground station should be optimized in terms of energy efficiency, robustness, Bit Error Ratio performance and capacity. One of the approaches to reduce the required energy consumption is to reduce the required Signal-to-Noise Ratio. We evaluate different coding schemes including LDPC and space-time codes. Due to the limited size of the CubeSat systems the use of cooperative schemes can be beneficial and shall be considered. Cooperative schemes in this context are schemes, in which several devices are virtually treated as to be a single one. Different system models for cooperative communication and basic results of the link budget calculation are presented in the introduction. A comparison of the Bit-Error- Ratio performance for different cases of using Alamouti codes as well as inter-satellite link budget calculations are shown in the main part of this paper. Keyword - Cubesat, QPSK, OQPSK, Rician fading, Reed- Solomon codes, convolutional codes, Turbo convolutional codes, LDPC, MIMO, MISO, Alamouti scheme satellites as one device. Fig. 1. System model for the cooperative MIMO case. Challenges of this idea are possible delays in inter-satellite links and difficulties with phase synchronization. To support stable inter-satellite link we can increase its throughput using higher order modulation schemes because for inter-satellite link an additive white Gaussian noise (AWGN) channel can be expected (no fading), phase synchronization can be provided by GPS signals [11]. I.INTRODUCTION The main idea of cooperative satellite schemes is observed in [1] - [3] and can be explained via simple system models (fig. 1-2). The main advantage of this approach is that we obtain MIMO (Multiple Input Multiple Output) or MISO (Multiple Input Single Output) benefits by using virtual (cooperative) MIMO/MISO techniques when we consider at least two Fig. 2. System model for the cooperative MISO case /18/$ IEEE

2 The selection of the channel model and its main characteristics and also the selection of the most appropriate modulation scheme are described in [4]. In [5] a more common approach for channel modeling was described. Briefly, we consider Rician flat fading channel with two cases: light shadowing (K = 4.0) and strong shadowing (K = 0.6) for primary evaluation of modulation and coding schemes capabilities. Main formula for Rician fading (randomly distributed value r) modeling may be obtained from Rician channel model: K K H = HLoS + HNLoS K+ 1 K + 1 K K r = + ( G1+ jg2) K + 1 2( K + 1) (1) where H is the channel matrix, K is the Rician factor, Line-of-Sight component H =e ( ) e ( ) = 1 (d is the antenna spacing, θr is the Direction of Departure, θt is the Direction of Arrival) and the Non-Line-of-Sight component H NLoS, actually, is the Rayleigh fading process. OQPSK as the most appropriate modulation scheme was selected [4]. The expected Bit Error Ratio is also justified in [4] and should not be larger than For the cooperative scenario we consider an additional case an asymmetric channel, where one propagation path is lightly shadowed, but another one is strongly shadowed. We assume that we use an open-loop case (without feedback) and therefore consider the Alamouti scheme as the most appropriate. Before we start to estimate the opportunities of cooperative schemes we should calculate the inter-satellite link budget. Actually, we can use formulas and main technical parameters that we used in [4] and presented in [5]. Main results are shown in the table 1. TABLE 1: EXPECTED SIGNAL-TO-NOISE RATIOS Range (in MHz) Bandwidth (in MHz) Uplink Power (in Watts) SNR (in db) Downlink Power (in Watts) SNR (in db) II.INTER-SATELLITE LINK BUDGET Firstly, we can calculate theoretical antenna gains for ideal K, Ka and V bands antennas to estimate possibilities of increasing inter-satellite distances: / antenna gains: dbi (ground) dbi (CubeSat) antenna gains: dbi (ground) dbi (CubeSat) antenna gains: dbi (ground) dbi (CubeSat) G A 10lg 4π λ tx a = 2 where λ is the wavelength and A tx = (π/4)d is the area of an ideal parabolic antenna with diameter d. According to this, we can expect the following values (table 2) for antenna gains (the values for 2.4 and 5.8 GHz obtained from technical specifications [6], [7]). (2)

3 TABLE II ANTENNA GAINS (APERTURE FOR THEORETICAL CASES IS FIXED ON 9 CM). Range (GHz) Antenna gain (db) For an inter-satellite link we do not expect a fading processes due to free space propagation and hence an AWGN channel for modelling can be used.. The expected SNRs can be estimated as a function of the inter-satellite distances (Fig. 4 5). Fig. 3. Expected SNRs in inter-satellite link for real equipment [6], [7] (Ptx = 30 dbm, antenna gains are shown in table 2). GHz means fairly pencil shaped beam pattern and therefore may be inappropriate due to Pointing, Acquisition and Tracking issues (the scenario is pretty similar to the optical case [12]). III.SPATIAL-TIME CODING METHODS AND DIVERSITY GAIN Improving the BER performance by exploiting diversity gain is a well known technique that is used in space-time codes. The widespread approach is the Alamouti scheme, which uses (3), for transmission: S c c = 1 2 t1, t2 * * c2 c1 Where S t1,t2 is the matrix of transmitted symbols c (rows correspond to time slots). A disadvantage of this method is that the Alamouti scheme takes an additional timeslot after each symbol. Hence, Alamouti transmission decreases the symbol rate to half in comparison with a spatial multiplexing approach. The MIMO channel can be represented as a tensor where the number of receive antennas Mr corresponds to the number of rows and the number of transmit antennas Mt is equal to the number of columns. Furthermore, the number of snapshots increases the lateral dimension. Moreover, we consider a channel matrix (one slice of the channel tensor) as uncorrelated. Each of the slices can be modeled via the formula (1) as MrMt Rician flat faded independent paths. For modeling we generate random binary message (the length is equal to bits), modulate it by OQPSK, multiply with Rician distributed channel matrix (assume that channel is time invariant for each couple of symbols [8]) for each snapshot, add White Gaussian Noise, equalize by Zero- Forcing method, demodulate and calculate BER. After that we can start to compare different cases for selected channel (fig. 5). (3) Fig.4. Expected SNRs in inter-satellite link for required equipment. (Ptx = 30 dbm, antenna gains are shown in table 2) Finally, we can see that the usage of K, Ka and V band antennas is a required condition for sufficiently large coverage area with minimal number of satellites and therefore design of the CubeSat antennas for these ranges is an extremely valuable branch of research. However, it should be taken into account that high frequency such as 60 Fig. 5. Bit-error ratio performance for simulated time invariant for each couple of symbols SISO/MISO/MIMO channels. IV. COMBINING SPACE-TIME CODES WITH CLASSICAL CHANNEL CODES. Main achievements of using coding schemes such as convolutional codes and Reed-Solomon codes were considered in [4]. Code rates that are equal to 1/3, 1/2, 2/3 and 3/4 are chosen for convolutional codes with octal generators (171, 133) (for code rate 1/3 octal generator is

4 equal to (171, 165, 133)), constraint length 7, and puncturing vector [110101] for code rate 3/4 and [1101] for code rate 2/3. For RS codes a (15, 9) structure with puncturing pattern [100101] is used. With a code rate close to 3/4, a (63,31) structure and with a code rate nearby 1/2 a (255,243) structure [9] are used (fig. 6, 7). Fig. 8. Comparison of Convolutional and Reed-Solomon codes in with light shadowing). Fig. 6. Comparison of Convolutional and Reed-Solomon codes (OQPSK, Rician fading channel with light shadowing). Fig. 9. Comparison of Convolutional and Reed-Solomon codes in with strong shadowing). Fig. 7. Comparison of Convolutional and Reed-Solomon codes (OQPSK, Rician fading channel with strong shadowing). The usage of only convolutional or RS coding does not allow to obtain large energy gains. More interesting to consider conjunction of space-time and channel coding schemes. Three cases for both MIMO (2x2) and MISO (2x1) are considered: a symmetric channel with light shadowing, a symmetric channel with strong shadowing and an asymmetric channel when we have one lightly shadowed and one strongly shadowed path (fig. 8-10). Note that for the MISO case an asymmetric channel is more realistic as it was considered above. Fig. 10. Comparison of Convolutional and Reed-Solomon codes in with asymmetric channel). To summarize we can construct table 3 with energy gains for estimation of opportunities of cooperative schemes. Values for uncoded case were obtained in [4]. Numerical results of the comparison are shown in [10].

5 Conjunction with more powerful coding schemes such as Turbo codes or LDPC codes is the following step of our research. Results of comparison of LDPC and Turbo codes were shown in [10]. For modeling of LDPC and Turbo convolutional encoders / decoders objects of MatLab s Communication toolbox were used (fig ). Fig. 14. Comparison of Turbo convolutional and LDPC codes in with strong shadowing, linear plot). Fig. 11. Comparison of Turbo convolutional and LDPC codes in with light shadowing, logarithmic plot). Fig. 15. Comparison of Turbo convolutional and LDPC codes in with asymmetric channel). Fig. 12. Comparison of Turbo convolutional and LDPC codes in with light shadowing, linear plot). Fig. 16. Comparison of Turbo convolutional and LDPC codes in with asymmetric channel, linear plot). Based on presented curves capabilities of coding schemes can be estimated. Numerical results are shown in [10]. Fig. 13. Comparison of Turbo convolutional and LDPC codes in with strong shadowing, logarithmic plot). V.CONCLUSION The obtained results show that CubeSat satellites can be used for communication systems. Firstly, the calculated link budgets show that existing equipment can provide sufficiently high SNRs both for uplink and downlink for voice transmission. Equipment for inter-satellite communication should be investigated for carrier frequencies higher than 10 GHz.

6 Different cases of the Alamouti space-time coding scheme in conjunction with CubeSat systems were considered. We can obtain up to 25 db energy gain for MIMO case in comparison with SISO, and up to 17 db for MISO case in comparison with SISO also. The modeling shows us also that only the MIMO case can ensure the required BER for typical SNRs. This problem can be resolved via a combination of channel coding and space-time coding (Alamouti). The cooperative case significantly outperforms the SISO case in terms BER performance. For the uplink convolutional codes with a code rate 2/3 or RS(255,243) codes for light shadowing can be selected and convolutional codes with code rate that is equal to 1/2 for strong shadowing should be chosen. For the downlink LDPC codes can be proposed because they outperform punctured Turbo codes and have relatively less computationally expensive encoders. The next step of the research is to include channel estimation and to further improve the channel model based on real measurements. REFERENCES [1] L. Jiang, G. Cui, S. Liu, W. Wang, D. Liu, Y. Chen, Cooperative Relay Assisted Load Balancing Scheme Based on Stackelberg Game for Hybrid GEO-LEO Satellite Network, 2015 IEEE [2] O. N. Challa, Dr. J. McNair, CubeSat Torrent: Torrent Like Distributed Communications For CubeSat Satellite Clusters, IEEE 2012 [3] Z. Guo-zhen, H. Bao-hua, M. Jing, One Scheme of Cooperative Diversity with Two Satellites based on the Alamouti Code, IEEE 2010 [4] Gaysin, A., Fadeev, V., & Hennhöfer, M. (2017, July). Survey of modulation and coding schemes for application in CubeSat systems. In Systems of Signal Synchronization, Generating and Processing in Telecommunications (SINKHROINFO), 2017 (pp. 1-7). IEEE. [5] Link budget calculation for CubeSat satellites [6] Flexible High Speed S-Band Radio Transceiver by GomSpace company (date of the application is ) [7] R. M. Rodriguez-Osorio, Enrique Fueyo Ramirez, A Hand s-on Education Project: Antenna Design for Inter-CubeSat Communications, IEEE Antennas and Propagation Magazine, Vol. 54, No. 5, October 2012 [8] Introduction to MIMO Systems (MathWorks) systems.html [9] Dr. Mahmoud Ahmed Atha Ali, Dr. Atef Abou-El-Azm, and Eng. M. F. Marie, Reed-Solomon codes and their performance for FDMA systems in fading satellite channel, 1999 IEEE [10] Fadeev, Vladimir. Design of Cooperative Communication System Based on CubeSat Satellites. Diss. Technische Universität Ilmenau, [11] Nie, G., Wu, F., Zhang, K., & Zhu, B. (2007, May). Research on LEO Satellites Time Synchronization with GPS Receivers Onboard. In Frequency Control Symposium, 2007 Joint with the 21st European Frequency and Time Forum. IEEE International (pp ). IEEE. [12] Zlata Gibalina, Vladimir Fadeev. Optical Inter-Satellite Link in Comparison with RF case in CubeSat system. Zhurnal Radioelektroniki - Journal of Radio Electronics No. 10. Available at