[ieee 2014 8th european conference on antennas and propagation (eucap) - the hague, netherlands...

Climatic-Dependent Energy Efficient Design of Satellite Links Operating above 10GHz: An Optimal

Stopping Approach Marios I. Poulakis and Athanasios D. Panagopoulos

School of Electrical and Computer Engineering, National Technical University of Athens (NTUA),

Athens, Greece Emails: [email protected], [email protected]

Abstract—The increasing demand for higher communication

data rates leads the operation of satellite systems to frequency bands above 10GHz. Moreover, it is very important for satellite systems to reduce the energy consumption of the communication part in order to maintain high energy efficiency, especially for remote satellite terminals that do not have a continuous power supply. This paper focuses on the energy efficient design of a satellite link that operates at the frequency range above 10GHz, where rain attenuation is the dominant fading mechanism. Specifically, we design an opportunistic transmission scheduler with a view to minimizing the energy consumption of a broadband satellite terminal or a gateway by exploiting the stochastic characteristics of the propagation conditions and more specifically the rain fading channel. The proposed scheduling policy, which is derived by employing the optimal stopping theory, postpones the communication up to an acceptable deadline until the best channel conditions are found. The energy efficiency gain that the proposed scheduler achieves and the effects of various satellite link parameters are examined. Significant conclusions for the optimization of satellite communication links in terms of energy efficiency are drawn.

Index Terms— Satellite communications, rain attenuation, energy efficiency, opportunistic scheduling, optimal stopping theory.

I. INTRODUCTION Modern satellite services increasingly demand for capacity

to support higher communication data rates. In order to satisfy the growing capacity requirements, frequencies above 10GHz are employed in the satellite communication systems. However, crossing the 10GHz limit gives rise to signal fading due to weather tropospheric phenomena with the dominant fading mechanism to be rain attenuation [1]. The exceedance probability is usually modeled with lognormal distribution showing very good behavior globally [2, 3].

Furthermore, given that the communication part of a wireless terminal consumes a significant portion of energy, the reduction of the transmission power is a very significant issue in energy-constrained terminals that do not have continuous power supply [4]. Towards this direction, the random channel fluctuations in time that are traditionally treated as a source of unreliability, can be opportunistically exploited, by scheduling data transmissions. This can lead to higher utilization of energy and achieve significant energy saving [4, 5].

This paper considers communication links from energy-constrained broadband satellite terminals (STs) to a Geostationary (GEO) satellite that operates above 10GHz (e.g. Ku and Ka bands). However, the results can be also applied to communication links from GEO satellite transponder to STs. By employing the optimal stopping theory [6], we find the optimal time instant for the ST to transmit under rain fades, depending on the channel conditions in order to minimize the ST’s energy consumption. Therefore, a climatic-dependent energy efficient opportunistic scheduler (CDE2OS), which is characterized by a multi-threshold policy, is proposed. Particularly, the CDE2OS postpones communication until it find the best expected channel conditions, considering specific quality of service (QoS) requirements: a tolerable time deadline for communication postponing and a required power level at the receiver. Moreover, in our analysis, we assume full channel-state information (CSI) that corresponds to the rain attenuation fading. The performance of the proposed scheduler is evaluated through simulation for different systems parameters, comparing it with other heuristic schemes. Simulation results manifest that the proposed scheme offers significant energy efficiency. Finally, it is noted that CDE2OS can be incorporated in modern satellite standards (e.g. DVB-S2, DVB-RCS2) to provide energy efficient data transmission or energy efficient transmission diversity.

The rest of this paper is organized as follows. Section II presents a short introduction on the optimal stopping theory. In Section III, we analyze the considered system and channel models as well as the link budget analysis, and also the proposed climatic-dependent energy efficient opportunistic scheduler is presented. Finally, Section IV presents the simulation results, while Section V concludes this paper.

II. OPTIMAL STOPPING THEORY The optimal stopping theory [6, 7] is concerned with

problems of choosing the optimal time to make a decision based on sequentially observed random variables, in order to maximize an expected payoff or to minimize an expected loss.

Specifically, an optimal stopping problem is defined by the following objects:

a sequence of random variables: {X1, X2, …} with known joint distribution;

The 8th European Conference on Antennas and Propagation (EuCAP 2014)

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a sequence of real-valued reward functions: {y0, y1(x1), y2(x1, x2), …, y (x1, x2, …)}

and it can be described as follows. The decision maker observes the sequence of random variables Xn=xn, and at each step n, the decision maker can choose to either stop observing and receive the known reward yn(x1, …, xn) or continue and observe Xn+1. The problem is to choose the best time 0 N to stop in order to maximize the expected reward [YN] (or, equivalently, minimize the expected loss), where YN= yN(x1, …, xN) represents the random reward for stopping at N, and

[.] corresponds to the expected value function. In more realistic problems (finite-horizon stopping problems), there is a known upper bound on the number of stages Nmax (horizon) at which one has to stop anyway.

III. CLIMATIC-DEPENDENT ENERGY EFFICIENT OPPORTUNISTIC SCHEDULER

A. System and channel model considerations For the system model under consideration, we assume the

uplink ST-GEO satellite link operating above 10GHz, however, the whole analysis can also be applied to the corresponding downlink configurations. Rainfall rate is considered the source of fading. The QoS requirements determine an upper bound time deadline Dmax within which the communication must be accomplished and a specified signal’s power level at the satellite receiver. In particular, in our communication scenario, the deadline constraint implies that the receiver must periodically get an amount of data up to the specific time bound, assuming that there are always data for transmission1. This deadline depends on the specific application/service scenario and may have various values from few seconds to several minutes. Furthermore, according to another perspective, if the same data may be re-transmitted multiple times (i.e. time diversity [8], [9]), the proposed scheduler can be viewed as an energy efficient improvement of the time diversity technique, since optimal re-transmission times are found before the time diversity fixed times.

1 Data are stored in the ST’s memory or the ST has the ability to instantaneously acquire them (e.g. by measuring).

Moreover, we assume that the ST is fully aware of the instantaneous CSI through pilot signals.

Fig. 1 presents the system model and the finite-horizon scheduling problem. The goal of the proposed CDE2OS is to minimize the transmission energy consumption of the ST by exploiting good channel opportunities. Specifically, the scheduling problem is a finite-horizon problem, where the horizon is an acceptable time deadline for transmission Dmax=Nmax· , until which we can postpone the communication. Thus, the ST checks the channel conditions at individual stages j=1,..., Nmax, every time intervals and this implies a maximum number of channel observations Nmax. The problem is to find the optimal stopping time N to start the transmission until Dmax that minimizes the energy consumption. If the time reaches Dmax and the ST has not yet transmitted, it transmits anyway. In order to exploit the channel fluctuations, the parameters of , that reflects the channel checks frequency, should be greater than the coherence time of the channel. Moreover, we assume invariant channel conditions during transmission by considering that the data transmission duration T is less than or equal to the coherence time. Additionally, the ST’s communication module can be set to the idle or sleep mode between two sequential channel checks in order to save more energy.

Furthermore, according to the link budget analysis, the received power at the satellite is given by [10]:

,r sat sat st stP G G P LG (1)

where LG denotes the total link gain, Gsat is the satellite’s antenna gain, while Gst and Pst are the ST’s antenna gain and transmission power, respectively. Regarding the total link losses, which are the reciprocal of LG, we consider both the free space losses (FSL) that are given by (4 d/ )2, where d is the distance to the satellite and is the wavelength of the signal, and the rain attenuation. Particularly, considering that g is the rain-induced fading channel coefficient, the rain attenuation in dB (AdB= –20log10g), is modeled as a lognormal random variable [2, 3]. Consequently, it can be proven [11] that the rain-faded channel power gain h=|g|2 (0,1) is modeled as a log-lognormal random variable with probability density function (pdf) that is given by:

2

2

ln ln ln1( ) exp2ln 2

mh

aa

h Af h

Sh h S (2)

where =-10/ln10, while lnAm and Sa are the statistical parameters of the link conditionally to rain lognormal distribution. These parameters can be estimated using the method in [3] or fitting the prediction method in ITU-R P.618 [12]. The point rainfall rate statistics are taken from ITU-R rainmaps [13]. Moreover, given the link characteristics and the application scenario requirements that induct the minimum Pr,sat, we have the required transmission power at ST:

1stP C h

(3)

where

t. . .Idle Mode

DataTransmissionIdle Mode Idle Mode

j=0 j=1 j=N 1 j=N Nmax

Satellite

Satellite Terminal

Time

Scheduling Problem

check

check

check

roundx

Fig. 1. System model and scheduling problem.


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,r sat

sat st

P FSLC

G G (4)

denotes the normalized power requirements at the satellite. Consequently, Pst should be greater than C, since h (0,1). Without loss of generality, we assume BPSK and QPSK modulation techniques. For those techniques, the QoS measure Bit Error Rate (BER) is given by 02 bBER Q E N [14]

for the uncoded signal, where Eb is the bit energy, N0 is the noise density at the satellite receiver and Q(.) is the Q-function. Thus, for a desired BER, the required received power at the satellite Pr,sat for the uncoded signal is given by

21, 00.5r sat bP Q BER R N , where Rb is the bit rate.

B. Propagation-based opportunistic scheduler In the following, considering that EN represents the energy

consumption of the ST at N, we formulate our scheduling problem as an optimal stopping problem of choosing a stopping rule 1 N Nmax that minimizes the expected energy consumption [EN]. In order our model to be more realistic, we assume that an amount of energy Ec is consumed every time the device checks the channel. Hence, if the ST stops at N, the total energy consumption EN can be expressed as the summation of the energy consumed for channel checks and the energy consumed during the data transmission as follows:

(3)1

N N c N cE P T N E C h T N E

(5)

where PN and hN denote the transmission power and rain-faded channel power gain at N, respectively.

The optimal stopping rule of this problem arises from the observation of the channel gain sequence of hj every and the sequence Ej, which is assumed to be j-measurable [7], where

j is the -field that is generated by the sequence of hj. We note that a stopping rule is defined to be a random variable N, such that the event {N=j} is in j. In our scheduling problem it can be easily proven that the optimal stopping rule exists, due to the finite horizon of the problem and the finite nature of Ej.

More specifically, after observing the channel conditions at each stage, the scheduler has to make the decision of whether it is optimal to stop and transmit or to continue. This decision depends on the expectation of better channel values in future moments. Thus, in order to solve our minimization problem, we compare the return for stopping PjT at each stage j, with the return that we expect to get by continuing and using the optimal rule for stages j+1 to Nmax, taking into account the cost Ec that we have to pay for continuing at every stage. Hence, considering that the cost Ec has already been paid when the decision has to be made, the following equation gives the function that represents the minimum return starting from a specific stage j, having observed H1= h1,..., Hj= hj:

max

max

( )maxmin , for 1,...,N

j j N j cV P T A E j N (6)

where max

max

( )1[ | ] N

N j j jA V that depends only on Nmax j, i.e. the number of stages to go. Consequently, the optimal stopping rule suggests stopping and transmitting at stage j, if

maxj N jP T A , which implies an optimal transmission power

threshold for each j that can be given by max

*,th j N jP A T .

In order to ensure that the transmission postponing (scheduling) deadline will be Dmax, we set A0= PmaxT at stage j=Nmax, where Pmax expresses the maximum output transmission power of the ST’s RF power amplifier. Following backwards induction, we can compute

maxN jA for each individual stage j=1,…, Nmax 1, as follows:

max

max max

1maxmax

max

1max

( )1 1

1

[ | ] = min[ , ] =

=

N j

N j

NN j j j j N j c

APT

P N j P cAC

T

A V P T A E

pTdF A dF E (7)

where FP(p) expresses the Pmax-normalized cumulative distribution function (cdf) of transmission power random variable. Consequently, it can be proven that the optimal power threshold *

,th jP at each stage is given by:

*, 1

* ** , 1 , 1 max

,

max max

1 , for 1,..., 1

, for

th jP

cP th j P th j

th j C

EpdF P F P j NP T

P j N

(8)

Hence, we result in an optimal multi-threshold policy that minimizes the expected energy consumption of the ST, according to which the current required transmission power Pj implied by the current channel conditions and the QoS constraints at the receiver, is compared with the corresponding power threshold at each stage. The multi-threshold policy is characterized by the following power threshold vector:

max

* * *,1 ,, ... , th th th NP P P (9)

To summarize, the optimal policy of CDE2OS can be described by the following expression for j=1,..., Nmax:

,

*if transmit at

else postponeth jjP P j

(10)

IV. SIMULATION RESULTS AND DISCUSSION In this Section, we evaluate the performance of CDE2OS

through extended simulations for different system parameters. The uplink ST – GEO satellite link is considered that operates at Ku and Ka bands. Realistic assumptions, which are summarized in Table I, are considered for the technical characteristics of the communication link. Moreover, the ITU-R rainmaps [13] are taken into account to calculate the rainfall rate parameters depending on the ST’s location. The long-term statistical parameters of rain attenuation have been calculated with the methodology presented in [3]. Without loss of


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generality, we consider Pmax=15W and elevation angle of 400. Moreover, in order to compare the results under different climatic conditions (different rainfall rate statistics), we consider two different geographical locations for the ST (Athens-GR / New Delhi-IN). With regard to the scheduling parameters, we assume that the channel checks occur every =30s, the transmission duration is T=30s and the time

deadline is Dmax=300s, unless it is clearly stated otherwise. Fig.2 illustrates the average energy consumption per round

that is achieved through CDE2OS versus the desired values of BER, which correspond to the minimum power requirements at the satellite receiver. The ST operates at Ku-band (14GHz) and at Ka-band (30GHz), while we consider two different geographical locations of ST to evaluate the proposed scheduler in different rain regions. As we can observe, the energy consumption increases at Ka-band in comparison with Ku-band, because the propagation losses and the fading phenomena are greater for higher frequencies. Furthermore, the average energy consumption is higher when the ST is located in New Delhi compared with Athens, due to the heaviest rain conditions. The differences between the two sites are small indicating the stability of CDE2OS and proving that it achieves climatic dependent energy efficient transmission. Moreover, at Ku-band, the average energy consumptions on the sites under investigation are almost the same.

For comparison purposes, we additionally consider two heuristic transmission schemes. Specifically, the first is the Deterministic Scheduler (DS) that schedules the transmission at constant equidistant time instants (every Dmax), while the second one is the Random Scheduler (RS) that prompts ST to transmit at a random time between the time length [0,Dmax]. The above described heurists can be considered as specific cases of time diversity technique, if the same data are transmitted at every transmission. Consequently, in this case CDE2OS can be viewed as an energy efficient time diversity scheme. To evaluate the energy efficiency of the proposed scheme, we employ the metric of energy efficiency gain ( EE). This metric is described as the percentage of energy consumption gain, comparing the average energy consumption by using the proposed scheduler and the average energy by using another scheduler X and can be expressed by:

( )1 ×100% ( )

2X

EEAvg. Energy Cons. CD EOS

Avg. Energy Cons. X (11)

Fig.3 presents the energy efficiency gain that the proposed scheduler achieves in comparison with the DS for several values of BER, considering a ST that operates at Ka-band in different rain regions. From the simulation results it can be observed, that CDE2OS attains significant energy gain which increases as the BER increases namely as the quality requirements become less strict. Particularly, for looser received power requirements at the satellite receiver, the parameter C decreases and consequently the power thresholds become stricter, improving the performance. Moreover, when the ST is positioned in a location with heavier rain phenomena (i.e. in New Delhi), the proposed scheduler attains significant higher gain. Specifically, for BER=10-3, which is a typical value for voice services, the proposed scheduler has an additional energy efficiency gain of 16% in New Delhi in comparison with the gain in Athens. This demonstrates the climatic stability of CDE2OS, which does not increase significantly the energy consumption for different rain regions (see Fig.2), in contrast with the DS. Similar results are also drawn for the RS, as it will be seen in the following.

Finally, Table II presents simulation results for different scheduling scenarios to demonstrate the effects of scheduling parameters on the proposed scheduler’s performance, considering the case of Ka-band for a ST located in Athens. Specifically, we consider three different scenarios: Scenario A (where =30s, T=30s and Dmax=300s), Scenario B (where =30s, T=30s and Dmax=600s) and Scenario C (where =60s,

T=30s and Dmax=600s). As we can see, Scenarios A and C have the same Nmax for different tolerable deadlines, while Scenario B has double Nmax. Particularly, Table II shows the normalized power requirements C at the satellite, the average energy consumption per round of CDE2OS and the corresponding energy efficiency gain in comparison with DS and RS, as well as the average performance and the average scheduling duration of CDE2OS. The average performance is given by the ratio of average power consumption to average throughput, with lower values to correspond to greater energy efficiency. Moreover, the average scheduling duration

10-5 10-4 10-3 10-2 10-10

50

100

150

200

250

300

Ave

rage

Ene

rgy

Com

sum

ptio

n pe

r Rou

nd (J

)

BER

Ku-band (14 GHz), Athens (GR)Ka-band (30 GHz), Athens (GR)Ku-band (14 GHz), New Delhi (IN) Ka-band (30 GHz), New Delhi (IN)

Fig. 2. Average energy consumption of CDE2OS per round vs BER fordifferent frequency band and ST’s locations.

TABLE I. TECHNICAL CHARACTERISTICS OF THE COMMUNICATION LINK.

Characteristics Typical Values Satellite GEO

Frequency Bands Ku (14GHz) / Ka (30GHz) Satellite Antenna Gain 60 dBi

Satellite G/T 35 dBK-1 ST Location Athens-GR / New Delhi-IN

ST Antenna Gain 10 dBi Rate 1 Mbps

Modulation BPSK/QPSK


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represents the average time that the data are postponed from transmission. As we can observe, Scenario B has slightly better performance in all evaluation metrics due to the larger Nmax which increases the opportunities to find better channel conditions; however the values for all scenarios are quite close, confirming the stability of the proposed scheduler.

V. CONCLUSION In this paper we propose a climatic-dependent opportunistic

scheduler, based on optimal stopping theory, with a view to minimizing the energy consumption of a ST that communicates with a GEO satellite. The considered communication link operates above 10GHz under rain fading. Specifically, the proposed scheduler postpones the data transmission until it finds good channel opportunities, according to an optimal stopping rule. This optimal rule suggests a multi-threshold policy that minimizes the transmission energy under specific time deadline and received power constraints. Simulation results for different system parameters have shown that the proposed climatic-depended scheduler achieves significant energy conservation comparing with other heuristics. Moreover, the stability of the proposed scheduler is confirmed in different rain regions and scheduling scenarios. Consequently, CDE2OS can provide energy efficient data transmission in modern satellite systems.

ACKNOWLEDGMENT This work was supported in part by GSRT funded project

“Cooperation 2011 - JASON” and in part by GSRT funded project “Innovative Enterprise Clusters” - ACRITAS”.

REFERENCES [1] A.D. Panagopoulos, P.-D.M. Arapoglou, P.G. Cottis, “Satellite

communications at Ku, Ka and V bands: Propagation impairments and mitigation Techniques,” IEEE Commun. Surveys & Tutorials, vol.6, no.3, pp.2-14, 2004.

[2] M. Filip, E. Vilar, “Adaptive modulation as a fade countermeasure. An Olympus experiment,” Int.J. Sat. Commun., vol.8, no1, pp.31-41, 1990.

[3] A.D. Panagopoulos, J.D. Kanellopoulos “On the rain attenuation dynamics: Spatial-temporal analysis of rainfall-rate and fade duration statistics”, Int.J.Sat. Commun. & Netw., vol.21, no.6, pp.595-611, 2003.

[4] M.I. Poulakis, A.D. Panagopoulos, P. Constantinou. “Advanced energy efficient communication techniques for wireless ad hoc and sensor networks,” in Advances and Applications in Mobile Computing, InTech, 2012.

[5] M.I. Poulakis, A.D. Panagopoulos, P. Constantinou, “Channel-aware opportunistic transmission scheduling for energy-efficient wireless links,” IEEE Trans. Veh. Technol., vol.62, no.1, pp.192-204, 2013.

[6] Y. Chow, H. Robbins, D. Siegmund, Great Expectations: Theory of Optimal Stopping. Boston, MA: Houghton Mifflin, 1971.

[7] T. Ferguson, Optimal Stopping and Applications. Math. Dept., Univ. Calif., Los Angeles, CA, 2006. [Online]. Available: http://www.math.ucla.edu/~tom/Stopping/Contents.html.

[8] H. Fukuchiand, T. Nakayama, “Quantitative evaluation of time diversity as a novel attenuation mitigation technology for future high speed satellite communication,” IEICE Trans. Commun., vol.87, no.8, pp.2119–2123, 2004.

[9] C.I. Kourogiorgas, A.D. Panagopoulos, S.N. Livieratos, G.E. Chatzarakis, "On the outage probability prediction of time diversity scheme in broadband satellite communication systems," Progress In Electromagnetics Research C, vol. 44, pp. 175-184, 2013.

[10] A.K. Maini, V. Agrawal, Satellite Technology: Principles and Applications. John Wiley & Sons Ltd, NJ, 2011.

[11] A.Papoulis, S.U.Pillai, Probability, Random Variables and Stochastic Processes. 4th ed. New York: McGraw-Hill, 2002.

[12] ITU-R Recommendation P.618-11, “Propagation data and prediction methods required for the design of Earth-space telecommunication systems,” 2013.

[13] ITU-R Recommendation P.837-6, “Characteristics of precipitation for propagation modeling,” 2012.

[14] A. Goldsmith, Wireless Communications. Cambridge Univ.Press, 2004.

TABLE II. SIMULATION RESULTS AT KA-BAND (30GHZ) FOR DIFFERENT SCHEDULING SCENARIOS (ST LOCATED IN ATHENS-GR).

Scenario A Scenario B Scenario C BER 10-4 10-2 10-4 10-2 10-4 10-2

C (W) 6.41 2.51 6.41 2.51 6.41 2.51 Avg. Energy

Cons. (J) 201.61 79.97 198.45 77.98 201.81 79.98

DSEE (%) 19.51 31.69 20.98 33.84 19.53 31.54

RSEE (%) 19.73 31.68 21.11 33.41 19.75 31.82

Avg. Performance

(mJ/MB) 53763 21326 52921 20796 53816 21328

Avg. Scheduling Duration (s)

172.1 161.3 327.5 279.1 344.7 322.7

10-5 10-4 10-3 10-2 10-10

10

20

30

40

50

60

70

80

90

Ene

rgy

effic

ienc

y ga

in (%

)

BER

Athens (GR)New Delhi (IN)

Fig. 3. Energy efficiency gain of CDE2OS at Ka-band (30GHz) comparedwith DS vs BER for different ST’s locations.


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