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Radio Resource Management Strategies for DVB-S2

Systems Operated with Flexible Satellite Payloads

Giuseppe Cocco∗, Tomaso De Cola∗, Martina Angelone†, Zoltan Katona∗ ∗ German Aerospace Center (DLR),

Institute of Communications and Navigation

82234, Oberpfaffenhofen, Germany

e-mail: {giuseppe.cocco, tomaso.decola, zoltan.katona}@dlr.de †Communications and TT&C Systems and

Techniques Section

ESA/ESTEC, Noordwijk, The Netherlands

e-mail: martina.angelone@esa.int

Abstract

The increasing demand for high-rate broadcast and multicast services over satellite networks has pushed for the development

of High Throughput Satellite (HTS) characterized by a large number of beams (e.g., more than 100). Moreover, the variable

distribution of data trafﬁc across beams and over time has called for the design of a new generation of satellite payloads, able

to ﬂexibly allocate bandwidth and power. In this context, this paper explores the technical challenges related to radio resource

allocation in the forward link of multibeam satellite networks and proposes a strategy based on a modiﬁed version of the simulated

annealing algorithm and a newly proposed objective function to meet as close as possible the requested trafﬁc across the beams

while taking fairness into account. Performance results conﬁrm the effectiveness of the proposed approach and also shed some

light on possible payload design implications.

I. INTRODUCTION

The advent of High Throughput Satellite (HTS) systems [1], [2] has revolutionized the concept of satellite communications

in that new systems operating in the Ka frequency band (and above) are being designed in order to provide geographical

coverage through a large number of beams. Such dramatic change has started upon the ever-increasing user demand for

broadcast/multicast services characterized by high rates and reliability performance. To meet these requirements, a natural

technology candidate is the Digital Video Broadcasting - Satellite - Second Generation (DVB-S2) standard [3], which is

nowadays one of the most widespread and preferred options from broadcasters of satellite systems in the forward link.

In spite of the attractive performance ﬁgures that can be attained by DVB-S2 (e.g., in terms of spectral efﬁciency), the

problem of optimally allocating bandwidth to beams and optimally operate the payload from a power perspective according to

the amount of requested trafﬁc is still not completely solved. This is because of the large number of variables that play a role

in the resulting radio resource allocation problem. Traditionally, this problem has been often addressed from a ground segment

viewpoint, by proposing optimization frameworks able to take into account propagation impairments (e.g., rain) and interference

contribution from other beams (e.g., co-channel interference (CCI)). For instance, reference [4] addresses the problem from a

scheduling viewpoint, allocating different ModCods to the satellite beams. However, the complex characteristics of data trafﬁc

(time- and space-correlation, heavily depending on the speciﬁc geographic area) have always represented a formidable obstacle

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against deriving closed-form solutions, hence requiring the introduction of approximated models or the use of numerical

optimization techniques.

On the other hand, the recent years have also witnessed an evolution of satellite system concepts from a space segment

viewpoint, which also have an important impact on the resource allocation problem [5]. Speciﬁcally, more sophisticated payload

designs have been introduced [6], so as to cope with the time and geographic variations of the bandwidth requested by each

beam. This mainly resulted in two possible design options, namely ﬂexible and beam-hopping payloads. The latter makes use

of a time-slotted illumination window so that it is possible to deﬁne the sequence of beam illumination and the number of slots

assigned to each beam according to the trafﬁc demands and the antenna radiation pattern. The former makes use of a dual

approach, consisting in allocating bandwidth or power to beams in relation to the offered and requested trafﬁc. Both options

have obviously important implications on the speciﬁc payload design (e.g., number of traveling-wave tube ampliﬁers (TWTA)

and structure of the payload connection matrix) and the related constraints (e.g., mass and available power) imposed by the

technology available nowadays. In [7], [8] the problem of time/beam allocation is studied in presence of trafﬁc asymmetry. In

the paper a closed form solution for the optimal resource allocation in a simpliﬁed setup with no interference is derived for

two different utility functions, aiming at matching the requested bitrate and maximizing the product of the ratios between the

offered and requested capacity across the beams, respectively.

In [8], [9] the advantages of multi-beam with respect to single beam satellite systems is studied under different performance

metrics. Speciﬁcally, the optimal power allocation is derived for two different objective functions, one leading to throughput

maximization and the other related to fairness. Although the aforementioned papers offer interesting hints on the problem of

resource allocation, the validity of the results is limited by the assumption of no co-channel interference, which is instead

removed in [10]. In the paper a phased array antenna is assumed at the satellite and call-admission control schemes are

investigated. Differently from the approaches adopted in the papers mentioned above, the studies contained in [11], [12]

explore the beneﬁts of power allocation. In particular, a two-stages sub-optimal algorithm is applied to solve a non-convex

optimization problem, whose solution offers some insights about the relations between power allocation and offered trafﬁc

on the forward link of satellite networks. Finally, beam-hopping and ﬂexible systems are compared in [13], where the latter

implement non-uniform bandwidth allocation and make use of sizable beams. It is worth noting that most of optimization

strategies considered in the available literature with respect to resource allocation make use of genetic algorithms or neural

networks. In [14] the Simulated Annealing (SA) algorithm [15], has been proposed to minimize the co-channel interference in

the uplink of two independent satellite systems. As a side remark, we point out that the problem of radio resource management

(RRM) has been studied also in the context of terrestrial networks [16] [17], although the payload constraints and the different

network topologies make the two optimization problems signiﬁcantly different.

With respect to the state of the art, the present paper proposes a novel resource allocation strategy, in which a multi-objective

optimization problem is addressed through the deﬁnition of an ad-hoc objective function. The optimization problem is addressed

using a modiﬁed version of the SA algorithm. Unlike in [14], the present paper applies a variant of SA to the forward link

of a multibeam satellite system adopting DVB-S2 technology and equipped with a ﬂexible (in power and/or in bandwidth)

payload. Furthermore, in our study we show the potentials of the proposed resource allocations scheme in presence of realistic

requested trafﬁc proﬁle and operative conditions by considering different conﬁgurations of ﬂexible payloads. Finally, the paper

also attempts to shed some light on the most appealing payload design approach in terms of ﬂexibility.

The remainder of this paper is structured as follows. Section II presents the system model and the formulation of the resource

allocation problem, whereas the proposed allocation strategies are illustrated in Section III. Performance analysis and discussion

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of the results are provided in Section IV. Finally, Section V draws the conclusions of the investigation presented in this work

and discusses some future research directions in the framework of radio resource management for next-generation satellite

systems.

II. RA DI O RESOURCE ALL OC ATIO N PRO BL EM

A. System Model

The present paper takes a multi-beam geostationary satellite system as reference. The satellite generates a geographical

footprint subdivided into Nbbeams, where each beam i,i= 1, . . . , Nb, serves Ni

uﬁxed satellite terminals. The population

of users active on beam igenerates an aggregate trafﬁc request which we denote as Ti

r. Let us denote with Gi,j the gain

of the signal transmitted in beam iand received by user j, where jcan take values between 1 and Ntot

u=PNb

i=1 Ni

u,Ntot

u

being the total number of users in the system. Such gains account not only for the transmitted satellite antenna power, but

also for the receiving and transmitting antennas gains and the propagation impairments (e.g., free space loss and atmospheric

attenuation). Ideally, each satellite terminal jis expected to receive only the signal transmitted by its reference beam, which we

denote as ˜

i(j). However, due to the secondary lobes of the satellite antennas, user terminals suffer from interference generated

by beams others than the reference one operating in the same frequency band (co-channel beams), leading to Gi,j 6= 0 for

some i6=˜

i(j). As far as the payload model is concerned, a single feed per beam (SFPB) architecture is considered. It is

assumed that a number of TWTA equal to NTWTA is available on-board the satellite and that each of them ampliﬁes the same

amount of bandwidth. Each tube has a total available DC power equal to Ptot. Each TWTA serves a subset of beams and

reuses the whole bandwidth. The association between beams and the TWTA’s is speciﬁed within the connection matrix. In the

conventional system, the total bandwidth Bof each TWTA is shared uniformly among the subset of ampliﬁed beams, so that

the bandwidth per beam depends only on the speciﬁc coloring scheme adopted (e.g.,B,B/2, or B/4for 1,2, or 4colours,

respectively). The TWTA bandwidth is shared among the connected beams in such a way that beams connected to the same

tube cannot have overlapping portions of bandwidth. Data is transmitted through a beam making use of multiple carriers, each

being assigned a fraction of the bandwidth allocated to the beam. The portions of data trafﬁc addressed to the different users

served by a given beam are multiplexed in time according to a time division multiplexing (TDM) framing.

B. Problem Formulation

Our aim is to allocate resources such that each beam receives an offered capacity Ti

o,i∈ {1, . . . , Nb}, that is as close as

possible to the requested capacity Ti

rwhile taking fairness into account. Ti

odepends on the bandwidth allocated to beam iand

the power settings of the TWTA to which beam iis connected, as well as on the co-channel interference generated by other

beams and on the channel gains (relative to both reference signal and interferers) of each single user. The optimization algorithm

is run at the gateway. We assume that the gateway has knowledge of the gains Gi,j ,i∈ {1, . . . , Nb},j∈ {1, . . . , N tot

u},Ni

u

being the number of users served by beam i. This assumption is a realistic one since ﬁxed terminals are considered, for which

the rate of channel variation can be assumed to be relatively slow. The channel gains are assumed to be periodically estimated

by the gateway through a return channel. Such gains are used to choose the ModCod which is best suited to each terminal’s

current channel condition, i.e., the ModCod with the highest spectral efﬁciency that can be supported by the channel.

We consider three different payloads. The ﬁrst payload can be optimized both in terms of bandwidth and power allocation.

The second one has only bandwidth ﬂexibility while in the third one only the TWTA operating conditions in terms of power

can be adjusted. For a fair comparison, both the number and the characteristics of the TWTA’s are the same for all payloads.

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We also assume that the connection matrix, which determines the subset of beams that are connected to each TWTA, is the

same in all payloads. The subset of beams connected to different TWTA’s are disjoint, i.e., one beam cannot be connected to

more than one TWTA. The ﬂexibility in terms of bandwidth allows to modify in each TWTA the spectrum assignment to the

subset of beams connected to it, under the constraint that the same portion of spectrum can not be assigned to more than one

beam connected to the same TWTA. Note that the same portion of spectrum can be assigned from different TWTA’s to one

of the beams in their relative subset, so that from a resource allocation point of view each TWTA acts as an independent unit.

The ﬂexibility in terms of power allocation consists in the possibility to change operating point (i.e., input back-off (IBO))

and power proﬁle of each TWTA independently of the others. The available set of power proﬁles is {0,1,2,3,4}. The power

proﬁle indicates the attenuation (in dB) of the peak radio frequency power delivered by the TWTA with respect to the peak

in the reference operation mode (i.e., power proﬁle 0). A larger power proﬁle indicates larger output back-off (OBO) for a

given IBO, which reduces the non-linear effects of the tube at the cost of a reduced power efﬁciency. Payloads with no power

ﬂexibility keep a ﬁxed IBO (equal to 3dB) and a power proﬁle equal to 2.

We ﬁx the bandwidth granularity to 31.25 MHz, i.e., the bandwidth allocated to a beam must be a multiple of Bch = 31.25

MHz. In the following we will refer to such elementary unit of bandwidth as chunk. The amount of bandwidth that can

be assigned to a certain beam can be expressed as NchBch , where Nch belongs to the set {1,2, . . . , N tot

ch },Ntot

ch being the

maximum number of chunks available in the system. In the present paper we assume an overall system bandwidth of 500

MHz, so that at most Ntot

ch = 16 chunks can be allocated to a beam. Transmission takes place on different carriers, each

corresponding to a chunk. The optimization problem that we aim to solve is:

minimize

v,p,Bf(v,p,B)

subject to vt∈ {−20,−19,...,5,6}, t = 1, . . . , NTWTA

pt∈ {0,1,2,3,4}, t = 1, . . . , NTWTA

B∈ B,

where NTWTA is the number of TWTA’s in the payload, f(., .)is the objective function to be minimized, which will be deﬁned

later on in this section, v= (v1, . . . , vNTWTA)and p= (p1, . . . , pNTWTA )are vectors containing the IBO’s and the power proﬁles

for all TWTA’s, respectively, while Bis the Nb×Nch bandwidth allocation matrix, which belongs to the set of feasible

bandwidth allocation matrices B.Bis a subset of the set of binary matrices whose structure depends on the speciﬁc payload

bandwidth constraints.

1) Key Performance Indicators: As a common practice in optimization problems, we aim at minimizing an objective function.

The objective function reﬂects the system key performance indicators (KPI). In order to deﬁne the KPI we start with some

general considerations. Our goal is to efﬁciently allocate the satellite resources with the aim of satisfying the requested trafﬁc

in all beams. The capacity request satisfaction can be looked at from a system (or global) perspective as well as from a beam

(or user) perspective. From a global perspective, a valid choice would be to take as objective function a measure of the error

in matching the requested capacity across the beams, i.e.,

E=

Nb

X

i=1

(Ti

o−Ti

r)2.

Although this may be a valid indicator to measure the error with respect to an ideal resources allocation condition (by ideal we

mean one in which the offered capacity matches the requested capacity exactly in each beam), the offered capacity exceeding

the requested one is treated in the same way as the missing capacity, which is not desirable. Moreover, the measure E is

5

20 40 60 80 100 120 140 160 180 200

0

1

2

3

4

5

x 108

Beam Id

Capacity [bps]

Conventional

Requested

Fig. 1: Example of requested capacity and offered capacity for the conventional payload plotted versus beam Id.

potentially unbounded (i.e., it can assume arbitrary positive values) and this makes it difﬁcult to evaluate the goodness of

the optimization solution. Furthermore, even if relatively good results are obtained in terms of matching error E, it can still

happen that trafﬁc requests are largely unmatched for a non-negligible number of beams. This may be the case mainly for

beams that present relatively low trafﬁc request and for which too little resources are allocated. As a matter of fact, beams

with relatively little capacity request may not have great impact on E and thus an optimization solution that performs well at a

global scale may neglect such beams. Although beams with higher capacity requests are likely to be the most proﬁtable ones

from the satellite operator perspective, low trafﬁc beams should be taken into account in the optimization process, since other

factors may make such beams appealing (e.g., presence in the territory, reputation of the operator, etc.). Fairness is indeed a

relevant parameter to be accounted for in the RRM optimization. Several different measures of fairness have been proposed

in literature, such as the Jain Index and the normalized entropy. Using one of these measures as (negative) objective function

would have the disadvantage of not accounting for the absolute value of the mismatch in terms of capacity (either excess or

missing).

Let us now deﬁne the satisfaction index of beam ias SIi=Ti

o

Ti

r. SI is a non-negative number which gives a measure of

the extent up to which the requested capacity is satisﬁed. If SI<1the beam has been allocated insufﬁcient resources for its

capacity needs, while SI>1indicates that the beam is being over-provisioned. Ideally it would be good to keep track of both

request satisfaction and absolute gap between the requested and the offered capacity. A way to visualize the system state in

such terms can be the representation of all beams on a scatter plot in a plane having as axis the satisfaction index and the

difference ∆i=Ti

o−Ti

r, which gives a measure of the missing (if negative) or wasted (if positive) capacity. We refer to such

plane as the satisfaction/gap (SG) plane. In Fig. 1 an example of requested and offered capacity for the conventional payload

plotted versus the beam Id is shown. The corresponding SG representation is depicted in Fig. 2.

2) Objective Function: The plot in the SG plane gives a qualitative idea of the goodness of a given resource allocation

solution in terms of both satisfaction and gap distribution. In order to have also a quantitative measure, we introduce a parameter

which is derived from the SG plot. We will refer to it as the satisfaction-gap measure (SGM). The measure has been created

so that the following hold:

1) Provide a measure of the mismatch with respect to the ideal case accounting for gap and satisfaction in all beams.

2) A beam with satisfaction lower than 1, say 1−δ, has more weight with respect to a beam with satisfaction 1 + δ(which

is also undesired but not as bad as having beams with missing capacity).

6

0 10 20 30 40 50 60

−3

−2

−1

0

1

2

3x 108

∆[bps]

SI

Fig. 2: Representation of beams in the SG plane. Each of the 200 beams is represented as a point (blue circle) in the plane having as xcoordinate the

satisfaction index and as ycoordinate the capacity gap ∆as deﬁned in this section.

3) Assume values in the interval [0,1],1being the desired situation (perfect match of offered and requested capacity through

all beams. 1).

The idea is to apply a transformation to the SG plane in such a way that the measure we look for satisﬁes the three conditions

above. Let us start with point 1). In order to take both SI and ∆into account, we treat the SG plane as a complex plane, in

which SI represents the real axis and ∆the imaginary axis. A beam/point is treated as a complex number in such plane. In

order to satisfy point 2), we apply the following transformation to the beams with real part lower than 1:

Re{c} → 1−1

Re{c},∀c:Re{c}<1.

Note that after this transformation smaller SI translate to larger distances from the origin. In order to satisfy point 3) we shift

the points with real part (satisfaction) larger than or equal to 1 towards the origin by applying the transformation c→c−1.

In this way the point representing the optimal solution becomes (0,0). In Fig. 2 it can be seen how, depending on the unit of

measure adopted to measure the excess/missing capacity (e.g., kbps, Mbps, Gbps) the range of the y axis can be quite wide

with respect to the x axis. This can be easily ﬁxed with a scaling operation. For each beam we do the following:

Im{c} → Im{c}

β,

with β > 0. The value of βcan be chosen, for instance, equal to (or a function of) the system throughput of the conventional

payload. In this way it is possible to make a comparison in terms of the goodness in the resource allocation solution between

systems with different total capacities.

In order to get a measure which takes values between 0and 1, we apply one last transformation to the plane which conﬁnes

all the points within the circle of radius 1 around the origin. This is done applying the following transformation to the absolute

value of each point, without modifying the phase of the number:

|c|→ 1−e−|c|.(1)

According to this transformation, a point at inﬁnite distance from the ideal condition (origin) will lie on the unitary circle after

the transformation while a point that has |c|=δ1before applying the transformation in expression 1, will have a distance

from the origin approximately equal to 1− | c|. The modiﬁed plot corresponding to the example in Fig. 2 is shown in Fig. 3.

1Note that such ideal condition can be achieved only in systems that are non-under-dimensioned in terms of total system bandwidth and power.

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−1 −0.5 0 0.5 1 1.5

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

y(∆)

x(SI )

Fig. 3: Representation of beams in the modiﬁed SG plane. Each beam is represented as a point (blue circle) in the plane having as xcoordinate a function

of the satisfaction index and as ycoordinate a function of the capacity gap ∆.

Starting from the transformed plot, we deﬁne the SGM as measure of the average distance from the optimal condition:

SGM = 1 −1

Nb

Nb

X

i=1

|ci|3.(2)

The third power rise in the sum on the right hand side of expression (2) is included in order to give more weight to beams

that are farther apart from the ideal condition (i.e., have SI which is either close to zero or much larger than 1or have a large

mismatch in terms of absolute capacity).

SGM is the complement to 1of the average (cube of the) distance from the origin of the points in the transformed scatter

plot. It can be easily seen that such measure takes values in [0,1] and is close to 1when all points are gathered around the

origin, which corresponds to the case in which the offered capacity matches almost exactly the requested capacity in each of

the beams and there is little difference among the deltas.

The optimization problem to be solved is, ﬁnally:

minimize

v,p,B−SGM (v,p,B)

subject to vt∈ {−20,−19,...,5,6}, t = 1, . . . , NTWTA

pt∈ {0,1,2,3,4}, t = 1, . . . , NTWTA

B∈ B.

III. RESOURCE ALL OC ATIO N STR ATEGY

Even assuming full channel state information at the transmitter, ﬁnding the optimal resource allocation is not trivial. This is

due, on one side, to the non-convexity of the objective function and on the other side to the large number of possible solutions,

which makes exhaustive search not viable 2.

We propose a suboptimal algorithm based on a slightly modiﬁed version of the Simulated Annealing algorithm [15]. The

algorithm tries to minimize the objective function deﬁned in Section II-B. This is done by running iteratively the SA algorithm,

each time using lower starting and stopping temperatures. The way the SA algorithm is applied at each run is described in the

following.

2For a ﬂexible payload with 50 beams, 8bandwidth chunks and 20 allowed IBO levels, the number of possible allocations (feasible points) is equal to

(256 ×20)50 which is on the order of 10185

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A. Perturbation of the Feasible Point

The SA algorithm uses as starting point the same bandwidth and power allocation as a conventional payload.

At each iteration the algorithm perturbs the feasible point. Depending on the payload to which the algorithm is applied,

either the bandwidth, the power or both can be modiﬁed. For the payload with full ﬂexibility the algorithm chooses randomly

at each iteration whether to modify one of the other.

The perturbation of the feasible point is done as follows. A beam is selected at random, then:

•If the bandwidth is to be modiﬁed, the number of bandwidth chunks Nch currently allocated to the beam is modiﬁed by

adding to such number a random variable u∈ {−1,0,+1}while keeping the number of allocated beams within the set

{1,2, . . . , N tot

ch −1, N tot

ch }. Once the new number of chunks Nch is selected, their location in the bandwidth is selected

at random among the Ntot

ch

Nch possible dispositions. Afterwards, the algorithms switches off the chunks allocated to the

selected beam from the other beams connected to the same TWTA (if necessary).

•If power is to be modiﬁed, the algorithm selects the TWTA to which the selected beam is connected and modiﬁes either

its IBO or its power proﬁle. Modifying the operating conditions of the TWTA induces a modiﬁcation in the amount of

power delivered by the TWTA, its power efﬁciency (i.e., the ratio of the delivered RF power to the absorbed DC power)

and the intermodulation interference associated with the TWTA nonlinearity. All these effects are taken into account by

the algorithm through realistic payload models. Note also that all the beams connected to the same TWTA are affected by

the same attenuation/ampliﬁcation of the signal on the selected beam. This is done in order to avoid the so-called capture

effect, which takes place in TWTA’s when carriers of different power are fed to the ampliﬁer [18].

B. SGM Evaluation

Once the resources of the selected beam and the corresponding TWTA have been modiﬁed, the resulting SINR for all users

are calculated for each bandwidth chunk 3. The new SINR’s are used to determine the ModCod with highest spectral efﬁciency

supported by the channel of each terminal in each chunk according to the DVB-S2 standard. Once the spectral efﬁciency for

all terminals and all allocated chunks are obtained, they are averaged out across users and chunks. More speciﬁcally, let us

consider a speciﬁc beam i. We call ηi

j,c the spectral efﬁciency achievable by terminal jin chunk cof beam i. The average

spectral efﬁciency in beam iis then:

ηi=1

Ni

uNi

ch

Ni

u

X

j=1

Ni

ch

X

c=1

ηi

j,c,(3)

where Ni

uis the number of users in beam iwhile Ni

ch is the number of chunks allocated to beam i. (3) follows from the

assumption that all users within a beam access their content in a TDM fashion on all chunks, such that each chunk is allocated

to a given user during the whole assigned reception slot. Finally, using the average spectral efﬁciency together with the number

of bandwidth chunks allocated to each beam (taking the roll-off αinto account), the offered capacity for beam iis calculated

as:

Ti

o=1

1 + αBchNi

chηi.

The Ti

oof all beams are then used to compute the new value of the SGM as described in Section II-B.

3The SINR is calculated on a chunk-by-chunk basis since each chunk is assumed to be a single carrier.

9

Initialization: allocate bandwidth

and power as in conventional

payload;

set ܶ

௦=T_start

Select a beam

Perturbate feasible point

ܵܩܯௗ <ܵܩܯ௪?

Keep new

point

With probability

݁ିௌீெିௌீெೢ

ௌீெ

்

ೞೌ

With probability

1െ݁ିௌீெିௌீெೢ

ௌீெ

்

ೞೌ

Decrease

ܶ

௦

Yes

No

Yes

No

Return point with

largest SGM and exit

Yes

No

Number of iterations

per temperature

reached?

ܶ

௦ > T_stop?

Fig. 4: Flow diagram for one call of the SA algorithm. At each call the initial and starting temperatures T_start and T_stop are decreased such that

T_start[l] = T_stop[l−1], lbeing the call index.

C. Feasible Point Update

Once the new SGM is calculated, there are two possibilities:

•The SGM obtained in the new point is larger than the old one. In this case the new point is kept and a new iteration

starts.

•The SGM obtained in the new point is smaller than the old one. In this case the new point is kept with a certain probability.

The probability of keeping the new point depends on a simulation parameter that is updated periodically. As common

practice in the literature related to simulation annealing, such parameter is called temperature and is indicated in the

following as Tsa. The new point is accepted with probability:

e−SGMold −SGMnew

SGMold Tsa .

Since we are considering the case in which the new point is worse than the previous one, in the expression above we

always have SGMold −SGMnew >0. Note also that such probability decreases as the temperature Tsa decreases.

The temperature is decreased once a predeﬁned number of iterations is reached. The cooling law at iteration nis:

Tsa(n) = ∆T×Tsa (n−1),(4)

where 0<∆T < 1. The block diagram describing one call of the algorithm is shown in Fig. 4.

As mentioned earlier in this section, the proposed algorithm is a modiﬁed version of the SA. The modiﬁcation consists in

that the SA algorithm is run iteratively, each time using lower starting and stopping temperatures. Speciﬁcally, if we indicate

with T_start[l] and T_stop[l] the starting and stopping temperatures at the l-th algorithm call, respectively, the following

holds:

T_start[l] = T_stop[l−1].

10

The reason behind such modiﬁcation is that, for the speciﬁc problem considered, we observed a tendency of the SA to converge

to local minima. This is a well known behavior of stochastic optimization algorithm with non-convex objective functions. The

typical solution usually adopted is to run the algorithm more than once, each time starting from a different starting point. In the

setup we study such solution showed limited advantages. For this reason we introduced a variant of such approach in which

i) the starting point of the new run is the feasible point output of the previous one, ii) rather than starting the simulator anew,

we decrease the starting and stopping temperature at each call. The overall effect is to break the path of the algorithm in the

feasible set, avoiding that it gets stuck in regions characterized by values of SGM that are lower than the last accepted one.

IV. PERFORMANCE ANA LYSI S

In the following we present the results obtained by applying the proposed algorithm to three different payloads. The ﬁrst

payload we consider has full ﬂexibility, in the sense that it can be optimized both in terms of bandwidth and power allocation.

The second payload has only bandwidth ﬂexibility, while in the third one only the power setting can be modiﬁed. The starting

point of the algorithm is the resource allocation used in the conventional payload. In all simulations we ﬁxed NTWTA = 50,

B= 500 MHz, Bch = 31.25 MHz, Nb= 200 and Ntot

u= 2000 (with Ni

u= 10,∀i= 1, . . . , Nb).

We compare the results for the different payloads in terms of both the effectiveness of the algorithm to meet the requested

capacity and the fairness with which the different beams are treated. Speciﬁcally, the Jain Index of the ceiled satisfaction index

is used to measure the fairness in the system. The ceiled satisfaction index is deﬁned as SI = min{SI,1}and is a measure of

the satisfaction level of a beam which focuses on the missing capacity. The JI is calculated as:

JI =PNb

i=1 SIi2

NbPNb

i=1 SI2

i

.(5)

Another relevant ﬁgure of merit for satellite communications systems is the unmet capacity (UC), which is the overall amount

of requested capacity that can not be met. UC is deﬁned as:

UC =

Nb

X

i=1 Ti

r−Ti

o+,(6)

where (x)+= max(x, 0). Similarly as for UC, we deﬁne the excess capacity as:

EC =

Nb

X

i=1 Ti

o−Ti

r+,(7)

which is the sum across the beams of the offered capacity exceeding the requested capacity. The UC and the EC give an

indication of the effectiveness of the resource allocation. Finally, we deﬁne the total offered capacity (TOC) as:

TOC =

Nb

X

i=1

Ti

o.(8)

In ﬁgures 5 and 6 the requested capacity is plotted against the beam Id together with the offered capacity obtained by

applying the proposed algorithm to different payloads. Speciﬁcally, the capacity offered by the payload with both bandwidth

and power ﬂexibility (Full), the one with only bandwidth ﬂexibility (Bandwidth) and the one with power ﬂexibility only (Power)

obtained with the proposed algorithm are shown. The offered capacity of the conventional payload is shown as a benchmark.

The requested capacity has been generated according to a trafﬁc model developed by the German Aerospace Center (DLR),

accounting for the geographical and time variations of trafﬁc requests as well as the availability of satellite network. The

model provides good matches with real requested trafﬁc statistics, as discussed in [5, section III-E], to which the interested

reader can refer for more details. In Table I and Table II the comparison among the four different payloads is presented for the

11

20 40 60 80 100 120 140 160 180 200

0

1

2

3

4

5

6

7

8x 108

Beam Id

Capacity [bps]

Full

Bandwidth

Power

Conventional

Requested

Fig. 5: Capacity versus beam number. The requested capacity at 00:00 h is shown together with the capacity offered by the conventional payload and the

three ﬂexible payloads considered.

TABLE I: SGM, Jain Index, unmet capacity and excess capacity at off-peak hour (00:00) for the four payloads. Values are rounded to the third decimal.

SGM JI UC [Gbps] EC [Gbps] TOC [Gbps]

Full 0.923 0.995 1.34 1.664 27.222

Bandw. 0.905 0.995 1.33 1.984 27.552

Power 0.62 0.978 4.263 13.26 35.895

Conv. 0.567 0.982 3.237 17.509 39.529

requested trafﬁc at off peak (00:00) and peak (19:00) hours, respectively. In order to have a deeper understanding of the SGM

as performance metric and the implications of using it as objective function, in the tables SGM, Jain Index, unmet capacity

and excess capacity are shown for each payload. All values are rounded to the third decimal. Since the last three parameters

have been previously used in literature or have an intuitive interpretation, they help to understand the SGM more in depth.

With reference to Fig. 5, the payload with bandwidth ﬂexibility and the payload with full ﬂexibility are able to provide an

offered capacity which closely follows the requested one in most of the beams. In beams with very low requested capacity,

such as beam with Id 194, the offered capacity is relatively larger than the requested one. This is in part due to the limited

granularity in terms of bandwidth. The payload with power ﬂexibility is not able to follow the requested trafﬁc as closely as

the other two ﬂexible payloads. One of the reasons for this is the fact that the power can be optimized only at TWTA level,

so that all beams experience the same power increase or decrease, while this is not the case for the payload with bandwidth

ﬂexibility, in which the number of bandwidth chunks assigned to a beam can be different from that of other beams connected

to the same TWTA (provided the same chunk of bandwidth is not allocated to more than one of the beams connected to it).

As a last remark, we notice that the offered capacity of the conventional payload shows some ﬂuctuations across the beams.

These are due to the slight differences in channel gains and interference levels experienced by the different users, that, on turn,

depend on the realistic satellite antenna radiation pattern used. From Table I we can see that the qualitative considerations

presented above are backed up by the numerical values in the table. As a matter of fact, the SGM is higher in the payloads with

full and bandwidth ﬂexibility. This corresponds to higher JI, lower UC and lower EC with respect to the other two payloads.

Comparing the Full and the Bandwidth payloads we see that the UC in the two payloads are almost the same while the smallest

EC is achieved by the Full payload, which leads to a larger SGM. This shows how the SGM jointly accounts for UC, EC and

fairness, although the mapping from SGM to the three measures is not straightforward.

In Fig. 6 we show the results relative to a more demanding pattern of requested capacity. The setup is much more challenging

12

20 40 60 80 100 120 140 160 180 200

0

1

2

3

4

5

6

7

8x 108

Beam Id

Capacity [bps]

Full

Bandwidth

Power

Conventional

Requested

Fig. 6: Capacity versus beam number. The requested capacity at 19:00 h is shown together with the capacity offered by the conventional payload and the

three ﬂexible payloads considered.

TABLE II: SGM, Jain Index, unmet capacity and excess capacity at peak hour (19:00) for the four payloads. Values are rounded to the third decimal.

SGM JI UC [Gbps] EC [Gbps] TOC [Gbps]

Full 0.912 0.978 8.514 1.161 37.415

Bandw. 0.884 0.966 10.692 1.081 35.157

Power 0.638 0.93 14.808 10.779 40.738

Conv. 0.603 0.914 15.765 12.166 39.529

than the one presented in Fig. 5 from an optimization perspective. This can be inferred from the peaks of requested trafﬁc

reaching more than three times the capacity offered by the conventional payload, and from the fact that the overall system

bandwidth and TWTA number in all the advanced payloads is the same as in the conventional one in both simulations. Also in

this case the payloads with full and bandwidth ﬂexibility can best follow the requested trafﬁc proﬁle, while the payload with

power ﬂexibility has only a limited adaptation capability. Interestingly, even though the power ﬂexibility alone is not able to

follow the requested trafﬁc, it provides an advantage to the payload with full ﬂexibility. This can be seen from the fact that

the Full payload can better approximate the highest peaks of requested capacity with respect to the bandwidth ﬂexible one.

This is further conﬁrmed by the results shown in the Table II. In the table we see that the payload with full ﬂexibility achieves

the best performance in all the four ﬁgures of merit considered, reducing the unmet and the excess capacity and increasing

the system fairness with respect to any of the other payloads. In this case we see how a higher SGM corresponds to a better

performance through the whole spectrum of ﬁgures of merits considered.

V. CONCLUSIONS

We studied the problem of radio resource management in multibeam satellite systems. A novel objective function has

been introduced with the aim to match the requested capacity across the beams as close as possible while taking fairness

into account. We proposed a stochastic optimization algorithm to minimize such function based on a modiﬁed version of

the simulated annealing algorithm. We applied the algorithm to three payloads having different degrees of ﬂexibility, namely

ﬂexibility both in bandwidth and power, in bandwidth only and in power only. Realistic payload models, antenna pattern,

co-channel interference and requested trafﬁc distribution were used in the simulations. Our results show that the proposed

approach is much more efﬁcient than the traditional conventional payload in matching the requested capacity across the beams

and leads to interesting results both under low and high trafﬁc demand. The goodness of the proposed approach has been

13

supported by measuring different ﬁgures of merit traditionally used in this kind of analysis, namely missing capacity, excess

capacity and Jain index.

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