Radio Resource Management Strategies for DVB-S2 Systems Operated with Flexible Satellite Payloads

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.

Full text

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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

2
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

3
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.

4
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|=δ1before 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.

7
−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

8
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
ܵܩܯ௢௟ௗ <ܵܩܯ௡௘௪?
Keep new
point
With probability
݁ିௌீெ೚೗೏ିௌீெ೙೐ೢ
ௌீெ೚೗೏
்
ೞೌ
With probability
1െ݁ିௌீெ೚೗೏ିௌீெ೙೐ೢ
ௌீெ೚೗೏
்
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 SIi2
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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