Limits of Smart Radio Resource Assignment inGEO Satellite Communications

Tedros Salih Abdu, Steven Kisseleff, Eva Lagunas and Symeon ChatzinotasInterdisciplinary Centre for Security, Reliability and Trust (SnT),

University of Luxembourg, LuxembourgEmail: {tedros-salih.abdu, steven.kisseleff, eva.lagunas, symeon.chatzinotas}@uni.lu

Abstract—In this paper, the limits in terms of offered capacityfor a non-precoded geostationary (GEO) satellite communicationsystem is investigated. In particular, we focus on the smart radioresource assignment as a technique to manage the interferenceacross the multi-beam pattern of the GEO system. In this context,a joint power and carrier allocation problem is formulated tomaximize the capacity of the system. The formulated optimizationproblem is non-convex and difficult to solve. Hence, we proposeto address the frequency allocation first by assuming an equalpower distribution, followed by the optimal power assignment tomaximize the sum-capacity. Numerical evaluations are presentedcomparing the proposed method with a precoded-based systemand with benchmark resource allocation schemes, showing thebenefits of the proposed technique and identifying the limits ofa non-precoded GEO satellite communications system.

Index Terms—GEO satellite, Radio Resource Assignment,Sum-Capacity Maximization

I. INTRODUCTION

Satellite communication systems have the capability ofproviding a handful of services, from TV broadcasting tobroadband internet, anywhere in the world at speeds of sev-eral megabits per second. As the world undergoes a digitaltransformation, satellite communications are expected to havea significant role in bridging the digital divide by providingconnectivity to remote areas in a quickly and easily manner[1].

The use of multi-spot beams have been introduced in mod-ern satellite communication systems to improve the spectrumutilization. While initial multibeam satellite systems consid-ered uniform and fixed power and bandwidth assignment,the recent advances in on-board payload technology (e.g.digital payloads) allow for an adaptive smart radio resourceassignment, where power and bandwidth can be distributedunevenly across beams depending on the channel qualityand/or expected beam demand [2], [3].

Several resource optimization techniques have been pro-posed in the multibeam GEO satellite literature focusingon the beam demand satisfaction. Demand-matching based

This work has been supported by the Luxembourg National Research Fund(FNR) under the project FlexSAT (C19/IS/13696663), DISBuS and the AFRGrant INSAT - “Power and Bandwidth Allocation for INterference-LimitedSATellite Communication Systems”.

bandwidth allocation has been proposed in [2] with the ob-jective of minimizing the difference between the requesteddemand and the offered capacity. In [4] power allocation isoptimized to maximize the energy efficiency of the systemby neglecting inter-beam interference. The latter is consideredin [5], [6]. Joint power and frequency allocation under ademand-matching perspective has been investigated in [7]–[9]. Regarding the maximization of the sum-capacity, severalworks have focused on the precoding design (including powerallocation) assuming full frequency reuse across beams [10],[11].

In this paper, we aim to investigate the limits of a non-precoded satellite system by means of proposing a joint powerand carrier assignment approach to maximize the sum-capacityof the system. Although the maximization of system capacityhas been extensively studied in terrestrial wireless commu-nications (e.g. [12]–[17]), this has not been fully addressedin the satellite communication area, where different systemmodel and payload constraints apply. In addition, the goal ofthis paper is to shed some light into the need of complexinterference mitigation techniques when flexible and smartresource assignment is available. The contribution the paperdescribed as follows:

• We mathematically formulate the joint carrier and poweroptimization problem for the system capacity maximiza-tion. The problem is shown to be non-convex and NP-hard. Therefore, we propose to solve the problem bysplitting it into two sub-problems which are sequentiallyaddressed. The achieved solution is a sub-optimal pointof the original problem.

• We provide extensive numerical results, where the perfor-mance of the proposed scheme is compared with differ-ent non-precoded radio resource management benchmarkschemes. In addition, we compared with the popularprecoded-based full-frequency reuse strategy [10], [18]and identified when precoding is needed to further in-crease the system capacity.

The remainder of the paper is organized as follows. SectionII introduces the system model. The problem formulation andthe proposed solution are presented in Section III and Section

IV, respectively. Numerical results are provided in Section V.Section VI concludes the paper.

Notation: Boldface of upper case and lower case lettersrefers to matrices and vectors, respectively. The transpose ofa vector and hermitian transpose of a vector are representedby [.]T and [.]H , respectively. Lastly, ‖.‖F represents theFrobenius norm.

II. SYSTEM MODEL

We consider a downlink multibeam GEO satellite systemwhich consists of N beams and K carriers. The total availabledownlink bandwidth is equal to Btot = K · Bsc where eachcarrier has bandwidth Bsc. We assume that a single userper beam is served at a given time instance. Furthermore,we denote xk =

[xk[1], xk[2], . . . , xk[N ]

]Tthe assignment

vector for carrier k, where xk[i] ∈ {0, 1} is a binary valuedvariable, with xk[i] = 1 indicating that carrier k is assignedto user i. The channel power gain vector between the satelliteand the ith user over the kth carrier is denoted as gi,k =[gi,k[1], gi,k[2], . . . , gi,k[N ]

]T.

The transmit power allocation vector for kth carrier is de-noted as pk =

[pk[1], pk[2], . . . , pk[N ]

]T. Hence, the signal-

to-interference-plus-noise ratio (SINR) of the ith user over kthcarrier can we expressed as

γi,k(xk,pk) =gi,k[i]xk[i]pk[i]∑N

j=1,j 6=i gi,k[j]xk[i]pk[j] + σ2k[i]

, (1)

where pk[i] is the transmit power assigned to the ith user overthe kth carrier, σ2

k[i] is the noise power received by the ithuser over the kth carrier and gi,k[j] is the channel power gainbetween the jth satellite antenna and the ith user over the kthcarrier. The power channel gain gi,k[j] is defined as

gi,k[j] =

∣∣∣∣∣√GRGi[j]

4π diλ

∣∣∣∣∣2

, (2)

where GR is the user terminal antenna gain, Gi[j] denotes thegain from the jth satellite feed towards the ith user and di isthe slant range between the satellite and ith user.

The offered capacity at to user i over carrier k is given by

Ci,k = Bsc log2(1 + γi,k(xk,pk)), (3)

and the overall offered capacity at beam i considering theaggregation of all available carriers of the system is

Ci =

K∑k=1

Ci,k. (4)

III. PROBLEM FORMULATION

In this section, the resource allocation problem is formulatedto maximize the total capacity of the system. For this, weselect the sum of the offered capacity as an objective functionsubject to different power and carrier constraints. Furthermore,we include a minimum SINR constraint for each user, whichprevents that only users with good channel conditions are

served while users with weak channels starve. The latter isalso achieved by ensuring that at least one carrier is allocatedper user. The optimization problem is given by

maximizexk,pk,∀k

f (γi,k(xk,pk))

s.t.

T1 : γi,k(xk,pk) ≥ xk[i]γmin,∀i,∀k,

T2 :

N∑i=1

K∑k=1

pk[i] ≤ Ptotal,

T3 :

K∑k=1

pk[i] ≤ Pmax,∀i,

T4 : xk[i] ∈ {0, 1},∀i,∀k,

T5 :

K∑k=1

xk[i] ≥ 1,∀i,

T6 : pk[i] ≤ xk[i]Pmax,∀i,∀k,T7 : pk[i] ≥ 0,∀i,∀k,

(5)

where

f (γi,k(xk,pk)) =

N∑i=1

K∑k=1

Bsc log2(1 + γi,k(xk,pk)).

Targeting the maximization of total offered capacity in (5),constraint T1 ensures that the SINR per carrier is not lowerthan to the minimum SINR γmin requirement of the system.Constraint T2 provides the upper bound for the transmit powergiven by the total available power at the satellite Ptotal. Inaddition, T3 indicates the per-beam power constraint, whereeach beam should not exceed the limit imposed by Pmax..The carrier assignment xk[i] is a binary variable as indicatedby T4. Furthermore, in order to serve all areas in the field ofview of the satellite, each beam has to be assigned at least onecarrier, which is guaranteed by constraint T5. Constraint T6guarantees that the power is allocated to beam i in carrierk only if the carrier is assigned, i.e. xk[i] = 1. Finally,Constraint T7 ensures that the allocated power is non-negative.At first, we rewrite problem (5) in standard form of convexoptimization:

minimizexk,pk,∀k

− f (γi,k(xk,pk))

s.t.

T1, T2, T3, T4, T5, T6, T7,

(6)

The non-linearity of γi,k(xk,pk) as well as the integer natureof xi,k makes the problem (6) to be non-convex. Problem(6) is a mixed integer non-convex optimization problem, forwhich it is difficult to find the optimal solution. In this section,we propose a sub-optimal solution for the aforementionedproblem (6).

IV. PROPOSED SMART RADIO RESOURCE ASSIGNMENT

We solve the problem by splitting it into two subproblems.In the first step, we propose an optimization problem to

find the carrier allocation vector xk by assuming a fixedand uniformly distributed power. Next, in the second stepand based on the previously obtained carrier assignment, weoptimize the power to maximize the system capacity.

A. Step 1: Carrier Assignment

In this section, we solve the carrier allocation problemwhile keeping the transmit power constant. We assume equalpower per carrier i.e. pk[i] = Ptotal

NK . The optimization problemformulated as

minimizexk,∀k

− f (γi,k(xk))

s.t.

R1 : xk[i] ∈ {0, 1},∀i,∀k,

R2 :

K∑k=1

xk[i] ≥ 1,∀i,

(7)

Constraints R1 and R2 represent the binary valued vari-ables and the guarantee that at least one carrier per beamis assigned, respectively. We convexify the constraint set of(7) by relaxing R1 constraint to be continuous between 0and 1, i.e. 0 ≤ xk[i] ≤ 1. Since R1 is relaxed, we observethat the value of xk[i] = 1/K also a feasible solution whichsatisfies the constraint R2. Hence, for this case, it is difficultto assign at least one carrier per beam. Therefore, to avoidthis problem, we replace R2 by equivalent representationof xk[i] ≥ χk[i],∀i,∀k, where χk[i] is the binary carrierallocation when K color reuse pattern is used1. Due to theinter-beam interference, the object of (7) is non-linear and non-convex. Hence, it is very challenging to determine a close-to-optimum solution. Therefore, we propose to use the quadratictransform to solve the problem iteratively [19]. The quadratictransform of f (γi,k(xk)) is given by

f̃ (γi,k(xk)) = log2(1 + γ̃i,k(xk)) (8)

γ̃i,k(xk) = 2yi,k

√gi,k[i]xk[i]pk[i]

−y2i,k

N∑j=1,j 6=i

gi,k[j]xk[i]pk[j] + σ2k[i]

(9)

yk[i] =

√gi,k[i]xlk[i]pk[i]∑N

j=1,j 6=i gi,k[j]xlk[i]pk[j] + σ2k[i]

(10)

where yk[i] is the quadratic transform variable for each carrierand xlk[i] is the previous value of xk[i]. Finally, we rewrite (7)as

1The value of χk[i] depends on K. For example if K = 4 and K = 7then χk[i] holds the property of four color reuse pattern and seven color reusepattern, respectively.

minimizexk,∀k

− f̃ (γi,k(xk))

s.t.

R1 : 0 ≤ xk[i] ≤ 1,∀i,∀k,R2 : xk[i] ≥ χk[i],∀k,∀i,

(11)

The problem (11) is convex and can be efficiently solvedwith advanced optimization toolboxes like CVX [20]. The pro-posed algorithm is provided in Algorithm 1. First , we test thealgorithm for different possible values xlk[i] and we observedthat a feasible point xlk[i] = 1,∀k,∀i gives best result. There-fore, we start with feasible point xlk[i] = 1, ,∀k,∀i. Then, thenew solution of xk[i] updates the value of xlk[i]. Accordingly,the algorithm iteratively updates the value of yk[i] until con-vergence. For this paper, the algorithm terminates when the ab-solute difference between the previous and the current value ofyk[i] undergoes 10−4 i.e.

∑Ni=1

∑Kk=1

∣∣yk[i]− ylk[i]∣∣ ≤ 10−4,

where ylk[i] is the previous value of yk[i]. Note that the finaloutput of the algorithm xk[i] may not be an integer numberdue to the applied relaxation of the variables. Therefore, weround it to the nearest integer number.

Algorithm 1: Carrier allocation

Input: feasible point xlk[i];yk[i]← 0;repeat

ylk[i]← yk[i];

Update: yk[i] =

√gi,k[i]xl

k[i]pk[i]∑Nj=1,j 6=i gi,k[j]xl

k[i]pk[j]+σ2k[i]

;

Solve (11) ;xlk[i]← xk[i];

until∑Ni=1

∑Kk=1

∣∣yk[i]− ylk[i]∣∣ ≤ 10−4;

Output:xk[i],∀i,∀k;

B. Step 2: Power AllocationAt this point, we have obtained the carrier assignment

vectors for each beam. In this section, we optimize thepower required per beam to maximize the system sum rateconsidering the potential inter-beam interference. Then, we re-formulate the optimization problem of (6) as follows,

minimizepk,∀k

− f (γi,k(pk))

s.t.

T1 : γi,k(pk) ≥ xk[i]γmin,∀i,∀k,

T2 :

N∑i=1

K∑k=1

pk[i] ≤ Ptotal,

T3 :

K∑k=1

pk[i] ≤ Pmax,∀i,

T6 : pk[i] ≤ xk[i]Pmax,∀i,∀k,T7 : pk[i] ≥ 0,∀i,∀k,

(12)

Problem (12) is still non-convex because of the non-linearityof γi,k(pk). Similar to section IV.A, we employ a quadratictransform of the objective function to solve the problem (12)iteratively [19]. The quadratic transform of f (γi,k(pk)) isgiven by

f̃ (γi,k(pk)) = log2(1 + γ̃i,k(pk)) (13)

γ̃i,k(pk) = 2zi,k

√gi,k[i]pk[i]

−z2i,k

N∑j=1,j 6=i

gi,k[j]pk[j] + σ2k[i]

(14)

zk[i] =

√gi,k[i]plk[i]∑N

j=1,j 6=i gi,k[j]plk[j] + σ2k[i]

(15)

where zk[i] is the quadratic transform variable for each trans-mit power per carrier and plk[i] is the previous value of pk[i].Note that we did not include xk[i] in (13) because we have theconstraint T6 which guarantees that the power is allocated tobeam i in carrier k only if the carrier is assigned, i.e. xk[i] = 1.Finally, we rewrite (12) as

minimizepk,∀k

− f̃ (γi,k(pk))

s.t.

T̂1 : xk[i]γmin

N∑j=1,j 6=i

gi,k[j]pk[j] + σ2k[i]

− gi,k[i]pk[i] ≤ 0,∀i,∀k,

T2 :

N∑i=1

K∑k=1

pk[i] ≤ Ptotal,

T3 :

K∑k=1

pk[i] ≤ Pmax,∀i,

T6 : pk[i] ≤ xk[i]Pmax,∀i,∀k,T7 : pk[i] ≥ 0,∀i,∀k,

(16)

Note that T̂1 is the equivalent form of T1. The problem (16)is convex and can be solved optimally. The calculation of theoptimal solution for (16) is repeated in each iteration, which isdepicted in Algorithm 2. First, we start with a feasible pointplk[i] = ptotal

NK . Then, we calculate zk[i] and by solving (16)we obtain a new point pk[i]. The algorithm terminates whenthe absolute sum of the difference between zk[i] and zlk[i]becomes very small (10−4 in this work), which indicates theconvergence of the algorithm (being zlk[i] the previous valueof zk[i]). Correspondingly, the power is optimized such thatmaximum capacity of the system attained. Accordingly, weobtain the total capacity as C =

∑Ni=1

∑Kk=1 Ci,k,∀i.

V. SIMULATION RESULTS

In this section, we evaluate the performance of the proposedJoint Power and Carrier Sum Rate Maximization (JPCSRM)

Algorithm 2: Power allocation

Input: feasible point plk[i];zk[i]← 0;repeat

zlk[i]← zk[i];

Update: zk[i] =

√gi,k[i]xk[i]plk[i]∑N

j=1,j 6=i gi,k[j]xk[i]plk[j]+σ2k[i]

;

Solve (16) ;plk[i]← pk[i];

until∑Ni=1

∑Kk=1

∣∣zk[i]− zlk[i]∣∣ ≤ 10−4;

Output:C =

∑Ni=1

∑Kk=1 Ci,k,∀i;

scheme. The main simulation parameters are summarized inTable I. A N = 100 GEO satellite beam pattern generated as-suming a Direct Radiating Antenna (DRA), with 750 elementsspaced 5 lambda and provided by the European Space Agency(ESA) is considered. The results have been generated withM = 100 Monte Carlo runs. In each run, a user is selectedrandomly from the considered beam coverage area.

TABLE ISYSTEM PARAMETERS

Parameter ValueSatellite Orbit 13◦E

Number of beams (N) 100Number of carrier (K) 4

System Bandwidth (Btot) 500 MHZSub-carrier bandwidth (BSC) 125 MHz

Noise power (σ2k[i]) -123 dBW

Minimum SINR (γmin) -2.2 dBMax. beam gain (Gi[j]) 51.8 dBiUser antenna gain (GR) 39.8 dBi

Total Power of the system (Ptotal) 5000WMaximum power for each beam (Pmax) 100W

For comparison, we consider the following benchmarkschemes:

1) Full color reuse scheme with uniform power alloca-tion (FullCUP): We assume all carriers are used in allbeams, i.e. xk[i] = 1,∀i,∀k, and we apply equal powerper carrier.

2) Four color reuse scheme with uniform power alloca-tion(FourCUP): One fourth of the available bandwidthwith uniform power allocation to each beam is assigned.

3) Minimum Mean Squared Error (MMSE) precoder:Full frequency reuse is assumed and the MMSE precoderis applied. The precoding matrix Wk is obtained fromthe channel matrix Hk as follows,

Wk =

√PtotalK

W̃ k

‖W̃ k‖F(17)

W̃ k = HHk (HkHH

k + βI)−1 (18)

where β > 0 is the regularizer factor, the channelmatrix is Hk =

[hT1,k,h

T2,k, . . . ,h

TN,k

]Tand the channel

vector is hTi,k =[hi,k[1], hi,k[2], . . . , hi,k[N ]

]T. Note

that hi,k[j] is the channel between the jth satelliteantenna and the ith user over the kth carrier. Hence,we define the channel as

hi,k[j] =√gi,k[j]e−iΦj , (19)

where Φj is the phase of the satellite jth antenna. TheSINR for the ith user over the kth carrier after usingMMSE precoder is

γi,k(wi,k) =|hHi,kwi,k|2∑N

j=1,j 6=i |hHi,kwj,k|2 + σ2

k[i]. (20)

Hence, the overall offered capacity at beam i consideringthe aggregation of all available carriers of the system is

Ci =

K∑k=1

Bsc log2(1 + γi,k(wi,k)). (21)

A. Random User Location

For each Monte Carlo realization, we choose the location ofusers randomly from a uniform distribution within the consid-ered beam coverage. Fig. 1 shows the distribution of possibleuser locations within a beam. Zone-based user location isproposed in Section V.B.

-9.5 -9 -8.5 -8 -7.5 -7 -6.5 -6 -5.5

Longitude [deg]

35.5

36

36.5

37

37.5

38

38.5

39

39.5

Latitu

de [deg]

Beam

Users

Fig. 1. Location of users within a beam

Fig. 2 shows the CDF of the sum rate for JPCSRM and thebenchmark schemes. We observe that the performance JPC-SRM outperforms the FullCUP and FourCUP schemes. Forexample, for 100% cases, JPCSRM achieves 77.66 Gbps whileFullCUP and FourCUP achieve 65.56 Gbps and 53.7 Gbps,respectively. However, the achievable rate with JPCSRM islower than with MMSE precoder by 38.4%. The reason isthat the selected user may be located at the beam edge andexperience strong interference from the neighboring beams.This interference can be reduced via precoding.

The geographic representation of the average achievable rateper beam for JPCSRM is shown in Fig. 3. We observed that

46% of the beams have a maximum rate between 500 Mbpsand 700 Mbps, 26% of the beams have a maximum ratebetween 700 Mbps and 800 Mbps, 10% of the beams havemaximum rate between 800 Mbps and 1000 Mbps, whereas18% of beams achieves more than 1000 Mbps. In general, weobserve that higher rates can be obtained at the border of thecoverage area. The reason for this lies in reduced number ofinterfering beams at the border compared to the center of thecoverage area, which leads to lower interference at the borderand a higher data rate.

50 60 70 80 90 100 110 120 130 140

Sum rate capcaity (Gbps)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CD

F

JPCSRM

FullCUP

FourCUP

MMSE precoder

Fig. 2. Comparison of schemes for random user selection

Fig. 3. Average achievable rate per beam for random user location

B. Zone-based User Location

In order to provide a deeper insight in the performance,we subdivide the beam area into two zones, i.e. Zone a andZone b, see Fig. 4. Zone a contains the users located close tothe beam center and Zone b contains the users close to thebeam edge. The latter is an important scenario, since usersat the beam edge suffer from strong interfering signals of theadjacent beams.

Fig. 5 provides the CDF of sum rate for the JPCSRM andthe benchmark schemes over different channel realizations forusers in Zone a. We observed that the proposed JPCSRMachieves higher sum rate compared to the FullCUP and Four-CUP schemes. For example, for 100% cases, the JPCSRM

-9.5 -9 -8.5 -8 -7.5 -7 -6.5 -6 -5.5

Longitude [deg]

35.5

36

36.5

37

37.5

38

38.5

39

39.5

Latitu

de [deg]

Beam

Users in Zone a

Users in Zone b

Fig. 4. Users clustered into two zones within a beam

provides 96.05 Gbps, whereas the sum rate FullCUP andFourCUP scheme is 91.93 Gbps and 62.65 Gbps, respectively.In contrast, the JPCSRM sum rate is lower than with theMMSE precoder by 30%. For Zone a, since the location ofthe users is near to the center of the beam, we expect thereceived interference signal from adjacent beams to be ratherweak. Hence, we observe a high sum rate.

60 70 80 90 100 110 120 130 140 150

Sum rate capcaity (Gbps)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CD

F

JPCSRM

FullCUP

FourCUP

MMSE precoder

Fig. 5. Comparison of schemes for Zone a

Fig. 6 shows the geographic representation of the averageachievable rate per beam. We observed that 18% of the beamshave a maximum rate between 700 Mbps and 800 Mbps, 40%of the beams have a maximum rate between 800 Mbps and900 Mbps, 11% of the beams have a maximum rate between900 Mbps and 1000 Mbps, whereas 31% of beams providesmore than 1000 Mbps. In general, we observe that the sum ratevaries much less than in Fig. 6, especially close to the centerof the coverage area. The reason is that the users experiencemuch less interference, if they are located close to the beamcenter. Thus, the data rate depends much less on the numberof adjacent interfering beams.

The performance of the schemes for Zone b is shown inFig. 7. The JPCSRM shows better performance compared toFullCUP and FourCUP. For instance, at 100% cases, the JPC-SRM provides 71.95 Gbps whereas, the sum rate of FullCUPand FourCUP is 55.72 Gbps and 50.52 Gbps, respectively.

Fig. 6. Average achievable rate per beam Zone a

But at 100% cases, the MMSE precoder provides 41.2% moresum rate compared with JPCSRM scheme. This is because theMMSE preocder mitigates the interference while the JPCSRMoptimizes the power to minimize the interference. For Zone b,since the location of the users is away from the center of thebeam, we expect the received interference signal from adjacentbeams to be high. Therefore, we observed that a lower sumrate achieved when the location of the user is near the edgeof the beam.

50 60 70 80 90 100 110 120 130

Sum rate capcaity (Gbps)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

CD

F

JPCSRM

FullCUP

FourCUP

MMSE precoder

Fig. 7. Comparison of schemes for Zone b

Fig. 8 depicts the geographic representation of the averageachievable rate per beam for JPCSRM. We observed that 72%of the beams have a maximum rate between 500 Mbps and 700Mbps, 4% of the beams have a maximum rate between 700Mbps and 800 Mbps, 5% of the beams have a maximum ratebetween 900 Mbps and 1000 Mbps, whereas 19% of beamsprovides more than 1000 Mbps. We notice that Zone b has alow achievable rate compared to random user distribution andZone a, because users experience a high level of interferencefrom adjacent beams. Furthermore, high data rates have onlybeen reached at the border of the coverage area, where thenumber of interfering beam is reduced. From this, we concludethat this scenario is interference-limited and precoding isrequired in order to enhance the system performance.

Fig. 8. Average achievable rate per beam Zone b

TABLE IIMAXIMUM SUM RATE AVAILABILITY

100% 50% 25% 10%Random Location (Gbps) 77.66 82.98 84.46 86.1

Zone-based Location (Gbps) Zone a 96.05 99.04 100.1 100.9Zone b 71.95 75.66 76.96 78.11

C. Maximum sum rate availabilityIn this section, we compare the maximum sum rate avail-

ability of the different user location distributions for theproposed JPCSRM technique. We can observe from Table IIthat the system provides 77.66 Gbps, 96.05 Gbps, 71.95 Gbps,in case of random user locations, users in zone a and usersin zone b, respectively, in 100% of cases. Similarly, in 50%of cases, the system provides 82.98 Gbps, 99.04 Gbps, 75.66Gbps, for the same scenarios. Generally, the maximum sumrate of Zone b is lower compared to Zone a and randomlocations. As described earlier, the reason is much higherinterference, which can only be mitigated using precoding

VI. CONCLUSIONS

In this paper, we proposed a joint carrier and power al-location to maximize the capacity of broadband GEO Sat-Com systems. The formulated optimization problem is non-convex in general and NP-hard. Therefore, we decomposedthe original problem into two subproblems. First, we findthe carrier assignment assuming a fixed uniform power dis-tribution. Next, we optimize the power required per carrier inorder to maximize the capacity of the system. With extensivesimulation results, we showed that the achievable capacity ofthe proposed smart radio resource assignment scheme givesbetter performance compared to the non-precoded benchmarkschemes. Furthermore, we observed that applying proper userselection can push further the limits of the low-complexitysmart radio resource assignment. On the other hand, weidentify the limits of non-precoded systems by comparing thiswith high-complexity precoded-based systems.

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