Linear and nonlinear techniques for multibeamjoint processing in satellite communicationsDimitrios Christopoulos1*, Symeon Chatzinotas1, Gan Zheng1, Joël Grotz2 and Björn Ottersten1,3
Abstract
Existing satellite communication standards such as DVB-S2, operate under highly-efficient adaptive coding andmodulation schemes thus making significant progress in improving the spectral efficiencies of digital satellitebroadcast systems. However, the constantly increasing demand for broadband and interactive satellite linksemanates the need to apply novel interference mitigation techniques, striving towards Terabit throughput. In thisdirection, the objective of the present contribution is to investigate joint multiuser processing techniques formultibeam satellite systems. In the forward link, the performance of linear precoding is investigated with optimalnonlinear precoding (i.e., dirty article coding) acting as the upper performance limit. To this end, the resultingpower and precoder design problems are approached through optimization methods. Similarly, in the return linkthe concept of linear filtering (i.e., linear minimum mean square error) is studied with the optimal successiveinterference cancelation acting as the performance limit. The derived capacity curves for both scenarios arecompared to conventional satellite systems where beams are processed independently and interbeam interferenceis mitigated through a four color frequency reuse scheme, in order to quantify the potential gain of the proposedtechniques.
1 IntroductionCurrent satellite systems, following the cellular para-digm, employ multiple antennas (i.e., multiple onboardantenna feeds) to divide the coverage area into smallbeams (spotbeams). To the end of limiting interbeaminterferences, these multibeam satellite communication(SatCom) systems spatially separate beams that sharethe same bandwidth. This multibeam architecture allowsfor a significant boost in capacity by reusing the avail-able spectrum several times within the coverage area,especially in the Ka-band. Subsequently, the capacity ofcurrent satellite systems can well exceed 100 GBps withstate-of-the-art architectures [1]. A large number ofrecent satellite systems procurements have clearly con-firmed the trend towards multibeam satellite systems asbroadband reference system architecture. Examplesinclude systems such as Wildblue-1 and Anik F2 (66Ka-band spot beams), Kasat (82 Ka-band spot beams)and recently Viasat-1 (72 spot beams in Ka-band) for
mainly fixed two-way (i.e., interactive) broadband appli-cations as well as the GlobalExpress system designed fora new generation of mobile services in Ka-band. Interac-tive services, in particular, benefit from these architec-tures since a finer partitioning of the coverage areaallows for parallel data stream transmissions.Despite the achievements of current SatComs, existing
systems are far from the future goals for terabit capacity.Two main obstacles towards the Terabit satellite arenamely the internal with respect to the system interfer-ences (i.e., intrasystem or interbeam interferences) andthe overwhelming number of spotbeams needed toachieve Terabit throughput. To alleviate these perfor-mance constrains, novel techniques need to be explored.Terrestrial systems, have introduced the paradigm of
multicell joint processing to mitigate interferences andboost system capacity. According to this paradigm, usersignals received in the uplink channel by neighboringbase station (BS) antennas are jointly decoded in orderto mitigate intercell interferences. Similarly, user signalsin the downlink channel are jointly precoded beforebeing transmitted by neighboring BS antennas for thesame purpose. However, one of the practical obstaclesin joint processing implementation is the existence of a
* Correspondence: [email protected] Centre for Security, Reliability and Trust (SnT), University ofLuxembourg, 6 rue Richard Coudenhove-Kalergi, L-1359 Luxembourg-Kirchberg, LuxembourgFull list of author information is available at the end of the article
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backhaul network which enables this form of coopera-tion amongst neighboring BSs.The interference limited nature of the multibeam
satellite channel is a commonality between SatCom andterrestrial systems. Also, considering the architecture ofmultibeam SatComs networks, a small number ofground stations is responsible for processing the trans-mitted and received signals that correspond to a vastcoverage area. This characteristic simplifies the applica-tion of joint processing techniques. In this context, theapplication of multibeam joint processing in SatComsystems is investigated in the present contribution. Themain purpose is to provide an overview of the perfor-mance of such techniques for the forward and thereturn link (RL) in specific realistic scenarios, as well asto quantify the potential gain of such techniques byusing the throughput performance of conventional fre-quency reuse schemes as benchmark.The rest of this article is structured as follows. An
overview of related work is presented in Section 2. InSection 3, the capacity performance of multibeam jointprocessing is examined, focusing on the forward link(FL) of fixed services. In Section 4 the RL of a satellitesystem serving mobile users and jointly decodes all thereceived signals is investigated. Finally, in Section 5, thecapacity performance is quantified through numericalsimulations and compared to the performance of con-ventional systems, while Section 6 concludes the article.
1.1 NotationThroughout the formulations of this article, ε[·], (·)†, (·)T,⊙ and ⊗ denote the expectation, the conjugate trans-pose matrix, the transpose matrix, the Hadamard pro-duct and the Kronecker product operations, respectively.The Frobenius norm of a matrix or vector is denoted by||·|| In denotes a n × n identity matrix, In×m a n × mmatrix of ones, 1n a n × 1 vector of ones, 0 a zeromatrix and Gn × m a n × m Gaussian matrix.
2 Joint processing techniquesThis section provides a review of related work in termsof multiuser multiple input multiple output (MU-MIMO) and multibeam processing techniques. Optimalnonlinear as well as suboptimal linear techniques havebeen investigated in the existing literature. In general,nonlinear techniques achieve channel capacity but theinduced complexity comes with high implementationcosts. Thus, reduced complexity linear techniques thatprovide sufficient performance can be employed.Starting from recent advances in information and
communication theory, an overview of the existing lit-erature on multibeam processing is provided, beforehighlighting the contributions of this article.
2.1 Multiuser joint processing techniquesThe concept of joint processing has the ability of con-verting the interference channel of the forward and RLof a multi-antenna system into a MIMO Broadcast (BC)and multiple access channel (MAC) respectively. Thestate-of-the-art on the receiver and transmitter architec-tures for the two channels follows.2.1.1 Transmitter architectures: MIMO BCIn MU MIMO communications, the capacity of theMIMO BC channel can be achieved by dirty paper cod-ing (DPC) as shown in [2]. DPCa, allows for the cancela-tion of the interferences of the previously, seriallyencoded users, thus causing no interference to followingusers. However, the implementation complexity of DPCleads to the investigation of linear precoding techniqueswith reduced complexity such as zero forcing (ZF) andregularized zero forcing (R-ZF). In these techniques, allusers can be encoded in parallel with the precoding vec-tors. In terms of performance, ZF cancels multiuserinterference, thus being suitable for the high signal tonoise ratio (SNR) regime [3]. On the other hand, R-ZFtechniques, also take into account the noise variance,thus making them suitable for any SNR [4]. The maindisadvantage of linear techniques, however, is that thenumber of simultaneously served single antenna userscan be at most equal to the total number of transmitantennas.More recently, several multi-cell processing methods
for the downlink of terrestrial systems were devised in[5-7]. In particular, assuming data sharing, the authorsin [5] studied the design of transmit beamforming byrecasting the downlink beamforming problem into aleast minimum mean-square-error estimation (MMSE)problem. However, the required signalling between theBSs is too high and global convergence is not guaran-teed. Later, in [6], a distributed design in Time-Divi-sion-Duplex (TDD) systems was proposed, using onlylocal channel state information (CSI) and demonstratingthat performance close to the Pareto bound can beobtained. However, the main issue with [5,6] is thatboth require data sharing between the BSs. Hence, theiruse with limited backhaul throughput is prohibited.Finally, in [7], distributed multicell processing withoutdata or CSI sharing was proposed, but with the require-ment for moderate control signalling among BSs.2.1.2 Receiver architectures: MIMO MACWith respect to the MIMO MAC, MMSE filtering fol-lowed by successive interference cancelation (SIC) per-formed at the receive side, is proven to be the sum-ratecapacity achieving strategy [8-10]. The reduced-com-plexity linear minimum mean square error (LMMSE)receiver [11,12] aims at minimizing the square errorbetween the transmitted and the detected signal with
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the use of MMSE filters. The outputs of the filters aresubsequently fed into conventional single-user decoders.The main limitation of the LMMSE receiver is that thenumber of users that can be effiectively filtered is lim-ited by the rank of the channel matrix, namely the totalnumber of receive antennas in the system.Multicell joint decoding was firstly introduced by
[13,14]. Since then, the initial results have beenextended for more practical propagation environments,transmission techniques and backhaul infrastructures inan attempt to better quantify the performance gain.More specifically, it was demonstrated in [9] that fadingpromotes multiuser diversity which is beneficial for theergodic capacity performance. Following that, realisticpath-loss models and user distribution were investigatedin [15,16], where closed-form capacity expressions basedon the cell size, path loss exponent and user spatialprobability density function (p.d.f.) where provided. Thebeneficial effect of MIMO links was established in[17,18], where a linear scaling with the number of BSantennas was proven. However, correlation betweenmultiple antennas has an adverse effect as shown in[19], especially when correlation affects the BS-side.Imperfect backhaul connectivity has also a negativeeffect on the capacity performance as quantified in [20].Finally, limited or partial CSI availability will result indegraded performance, as proven in [6,21,22]. The topicof CSI will be further discussed in Section 2.4.
2.2 Joint processing in SatComsA multibeam satellite operates over an interference lim-ited channel, for which the optimal communicationstrategy in general is not yet known [8,23-25]. Hence,orthogonalization in the frequency and polarizationdomain is used to limit interbeam interferences. How-ever, the concept of multibeam joint processing can beapplied and the system can benefit from reusing the fullfrequency in all beams.2.2.1 Multibeam joint processing in the FLIn the context of SatComs, multibeam joint processingscenarios have been studied in various settings. Specifi-cally, the FL case has been examined in [26-33]. Variouscharacteristics of the multibeam satellite channel weretaken into account such as beam gain [28,29,34], rainfading [30], interference matrix [29] and correlatedattenuation areas [28]. Joint processing studies concern-ing the FL of SatCom systems usually assume fixedusers. This assumption originates from the difficulties inacquiring reliable and up to date CSI for the FL of satel-lite systems. During the CSI acquisition process, thepilot signals need to be broadcasted to the users andthen fed back to the transmitter, thus doubling theeffect of the long propagation delay of the satellite chan-nel and rendering the acquired CSI outdated.
Subsequently, the adoption of the slow fading channelof the fixed satellite services (FSS), partially alleviatesthis obstacle since CSI needs to be updated lessfrequently.In terms of precoding techniques, Tomlinson Hara-
shima precoding (THP) was studied in [29,34], while lin-ear precoding schemes such as ZF and R-ZF wereevaluated in [30,34]. Furthermore, authors in [31] haveinvestigated generic linear precoding algorithms underrealistic power constraints for single and dual polarizedsatellite channels. The effect of flexible power con-straints rising from flexible and multiport amplifiers hasbeen evaluated in [33] and an energy efficient schemefor MMSE beamforming was proposed in [32]. Finally,authors in [28] have considered an Opportunistic Beam-forming (OB) technique based on a codebook of ortho-normal precoders and low-rate feedback.In the present article, linear R-ZF and nonlinear DPC
techniques are considered, while optimization methodsare employed to deduce the best power allocation andprecoder design, to the end of maximizing systemthroughput. In contrast to the existing literature, a per-beam power constraint (i.e., individual amplifier perbeam) is considered instead of the commonly assumed,less realistic sum-power constraint (i.e., total on boardpower can be allocated in one beam).2.2.2 Multibeam joint processing in the RLFirst attempts to study multibeam joint processing inthe RL, onwards referred to as multi-beam joint decod-ing, have been carried out in [35-37]. The RL of asatellite system employing multibeam joint decodingwas studied via simulations in [37] from a systempoint of view, where MMSE and optimal multiuserreceivers were considered, on a simplistic channelmodel basis, demonstrating a considerable improve-ment in both availability and throughput. The firstanalytic investigation of the uplink capacity of a multi-beam satellite system was done by [35], where closed-form expressions were derived for the capacity of mul-tibeam Rician channels. Asymptotic analysis methodsfor the eigenvalues of the channel matrix were used in[38] to determine upper bounds for the ergodic capa-city and calculate the outage probability of a MIMOland mobile satellite (LMS) channel which is repre-sented by Rican fading with a random line-of-sight(LoS) component. Similarly, in [39] the statistics ofminimum and maximum eigenvalues were derived forRician fading with Gamma distributed LoS component.Finally, it should be noted that a multiuser decodingalgorithm was presented in [36].2.2.3 Practical constrains in the system design levelAlbeit the throughput enhancement the cooperativetechniques can provide in satellite networks, as it will beshown in the following, several issues arise with the
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adoption of these techniques in SatComs and need to beaddressed.Firstly, multibeam satellite systems with a high num-
ber of beams need to employ multiple GWs. The futureof broadband SatComs is without any doubt connectedwith multibeam satellites. As throughput demandincreases, the number of beams needs to be increasedso that the same spectrum segments can be reused inspatially separated beams. Due to feeder link limitations,one single gateway cannot accommodate the total num-ber of employed beams thus emanating the necessity formultiple GWs to serve large multibeam systems. In thepresent publication, to perform multibeam joint proces-sing, both for the forward and the RL, a centralized pre-coder and decoder respectively is assumed. Thistheoretical assumption can be supported by a real sys-tem implementation via two approaches. One solutionwould be the exploitation of higher frequency bands forthe feeder link (optical feeder links), assuming that sucha system can be practically employed. As a result, a sin-gle gateway could serve the multibeam satellite system.Alternatively, another approach is the full interconnec-tion amongst the multiple GWs so that they all sharethe same data (CSI and data). The second approach iseasier to implement if we consider the bandwidth cap-abilities of broadband cable networks. Of course, theadded delay is an issue to be considered, especially inthe SatCom context where delay is already a majorissue. Subsequently, both approaches lead to the verifi-cation of the simplistic assumption of cooperative sys-tem that utilizes a central precoder/decoder.Additionally, although this contribution does not tacklethe subject of decentralized precoding/decoding, worksin the existing literature examine the performancedegradation effects of the adoption of decentralized pre-coder designs, for the case where full gateway intercon-nection cannot be assumed. An example of such anapproach for multibeam satellite systems can be foundin [40] where the level of cooperation amongst GWs isexamined and the most promising technique is shownto be partial data and CSI exchange among the inter-connected GWs.A second major issue is the payload implications of
the adoption of full frequency reuse. Multibeam JointProcessing can be classified in the more general categoryof multi-user detection (MUD) techniques. Interferingusers are successively decoded/precoded thus allowingfor the subtraction of the known interfering signals.This alleviation of interferences enables the full fre-quency reuse in multibeam system allowing for moreaggressive exploitation of the available bandwidth thusleading to higher spectral efficiency. Nevertheless, theadded on-board complexity that results from theincrease of the frequency reuse in a multibeam satellite
system needs to be noted. More aggressive reuse of thespectrum is translated in a proportional increase in thenumber of amplifiers accommodated in the satellite pay-load. Indeed, when advancing from a specific frequencyreuse scheme (e.g., four color frequency reuse) to fullfrequency reuse, the number of on board high-poweramplifiers (HPAs) needs to be increased (e.g., four timesmore HPAs) since each beam will occupy the holebandwidth of the amplifier. Currently, this proves aheavy burden for the satellite payload hence more sim-plistic approaches need to be investigated. Added tothat, a fairness issue arises in the comparison of multi-beam joint decoding to conventional single beam decod-ing since the first, requires increased power and payloadmass compared to the latter.The above noted issues will not be further addressed
in the present contribution but they will be part of theauthors’ future work. In the following, the achievable RLthroughput by the means of MMSE filtering followed bynonlinear SIC and of Linear MMSE, is calculatedthrough simulations. The novelty of this work is theconsideration of the multibeam antenna pattern over acorrelated Rician channel. Additionally, lognormal sha-dowing is incorporated in the channel model to investi-gate the effect of user mobility.
2.3 SatCom standardsThe second generation of the digital video broadcastingover satellite standard (DVB-S2) is the latest generationstandard for SatComs enabling broadband and interac-tive services via satellite [41]. It has been designed forbroadcasting services (standard and high definition tv),Internet and professional services such as TV contribu-tion links and digital satellite news gathering [42]. Dur-ing the formulation of DVB-S2, three main conceptswere carefully considered: (a) best transmission perfor-mance approaching the Shannon limit, (b) total flexibil-ity and (c) reasonable receiver complexity [43]. Highperformance and low complexity iterative decodingschemes like Low Density Parity Check codes (LDPC)along with high order Amplitude and Phase Shift Keying(APSK) modulations were adopted for efficient opera-tion over the nonlinear satellite channel in the quasierror free region. Compared to previous standards, thesecond generation standard attains 20-35% capacityincrease or alternatively 2-2.5 dB more robust receptionfor the same spectrum efficiency by virtue of theadvanced waveforms. Furthermore, to facilitate the pro-vision of interactive services, the standard featuresoperation under Adaptive Coding and Modulation(ACM) parameters. When used for interactive services,ACM allows optimization of the transmission para-meters adaptive to varying path conditions [44,45].Hence, resources are optimally exploited, since
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operation under a constant fading margin according to aworst case scenario design, is no longer necessary.Moreover, DVB-RCS NG is a next generation (NG)return channel over satellite, Very Small ApertureTerminal (VSAT) standard that has recently beenapproved by the DVB technical module as commonphysical layer standard within the RCS2 context. Thisstandard improves the existing mature DVB-RCS stan-dard by including state of the art channel coding andhighly efficient, nonlinear modulation schemes. Hence,the efficiency and the flexibility of the return channeloperational modes is enhanced. All of these standardshave been devised for large multiuser satellite two-waysystems and can be adapted to the proposed multibeamprocessing techniques.
2.4 CSI acquisitionChannel state information is one of the most impor-tant enablers for the application of the multibeam jointprocessing techniques. A specific part of the existingliterature addresses the importance of CSI in MIMOsystems, such as [21,46-49]. In the context of SatComs,channel knowledge can be acquired at the end-userground stations for the FL and then fed back to thegateway station (GS) for the RL. More specifically, CSIshould be available at the GS so that multiuser precod-ing can be performed for the FL and joint decoding atthe RL. Current standards are using pilot sequences,either available within the standard as an optional fea-ture (i.e., for DVB-S2) or defined within the specifiedrequirements for the transmission burst structure ofthe Multi-Frequency Time Division Multiple Access(MF-TDMA) return channel (i.e., for the DVB-RCSNG). A recent study for the effect of CSI in the satel-lite context can be found in [50], where the satellitelink performance with and without CSI is comparedand a technique for estimating CSI is proposed. Subse-quently, the current state of the art reference transmis-sion standards are well suited for the adaptation of theproposed multibeam satellite systems.In more detail, CSI is acquired by broadcasting pilot
signals through the FL to all ter-minals which in turnmeasure them and feed the quantized measurementsback to the GS through the RL. In most cases, FL andRL operate in different frequency bands and thus thedescribed process yields the FL CSI. Nevertheless, it isoften assumed that the two link are reciprocal (espe-cially if they are adjacent in frequency) and as a resultthe measured CSI can be also used for the RL. Further-more, the CSI acquisition process in SatComs intro-duces a long delay which may result in outdated CSI.This complication is especially acute for the FL whereCSI is needed before transmission in order to calculatethe precoding vectors. In the RL, CSI is only needed for
decoding and therefore it can be transmitted by theterminals along with their data.Based on this discussion, in the following sections we
focus on fixed terminals for the FL (slow-varying chan-nel) and mobile terminals for the RL. In the RL case, thejoint decoding techniques can be applied either for fixedor mobile satellite services. As a matter of fact, the slowfading channel would even lead to simple practical imple-mentation since CSI is easier to acquire. However, thisdistinction has been made in order to point out one maindifference between the forward and the RL. In the RL,the channel estimates can be sent along with the trans-mitted data. This introduces much less delay when com-pared to FL case, where the pilot signal needs to betransmitted and fed back to the GW before the precodingmatrix can be calculated, leading to approximately dou-ble time delay compared to the RL case. This substantialdifference in the CSI acquisition procedure, leads to thedefinition of the specific scenarios. Added to that, theFSS case for the RL has been also studied by [35]. Never-theless, the proposed analysis is straightforwardly applic-able to FSS, by omitting the shadowing coefficients in thedefinition of the channel matrix. Finally, it should also benoted that the feeder link, i.e., the link between the gate-way and the satellite, is considered ideal.
3 Capacity performance of multibeam jointprocessing: FL for fixed servicesThe first system example scenario discussed is a Ka-bandmultibeam scenario for fixed Sat-Com and high speedapplications. These scenarios can include, for example,multiuser systems such as broadband internet access sys-tems. In such scenarios mainly the FL is the limiting fac-tor of the overall system dimensioning. Thus, theproposed techniques for this FL scenario, with para-meters given in Table 1, will be studied in the followingsection. The modeling of conventional systems is alsoincluded to assist in the evaluation of the potential gainof these techniques. The considered figure of merit is theaverage per user achievable throughput, namely the sumthroughput for all beams divided by the number of users.
3.1 Channel modelOne of the main differences between SatCom and ter-restrial systems are the inherent characteristics of thechannels they are operating over. The most fundamentalattributes of the satellite channel are the high LoS com-ponent of the signal and the multibeam antenna radia-tion pattern. Additionally, satellite systems operating infrequencies over 10 GHz are prone to atmosphericattenuation. Especially, rain fading is the dominant fac-tor and will be taken into account in the course of ouranalysis. It is modeled via the latest empirical modelproposed in the International Telecommunications
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Union–Radiocommunications Sector (ITU-R), Recom-mendation [[51], p. 618]. The distribution of the powergain ξ in dB, ξdB = -20 log10(ξ), is commonly modeledas a lognormal random variable, i.e., ln(ξdB) ∼ N (μ, σ) , where μ and s depend on the loca-tion of the receiver, the frequency of operation, thepolarization and the elevation angle toward the satellite.The p.d.f. of a lognormal variable ξ reads as
p (ξ) =1
ξ√2πσ 2
exp
(− (ln ξ - μ)
2
2σ 2
), ξ ≥ 0. (1)
Variables μ (dB) and s (dB) are the mean and stan-dard deviation of the variable’s natural logarithmrespectively.The corresponding K × 1 rain fading coefficients from
all antenna feeds towards a single terminal antenna aregiven in the following vector
h̃ =√
ξ−1
e−jφ1N (2)
where j denotes a uniformly distributed phase. Thephases from all antenna feeds are hard to differentiateand assumed to be identical. This is because we con-sider a LoS environment and the satellite antenna feedspacing is not large enough compared to the communi-cation distance [52].Since rain attenuation is a slow fading process that
exhibits spatial correlation over tens of kilometers [53],we assume that users among different beams undergoindependent fading. In other words, we assume thateach correlated area [28,53] cannot extend over the cov-erage of a single beam. This is a valid assumption if weconsider that beam sizes are typically of the size of
hundreds of kilometers. Moreover, the commonassumption of user scheduling, according to which onlyone user per beam is served during a specific time slot,is adopted thus rendering the fading coefficientsamongst users independent.The link gain matrix defines the average SINR of the
each user and it mainly depends on the satellite antennabeam pattern and the user position. Define one user’sposition based on the angle θ between the beam centerand the receiver location with respect to the satelliteand θ3 dB is its 3-dB angle. Then the beam gain isapproximated by [34]:
b (θ , k) = bmax
(J1 (u)2u
+ 36J3 (u)u3
)2
(3)
where u = 2.07123 sin θ/sin θ3 dB, and J1, J3 are the firstkind Bessel functions, of order one and three respectively.The j-th user corresponds to an off-axis angle θ withrespect to the boresight of the i-th beam where θi = 0°.
The coefficient bmax =(
λ4π
)2 1d0
2 , where l is the wave-
length and d0 ≃ 35, 786 Km, is the satellite altitude.Collecting one user’s beam gain coefficients from all
transmit antennas into the K × 1 vector b, the overallchannel for that user can be expressed as
h = h̃ � b12 . (4)
3.2 Problem formulationLet us denote the complex signal intended for user k as
sk with E[|sk|2] = 1 . Before transmission, the signal to
be transmitted is weighted by the beamforming vector√pkwk where wk is a complex vector with ||wk|| = 1
and pk is the transmit power for the k-th user signal.The total transmit signal is given by
x =K∑k=1
√pk wksk. (5)
The received signal at user k is
yk = h†k
K∑k=1
√pkwksk + nk (6)
where nk is the independent and identically distributed(i.i.d.) zero-mean Gaussian random noise with powerdensity N0. Then the received SINR at the k-th user is
�k =pk∣∣∣w†
khk
∣∣∣2∑
j�=k pj∣∣∣w†
khk
∣∣∣2 + WN0
, (7)
Table 1 Link budget parameters–FL
Parameter Value
Orbit GEO
Frequency band Ka (20 GHz)
User link bandwidth 500 MHz
Number of beams 7
Beam diameter 600 Km
TWTA RF power @ saturation 130 W
Frequency reuse factor (conventional scheme) 4
Free space loss 210 dB
Receiver noise power N -118 dBW
Max satellite antenna gain GT 52 dBi
Max user antenna Gain GR 41.7 dBi
Downlink free space loss 210 dB
Fading margin 3 dB
Rain fading mean -2.6 dB
Rain fading variance 1.63 dB
Receive SNR 21 dB
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where Bu is the total user-link bandwidth. The achiev-able average per user throughput is then expressed as
R =Bu
K
K∑k=1
log2 (1 + �k). (8)
In this section, the problem of interest is to maximizethe system throughput by optimizing the precoding andpower allocation subject to individual power constraintsPk = [p1, p2, ... pK ] on beam k. This problem can be for-mulated as
max{pk,wk}R
s.t.K∑k=1
pkw†kQjjwk ≤ Pj, j = 1, . . . ,K.
(9)
where Qjj is a k × k matrix full of zeros, besides its (j,j) element which is unitary.The described throughput maximization problem is
difficult to tackle and the optimal solution is unknownin the literature. Next we will separate the optimiza-tion of precoding from the power allocation, then pro-vide simple and sub-optimal solutions for each ofthem.3.2.1 Regularized zero-forcing and sub-optimal powerallocationZero forcing is a simple but suboptimal linear precod-ing strategy that mitigates multiuser interference, whileits design only depends on the channel regardless ofthe noise. Although it is asymptotically optimal in thehigh SNR regime, the drawback of ZF precoding isthat the throughput does not grow linearly with K[54]. R-ZF was proposed as a simple precoding techni-que with substantial performance. This method intro-duces a regularization parameter that takes intoaccount the noise effect. Thus, the resulting through-put is proven to grow linearly with K [55]. More speci-fically the precoding vector wk is taken from thenormalized k-th column of
W =(H†H + αI
)−1, (10)
where a is the regularization factor, that needs to becarefully chosen to achieve good performance. Based onthe large system analysis, the optimal a (in the statisticalsense) to maximize the SINR is given by [56],
αopt =N0Bu
max Pk. (11)
With R-ZF precoding, the throughput maximizationproblem (9) reduces to a power allocation optimizationproblem:
max{pk}R
s.t.K∑k=1
pkw†kQjjwk ≤ Pj, j = 1, . . . ,K.
(12)
Subsequently, the applying R-ZF the power and pre-coding matrix optimization problems are separated anda solution can be found. However, although the con-straints are linear, the throughput is non-convex withrespect to the power vector thus and hard to find theoptimal solution. To overcome this restrain, we proposethe use of simple gradient-based algorithms, such as thesteepest descent algorithm to find a locally optimal solu-tion for the power allocation optimization problem. Sub-sequently the average per user throughput for the R-ZFtechnique will read as
RRZF =Bu
K
K∑k=1
log2
(1 +
pk|w†khk|2∑
j�=k pj|w†j hk|2 + BuN0
). (13)
3.2.2 Dirty paper codingDirty paper coding is known to be the sum-rate capa-city-achieving technique in MU MIMO downlink.Hence, it is used as an upper bound for the suboptimal,linear techniques. As a nonlinear technique, DPC isbased on the idea of known interference precancelationwhile serially encoding user signals.Let us now assume that π0 = {1, 2, ..., K} is a trivial
user encoding order. Then the received SINR at user kis
�DPCk =
pk|h†k wk|2∑
j>k pj|h†k wj|2 +N0Bu
(14)
With DPC, the throughput maximization problemwith individual power constraints (9) has been solved byconverting it into a dual uplink with sum power con-straint across users and uncertain noise and employingan interior-point algorithm [57]. It should be noted thatthe sum-rate capacity can be achieved by all user encod-ing orders, but the individual user rates vary accordingto the employed encoding order.According to (14) and (8) the achievable average peru-
ser throughput will read as
RDPC =Bu
K
K∑k=1
log2(1 + �DPC
k
). (15)
3.2.3 Conventional frequency reuse schemeTo the end of providing a benchmark scenario so thatthe performance enhancement can be quantified a con-ventional system will also be studied. As already dis-cussed in Section 1, the norm in multibeam satellite
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systems is the use of conventional single beam decoding.In order to achieve acceptable SINR ratios at the receiveside, orthogonalization in the frequency domain isemployed. In the present contribution, the polarizationdomain has not been examined for simplicity reasons.Hence, the usual case of a four color frequency reusescheme has been assumed, where interferences are alle-viated by allocating different spectrum segments to adja-cent beams. Despite this spatial separation, thepotentially large number of beam in a multibeam satel-lite system emanates the need of accounting for interfer-ences originating from non-neighboring co-channelbeams. To this end, the conventional system throughputfor each beam is calculated as
RFL4c = BuE
⎧⎪⎨⎪⎩14
K∑k=1
log2
⎛⎜⎝1 +
|hk|2∑j�=k,j∈AC
|hj|2 +(4 PkN0Bu
)−1
⎞⎟⎠⎫⎪⎬⎪⎭ , (16)
The channel coefficients hj, for the k-th user are given
by (4), while AiC is the set of the co-channel to the k-th,
users.
4 Capacity performance of multibeam jointprocessing: RL for mobile servicesThe second scenario considered involves an S-bandsatellite network for mobile applications. In fact, suchnetworks are typically bandwidth limited and the usageof joint multibeam processing promises to increase over-all system capacity by exploiting the full frequency reusewhile mitigating the challenging interbeam interferencelimitation requirements within the overall system con-cept. More aggressive reuse of the available spectrumreuse is consequently possible through smaller beamswith no requirements on co-channel isolation leading topotentially increased overall system capacity. The RL isanalyzed in this context hereafter.
4.1 Channel modelTo the end of accurately modeling the LMS channel theimportant parameters of the actual system need to beaccounted for. Mobile users, due to size limitations, areequipped with low gain antennas and low power ampli-fiers. Added to that, user mobility, prohibits the use offrequencies over 3 GHz since the link budget would becompromised by the lack of orbital pointing accuracy,the increased free space losses and the high atmosphericattenuation due to rain fading. Finally, the importanceof the LoS component of the received signal, an inher-ent characteristic of SatComs, will be accounted for byassuming Rician fading coefficients.More specifically, in the following we consider a clus-
ter of K spot-beams covering K user terminals, eachequipped with a single antenna, under the limitation of
a single transmitting user per bean, during a specificchannel instanceb. Hence, a MIMO MAC is realized.Subsequently, the input-output analytical expression forthe i-th beam reads as
yi =K∑j=1
zijxj + ni, (17)
where zij is the complex channel coefficient betweenthe i-th beam and the j-th user and ni is the AdditiveWhite Gaussian Noise (AWGN) measured at the receiveantenna. To the end of investigating the adverse satellitechannel the following characteristics will be incorpo-rated in the channel model: beam gain bij, lognormalshadowing ξj, Rician fading hij and antenna correlation.Hence, (17) becomes
yi =K∑j=1
bijhijξjxj + ni. (18)
Shadowing ξj only depends on the j-th user position asa result of the practical collocation of the satellite anten-nae. The general baseband channel model for all beamsin vectorial form reads as
y = Zx + n, (19)
where y, x, n are K × 1 vectors. The channel matrixZK×K will be:
Z = B · HR � �1/2d , (20)
where each line of the satellite antenna gain matrixBK×K contains the square roots of the normalized coeffi-cients given by (3) as described in Section 3.1. Thematrix HR is the channel gain matrix that consists ofrandom i.i.d nonzero mean Gaussian elements and mod-els the Rician satellite channel [35]. Due to rank defi-ciencies introduced by LoS signal components and thehigh receive correlation at the satellite side (20) canreduce to [35,58]
Z = B · HRd · �1/2d , (21)
where the diagonal matrix HRd is composed of the ele-ments of the unit rank matrix HR. Finally, random fad-ing coefficients following a lognormal distribution havebeen employed to model shadowing due to user mobi-lity. Owing to the practical collocation of the on boardantennae, possible obstructions affect equally allreceived signals. Subsequently, Ξd is a diagonal matrixcomposed of random elements that represent shadowingdue to user mobility: Ξd = diag{ξ}, where ξ = [ξ1, ξ2 ...ξK ]. The p.d.f. of the random fading coefficients ξmreads as in (1).
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4.1.1 Single-beam decodingIn the same direction as in Section 3.2.3 the benchmarkperformance metric will be given by the throughput of aconventional single beam decoding system, which foreach beam reads as
RRL4c = BuE
⎧⎪⎨⎪⎩14
K∑i=1
log2
⎛⎜⎝1 +
|zii|2∑j�=i,j∈AC
|zij|2 +(4 PkN0Bu
)−1
⎞⎟⎠⎫⎪⎬⎪⎭ , (22)
The channel coefficients zij are given in (18), while AiC
is the set of co-channel to the i-th, beams.4.1.2 MMSE filtering with SICConventional single beam decoding sacrifices bandwidthto cope with interferences. However, the almost lineardependence of channel capacity with respect to band-width motivates the study of more advanced decodingtechniques that allow for the full exploitation ofresources. The optimal decoding strategy when full fre-quency reuse is employed is proven to be SIC. Followingthe MMSE filtering of the strongest user, it’s signal isdecoded and then subtracted from the aggregate signaland so on. Hence, the second in order user will copewith less interference. The achievable capacity for thiscase reads as:
RSIC =Bu
KE {
log2 det(In + γZ†Z
)}, (23)
where g stands for the transmit (SNR) and all theusers are transmitting with the same power.Due to the high implementation complexity of such
techniques, suboptimal methods need to be examined aswell. Added to that, imperfect channel estimates lead toresidual cancelation errors and practical coding schemesare imperfect hence decoding errors can propagate tothe following users. For the above reasons, suboptimalsolutions can be applied and their potential gains areexamined in the following section.4.1.3 Linear MMSE filteringA more practical receiver implementation would onlyconsider MMSE filtering of the received signals followedby singe user decoding. In this case, linear MMSE capa-city reads as:
RMMSE =Bu
KE{
K∑i=1
−log2([(
IK + γZ†Z)−1
]ii
)}. (24)
5 Numerical resultsIn this section, numerical results are provided in orderto study the performance of multibeam processing forboth the forward and the RL. The considered metric isthe per user throughput, averaged over the channel sta-tistics, in bits/s. Since signals from adjacent beams are
no longer harmful when multicell processing is in place,we consider a set of feed antennas which allow for theillumination of beams with variable overlap. In otherwords, we assume a number of beams with fixed centersof the earth surface but variable diameter. The formulaspresented in Section 3 are used to calculate the spectralefficiency of each architecture for every value of thevariable overlap, i.e., for every instance of the matrixcontaining the beam gain coefficients. The objective isto evaluate the effect of beam overlap on systemthroughput and investigate whether there is an optimaloverlap point which optimizes the multibeam processingthroughput.During the simulations, a satellite system with only
seven beams were considered for reasons to beexplained and justified hereafter. The computationalcomplexity of the employed optimization algorithm,namely the ‘the steepest descent algorithm’, grows withthe number of beams since the algorithm performschannel matrix inversions and multiplications. Toovercome this obstacle, a small number of beams sym-metrically arranged over a cellular-like coverage areawas employed. Subsequently, the achieved total systemthroughput has been averaged over the number ofbeams, providing the average per beam achievable rate.This performance metric facilitates the extension ofthe results into larger systems, assuming the lineardependence of the system throughput with respect tothe number of beams; a solid assumption for conven-tional systems [1]. For the proposed systems, the lineardependence of capacity with respect to the channeldimensions assumption can be justified by the MIMOliterature. The prelog of the channel capacity growslinearly with the rank of the channel matrix, i.e., thenumber of beams in our case. This fact can supportthe assumption that the broadcast MIMO channel(MIMO BC) capacity will scale approximately linearlywith the number of beams. Hence, the average perbeam capacity can provide a good estimation for thetotal capacity of a larger multibeam channel. Addition-ally, if a larger system was addressed, the approachwould have been similar. The precoder matrix shouldhave smaller dimensions than the full channel matrixin order to perform the optimization, since the highlydirective antennas lead to very good beam isolation.This means that if the precoder matrix had dimensionsequal to the number of beams (i.e., interferences fromall beams are taken into account) it would be a matrixwith very small, decreasing entries away from the maindiagonal, resulting in an ill-conditioned precodingmatrix that cannot be accurately handled. The solutionis to take into account the first or maybe the secondtier of interfering beams by employing smaller precod-ing matrices.
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5.1 Forward linkFor the multibeam joint precoding, a satellite FL wasconsidered as described in Section 3.1 with detailedparameters listed in Table 1. According to the discus-sions of Section 2 optimization algorithms were used tosolve the problem of power allocation and precodingmatrix calculation, in the case of the linear R-ZF. Subse-quently sub-optimal R-ZF throughput could be evalu-ated using (13). The capacity achieving nonlinear DPCis evaluated using (15). Moreover, the conventionalspotbeam system has the same user-link bandwidth Bu
and noise density while it employs a frequency re-usescheme with factor 4 in order to mitigate inter-beaminterferences. The achievable capacity is given by (16).The results are plotted in Figures 1 and 2 versus thevariable, normalized to the nominal 3 dB, beam overlap.In Figure 1, the optimized sum rate results are shown
for the FL when users are uniformly located within cells.First it is noted that for all schemes, the maximum ratesare achieved when the normalized beam angle is lessthan the nominal one and for both R-ZF and DPC pre-coding the optimal beam angles are only 30% of thenominal one. This is because users are randomly locatedin the cells and it is preferred for satellite antenna feedsto focus on a smaller beam size in order to reduce inter-ference to neighboring cells while users outside the cellcan be jointly served by all feeds. As can be seen, whenthe normalized beam angle is less than the nominal one,more than double rates are achieved by joint beam pro-cessing using R-ZF precoding or DPC precoding, com-pared to conventional single beam processing. Also dueto the smaller beam size, interference is not the domi-nant factor therefore the linear R-ZF precoding per-forms almost as well as DPC precoding. When thenormalized beam size increases, beams become
overlapped and achievable rates decrease due to thestrong interferences. In this case, DPC clearly shows theadvantage of nonlinear interference pre-cancelation overthe linear R-ZF precoding.In Figure 2, the optimized sum rate results are shown
for the FL when users are on cell edges which is a worstscenario and results in much lower rates for all schemes.Again substantial rate gains are achieved by multibeamjoint processing using R-ZF and DPC precoding. Theoptimal beam sizes are the nominal one or close to it,which is reasonable to cover users that are on the edge.
5.2 Return linkWith respect to the RL scenario, a set of Monte Carlosimulations were carried out to evaluate the behavior ofthe proposed optimal and sub-optimal schemes given inSection 2. The RL scenario follows the parameters of
Figure 2 Average per beam rate in the FL where users are onbeam edges.
Table 2 Link budget parameters–RL
Parameter Value
Orbit GEO
Frequency band S (2.2 GHz)
User link bandwidth Bu 15 MHz
Number of beams 7
Beam diameter 1,200 km
Mobile terminal RF power [-3-24.5] dBW
Frequency reuse factor (conventional scheme) 4
Free space loss L 193 dB
Receiver noise power N -133 dBW
Mobile antenna gain GT 3 dBi
Max satellite antenna gain GR 52 dBi
Mobile antenna gain GT 3 dB
Fading margin 3 dB
Receive SNR [-5-20] dB
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Table 2. The goal of the simulations is twofold. Firstly, itserves as a benchmark to measure the gain of the theo-retical SIC given by (23) and the more realistic mini-mum mean square error method given by (24), over theconventional four color frequency reuse schemes asgiven by (22) Secondly, the effect of beam overlappingon the performance of the system is investigated. Thusthe achievable per user throughput is plotted in Figures3 and 4, for the three different receiver implementations,as the percentage of beam overlap changes. The inde-pendent variable is normalized over the nominal 3 dBbeam size. For beam size less than one, the satellitereceives less then half of the maximum gain from eachuser, hence gaps appear between beams in the coveragearea. For more then one, beams overlap and the satelliteis receiving more useful as well as interfering signalpowerc. The metric utilized is average per user achiev-able throughput, expressed in Mbps.
In Figure 4, mobile users are assumed on the celledge. In this worst case scenario, results indicate thatmultibeam joint decoding techniques with SIC can theo-retically achieve more than twofold gain over conven-tional techniques. More realistic receiverimplementation techniques with linear MMSE filteringstill achieve two times more throughput than the fourcolor frequency reuse scheme. Additionally, systemoptimality is as expected very close to the nominal valueof the beam size. In the same figure, we notice that forhigh beam separation (i.e., percentage of beam overlapless than 0.6) linear MMSE performs the same to theSIC. This is justified by the fact that when beams do notoverlap, interferences become negligible. Taking intoaccount that a characteristic of LMMSE is its optimalityat the noise limited regime, the above observation is jus-tifiable. Furthermore, when receive (SNR) increases,interferences become important and linear MMSE tech-niques prove suboptimal compared to SIC. However,they still manage to maintain a twofold gain over theconventional systems. Finally, an important observationis that the performance of conventional schemes quicklydegrades as they are highly affected by interferences.Alternatively, the proposed schemes show higher toler-ance to interferences, hence making them appropriatefor a real system implementation where practical restric-tions prevent ideal multibeam coverage areas.According to Figure 3, when users are randomly allo-
cated within each beam, then the optimal solution is toincorporate highly directive antennas that better serveusers close to the beam center. Hence, optimal through-put is achieved for 0.2 of the nominal beam size. Asexpected, achievable throughput is higher, compared tothe worst case scenario with cell edge users. Again,more than twofold gain can be realized of conventionalschemes.
6 ConclusionsThe present article provides an overview of the applica-tion of joint processing techniques in SatComs. The pre-sented schemes, here in referred to as multibeam jointprocessing techniques, have the potential of being incor-porated in existing satellite payloads with some modifi-cations on the ground segments of multibeam satellitesystems, in the existing SatCom standards, in the satel-lite payload and in the capacity of the feeder link (i.e.,the link between the gateway and the satellite). Both theforward and the RL of these systems have been exam-ined under realistic link budget assumptionsrespectively.Concerning the FL, precoding along with optimal
power allocation amongst beams can provide substantialgains by pre-canceling interferences. Nonlinear DPC hasbeen applied to provide an upper bound for the
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
1
2
3
4
5
6
7
8
Normalized beam size
Per
Use
rA
vera
geR
ate
(Mbp
s)
Conv. SchemeSICMMSE
Figure 3 Average per user rate in the RL for random users.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Normalized beam size
Per
Use
rA
vera
geR
ate
(Mbp
s)
Conv. SchemeSICMMSE
Figure 4 Average per user rate in the RL for beam edge users.
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performance of this approach. Linear R-ZF provides amore realistic value for the potential gain of joint pro-cessing techniques. Performance results were comparedto current conventional architectures so that the poten-tial gain could be quantified. More than twofold gain isexpected with the implementation of multibeam jointprocessing in the FL. Finally, the performance of theaforementioned schemes was examined versus animportant system design parameter, namely the percen-tage of beam overlap, where the optimal values of beamoverlap for throughput maximization have beendeduced.In the RL, nonlinear MMSE filtering followed by SIC
acts as the performance upper bound for the jointdecoding approach. Linear MMSE filtering is the subop-timal scheme that depicts the more realistic perfor-mance. The conventional single beam decoding schemewith frequency reuse acts a performance benchmark.Multibeam joint processing in the RL can potentiallyachieve more than twofold gain over current systemarchitectures. Again, the performance was studied versusvariable beam overlap and the optimal values of thisparameters have been extracted.
EndnotesaOr alternatively: Known Interference Precancelation.bThis assumption is accurate for existing standards suchas DVB-RCS where in every beam, each user transmitsduring one timeslot. cAn appropriate threshold for thebeam gain is -4.3d dB of the maximum beam gain toavoid gaps in the coverage area.
AcknowledgementsThis work was partially supported by the National Research Fund,Luxembourg under the CORE project “CO2SAT: Cooperative and CognitiveArchitectures for Satellite Networks” and the SatNEx-III European Network ofExperts.
Author details1Interdisciplinary Centre for Security, Reliability and Trust (SnT), University ofLuxembourg, 6 rue Richard Coudenhove-Kalergi, L-1359 Luxembourg-Kirchberg, Luxembourg 2SES, Chateau de Betzdorf, Betzdorf 6815,Luxembourg 3Signal Processing Laboratory, ACCESS Linnaeus Center, KTHRoyal Institute of Technology, SE-100 44 Stockholm, Sweden
Competing interestsThe authors declare that they have no competing interests.
Received: 15 November 2011 Accepted: 4 May 2012Published: 4 May 2012
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doi:10.1186/1687-1499-2012-162Cite this article as: Christopoulos et al.: Linear and nonlinear techniquesfor multibeam joint processing in satellite communications. EURASIPJournal on Wireless Communicationsand Networking 2012 2012:162.
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Christopoulos et al. EURASIP Journal on Wireless Communicationsand Networking 2012, 2012:162http://jwcn.eurasipjournals.com/content/2012/1/162
