Improving the Spectral Efficiency of Nonlinear Satellite Systems through Time-Frequency Packing and Advanced Processing

0.19 MB·English

by  Amina Piemontese

1
Improving the Spectral Efficiency of Nonlinear
Satellite Systems through Time-Frequency Packing
and Advanced Processing
Amina Piemontese, Member, IEEE, Andrea Modenini, Student Member, IEEE, Giulio Colavolpe, Senior
Member, IEEE, and Nader Alagha, Member, IEEE
Abstract—We consider realistic satellite communications sys- relaxing the orthogonality condition. Faster-than-Nyquist sig-
tems for broadband and broadcasting applications, based on naling(FTN,see[2]–[5])isawellknowntechniqueconsisting
frequency-division-multiplexed linear modulations, where spec-
ofreducingthetimespacingbetweentwoadjacentpulseswell
tral efficiency is one of the main figures of merit. For these
below that ensuring the Nyquist condition, thus introducing
systems, we investigate their ultimate performance limits by
3 using a framework to compute the spectral efficiency when ISI. If the receiver is able to cope with the interference, the
1
suboptimalreceiversareadoptedandevaluatingtheperformance efficiency of the communication system will be increased. In
0
improvements that can be obtained through the adoption of theoriginalpapersonFTNsignaling[2]–[5],thisoptimaltime
2
the time-frequency packing technique. Our analysis reveals that
spacing is obtained as the smallest value giving no reduction
n introducingcontrolled interferencecan significantlyincrease the
oftheminimumEuclideandistancewithrespecttotheNyquist
a efficiency of these systems. Moreover, if a receiver which is able
J toaccountfortheinterferenceandthenonlinearimpairmentsis case. This ensures that, asymptotically, the ISI-free bit-error
7 adopted, rather than a classical predistorter at the transmitter rate (BER) performanceis reached, at least when the optimal
1 coupled witha simplerreceiver, thebenefitsin terms of spectral detector is adopted. The i.u.d. capacity or information rate
efficiencycanbeevenlarger.Finally,weconsiderpracticalcoded (IR), i.e., the average mutual information when the channel
schemesandshow thepotentialadvantages of theoptimizedsig-
] inputs are independent and uniformly distributed (i.u.d.) ran-
T nalingformatswhencombinedwithiterativedetection/decoding.
dom variables, is then computed, still assuming the adoption
I
. of the optimal detector [6], [7]. However, the complexity of
s Index Terms—Nonlinear satellite channels, interchannel in-
c this optimal detector easily becomes unmanageable, and no
terference, intersymbol interference, information rate, spectral
[ efficiency. hints are provided on how to perform the optimization in the

1 more practical scenario where a reduced-complexity receiver
v is employed.
4 I. INTRODUCTION In [8], for the AWGN channel, a different approach for
8
improvingtheSEhasbeenconsidered.Theapproachrelieson
1 In satellite systems, orthogonal signaling is often adopted
bothtimepackingofadjacentsymbolsandreducingthecarrier
4 to avoid intersymbolinterference(ISI),at least in the absence
1. of nonlinear distortions. For example, in the 2nd-generation spacingoftheadjacentchannelswhenapplicable(multicarrier
transmission), thus introducing also interchannel interference
0 satellite digital video broadcasting (DVB-S2) standard [1], a
(ICI). In [8] it is assumed that a symbol-by-symbol detector
3 conventional square-root raised-cosine (RRC) pulse shaping
1 workingonthesamplesatthematchedfilteroutputisadopted
filter is specified at the transmitter. For an additive white
: atthereceiverside,andthecorrespondingIRiscomputed,by
v Gaussian noise (AWGN) channel and in the absence of other
i impairments,theuseofaRRCfilteratthereceiverandproper also optimizing time and frequencyspacings to maximize the
X
achievable SE. Hence, rather than the minimum distance, and
sampling ensure that optimal detection can be performed on
r thus the BER, the SE is the performance figure of merit. In
a a symbol-by-symbol basis. On the other hand, it is known
addition, a low-complexitymemorylessreceiveris considered
that, when finite-order constellations are considered (e.g.,
rather than the optimal detector employed in [2]–[7]. More
phase-shift keying (PSK)), the spectral efficiency (SE) of the
complexdetectionalgorithmshavebeenalsoconsideredin[9]
communication system, defined here as the information rate
for the case of linear channels.
normalized to the spectral bandwidth assigned to the channel
In this work, we apply the time-frequency packing (TF
and the time spent to transmit a symbol, can be improved by
packing) technique to nonlinear satellite channels. In particu-
lar, we design highly efficient schemes by choosing the time
G.Colavolpe,A.Modenini,andA.PiemontesearewitharewithConsorzio
Nazionale Interuniversitario perleTelecomunicazioni (CNIT)andUniversita` andfrequencyspacingswhichgivethemaximumvalueofSE.
diParma,Dipartimento diIngegneria dell’Informazione, VialeG.P.Usberti, We assume a realistic satellite channel where nonlinear dis-
181A, I-43124 Parma, Italy, e-mail: [email protected], [email protected],
tortionsoriginatefromthe presenceof a high-poweramplifier
[email protected]. N. Alagha is with the European Space Agency
(ESA-ESTEC),Noordwijk, TheNetherlands (HPA). The considered system is also affected by ISI, due
ThisworkisfundedbytheEuropeanSpaceAgency,ESA-ESTEC,Noord- to the presence of input and output multiplexing (IMUX and
wijk,TheNetherlands, undercontract no.4000102300.
OMUX)filtersplacedbeforeandaftertheHPAandintention-
The paper was presented in part at the IEEE Intern. Conf. Commun.
(ICC’12), Ottawa, Canada, June2012. ally introducedby the adoptionof the time packingtechnique
2
aswell.AlthoughICIisalsopresentduetofrequencypacking,
Satellitetransponder
we limit our investigation to systems in single-carrier-per
transponderoperation(i.e., each transponderis devoted to the x(t) h(ℓ)(t) HPA h(ℓ)(t)
i o
amplification of the signal coming from only one user) where
a single-userreceiveris employed,and considertwo different
Fig.1. Satellite transponder foruser ℓ.
approaches to detection for nonlinear channels, namely the
use of a detector taking into account the nonlinear effects
and a more traditional scheme based on predistortion and where x(ℓ) is the symbol transmitted by user ℓ during the
memorylessdetection.Inthecaseofpredistortion,weconsider k
kth symbolinterval,and F is the frequencyspacing between
u
the dynamic data predistortion technique described in [10],
adjacentchannels.1Thetransmittedsymbolsbelongtoagiven
[11], whereas in the case of advanced detection we consider
zero-meanM-arycomplexconstellation.InDVB-S2 standard
a receiver based on an approximate signal model described
the base pulse p(t) is an RRC-shaped pulse with roll-off
in [12]. In this latter case, we also employ the channel short-
factor α (equal to 0.2, 0.3, or 0.35 depending on the service
ening technique (CS) [13], recently proposed for nonlinear
requirements).Noticethat,inordertoleaveoutbordereffects,
satellite channels, to limit the complexity of the detection
the summations in (1) extend from −∞ to +∞, namely an
algorithm. It should be noted that we apply the TF packing
infinite number of time epochs and carriers are considered.
technique to nonlinear satellite channels for which, usually,
As commonly assumed for broadband and broadcasting
even by using RRC pulses there is still ISI at the receiver.
systems, on the feeder uplink (between the gateway and the
The proposed TF packing technique promises to provide
satellite) the impact of thermal noise can be neglected due
increased SEs at least for low-order modulation formats. In
to a high transmit signal strength. Hence, in our analysis, we
fact, when dense constellations with shaping are employed,
have considered a noiseless feeder uplink. Although the TF
we fall in a scenario similar to that of the Gaussian channel
packing can be applied to other and more general scenarios,
with Gaussian inputs for which orthogonal signaling with
we consider here a single-carrier per transponder scenario,
no excess bandwidth (rectangular shaping pulses) is optimal
where differentcarriersundergoindependentamplification by
(although this is mainly true for the linear channel and not
different transponders on board of satellite, each of which
in the presence of a nonlinear HPA, since shaping increases
works with a single carrier occupying its entire bandwidth.
thepeak-to-averagepowerratio).ImprovingtheachievableSE
In this case, the on-board power amplifier can operate closer
withoutincreasingthe constellationordercanbe considerably
tosaturationandhenceimproveitsefficiency.Thetransponder
convenientsinceitiswellknownthatlow-orderconstellations
model for user ℓ, shown in Fig. 1, is composed of an IMUX
are more robust to channel impairments such as time-varying filter h(ℓ)(t) which selects the ℓth carrier, an HPA, and an
phase noise and non-linearities. It is expected that the use of i
OMUXfilterh(ℓ)(t)whichreducestheout-of-bandpowerdue
low-ordermodulationinconjunctionwithTFpackingprovides o
to the spectral regrowth after nonlinearamplification [1]. The
similar advantages in terms of robustness against channel
HPA is a nonlinear memoryless device defined through its
impairments.
AM/AMandAM/PMcharacteristics,describingtheamplitude
The proposed approach to improve the SE is very general
and phase distortions caused on the signal at its input.
andthe caseofsatellite systemsforbroadbandandbroadcast-
The outputsof differenttranspondersare multiplexedagain
ing applications must be thus considered just as an example
in the downlink to form the signal s(t), and we assume
to illustrate the benefits that can be obtained through the
that the adjacent users have a frequency separation of F ,
applicationoftheTFpackingparadigmcoupledwithadvanced d
usually equal to that in the uplink. The useful signal at the
receiver processing.
user terminal is still the sum of independent contributions,
The remainder of this paper is organized as follows. In
one for each transponder (although these contributions are
Section II, we introduce the system model. The framework
no more, rigorously, linearly modulated due to the nonlinear
that we use to evaluate the SE of satellite systems is detailed
transformation of the on-board HPA). The received signal
inSectionIII,whereasdifferentapproachestothedetectionfor
is also corrupted by the downlink AWGN, whose low-pass
theconsideredchannelaredescribedinSectionIV.Numerical
equivalent w(t) has power spectral density (PSD) 2N . The
results are reported in Section V, where we show how the 0
low-passequivalentof the receivedsignalhas thusexpression
proposed technique can improve the SE of DVB-S2 systems.
Finally, conclusions are drawn in Section VI. r(t)=s(t)+w(t).
II. SYSTEMMODEL We evaluate the ultimate performance limits of this com-
We consider the forward link of a transparent satellite munication system when single-user detection is employed at
system, where synchronous users employ the same linear thereceiverside.Theproposedtechniqueconsistsofallowing
modulation format, shaping pulse p(t), and symbol interval interference in time and/or frequency by reducing the values
(or time spacing) T, and access the channel according to of T, Fu, and Fd, (partially) coping with it at the receiver,
a frequency division multiplexing scheme. The transmitted in order to increase the SE. In other words, T, Fu, and Fd
signal in the uplink can be expressed as are chosen as the values that give the maximum value of the
x(t)= x(ℓ)p(t−kT)ej2πℓFut, (1) 1Inthisscenario,wewillusetheterms,“channels”,“users”,and“carriers”
k
interchangeably.
ℓ k
XX
3
SE.Thesevaluesdependontheemployeddetector—thelarger The aim of the proposed technique is to find the values of
the interferencethat the receivercan cope with, the larger the F and T providing,foreach value of the signal-to-noiseratio
SE and the lower the values of time and frequency spacings. (SNR),themaximumvalueofSEachievablebythatparticular
Notice that, since we are considering single-user detection, receiver,optimalfortheconsideredspecificauxiliarychannel.
thereceiverisnotabletodealwiththeinterferenceduetothe Namely, we compute
overlap of different channels. In this case, the optimization
η = max η(F,T). (4)
of the frequency spacings is actually an optimization of M
F,T>0
the frequency guard bands generally introduced in satellite
Typically, the dependence on the SNR value is not critical,
systems to avoid the nonlinear cross-talk, since a single-user
in the sense that we can identify two or at most three SNR
receiver can tolerate only a very small amount of ICI.
regions for which the optimal spacings practically have the
The considered nonlinear satellite channel reduces, as a
same value.
particularcase,tothelinearchannel,providedthattheHPA is
For fair comparisons in terms of SE, we need a proper
drivenfarfromsaturation.Hence,alltheconsiderationsinthis
definition of the SNR. We define the SNR as the ratio P/N
paper can be straightforwardly extended to the linear channel
between the transmit power when the HPAs are driven at
case. A few results can be found in [9].
saturation and the noise power(in the consideredbandwidth).
Denoting by U the number of users and by W the signal
III. OPTIMIZATION OF THESPECTRALEFFICIENCY bandwidth, P/N can as written as
We describe the framework used to evaluate the ultimate P UP P
= lim sat = sat , (5)
performance limits of the considered satellite system and to
N U→∞N0((U −1)F +W) N0F
perform the optimization of the time and frequency spacings.
where P is the peak power at the output of an HPA in
To simplify the analysis, we will assume F = F = F. We sat
u d
response to a continuous wave input, denoted as the ampli-
perform this investigation by constraining the complexity of
fier saturation power. P is independent of the bandwidth
theemployedreceiver.Inparticular,asmentioned,weassume sat
W. The SNR definition as given in (5) is independent of
that a single-user detector is used. For this reason, without
the transmit waveform and its parameters. This provides a
loss of generality we only consider the detection of symbols
x(0) = {x(0)} of user with ℓ = 0.2 In addition, we also common measure to compare the performance of different
k solutions in a fair manner. The output back-off for each
consider low-complexity receivers taking into account only a
waveform (or modulation scheme) is defined as the power
portionoftheactualchannelmemory.Undertheseconstraints,
ratio (in dBs) between the unmodulated carrier at saturation
we compute the IR, i.e., the average mutual information
and the modulated carrier after the OMUX. We point out
whenthechannelinputsarei.u.d.randomvariablesbelonging
that equations (3)-(5), although derived for nonlinear satellite
to a given constellation. Provided that a proper auxiliary
channels, can be used for linear AWGN channels also, by
channelcan be definedforwhichthe adoptedlow-complexity
replacing P in (5) with the user’s transmitted power.
receiver is optimal, the computed IR represents an achievable sat
Without loss of generality, T and F in (3)-(5) can be
lower bound of the IR of the actual channel, according to
normalized to some reference values T and F . We will
mismatched detection [14]. B B
denoteν =F/F andτ =T/T .Inthenumericalresults,we
Denoting by y(0) a set of sufficient statistics for the detec- B B
will chooseT and F as the symboltime andthe frequency
tion of x(0), the achievable IR, measured in bit per channel B B
spacingadoptedin the DVB-S2standard,whichis considered
use, can be obtained as
as a benchmark scenario.
1 p(y(0)|x(0))
I(x(0);y(0))= lim E log , (2)
K→∞K ( p(y(0)) ) IV. AUXILIARYCHANNELMODELS
The system model described in Section II is representative
where K is the numberof transmittedsymbols.Theprobabil-
of the considered scenario and has been employed in the
ity density functions p(y(0)|x(0)) and p(y(0)) are computed
information-theoretic analysis and in the simulations results.
by using the optimal maximum-a-posteriori (MAP) symbol
In this section, we describe the employed auxiliary channel
detectorfortheauxiliarychannel,while theexpectationin (2)
modelsandthecorrespondingoptimalMAPsymboldetectors.
is with respect to the input and output sequences generated
As explained in Section III, they are used to compute two
accordingtotheactualchannelmodel[15].Inthenextsection,
lowerboundsontheSEfortheconsideredchannel[15].Since
we will discuss two different low-complexity detectors for
these lower boundsare achievable by those receivers,we will
nonlinearsatellitechannelsandwewilldefinethecorrespond-
say that the computed lower bounds are the SE values of the
ing auxiliary channels.
considered channel when those receivers are employed.
We can define the user’s bandwidth as the frequency sepa-
ration F between two adjacent carriers. The achievable SE is
A. Memoryless model and predistortion at the transmitter
thus
η = 1 I(x(0);y(0)) [b/s/Hz]. (3) When the HPA AM/AM and AM/PM characteristics are
FT properly estimated and feeded back to the transmitter, the
sequence of symbols {x(ℓ)} can be properly predistorted
2Assuming a system with an infinite number of users, the results do not k
dependonaspecificuser. to form the sequence {x′(ℓ)} that is transmitted instead,
k
4
in order to compensate for the effect of the non-linearity from the classical one by neglectingsome selected terms. For
and possibly to reduce the ISI. Here we consider the dy- further details, the reader can refer to [12]. We are looking
namic datapredistortiontechniquedescribedin [10], [11] and for an auxiliary channel and the corresponding optimal MAP
also suggested for the application in DVB-S2 systems [1], symbol detector. As mentioned, only single-user receivers
where the symbol x′(ℓ) transmitted by user ℓ at time k is are considered here. Hence, we will assume that, apart from
k
a function of a sequence of 2L + 1 input symbols, i.e., AWGN, only user ℓ = 0 is present and that the simplified
p
x′ = f(x ,...,x ,...,x ). The mapping f at the model (7) holds. Optimal single-user MAP symbol detection
k k−Lp k k+Lp
transmitter is implemented through a look-up table (LUT), for this case can be performed through a bank of filters
which is computed through an iterative procedure performed followed by a conventional BCJR detector [18] with proper
off-line and described in [10], [11]. This procedure searches branchmetricsandworkingonatrelliswhosenumberofstates
the best trade-off between the interference reduction and exponentially depends on the channel memory [12].
the increase of the OBO. The complexity at the transmitter Inthe case of PSK modulations,being|x |2 =1,the signal
i
dependson the numberof symbolsaccounted for throughthe model(7)simplifiestoalinearmodulationwithshapingpulse
parameter L . The transmitted signal is thus h¯(t) = NV−1h(2i+1)(t) [12]. An approximate (being the
p i=0
modelin (7) an approximation)set of sufficient statistics y(0)
x(t)= x′k(ℓ)p(t−kT)ej2πℓFt canthusPbeobtainedbysamplingtheoutputofafiltermatched
Xℓ Xk to h¯(t). Under the assumption that only user with ℓ = 0 is
whereas, at the receiver, a simple single-user memoryless present, the kth element of y(0) is
channelisassumedcorrespondingtotheauxiliarychannel(for
user with ℓ=0) yk(0) = x(k0−)igi+ηk,
yk(0) =x(k0)+nk (6) Xi
where
where n is azero-meancircularlysymmetricwhiteGaussian
k g = h¯(t)h¯∗(t−iT)dt
process with PSD 2(N +N ), N being a design parameter i
0 I I
which can be optimized through computer simulations—an Z
andη isaGaussianprocesswithE{η η∗}=2N g .Vector
increase of the assumed noise variance can improve the com- k k+i k 0 i
y(0) can be written as
puted achievable lower bound on the spectral efficiency [8].
y(0) =Gx(0)+η (8)
B. Model with memory and advanced detection
whereGisaToeplitzmatrixobtainedfromthesequence{g }
i
A valid alternativeto nonlinearcompensationtechniquesat
whereasη is a vectorcollectingthe noisesamples. According
the transmitter relies upon the adoptionof advanceddetectors
to the CS approach,the consideredauxiliary channelis based
which can manage the nonlinear distortions and the ISI. In
on the following channel law [17]
this work, we consider detection based on an approximate
signalmodeldescribedin[12],whichcomesfromasimplified p(y(0)|x(0))∝exp 2R(y(0)†Hrx(0))−x(0)†Grx(0) ,
Volterra series expansion of the nonlinear channel. In the
(9)
(cid:16) (cid:17)
following, we will consider PSK and amplitude/phase shift where Hr and Gr are Toeplitzmatricesobtainedfromproper
keying (APSK) modulations typically employed in satellite sequences{hr}and{gr},andareknownaschannelshortener
i i
systems [1]. To limit the receiver complexity with a limited andtargetresponse,respectively[17].Matrix Hr representsa
performance degradation, we also apply a CS technique [16]. linearfilteringofthesufficientstatistics(8),and Gr istheISI
In fact, when the memory of the channel is too large to be
to be set at the detector (different from the actual ISI) [17].
taken into account by a full complexity detector, an excellent
In (9), the noise variance has been absorbed into the two
performancecanbeachievedbyproperlyfilteringthereceived
matrices. In order to reduce the complexity, we constrain the
signal before adopting a reduced-state detector [16]. A very
target response used at the receiver to
effectiveCStechniqueforgenerallinearchannelsisdescribed
in [17], while its extension to nonlinear satellite systems is gr =0 |i|>L , (10)
i r
reported in [13].
which implies that the memory of the detector is L instead
The approximatemodel (employedfor receiverdesign pur- r
poses only) of the contribution s(0)(t) of user ℓ = 0 to the of the true memory of the channel. The CS technique finds a
closed form of the optimal {hr} and {gr} which maximize
receivedusefulsignals(t),canbebasedonthefollowingvth- i i
the achievable IR (2). We point out that if the memory L is
order(with v beingany oddinteger) simplified Volterra-series r
larger than or equal to the actual channel memory the trivial
expansion [12]
solution is Hr = I/2N and Gr = G/2N , where I is the
0 0
NV−1 identity matrix.
s(0)(t)≃ x(0) |x(0)|2ih(2i+1)(t−nT) , (7)
n n For APSK modulations, an approximate set of sufficient
Xn Xi=0 h i statistics can be obtained through a bank of filters matched
whereN =(v+1)/2,andh(2i+1)(t)arecomplexwaveforms to the pulses h(2i+1)(t), i=0,...,N −1. The CS technique
V V
givenbyalinearcombinationsofthetheoriginalN Volterra has been recently extended to this case in [13], and leads to
V
kernels. This simplified Volterra-series expansion is obtained an auxiliary channel whose law has the same form of (9),
5
r(t)
h¯∗(−t) Hr 5
a) detGe
trion QPSK
8PSK
16APSK
r(t) h(1)∗(−t) soft 4 32APSK
Hr inform. 64APSK
b) ... NV ×NV ... detGe
rtion Hz] 3
h(v)∗(−t) b/s/
η [ 2
Fig. 2. Block diagram of the considered suboptimal receivers for a) PSK
andb)APSKmodulations. 1
0
where the channelshortenerand the targetresponseare block -12 -8 -4 0 4 8 12 16 20 24
matrices (see [13] for details). Psat/N0F [dB]
The resulting receivers for PSK and APSK modulations
are shown in Fig. 2. They are optimal for the considered
Fig. 3. Spectral efficiency of DVB-S2 modulations with roll-off 0.2, data
auxiliary channel models. Interestingly, when L = 0 the
r predistortion, andmemoryless detection. Comparison with aconstellation of
optimalchannelshortenerbecomestheminimummeansquare increased cardinality (64APSK).
error (MMSE) feedforward equalizer of [19], applied to the
signal model (7).
cardinality,andinFig.3wealsoshowtheSEforthe64APSK
V. NUMERICAL RESULTS modulation[20]. It can be seen that the 64APSK modulation,
due to the higher impact of the nonlinearities, allows to
A. Spectral efficiency
increase the SE only at high SNR values and it seems there
Considering the DVB-S2 system as a benchmark scenario,
is no hope to improve the SE in the low and medium SNR
we now show the improvement, in terms of SE, that can be
regions.
obtained by adopting the TF packing technique joint with an
An alternative way of improving the SE is based on a
advanced processing at the receiver. Let us consider a typical
reduction of the roll-off factor. In Fig. 4, we consider QPSK
DVB-S2 scenario where, at the transmitter, the shaping pulse
and16APSK modulationsin a scenariowherepredistortionat
p(t) has a RRC spectrum, whereas the IMUX and OMUX
thetransmitterandsymbol-by-symboldetectionatthereceiver
filters and the nonlinear characteristics of the HPA are those
are still employed. We show the SE improvementthat can be
reported in [1, Figs. H.12 and H.13]. The standard considers
obtainedbyreducingtheroll-offtoα=0.05.4Wecanobserve
the following modulation formats: QPSK, 8PSK, 16APSK,
that the roll-off reduction improves the SE with respect to
and 32APSK. To combat ISI and nonlinear distortions, a
DVB-S2 for all SNR values. On the other hand, as shown
data predistorter is employed at the transmitter whereas at
in Fig. 4, better results can be obtained by allowing TF
the receiver a symbol-by-symbol detector is assumed. Here,
packing.ThevaluesofT andF arechosenasthoseproviding
we consider the predistorter described in Section IV-A, with
the largest SE. This search is carried out by evaluating (4)
L =2 for QPSK, 8PSK 16APSK, andL =1 for 32APSK.
p p on grid of values of T and F (coarse search), followed by
TheSEresultshavebeenobtainedbycomputingtheIR in(2)
interpolation of the obtained values (fine search). We point
by means of the Monte Carlo method described in [15]. For
out that these curves have been obtained without reducing
each case, we also performed a coarse optimization of the
the roll-off factor, which is still α = 0.2, and employing the
noise variance to be set at receiver [8], and of the amplifier
same predistorter and symbol-by-symbol receiver adopted in
operation pointthroughthe OBO. Unless otherwise specified,
the DVB-S2 system.
the roll-off factor of the RRC pulses is α=0.2, which is the
With the aim of further improving the performance, we
lowest value considered in the standard.
now consider TF packing and a system without predistortion
We first consider the achievable SE of our benchmark
at the transmitter but using the advanced detection algorithm
scenario,andin Fig.3we report η asafunctionofP /N F
sat 0 described in Section IV-B, joint with CS (L = 1). The
r
forthefourmodulationformatsofthestandard(QPSK,8PSK,
Volterra order of the model (7) is v = 5. The results for
16APSK, and 32APSK). We verified that comparable SE val-
QPSK and16APSKmodulationsarereportedinFig.5,where
ues can be also obtained by using, instead of the predistorter,
we also showthe DVB-S2benchmarkcurvesdiscussedabove
the advanced detection scheme of Section IV-B with L = 0
r andthecurvesrelatedtoTFpackingwhenpredistortionatthe
(MMSE detection). We also consider two alternative ways
transmitterandmemorylessdetectionat the receiverare used.
that, at least in the case of a linear channel, can be used
Theseresultsshowtheimpressiveimprovementachievableby
to improve the SE without resorting to TF packing.3 The
simplest approach relies on the increase of the modulation 4We properly modify the transmitted signal such that it occupies the
same bandwidth as that of the signal with roll-off 0.2. We verified that no
3On a nonlinear satellite channel, due to the increased peak-to-average improvement can be obtained by resorting to a more sophisticated receiver
power ratio, their application must be carefully considered since not nec- based on linear ornonlinear equalization in addition to orin substitution of
essarilyproduces theexpected benefits. thepredistorter.
6
5 4
QPSK, DVB-S2 QPSK, T pack.
QPSK, α=0.05 3.5 QPSK, W opt.
QPSK, TF pack. QPSK, T pack., W opt.
4
16APSK, DVB-S2 3 QPSK, TF pack.
16APSK, α=0.05 QPSK, TF pack., W opt.
z] 3 16APSK, TF pack. z] 2.5
H H
b/s/ b/s/ 2
[M 2 [M
η η 1.5
1
1
0.5
0 0
-12 -8 -4 0 4 8 12 16 20 24 -12 -8 -4 0 4 8 12 16 20 24
Psat/N0F [dB] Psat/N0F [dB]
Fig. 4. Improvements, interms ofspectral efficiency, that can be obtained Fig. 6. Spectral efficiency of QPSK modulation with TF packing and
forQPSK and 16APSK modulations byreducing ofthe roll-off (α=0.05) bandwidthoptimizationbyadoptingtheadvancedreceiverwithCS(Lr =1).
or by adopting the TF packing technique. In all cases, predistortion at the
transmitter andmemoryless detection atthereceiver areemployed.
decreasing F, this is no more true for our nonlinear channel
5 since IMUX and OMUX bandwidths are kept fixed. Hence,
QPSK, DVB-S2
an increased value of W also increases the ISI. The benefit
QPSK, TF pack., pred.
QPSK, TF pack., adv. det. of the bandwidth optimization is twofold: it can be used as
4
16APSK, DVB-S2 an alternative to frequency packing (e.g., in cases where the
16APSK, TF pack., pred.
z] 3 16APSK, TF pack., adv. det. frequenciesoftheon-boardoscillatorscannotbemodifiedand,
H hence, frequency packing is not an option), or it can be used
s/
b/ to improve the results of TF packing. In Fig. 6, we consider
[M 2 QPSK modulationandtheadvancedreceiverwith L =1.As
η r
expected, the combination of TF packing with the bandwidth
1 optimizationgivesthebestresults.Wealsoshowtheresultsin
caseonlytimepackingoronlythebandwidthoptimizationare
adopted.Interestingly,theSE oftimepackingwith bandwidth
0
-12 -8 -4 0 4 8 12 16 20 24 optimizationisquitesimilartothatachievablebyTFpacking.
Psat/N0F [dB] Finally,tosummarizetheresults,Fig.7showstheSEforall
DVB-S2 modulations (QPSK, 8PSK, 16APSK and 32APSK)
with TF packing, bandwidth optimization, and the advanced
Fig. 5. Spectral efficiency for QPSK and 16APSK modulations with TF receiver. For clarity, we show only one curve which, for each
packing and advanced detector (TF pack., adv. det.). Comparison with the
abscissa, reports only the largest value of the four curves
DVB-S2 scenario and the case of TF packing when a predistorter and a
symbol-by-symboldetector areadopted(TFpack.,pred.). (the “envelope”). In the same figure, we also plot three other
SE curves obtained by using predistortion and a memoryless
receiver. The lowest one is that corresponding to the DVB-
TF packing combined with the considered advanced receiver, S2 scenario (one curve which is the “envelope” of all four
which, with a memory of only one symbol, can cope with curves in Fig. 3), the SE curve for the 64APSK modulation,
much more interference than the schemes employing the andtheSEcurveincaseofroll-offα=0.05reduction.Inthis
predistorter and a memoryless detector. latter case, we considered all modulationswith cardinality up
Havingremovedthe constraintoforthogonalsignaling,one to 64, and hence this curve represents the effect of both roll-
more degreeof freedomin the SE optimizationis represented off reduction and cardinality increase with respect to DVB-
by the bandwidth W of the shaping pulse p(t) (in case S2. The figure shows that TF packing and advanced receiver
of orthogonality, it is W = (1 + α)/T instead).5 Hence, processing allows a SE improvement of around 40% w.r.t.
guided by the same idea behind the TF packing technique, DVB-S2 at high SNR.
we also optimized W, further increasing both ICI and ISI
duetotheadjacentusersandtotheIMUXandOMUXfilters,
B. Modulation and coding formats
respectively.WhereasontheAWGNchannelthisoptimization
What information theory promises can be approached by
is implicit in TF packing, in the sense that we can obtain the
using proper coding schemes. All the considered modulation
same ICI by fixing F and increasing W or by fixing W and
and coding formats (MODCODs) use the low-density parity-
check (LDPC) codes with length 64800 bits of the DVB-S2
5Thesymbolrate,orequivalently thebandwidth,ofconventional DVB-S2
canalsobefurtheroptimized foraperformance improvement. standard.WeadopttheoptimizedvaluesforT,F,andW and
7
5 5
DVB-S2 SE, DVB-S2
4.5 64APSK 4.5 SE, TF pack, W opt.
α=0.05 MODCODs, DVB-S2
4 4
TF pack., W opt. MODCODs, TF pack, W opt.
3.5 3.5
Hz] 3 z] 3
H
[b/s/M 2 .25 η [b/s/ 2 .25
η
1.5 1.5
1 1
0.5 0.5
0 0
-12 -8 -4 0 4 8 12 16 20 24 -12 -8 -4 0 4 8 12 16 20 24
Psat/N0F [dB] Psat/N0F [dB]
Fig.7. Spectral efficiency ofTFpacking withbandwidth optimization (TF Fig. 8. Modulation and coding formats of the DVB-S2 standard and
pack.,W opt.).ComparisonwithDVB-S2,64APSK androll-offreduction. comparisonwiththosedesignedfortheproposedTFpackingtechniquewith
optimized bandwidth.
TABLEI
DETAILSOFTHEMODCODSBASEDONTFPACKING. TABLEII
DETAILSOFTHEDVB-S2MODCODS.INTHISCASE,τ =1ANDν=1.
rate τ ν Wopt P/N0F η
[dB] [b/s/Hz] rate P/N0F [dB] η [b/s/Hz]
1/3 0.833 1.00 +20% -1.7 0.53 1/2 0.1 0.66
QPSK 1/2 0.750 0.90 +20% 2.2 0.98 QPSK 3/5 1.4 0.79
3/5 0.750 0.90 +20% 3.6 1.18 3/4 3.2 0.99
1/2 0.731 0.95 +30% 5.3 1.43 3/5 4.6 1.19
8PSK 3/5 0.731 0.95 +30% 7.4 1.72 8PSK 3/4 7.3 1.49
2/3 0.731 0.95 +30% 8.5 1.91 8/9 10.0 1.77
2/3 0.792 0.90 +20% 11.1 2.48 3/4 10.9 1.99
16APSK 16APSK
3/4 0.750 0.90 +20% 14.1 2.94 4/5 12.0 2.12
2/3 0.731 0.95 +30% 15.3 3.18 5/6 12.7 2.21
3/4 0.731 0.95 +30% 17.5 3.58 8/9 14.6 2.35
32APSK
5/6 0.731 0.95 +30% 19.5 3.98 3/4 14.3 2.48
8/9 0.731 0.95 +30% 21.2 4.24 4/5 15.6 2.65
32APSK
5/6 16.5 2.76
8/9 19.2 2.94
9/10 19.9 2.98
the advanced detector described in Section IV-B. We assume
that1/T =27.5MbaudandF =41.5MHz, and use these
B B
values to normalize the time and frequency spacings. Due to
efficiency of a nonlinear satellite system employing linear
the soft-input soft-output nature of the considered detection
modulationswith finite constellations. As a first step, through
algorithm, we can adopt iterative detection and decoding. We
an information-theoretic analysis, we computed the spectral
distinguishbetweenlocaliterations,withintheLDPCdecoder,
efficiency achievable through this technique showing, with
and global iterations, between the detector and the decoder.
reference to the DVB-S2 scenario, that without an advanced
Here,weallowamaximumof5globaliterationsand20local
processingatthereceiver,the potentialgainsareverylimited.
iterations.
On the other hand, a detector which takes into account a
BER resultshavebeencomputedbymeansofMonteCarlo
memory of only one symbol, and thus with a very limited
simulationsandarereportedintheSEplaneinFig.8using,as
complexity increase, it is possible to obtain a gain up to 40%
reference,aBERof10−6.Inthesamefigure,theperformance
intermsofspectralefficiencywithrespecttotheconventional
oftheDVB-S2MODCODsisalsoshownforcomparison.We
use of the current standard. All these considerations can be
recallthatforthempredistortionatthetransmitterandsymbol-
extended to other channels and scenarios.
by-symboldetectionatthereceiverareadopted.Moreover,for
them we have τ =1 and ν =1. The details of the considered
REFERENCES
MODCODs are reported in Tables I and II. These results are
in perfectagreementwith the theoreticalanalysisand confirm [1] ETSIEN301307DigitalVideoBroadcasting(DVB);V1.1.2(2006-06),
Second generation framing structure, channel coding and modulation
that the TF packing technique can provide an impressive
systems for Broadcasting, Interactive Services, News Gathering and
performance improvementw.r.t. the DVB-S2 standard. other Broadband satellite applications, 2006. Available on ETSI web
site(http://www.etsi.org).
[2] J.E.Mazo,“Faster-than-Nyquistsignaling,”BellSystemTech.J.,vol.54,
VI. CONCLUSIONS pp.1450–1462, Oct.1975.
[3] J. E.Mazo and H. J. Landau, “On the minimum distance problem for
We have investigated the TF packing technique, joint with
faster-than-Nyquist signaling,” IEEETrans. Inform. Theory, pp. 1420–
anadvancedprocessingatthereceiver,toimprovethespectral 1427,Nov.1988.
8
[4] A. Liveris and C. N. Georghiades, “Exploiting faster-than-Nyquist
signaling,” IEEETrans.Commun.,vol.47,pp.1502–1511,Sept.2003.
[5] F. Rusek and J. B. Anderson, “The two dimensional Mazo limit,” in
Proc.IEEEInternationalSymposiumonInformationTheory,(Adelaide,
Australia), pp.970–974,Nov.2005.
[6] F. Rusek and J. B. Anderson, “On information rates of faster than
Nyquist signaling,” in Proc. IEEE Global Telecommun. Conf., (San
Francisco, CA,U.S.A.),Nov.2006.
[7] F. Rusek and J. B. Anderson, “Maximal capacity partial response
signaling,” in Proc. IEEE Intern. Conf. Commun., pp. 821–826, June
2007.
[8] A. Barbieri, D. Fertonani, and G. Colavolpe, “Time-frequency pack-
ing for linear modulations: spectral efficiency and practical detection
schemes,”IEEETrans.Commun.,vol.57,pp.2951–2959,Oct.2009.
[9] A. Modenini, G. Colavolpe, and N. Alagha, “How to significantly
improve the spectral efficiency of linear modulations through time-
frequency packing and advanced processing,” in Proc. IEEE Intern.
Conf.Commun.,pp.3299–3304, June2012.
[10] G.Karam andH.Sari, “AData Predistortion Technique with Memory
forQAMRadioSystems,”IEEETrans.Commun.,vol.39,pp.336–344,
Feb.1991.
[11] E.Casini,R.DeGaudenzi,andA.Ginesi,“DVB-S2modemalgorithms
design and performance over typical satellite channels,” Intern. J.
of Satellite Communications and Networking, vol. 22, pp. 281–318,
May/June 2004.
[12] G.ColavolpeandA.Piemontese,“NovelSISODetectionAlgorithmsfor
Nonlinear Satellite Channels,” IEEEWireless Commun.Letters, vol. 1,
pp.22–25,Feb.2012.
[13] G. Colavolpe, A. Modenini, and F. Rusek, “Channel shortening for
nonlinearsatellitechannels,”IEEECommun.Letters,vol.16,pp.1929–
1932,Dec.2012.
[14] N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai, “On information
rates for mismatched decoders,” IEEE Trans. Inform. Theory, vol. 40,
pp.1953–1967,Nov.1994.
[15] D.M.Arnold,H.-A.Loeliger,P.O.Vontobel,A.Kavcˇic´,andW.Zeng,
“Simulation-based computation of information rates for channels with
memory,” IEEE Trans. Inform. Theory, vol. 52, pp. 3498–3508, Aug.
2006.
[16] D.D.FalconerandF.Magee,“Adaptivechannelmemorytruncationfor
maximumlikelihoodsequenceestimation,”BellSystemTech.J.,vol.52,
pp.1541–1562,Nov.1973.
[17] F.RusekandA.Prlja,“OptimalchannelshorteningforMIMOandISI
channels,” IEEETrans. Wireless Commun., vol. 11, pp. 810–818, Feb.
2012.
[18] L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of
linearcodesforminimizingsymbolerrorrate,”IEEETrans.Inform.The-
ory,vol.20,pp.284–287,Mar.1974.
[19] S.BenedettoandE.Biglieri,“Nonlinearequalization ofdigitalsatellite
channels,”IEEEJ.Select.AreasCommun.,vol.1,pp.57–62,Jan.1983.
[20] K. P. Liolis and N. S. Alagha, “On 64-APSK constellation design
optimization,” Proc. Intern. Work. on Signal Processing for Space
Commun.,pp.1–7,Oct.2008.