4.5 Numeri al results
4.5.4 SATMODE phase noise ee ts at large spe tral e ien y 172
10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0
6 7 8 9 10 11 12
BER
E b /N 0
FC-COH MM-DP
slow-AR1, MM-DP fast-AR1, MM-DP LP
Figure4.8: 2RC modulationwith
h = 1/5
andM = 4
and oderater = 0.88
.1.5
dBatBER= 10 −5
withrespe tto the FCalgorithm.InFig.4.4,foraSC-CPMs hemewith
η = 0.925
bps/Hz,thesamealgorithmexhibitsonly0.5
dBoflosswithrespe ttothe FCdete tor,andthusthe onsideredalgorithm gets
worse performan e when employed with a system of large spe tral e ien y.
In Se tion 2.4.4,it is demonstrated that, for the onsidered CPM format, all
thealgorithmsbasedonasinglephasenoisedis retization(i.e.,algorithmslike
theDP inSe tion 2.4.3 orthe MM-DP)and workingona hannel ae tedby
a double-AR1 PN, exhibit an IR loss with respe t to the IR of the oherent
ase. Su h a IR degradation is of about half dB at medium IR values, and
almost
1
dB at large IR values. Hen e, the large BER degradation we have noted,isonlypartiallyjustiedbyinformation theoreti arguments.Probably,theBERlossislargerthanwhatwasexpe tedbe auseoftheredu ednumber
of quantization levels in the MM-DP we have employed in BER simulations
(
D = 30
), withrespe t to the largerD
valueemployed inthe IRsimulations.Moreover,inFig.2.14,weseethattheIR urve onstrainedtotheDPdete tor
loseslessthan
0.5
dBat a spe trale ien yη
of0.925
bps/Hz,andapproxi-mately
0.8
dBwhenη = 1.76
bps/Hz;thus, thelarger BERdegradationwhen onsidering a more spe tral e ient SCCPM s heme, is justied by IRargu-ments. In Fig.4.8, we also provide the two BER urves orresponding to the
appli ation ofthe MM-DPalgorithm when justthe slow-AR1 omponent (or
thefast-AR1 omponent)impairs the hannel,inordertoisolatetheee tsof
thesinglePNpro esses.Asexpe tedfromthe IRresultsreportedinFig.2.14,
most of the BER degradation is due to the fast omponent, whi h is hard to
betra ked.
In prin iple, there are two dete tors by whi h we an re over the BER
performan eloss:
the rstoneis toemployanalgorithm basedon adoublePN
dis retiza-tion, one for ea h omponents (Se tion2.4.3);
these ondoneistoresorttoanimproved-DPalgorithm(inSe tion2.4.3).
The rst wayis not a eptable, due to the very large amounts of trellisstate
ne essary to des ribe two phase dis retizations. Hen e, we resort to the
im-proved DP algorithms; inparti ular we an employ theI-DP algorithm
(Se -tion 2.4.3), basedon thefull- omplexitytrellis, aswellas theMM-I-DP
algo-rithm (Se tion 4.4.4), based on the trellis deriving from MM de omposition.
However, from some BER simulations (notreported here),we found thatthe
BERofthe I-MM-DPand oftheI-DPareoverlappedto theBERofMM-DP
inthes enarioofFig.4.8.Thus,inthis aseBERresultsperfe tly onrmthe
IRresultsof Fig.2.14,where I-DP onstrained IRispra ti allyoverlappedto
theDP onstrained IR.
Finally, in Fig. 2.14 we also show the performan e of the LP algorithm
des ribed in Se tion 4.4.4, where the predi tor oe ients are omputed
as-suminga double-AR1phasenoise modeland a predi tion order
C = 4
.Evenif su h dete tor is mat hed to the hannel, due to the approximations
intro-du ed inits derivation, it has a performan e worse than that of the MM-DP
algorithm.
Multi arrier s hemes over
doubly-sele tive hannels
In the following hapter we ompare four dierent multi arrier s hemes in
a dis rete-time, oversampled domain over doubly-sele tive hannels. We nd
that all s hemes an be implemented in a redu ed omplexity way, resorting
to suitablefasttransformslike DFT(Dis reteFourier Transform), DCT
(Dis- rete Cosine Transform), or DST (Dis rete Sine Transform). For all models
we assume either a re tangular base pulse or a properly designed prototype
pulse, well lo alized in both time and frequen y domains, and we show that
su h a te hnique an be applied to our dis rete-time blo k-based model. We
highlight the similarities and the dieren es between some re ently proposed
multi arrier modulations based on DCT and DST to mathemati al on epts
su h as the Wilson base, that inturn will be used to develop a novel and
ef-fe tive multi arrier format,ready to be employed in pra ti al ommuni ation
systems.
5.1 Introdu tion
Orthogonal Frequen y-Division Multiplexing (OFDM) is an e ient
modula-tion te hnique belonging to thewide lassof multi arrier modulations, and is
parti ularly suitedfor transmissionoverlinearfrequen y-sele tive hannels. It
isinfa twellknownthat,bymeansofOFDM,alineartime-invariant hannel
anbede omposedintoasetoforthogonal,interferen e-freesub- hannels[74℄,
and exa t maximum a posteriori (MAP) dete tion an be arried out on a
symbol-by-symbolbasis,thus withouttheneedfor omplexequalization
te h-niques. Other advantages of OFDMin lude,among others,improved spe tral
e ien y on frequen y-sele tive hannels by means of power allo ation and
easierresour eallo ationinmultiusers enarios.Asa onsequen e,OFDMhas
beenalready implementedinboth wirelineappli ations (asinthedigital
sub-s riberline(DSL)standards)aswellasinawiderangeofwirelessappli ations,
rangingfromthedigitalaudioandvideobroad asting(DAB-T,DVB-T,
DVB-SH,DVB-H)standards, tothe lo aland metropolitan areanetworks(WLANs
and WMANs).
Onthe otherhand,oneofthe OFDMmost riti aldrawba ks,namelythe
in reasedsensitivitytothe hannelimpulseresponse(CIR)timevariations,has
restri ted the appli ation of OFDM to s enarios hara terized by su iently
slowvariations. Inthepresen eof arapidly time-varyingCIR, where time
se-le tivity stems for example from the Doppler ee t or the os illators' phase
noise, the orthogonality between thesub arriers is destroyed, inter- arrier
in-terferen e(ICI)appears[75,76℄,and omplex equalizationte hniquesmustbe
employed to opewiththelatter ee t [77,78℄.
Re ently, multi arrier modulations dierent from OFDM have been
pro-posed to redu e the sensitivity to time-variations, in order to be able to
ef-fe tively employsu h modulations on doubly-sele tive hannels. For example,
some authorshave proposedto useeithertheDCTor theDSTasan
alterna-tivetotheDFTinthemodulator/demodulator implementation,forwhi hfast
implementations exist (the resulting modulation formats are denoted
respe -tivelyasDCT-OFDMandDST-OFDM,inorderto distinguishthemfromthe
previously mentioned DFT-OFDM s heme). Inparti ular in [79℄,theauthors
derive onditions on a guard sequen e and a front-end prelter for whi h a
frequen y sele tive hannel an be diagonalized into orthogonal,
interferen e-free, parallel sub- hannels when DCT-OFDM is onsidered. Moreover, in[80℄
it is shown that DCT-OFDM outperforms DFT-OFDM system over AWGN
hannelae tedbya arrierfrequen yosetandoverafrequen y-sele tivefast
Rayleighfading hannel,whilein[81℄itisprovedthatDCT-OFDMand
DST-OFDMaremorerobusttotheinterferen e, atthepri eofadramati de rease
of thespe trale ien y dueto a largeoverhead. It wasalsopointedout that
su h overhead an be avoided byinterspersing the two above mentioned
dis- rete trigonometri transforms(DTT) inthe modulator stage (DTT-OFDM),
bytransmitting theDCT oe ientsonthe even sub arriersandtheDST
o-e ientson theoddsub arriers [81℄.However, thisapproa hwasnot pursued
further due to thefa t that it leads to signals no longer orthogonal on linear
time-invariant(LTI) hannels(thoughorthogonalityisinsteadensuredon
non-dispersive hannels).Weremarkthatnos hemeabletomaintainorthogonality
onadoubly-sele tive sto hasti hannelexists[82℄,thus orthogonalityisnot a
realisti performan e measurewhen doubly-sele tive hannels are onsidered.
An alternative approa h to ombat ICI, re ently pursued by several
au-thors and denoted as pulseshape OFDM (see, for example, [83 86℄ and
ref-eren es therein), onsists in a suitable design of the prototype pulse, so as
to obtain a better time-frequen y lo alization withrespe tto there tangular
pulse employed in standard OFDM, and thus redu e ICI. These approa hes,
that an be applied to any of the above mentioned multi arrier formats,
al-lowlow- omplexitysymbol-by-symboldete tion, even onrapidlytime-varying
hannels.
The aim ofthis hapteris threefold.
Firstly, starting from a general lter-bank system, we propose an
over-sampleddis rete-timetransmitterandre eivermodelaimingatthe
pra -ti alimplementation of various multi arrier modulationformatsin
real-isti ommuni ation systems.
Se ondly, we show that all the multi arrier modulation formats an be
derived from su h adis rete-time model, with ageneral prototype lter
(rather than with the standard re tangular lter) and a general time
and frequen y spa ing between the information symbols; inotherword,
we apply pulseshaping te hnique to all the s hemes, so extending the
DCT-OFDM,DST-OFDM andDTT-OFDMs hemesalreadypresentin
literature.
Finally,inspiredbytheWilsonbase[87,Se tion4.2℄,thatturnsouttobe
a leverwayto design well-lo alized orthogonalGaborframeswithhigh
time-frequen ye ien ythatavoidthelimitingfa torduetothe
Balian-Lowtheorem[87℄,[88℄,wederiveapra ti almulti arriermodulationwith
ex ellent performan e on doubly-sele tive hannels.
For all the above mentioned modulation s hemes, we rst assume a
re t-angular prototype pulse, as is usually done in the literature [74,81℄, then we
designasuitableprototypepulse,welllo alizedinboththetimeandfrequen y
domains, by meansof thete hnique proposedin[89℄ or in[90℄.