Iterative Joint Dete tion/De oding S hemes

Whenwe onsider a ommuni ationsystem hara terized byan error

orre t-ing ode together with a hannel with memory, the ardinality of the

over-all system state an be very large, and thus, optimal MAP symbol dete tion

strategy at the re eiverbe omesunfeasible.In these ases,we an resort to a

suboptimaliterativejointdete tion/de odings heme,whi hexhibits

omputa-tional omplexityabsolutelylowerthanthe omplexityoftheoptimals heme,

but a performan e whi h tends to the optimal one (as veried by numeri al

results)[9℄.Inparti ular,herewedes ribetheoperationsofaserially

on ate-nateds heme, whi h is thes heme adoptedinChapters 3 and4 for dete tion

of CPMsignalinthe presen eof anouter error orre ting ode.

In an iterative on atenated joint dete tion/de oding s heme, ea h

om-ponent blo k (i.e.,the dete tor and the de oder) works separately, by

imple-mentingthe MAPsymbolstrategyoptimal forthesingleblo k,assumingthat

no other memory sour esarepresent inthe system.They employ a dete tion

(de oding)algorithmbasedontheMAPsymbolrule,whi hprovidesreliability

estimatesonthealgorithmde isions (Se tion1.3.1), sin eweneed soft-output

de isions in orderto on atenatethe two blo ks.In general, an iterative

on- atenated s heme is based on the following basi on ept: ea h omponent

blo k exploits the suggestion provided by the other omponent blo k, in

or-der to derive de isions whi h be omes more reliable with the iteration. In

detail, a serially on atenated s heme worksas follow. First of all, the

dete -torperformsan instan eof thedete tionalgorithm, operatingon the hannel

su ient statisti s

y

^{.Then, the}soft-de isionsitprodu es onea h symbol

x n

^,

are forwarded to the de oder, whi h employs the dete tor a posteriori

prob-abilities, as a priori probabilities on

{x n }

^{while performing de oding. Thus,}

it also produ es soft-de isions on the

x _n

^{symbols, whi h are in turn passed}

to the dete tor. The dete tor exploits su h reliability estimations as a priori

probabilities on

{x ⁿ }

^{and itstartsanewiterationof theserially} on atenated s heme. Thejointdete tion/de odingstrategy ontinuesforaxednumberof

y les;then, hard nalde isions onthe symbols

{x n }

^arederived.

In order to a elerate the onvergen e of theiterative dete tion/de oding

pro ess, ea h omponent blo k must re eive as input an information whi h

is not self-produ ed. With this aim,in [10,11℄ the on ept of extrinsi

infor-mation is introdu ed, whi h identies the reliabilityinformation produ ed by

a omponent blo k whi h does not depend on the information it re eived as

input. Indetail, ifwe denote by

ℓ _a,n

^{out theLLRsdened in(1.28), produ ed by}

a blo k and representing the reliability measure of a MAP symbol algorithm

onthede isiononthesymbol

x _n

^,theextrinsi information

ℓ _a,n

^{e,out generated by}

su h blo k,is given by

ℓ _a,n

^e,out

= ℓ _a,n

^out

− ℓ a,n

^e,in

.

^(1.32)

The FG/SPA toolintrinsi ally propagates extrinsi information, asdes ribed

by(1.30)-(1.31).

Capa ity Evaluation for CPM

signals

2.1 Introdu tion

Continuousphase modulations (CPMs)form a lass of onstant envelope

sig-naling formatsthataree ient inpowerand bandwidth[1℄.Inorder to

om-pare CPMs against linear modulations, e.g., phase-shift keying (PSK) and

quadrature-amplitude modulations(QAMs),aswellastooptimizethevarious

parameters whi h des ribe a CPM signal, namely phase response, alphabet

size,andmodulationindex,information theoreti arguments ouldbeused.In

parti ular, the availabilityof expressions for the hannel apa ity,interms of

bits per hannel use, and bandwidth o upan y of thesignal, would allow to

evaluate theamountof b/s arriedperbandunit (Hz),whi h isanimportant

omparison riterion for system designer. Unfortunately, neither losed-form

results for the apa ity of a CPM signal nor simple expressions for its

band-widthexist.

In[12℄and[13℄ananalyti alstudyoftheinformationtransferoveradditive

white Gaussian noise (AWGN) hannels for envelope onstrained waveforms

under a xed bandwidth denition is des ribed; however the results do not

seem beimmediately appli ableto theCPMs.Firstresultson CPMs apa ity

arereportedin[14℄,wheretheyarepresentedtojustifythe hooseofa ertain

outer odeinaserially- on atenated CPM(SCCPM)s heme. Theauthors do

not des ribe the method by whi h CPM apa ity is omputed and moreover,

the results they arry out do not mat h with results we will obtain in the

present work.In[15℄ multi- hannel apa ity resultsareapplied to the

de om-position [16℄ of CPM signal; unfortunately that method provides bounds too

looseon CPM apa ityto be onsidered of pra ti alinterest.

Finallyin[17,18℄and[19℄CPM apa ityis omputed byusingthemethod

by Arnold and Loeliger in 2001 [20℄ and in2006 [21℄. By this te hnique, the

information rate (IR) over a hannel with memory an be omputed by the

forward metri of a BCJR algorithm (explained in Se tion 1.3.1) applied at

theoutputofsu ha hannel. Thisworkwaspresentedinthe ontext oflinear

modulationsover hannels withmemory,but anbetransposedtoall hannels

withmemory.Hen e,representingCPMsignalsasasuitablenite-state,

nite-dimensional Markov pro ess (as done in Se tion 1.2), it is possible to derive

theinformation rateof the hannel omposedbythe on atenationof aCPM

modulator andan AWGN hannel. Moreover,in[19℄ theinformation rateof a

CPMsignalis omputedinthepresen eofaphasenoise(PN)pro ess,modeled

as a dis rete time Wiener random pro ess, whi h is a ommonly used model

intele ommuni ation s hemes.

The remainder of this hapteris organized as follows. First ofall, we

pro-vide a more exhaustive des ription of thealgorithm proposed byArnold and

Loeliger and we exploit it to derive the IR apa ity of a CPM signalover an

AWGN hannelandoveranAWGN hannelae tedbyphasenoise,modeledas

adis retetimeWienerpro ess.Then,weresorttoaphasenoise(PN)modelof

pra ti al interest, i.e.,the SATMODEphasenoisemodel,whi himpairs

satel-lite ommuni ations hara terized bylow- ost transmitter and re eiver.

SAT-MODEPN isamodelusually employedto testtheperforman eofDVB-RCS

(Digital Video Broad asting-Return Channel Satellite) systems.In parti ular,

inspe ting the phasenoise powerspe traldensity (PSD) [22℄,we see thatthe

dis rete-time phase pro ess an be well approximated by the sum of two 1st

orderauto-regressive (AR1)pro esses,andwe derive CPM'sIRinsu ha

s e-nario.Finally,we proposea novel iterative method,similarto thegeneralized

Blahut-Arimoto algorithm re ently proposed by Kav£i [23℄, to evaluate the

Markov apa ityofa CPMsignalover anAWGN hannel. Oneof thenovelty

of our approa h is that we maximize, with respe t to the input distribution,

thespe trale ien yinbps/Hzratherthanthemutualinformationinbitsper

hannel use. We address this problem by taking into a ount the bandwidth

o upan y of the CPM signal by means of the (properly modied) Carson's

rule bandwidth denition, and solving a linearly onstrained non-linear

opti-mization problem. The results show that Markov apa ity obtained with the

proposed input optimization algorithm strongly outperforms the apa ity for

independent and uniformly distributed inputs. In the numeri al results, we

also onsidera properbandwidth denitionrelatedtothespe tralpower

on- entration(SPC),although inthis asetheoptimization an beperformedby

resorting to abrute-for e approa h only.

Nel documento Advanced Modulation/Demodulation Schemes For Wireless Communications (pagine 30-35)