BSTJ 60: 9. November 1981: Adaptive Cancellation of Intersymbol Interference for Data Transmission. (Gersho, A.; Lim, T.L.)

9.3 MB·English

THE BELL SYSTEM
TECHNICAL JOURNAL

Adaptive Cancellation of intersymbol
Interference for Data Transmi

By A. GERSHO and T. LLM
(teruscretrcoives Apr 22, 1981)

In this paper, we anatize « techaigue for accurately detecting
transmitted data symbols contained in e modulated signal that has
‘een degraded by a linear dispersice channel end wdiitive Gaussian
noise. The approach uses an adaptice equalizer which provides
preliminary decisions to an adaptive canseller, The canceller output
{usd to remove the interference from an adaptice matching filter,
resulting in the desired signal. Channel equalization atlempls 10
Invert the channel transfer function, while avoiding excessive noise
enhancement. However, cancellation {as used in echo canceller),
‘attempts to generate a replice of the ierfering signal and aubtract
it from the actual received signal containing the sim of the desired
signal and interference. The cancellation approach, unlike equali-
2ation, offers the possibility of removina interference without enhanc

ing the level of noise already present in the received waveform,
‘Simulation results for tranamission over practical channels show
significant improvement of linear cancellation over both linear for
‘ward and decision feedback equalization,

|. wTRODUCTION

For the past twenty years engineers have been seeking new tech-
niques to combet the intersymbel interference us) in data transmie
sion over band-limited channels. Adaptive equalization withthe mean
square algorithm has been the waaor (wchniquw thal. lowe abe
‘stantial increase in alsinable (rrseimion rate If Ue channel has

1997
‘only phase distortion, then the Linear fractionally spaced equalizer can
‘liminate virtually all of che Ist without enhancing the nose level *
However, when amplitude distortion is pretent in the channel, any
‘adaptive linear equalizer (LE) must compromise betwoen inverting the
‘channel transfer fumetion and nvoiding exceaive noise enhancement.
Inevitably, some noise enhancement occurs, Decision feedback equal-
ination can offer somewhat improved performance when amplizade
distorcion ie present. By using the Viterbi algorithn,* maximum-
Iikeihond receivers in principle, offer the best performance posible
‘but depend on adaptive estimators of the channel and require an
Impractically high complexity when the channel impulse response is
Jong, a in the case of the typical telephone channel

there were no iat, the probability of error in detecting the trans
‘mite data level (Le, £1 or 3) would he the same as if oly one such
pulse were transmitted in lation In that cace, the optimal receiver
{for Gaussian noise) would be a matched filer and would yield «
‘certain error probability, Ps. When pulsos are sent sequentially, the
‘tfoct of tor cannot be totally eiinated, The maximum likelihood
‘esimator ofthe enlio soquence of wansmitted symbol is known to
‘emule nan error probly that ia somewhat larger than Pe

Tn this paper, we describe cancellation technique dosigned to
achieve ncated-pulve, matched-flter performance. Extensive simula
‘don reslts confirm that chere is asgnficant improvement over linear
bor decision-fedback equalization fr severe amplitude distorting chan
els of practical intorst

1. BACKGROUND AND MOTIVATION

‘The ide of cancellation was use for the echo problem in two-wite
telephony (eee Ref. 7), where the received signal contains an intarfer-
fence component that ew ered and delayed version ofan “orginal-
ing” signal In that application, the originating signal is accualy
fvailable the same Toeation, However, in data transmission the
‘riginating signal—the tranmitred data stream—Ie not dinectly ob-
servable at the tecaiver, The idea of using preliminary decisions
(generate an intermediate elimate of che transmitted data signal was
{independently proposed by various investigators. Allo the proposals
‘ncuded adapting tha ooefclents of after that forms a replica ofthe
tar, Adaptation i, of course, needed since the appropriate fering
‘operation is not known in advance and can vary with line, Hirsch and
‘Proskis proposed the cancellation echeme wilh che essential structure
in Figure 1°” Here the anceller attempts to remove the ts directly
from the reocived line signal. "This approach doesnot achieve improved
performance over linear enulization if there is phate distortion. Tn
thie paper, me describe w linear eaneller (xe) structure where a

4900 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1981
sO) [FF]

ig Fn eee ina ane

taneversl fer Wis uae instead of the delay in Fig. 1, Both C and
‘Ware adapted simulcaneously with the ror signal between the input
ve the final detector and the appropriate reterenoe.

‘The motivation for this structure sie from the need lo effectively
elect higtvepeed data on channel Unat have both high noise level
and substantial amplitude (lope) and phase distortion. In cern
Condivins of practical interest, even ifthe equalizer were of infinite
Tength, the noise enhancement of Linea or decision Feedback equal:
aation makes impossible to achieve the required errar rate. Never:
‘theless, incar equalization is sufficient to obtain fairly moderate error
rates o that the detected symboix may he adequate a preliminary
‘decisions for a cancellacion scheine.

Tm Section 3, we provide intuitive rearing thatthe optimal choice
for Win a matched fiver, and the optimal (isa canciler whose tap
‘weightsare the aamplesof the channel autocorrelation function, except
Tor the center tap, which han zea weighl. We show in Section 4 that
this ia true under the ascumsptian that the pectiminnry decision Ay are
comet. Section § covers adaptive operation snd Sion 6, mulation
eau

1M, FORMULATION
‘Let the transmitted data symbole be denoted Ay, Ay Ay, «+= with
‘each complex valued syrahol having real aru iaginary pars retrcted
to one ofa finite set vf values (ie. 41,18). A complex-valued pulse
shape plt) is uted to gencente the baachand tranmmiteed data signal

INTERSuBO! INTERFERENCE 1900
M0) = Anple = RP. o

‘The linear distrtion ofthe channel resuls in the received waveform,
XW = Ade a7 + Via, e

ere V(t) is white noine and A(t) is the overall channel impulse
response
unooe intially that the receiver consists of a matched fter and a
sampler rate 1/7) followed by a symbol detector as shown in Fig. 2
"The matched fier his impulse eaponse
w= hr), o
‘where *denstes complex conjugation and the integer Lis chosen large
‘ough so thatthe output ix amall for 2 <0. The output ofthe sampler
isthen
Ulm) = Lavin? — AP LT) + nT, o

ushere V4 i the colerod noses the matched filter output and rit)
is the autocorrelation function of the pulse Ald); that is 7) =
Ee Alege + elds, Kqation (4) can be writen as

UimT) = Ani Oh-+ VAT) + Tote o
where
= EB Avi? - AP ED) 6

‘Suppose vba at time ¢— mf the reeciver must detect the currently
otwervable symbol ae 1 amd it Knows all prior symbols Ans
(Anis ata all eabaequent symbols Ay-tsiy Amato,» Are that
fltermine the value Jp ofthe total Tn this case, Jn na known
fonstant and can be aberacted fur Clim). What remains is exactly
the output value that the matched filler would produce ifthe erans-
tater scot single isolated pulse An ple — (m ~ L)T), Hence, che
‘eal performance, with eror probability Ps, would be achieved

1g +-Moda of tama chan and matched le

2000 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1981
iF crc

aad He

"The above reasoning auggeste that we could approach the ideal—
isolated eymbol— performance with each symbol fleision if we could
‘generate a good estimate ofthe total 1, a each vampling instant,
f= mT. The decision feedback approach can be viewed as a partial
step this dieetion. This appreach ia based on the iden that we ean
estimate the prior symbols called precursors by suring and processing
the outputs Ay-t-n, Aga sleady produced by the detector. The
are of fa-r detorminod by the precursors can then be constructed, BY
‘applving the decision A to « feodback Ber, che oorput is subtaacted
from Une?) and the resultant signal is applied to the detector. The
decison feedback equalizer (DFE) ia shown in Fig. 3. Since we have
pot removed all ofthe is, cheesulting performance willbe inferior to
that ofthe ialated-palse cae, ‘Thi diacusion shows that the DFE
fechnigue can be rogarded at partial step towards the goal of totally
emaving Ist, We next examinr how we go beyond the stage of
postcursor eancellain ta include precurser cancellation,

‘Suppose at time mT we could aleo eliminave the subeequent, pos
cursor syrabols Ay-taiyw-rot Aw that also contribute to the total
Interferonee at time m7. Then, using eq (6), am etimat of the total
11, To, would be aunilable at Game instant m7. This ia not possible
tusing the output ofthe decovtorin Pig. Howaver, suppose a separate
‘equlizer operates om the recrived dain signal y() sx shown in (a) of
Fig. 4 1 optimally designed, it will have a modest error rate, and we
can use it decision do, as preliminary ur Vntative deision forthe
parpose of consracting our etimate of Ty. Now there brno problem
in obisining both precursor and posceursor estimates needed to for
Tz By introducing a fred time delay, D, to the received signal prive
@ the matched filter us shown in (@), the Le has @ head-sart in
estimating data symbols. A practical implementation of an adaptive
‘esbond eanceller would tle the form ebown in (b) of Fig. 4

‘The delay D can actully be incorporated into the matched filter by
chouning suitably lege. ‘Tho cancellation filter (2 produces the
estimate fy cof the actual inverforence

Iam B Aertmt — 10 -

LT), °

INTERSYHGOL INTERFERENCE 2001
igo wae an) Pasha ar cancel sacs

2002 THE BELL SYSTEM TECHNICAL JOURNAL, NOVENBER 1861
swhare Ay is tho sequence of prlininary decisions. Note that the
Aransverel filer whieh lakes as input A and produces the ouput
Ts at cone mT, bas an impulse response

eft OP] temo
0 moe

®

‘We shall see in Section IV that, under the assumption of perfect
preliminary decisions, this is indeed the optimum impulse response in
the mean-square sense

1, OPTIMAL CANCELLATION
‘41 Daruation of opts Miter coemneients
"To determine the optimal par of filters W and Cfor the cancellation

scheme, we make the simplifying assumption that the preliminary
‘decisions available from the ua are correct. We focus onthe structure
‘shown in Fig. 5, where the filter W, called the matching filter, is &
‘T/espaced Infinice length craneversal ker preceded by’ a campler
‘operaling at rate 2/7 sammplea per second. ‘The filter C, called the
ceanceller, isa

(11/2), where (0)
the received line signal, and the oulpul, Ux of Wis taken ai ime
Insta, # = #7, ax indicated in Fig. 5 by the 1/7 rate sampler. The
Input to caneeller Cis the true data sequence (4s) since we have
sured Ue tentative decisions are err lay Fg: shown being
fed dinectly by the tanamitzed data symbols Te ia not necessary to
explicidly consider che time delay D since we are allowing infinite
length filters: The output of the canceller Vy is subtracted trom the
matching filter output. This dilferenee producing U.~ Vz tobe applied
(oa slicer may be viewed ne linen timtar of the duis ymbol dy.
"The goal i to determine the fitere W and C that minimize

= Bile, ®
the mean -aquare ear (re), where ey = Us — Va ~ Ay

Fig 5 Mocel ofa incr cnet.

INTERSYMBOL INTERFERENCE 2000
‘Lec alt) denote the additive rxeiver noise aa shown in Fig. 6."Then,
‘the input to the matching tar is given by

pm expla TI) Y AMET 00) a2)

0)

‘where hit) athe eomples impulse response ofthe channel and include
the effect ofthe tramilicr shaping filter p(t) we trested in Section
IIL The term a) is the complex Deseband noiso sample. All sum:
‘mations are over the integers rom — t0-,unlea otherwise indented,
‘The output Uy oF tha mating ter 8

Uy= capt ian) § Wis a
‘where W denotes the tap weighta of W: Let hi= AUT) and define
bE Whe a
‘Then Uy may be waite in be for
U-Pb oot Ne on)
whore
2 Whew ao
{nthe noi atthe omput ofthe mntching fer.

‘Weshall et C; denote the ith lap weight ofthe cancellation fitr for
cach intoger é exoopt i = 0. We make the constrain chat the center
tap toeight of the cancellation [iter is ero, This restricts tho role of
the cenceller to removing I6t srl prevents the cancelle from making
‘use ofthe errent data symbol which must be estimated bythe output
signal rom the matching ter. The caneellr output Vs is given by

We ETA 5)

and we assume that

FAR a6)

‘which ie a convenient normalization ofthe date symbol power lvel,

"To minimiav the mein e, (8), We differentiate with respect to
the complex cap weights (Ca) and {Ws} and st the derivatives to zero,
Using og (15), ica be shown to yield

2004 “HE RELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1981
Fut Awd=0 mau, an
snd using 69.10),
exp jun TELE,

=o am. as)

‘Ths, these aptirality conditions roguire Unt dhe wet vgn € be
rdhoonal to the ubservable ins un the C und W Evers, namely.
Aa) and)

‘We discuss ca eases of interest. n Case , the chanel is wideban
‘We meme that the BAe process he Tie signal cell from
channel without prior band-limicing so that even when samplod at a
rate of 2/7, the noise samples aze uncorrelated, Ia Cie 2, which is
‘more relevant to our situation of a channel band-limited to the voice
‘roquoney range, tho noise samples at 7/2 spacing are coralated.

Case 1. Uncorelatad noe samcies
Tn Case 1,
Flatt 2a (AT/2)| = oe,
‘whore oi the noise vaviance. We uso define u now term,
RAD = AUTPMUTR + ITP), a9)

whieh 8 the autocorrelation funetion of the T/2sueupled impulse
response, (77/2). Than, wth

3 [4(/9)
= Ryo, am

sre ahow in the Appendix thatthe matching filter has 7/2-apaced tap
weighs

Aim

Rte

all, on

spf D7

\shich is learly proportional Loa mee -Filer ape respon, The
Capa are shown in the Appendix to he

Coma

Rion, me0. co

Tee

‘Thus, the eancellerimpolse response, form #0, i that of che overs
‘P-spaced impulse response of che channel and matching Hse.

(cave 2, Corelated note eamples
‘Aa desribed earlier, Case 2 comesponds othe voiceband telephone

INIERSYMBOL INTERFERENCE 2008,
channel, where (he noise has approximately the same bandwidth as
‘he signal wo thal ole samples at 7/2 spacing are correlated.
The noize corelation is
ELA T/2)0° UTD) = Rak ~D.
We define Wie) a the Fourier transform ofthe Wap weights, $3)
is the sampled noice specizim, and Fu) is che Fourier tranaform of
the channel-sampled impulse response "hen, with

PT [wal 4
eo E [La os
veoshow nthe Append ha
ri Aw wu)
WO Ty DR ee

"The corresponding Fourier transform of the cancller is
ro)

[Note that since

Ri (2m) = Rion),

sad (ie + op) is real, we see from eqs, (22) and (25) that the
‘ptimnom, infinitely long caneeller aampled impulse response in Her
tniian aymumerie abou the center, Le.

Can

5

4:2 Dorbation of mse

‘We now derive the mae achieved for Cage 1, under the nssumption
that, W and (have the uplinal impulse responses given by eas (21)
nod 2), respectively. The malching Blter eutpat is given by

Ly Alen — ts) 4 By wn

BepgE Alita ~ ts) + Ne cn
‘Tihs ning, Noi eh result of applying white noiso with variance a to
he macching Slter oy. (66), Hence, using eqs. (06) and (67), we Gnd
hat

te

By
BUN" = ete
IN = aS (23)
‘Also, he canclle output iv gin by

1
Va= poig ¥ AeRalan — 20), 2%

2006 THEBELL SYSTEM TECHNICA. JOURNAL, NOVEMBER 1081