7.an Adaptive Decision Feedback Equalizer

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IEEE TRANSACTI ONS ONCOMMUNICATIONTECHNOLOGY,VOL.COM-19, NO. 3, JUNE 1971 281

An Adaptive Decision Feedback Equalizer

Abstract-An adaptive decisioxi feedback equalizer to detect

digitalnformation transmitted by pulse-amplitude modulation

(PAM)hrough a noisy dispersive linear channel is described, and

its performance hrough several channels is evaluated by means

of analysis, computer simulation, and hardware simulation. For

the channels considered, the performance of both the fixed and

the adaptive decision feedback equalizers are found to be notably

better than that obtained with a similar linear equalizer.

The fixed equalizer, which may beused when the channel

characteristics are known, exhibits performance which is close

to that of the optimum, but impractical, Bayesian receiver and is

considerably superior to that of the linear equalizer. The adaptive

decision feedback equalizer, which isused when the channel

impulse response is unknown or time varying, has a better transient

and steady-state performance than the adaptive linear equalizer.

The sensitivity of the receiver structure to adjustment and quanti-

zation errors is not pronounced.

A

I. INTRODUCTION

N ADAPTIVE decision feedback qualizer is de-

scribed, and it,sperformance is discussed in his

paper. The equalizer is used to recover a sequence of digits

that has been transmit ted at a high rate overa noisy

dispersive linear communications channel by some linear

modulation process. The channel s used efficiently bysending the digital information at such a high rat e that

there is intersymbol nterference at he receiver input

between several successive digits. The receiver is able to

combat both t,he additivenoise and the intersymbol inter-

ference, and also to adapt itself to an unknown or slowly

varyingchannelwithout the aid of a training digit se-

quence. Thus it can “track” a continual slow dri ft in chan-

nel characteristics without interrupting themessage trans-

mission. Past decisions about the digits are used in mini-

mizing the intersymbol nterference by coherentlysub-

tracting the interference from previously detected digits,

and also are used in adapting the equalizer parameters to

a change in channel characteristics. It is shown that this

receiver is insensitive to quantization of the input signal

and quantization and adjustment of its own parameters,

and SO can be constructed at reasonable cost.

of the IEEE Communication Technology Group for publicationPaper approved by the Data Communication Systems Committee

after presentation at the 1970 IEEE International Conference on

received September 25, 1970; revised December 23, 1970.Communications, San Francisco, Calif., June 8-10. Manuscript

D. A. George is with the Department of Electrical Engineering,Carleton University, Ottawa, Ont., Canada.

R .R . Bowen and J. R . Storey are with Communications Re-search Center, Department of Communications, Ottawa, Ont.,

Canada.

The adapt,ive linear transversal equalizer [1]-[3] has

been developed in recentyears to accomplish the task

outlined previously. With that receiver it has been pos-

sible to utilize unknown or slowly varying dispersive chan-

nels much more effectively than was possible with fixed

lumped-parameter equalizers. Concurrently, however, it

has been shown [4]-[7] tha t the statistically optimum

receiver for the recovery of the digit sequence, when the

dispersivechannel is known, is nonlinear. At high da ta

rates the performance of this receiver is much bett er than

th at possible with the transversal equalizer, which is theopt,imum inear receiver. Unfortunately, t he statistically

optimum receiver is very complex when there is a large

amount of intersymbol interference, and is not practical

with oday’s technology. This suggests that one seek a

statisticallysuboptimum receiver that is practicaland

has a performance that is significantly be tter tha n that

of any receiver that is constrained to be linear. A decision

feedbackequalizer, described by Austin [SI, is sucha

receiver. It is shown in Fig. 1. This equalizer is not adapt-

ive but an adaptive version may readily be obtained, as

is shown in this paper.

The decision feedback equalizer is similar to the trans-

versalequalizer in hat bot,h havea iltermatched to

the isolated received pulse, followed by a baud-rate tapped

delay line. However, it makes use of the fact tha t at the

transversalequalizeroutput here is intersymbol nter-

ference caused by both undetected digits and previously

detected digits. If the previous decisions are correct, they

can be used to coherently substract the intersymbol inter-

ference caused by t,he previously detected digits. This is

done by passing the past decisions through the feedback

t,apped delay line. The feedback delay line tap values are

chosen on the assumption that these past decisions are

all correct. The matched ilter and he forward tapped

delay line are used to minimize the effects of the additivenoise and t.he intersymbol nterference from undetected

digits. Errorsat heoutput of this equalizer occur in

bursts, of course, because a decision error in the feedback

delay line tends o cause yet more incorrect decisions.

However, the equalizer s able to recover spontaneously

from his condition.Simulation tudies show that he

performance of the decision feedbackequalizercanbe

considerably bet ter than that of the linear equalizer even

though it,s output errors occur in bursts.

In Section I1 of this paper the decision feedback equal-

izer is described, and its performance is compared with

the performance of a number of other receivers. This com-



282 IEEE TRANSACTIONS ON COMMUNICATION TECHNOLOGY, J U N E 1971

!! fGf.(llDT T T

T A PPEDD EL A Y IN E

Fig. 1. Decision feedbackequalizer.

parison is done both analyt,ically and by digital computer

simulat,ion.It is shown by example ha t thedecision feed-

back equalizer is an attractive compromise between what

is theoret,ically possible and what is now in use. Next, in

Section 111, it is demonstrated that the decision feedback

equalizer may be made adaptive to an unknown channel.

Twodifferent adaptationalgorithmsare described and

comparedbyhardwaresimulationstudies. In th e cases

considered, the adaptive decision feedback equalizer sig-

nificantly outperformed the adaptive linear equalizer, and

a raining equence was not required or adapt,ation.

Rat ,her , the decisions can be used for adaptation as well

as o coherent.ly substract he ntersymbol interference.

Finally, inSect.ion IV, the practical naturef the equalizer

is demonstratedbyshowing hat henumber of delay

line taps tha t it requires s modest, and that its digita l

implementat.ionrequires no finerquanbization han he

linear equalizer.

11. FIXED QUALIZER

In this section t.he fixed nonadaptive decision feedback

equalizer for a known dispersive channelwill be examined.

The error rate of this equalizer is a lower bound on the

error rate of an equalizer t,hat must also adapt to random

changes in the channei characteristics. The basic assump-

tion made in deriving the receiver is tha t the decisions

made by t,he receiver as to the transmitted signal samples

are essentially correct. Given the bit error rate require-

ment.s in modern communication systems, this is a valid

assumpt,ion. It is furthermoreassumed hat heanalogsignal rom thecomhunicationschannelhas been de-

modulated, filtered, and sampled at th e digitbaud rate

with ,he appropriate phase. Previous work [l], [SI has

indicated the desirability of a matched filter before the

sampler, as shown in Fig. 1. In the approach taken in this

paper, any suitable band-limit’ing filt,er may be used, at

the price of some loss inperformance. It remains to

determineheap gains { a ( k ); = 0,1, - , N } and

{ b(m) ; m = 1,2,3, - . , M ) , as illustrated in Fig. 1. In the

adaptive formof the equalizer these aps are automat ically

adjusted; for the fixed equalizer the tap gains must be

calculated and manually adjusted after the channel char-

acterist.ics are determined.

The equalizermakes the stimate ’ ’

N MYe ( j ) = a ( k ) y ( j+ k) - b ( z ) J ( j - ) ( 1 )

k-0 z=1

about e( j ) , he digit th at is sent at time = j T , and then

converts this estimate to a final decision e^( j ) with a non-

linear memoryless circuit,. (If the digits { e ( j ) are binary

this circuit is a clipping circuit with zero bias. If the digits

are m-ary the circuit is an m-output quantize r.) In ( 1 )

y ( + k ) is the output of the initial filter a t time t =

( j + k )T.One met.hod of choosing the tap values is to

adjust for’heminimization of the robabili tyhat

e ( j ) # e( j ) . However, this direct opt,imizations difficult

because an analytical expression for the error probability

in erms of the equalizer tap valuesis

notknown.Apracticabie way to “opt’imize” the tap values is to choose

them such t.hat the output mean-square errorE [ e 2 (j ) ] s

minimized, where

e ( j )~ - e ’ ( j >e ( j > . ( 2 )

As shown later , t.his leads to a set of linear equa tions that

specify the ap values. Thismethod of optimization is

also attractive because it canbe used to make theequalizer

self-optimizingor adaptive oanunknownora slowly

varying channel. While this optimization does not mini-

mize t.he digit error probability directly, computer simu-

lation studies SI have shown that the probability density

function of the error e ( j ) is close to Gaussian, and sothe two performance criteria are similar.

The process of determining the tap values starts with

the evaluat ion of the mean-square error:

E C ~ ~ ( O I E C $ ( ~ ) ( j > ~ ~ l

N

= EC{C a ( k ) y ( j+ k)k-0

M

- c b ( o J ( j- ) - ( j ) 1 2 1 (3)1-1



GEORGE et al.: ADAPTIVE DECISION FEEDBACK EQUALIZER283

where the signalample y ( j + k ) is In general, it is quite difficult to calculate the digitrrorprobability at he equalizer output.The calculation is

( j + k ) = e( j + k - qZ( i )+ n( + k ) (4) particularly difficult because the assumption tha t all pastM

i=O digitsretrictlyorrect will, of course,eiolated, and

and x ( i ) is t.he value of the impulse response of the linear

modulator, the channel, and the initia l eceiver filter after

a delay iT, nd n( + k) is the additive noise at th eout-

put of the initial filter a t time t = ( j + k ) T. The for-

ward tap a ( n ) is optimum when

the errors may tend to occur in bursts. Nonetheless, some

id& of the improved performance of the decision feedback

equalizer over the transversal equalizer can be obtained

by assuming an ideal equalizer with an infinite numberof taps and a matched filter in an environment of white

additive noise with spectral density N o . In this case the

equations or the optimum tap values of a ransversal

equalizer are

for all k ( 1 0 )

= 0, n = 0 , 1 , . . - , N . (5) where 6 ( - ) is the Kronecker deltaunctionnd

Similarly, the feedback tap b(m) is optimum when

a E C e 2 ( j ) 1= 2EC( a ( k ) y ( + k )N

ab (772) k=O

the channel ncascade.Themean-squareerror of the

output of this equalizer isM

- 6(z)8( j - ) - e( j ) . e ( j - m ) ]1-1

E [ e 2 ( j ) ]= N o c ( 0 ) .1 2 )

= - 2 ~ [ e ( ) e ( j- m ) ]In th e same situat ion he forward ,aps of the decision

= 0, m = 1 , 2 , . . . , M . ( 6 ) feedbackqualizer are given by

The M + N + 1 ( 5 ) and (6) canbewritten s et of 01

M + N + 1 linear,equat,ionswith the unknowns a ( i ) a ( j ) ( + q ( j- 72) + N o S ( j - nz) ) = ~ ( ~ ~ ~

i = O , l , - . . , N and b ( k ) , k = 1 , 2 , . - - , M .This is done by

reversing,herder of t,heummationnd the averagingor 772 2 0. ( 1 3 )

j=O

in (5) and ( 6 ) and by assuming that e ( j ) = e( j ) and

that E[e( ) e ( j + k ) 3 is zero if k # 0. The resulting

equat’ions are

As before, the feedback tap values are given by (8). If the

past decisions (e^( j - 72) ) are all correct, he decision

feedback equalizer out’put mean-square error is

and

N

c a ( i ) *( i l k ) + dn(k - ).) = Z ( k ) , E [ e2 ( ) ] = N o a ( 0 ) .1 4 )i=O

k = 0,1, * . , N ( 7 )The performances of the wo equalizerscan nowbe

compared by comparing ( 1 2 ) with ( 1 4 ) through the

medium of an equivalent eceivedpulse” which has

b(nl) = a ( i ) x (m+ i), 772 = 1 , 2 , .. ,M (8) sampled datanotationand he z transform is convenient

N samples p ( i ) athe sampling instants t = iT. Use of

i= O here. The transformedulsehape P ( z ) is defined to be

where & ( k - ) is the autocorrelation unction of the

noise n ( t ) at delay T = ( k - )T , and \k (ilk) s defined

by the equation

i\ k ( i , k ) g x(Z)x(Z + k - ). (9 )

2 4

In th e articular case where a matched filters used ahead

of the tapped delay lines, the x ( t ) is the autocorrelation

function of the impulseresponse of the modulator and

channel in cascade, and (7)-(9) become equivalent to

those given by Austin [ S I .

w

P ( z ) p ( i ) z - i . ( 1 5 )i=O

With this notation, the equivalent received pulse for the

problem at hand is given by

where



284 IEEE TRANSACTIONS ON COMMUNICATION TECHNOLOGY, JUNE 1971

The quant ,i ty of significance here s the inverse of the

“equivalent received pulse”, which is defined by

and ther ( i ) can be determined by simple long ivision.

into (12) and (14)) gives the mean-square error

Substi tuting the results of this series of definitions back

01

E r e 2 ( ) ] = No r 2 ( i ) (19)i=O

for the transversal equalizer and

Ere2( ) = N o r 2 ( 0 ) (20)

for the decision feedback equalizer. It should. be noted

th at these results are for an idealized situation, and as I

such form a lower bound on t’he actual mean-square error;

however, they do allow ready comparisons. For example,

for th e simple case where p (i) = P exp ( -ir) , i 2 0,

the advant.age of the decision feedback equalizer is limited

to 3 dB, since

r 2 ( i )= P (1+ exp (-27)) (21)

00

i s 0

and

r2(0) = P. (22)

In cont rast, if the background noise spectral density N ois small and the actual pulse q ( r ) is a rect(angu1ar pulse

of length L, where the int,erpulse period T is aL, 1/2 5a _< 1, then t.he ratio of the mean-square errors is

where

P2

1 + p =A I - a .

The ratio becomes very large as a4 1/2. Thus the ad-

vantage achieved by using the decision feedback equalizer

depends on the hannel impulse response, and can, in some

cases, be quite large.

The performance of the equalizers were compared alsobyMonte Carlosimulation of th e twoequalizers on a

digitalcomputer. In addition, the statistically optimum

or Bayesian demodulator [SI was simulated to determine

how close to the optimumperformance were the perform-

ances of t.he statistically suboptimum, but much simpler,

equalizers. In one series of simulation tes ts the isolated

received pulse was Are- and headdit ive noise was

Gaussian and white with power spectral density N o . The

message was a sequence of independent binary digits. The

measured error probabilit,ies at the outputof the decision

feedback equalizer, the linear equalizer, the Bayesian

1q ( r I =7e-r

BAUD INTERVAL T = I O

0 3

Pe

3

20 4.0 6.0 80 0.0 12.0 140 160EINo. dB

Fig. 2 . Comparison of receiver errorprobabilities as functions ofsignal t o background noise ratio.

PF5

0

s0

210

pe =

LINEAREQ U A L IZ ER

DECISIONFEEDBACK

12.0 E Q U A L I Z E R

BAYESIAN

D EM O D U L A T O R

0 0

-3 0 - 2 0 -1.0 0 0 1.0 2 0 3 0 4 0 5 0 6.0 70

T R A N SM ISSIO NRATE R

lo [ 3de+B- -1Fig. 3. Effect of dat,a transmission rate change on receiver

performances.

demodulator, and a matched filter with clipper are shown

in Fig. 2, as a function of the signal to background noise

level E/No. ( E s the isolat.ed pulse energy, equal to & ( O )

of (11) .) Also shown is t.he error function curve, the per-

formance that one could achieve if there was no nter-

symbol nterference. I n this series of tests hechannelparameter a was unity.Afiltermatched o Are-‘ was

used as part of both the linear and the decision feedback

equalizer. Approximately one hundrederrors were ob-

served in making each error probability measurement. A

sequence of tests was donewithdifferentnumbers of

forward and feedback equalizer taps. It was found that

the linear equalizer performance improved as the number

of taps was increased to 5 , but a further increase did not

appreciably improve the performance. I n the same way,

3 forward taps and 6 feedback taps were found for the

decision feedback equalizer. (The question of the number



GEORGE et al.: ADAPTIVE DECISION FEEDBACK EQUALIZER 285

0 4 8 12 16 x ) 24 28 32 36 40 44 48

TIME, NANOSECONDS

Fig. 4. Impulse response of coaxial cable PCM channel.

of taps is discussed in more detail nSection V.) As

expected, it was observed t ha t the errors a t t,he decision

feedback equalizer output occurred in short, burst,s. At low

signal to background noise ratios, 5 6 dB in ’his case, the

bursts occur so frequently th at the linear equalizer per-

formance is better. However, a t higher signal-to-noise

rat ios (SNRs) the improved ability of the decision feed-

back equalizer to reduce the intersymbol nterference s

more important than the tendency t.0 produce errors in

bursts.

It was found t,ha t at low error probabilities, wherever

the digiterrorprobability was less than he perform-

ance of t,he decision feedback equalizer, the linear equal-

COAXIAL PC M HANNEL

I6 0

ERROR PROBAEILITY :1 6 ~

I 4 O j2 0

izer, and t,he Bayesian demodulator could all be accurat’ely

described by t,he empirical formula0 I I I

0 100 200 300 400 50 0 600

{ [ 2No 11DATA RATE R, MEGAEITS/SECOND

T(R)EP[e] = 0.5 1- erf- ( 2 5 ) Fig. 5 . Effect, of data transmission rate changehrough PCM

channel.

where R is the dat a transmission ate, defined for this

example to be equal to (aT)-l. q ( R ) may be considered

to be the efficiency of the modem, and must, be in the

range 0 5 q ( R ) 5 1.0. In all cases q -+ 0 as R -+ and

q -+ 1.0 as R -+ 0. q ( R ) for t’he hree demodulators, meas-

ured at digiterrorprobability, is shown in Fig. 3 asa funct,ion of R. At all transmission rates the efficiency

of the decision feedback equalizer was greater tha n th at

of t,he linear equalizer and less than tha t of the Bayesian

demodulator. At high transmission rates t.he efficiency of

both nonlinear receivers decreased by 4.0 dB when the

rate was doubled. The efficiency of the Bayesian demodu-

lator was 2.0 dB bet ter than that f the decision feedback

equalizer a t all high rates. In contrast’, bhe efficiency of

the linear equalizer decreased by 9.0 dB when t,he rate

was doubled. This difference in rate of efficiency decrease

becomes very important, of course, if t,he channel is used

a t very high rates and at high SNRs.

The usefulness of the decision feedback equalizer in a

coaxial cable pulse-code modulation (PCM) link was also

evaluated with a computer Monte Carlo simulation pro-

gram. In t.his series of tests the “channel” included the

transmitter, a solid coaxial cablewith an air dielectric,

and a fixed lumped-parameter equalizer. This channel has

no dc response, a 100-MHz bandwidth at th e -3.0-dBpoints,a 240-MHz bandwidth at th e -20.0-dB points,

and a 70.0-dB per octave roll-off a t higher frequencies.

(Thiscontrastswith he previous example, where the

roll-off was 12.0 dB peroctave.) The channel impulse

response is shown in Fig. 4. The nominal data rate through

this channel without further equalization is 225 Mbit/s.

Simulation tests showed th at inclusion of a linear trans-

versal equalizer with a matched filter would allow one to

increase the data rate to 400 Mbit/s, but not beyond.

I n contrast, the decision feedbackqualizerwith a

matched filter can be used a t 450 Mbit/ s with only 6.0

dB more signal strength than that required a t low data

rates, and even higher rates if the signal strength is in-

creased further. The efficiency q ( R ) of the linear and the



286 IEEE TRANSACTIONSNOMMUNICATIONECHNOLOGY, JUNE 1971

decision feedback qualizer fo r t,his hannel example,

measured at digitrrorrobability, is shown in

Fig. 5 .

Thus both theperformance analysis and the simulation

results indicate th at th e decision feedback equalizer per-

formance is considerably better ,han hat of the linear

equalizer. Moreover, in the examples in which the much

more complex statistically optimum demodulator was also

evaluated, the decision feedbackequalizerperformance

was quite close, o his imiting performance. However,

these results cannot be extended to other channels with-

out either a simulation study in each case or the develop-

ment of an appropr iate analysis technique.

111. ADAPTIVEQUALIZER

I n this section i t is shown that the decision feedback

equalizercan be madeadaptive o unknown or slowly

varying channels, i.e., channels in which the impulse re-

sponse does not change appreciably during the transmis-

sion of several hundred digits. The dynamic performance

of the decision feedback equalizer, th at is, th e performanceof the equalizer while it is adapting, is described.

A method by which the decision feedback equalizer can

bemadeadaptivecan be seen from ( 2 ) , ( 6 ) , and ( 7 ) .For any set of tap values

and

If e ( j ) of ( 2 ) is replaced by

Z ( j ) = 7 ( j ) - ( j ) (28)

by assuming that the decisions are correct, then all the

signals n (26) and (27) are available at he receiver.

When t.he error probability is low this subst itution does

not change thevalue of (26) or (27) appreciably. By

changing the forward tap values byamounts approxi-

mately proport,ional to -E[;( j ) y ( j + k ) ] , and the feed-

back ta p values by amounts approximately proportional

to E[;( j ) i ( - m ) ] , the taps are automatically adjusted

to near their optimum values. Thus the forward t aps are

adjusted by means of measurement of the cross correla-tion between the error and the input signals, just as for

the linear ’ransversal equalizer. On the othe r hand, ad-

justment of the feedback taps makes use of the cross

correlation between the error and the output signal, i.e.,

t.he decisions.

The potenti al of this type of algorithm can be seen by

observing how t,he mean-square error E [ e 2 ( ) ] depends

on ap value rrors. Let ( a ( k ) ; k = 0 , 1 , . - - , N )and

{ b ( Z ); Z = 1,2,- .,MI be theactual ap values, and

( a o ( k ) ; = O , l , - . . , N } and ( b o ( Z ) ; = 1,2, . . . ,M) be the

opt imum tap values, specified by (7) and (8). Then the

_ - - __ - _- _ _ -

ADAPTATIONTEADY STATET IM E M S E PER FO R MA N C E L OW EROUND

KNOWNCHANNEL

TIME

Fig. 6. Adaptation to step change in channel impulse response.

tap value error is

d ( k ) 4 a ( l c ) - a o ( k ) , k = 0 , 1 , . . . , N

-b ( - k ) - b o ( - k ) , k = - l , . . * , - M . (29)

1,c.t 11salso define a set, of signals ( z j + i) by

z ( j + i) = y ( + i), i = O , l , . * . , N

=d ( j +

i), i =-l , .*. , --M .

(30)

Then it, can be shown th at if the tap values are in error

t,he mean-square error is

M N

+ c c ( i ) d ( k ) E [ z ( j+ i ) z ( j+ k) ]

(31 )

where eo ( j ) would be the error if the tap values were all

correct.. (The assumption was made that e ( j - 71 ) =

e ( j - m ) , 11 1 = 1,2,. . ,M, to derive ( 3 1 ) . ) Thus he

mean-square error is a quadratic function of the ta p gainerrors,,in the same way that the mean-square error of t he

linearequalizer is aquadrat,ic unction of it s ap gain

errors. Because of t,his, thereare no “locally optimum”

ta p gain settings, and a hill-climbing adaptation can be

made to readily converge close to the correct set of tap

values given by (7 ) and (8).

Of course, tJhecross correlations E[;( j ) y ( j + k ) ] and

Ere”( ) g ( - n z ) ] cannot be measured exactly in a finite

time, so any particular sequence of tap adjustments is a

sample function of a random process. A Robbins-Monro Iprocedure [9] would beapplicable if t,hechannel were

unknown but t,ime invariant . However, if t,he channel is

slowly varying then the adaptive algorithm must be ca-pable of “tracking” slowly varying hannel and of

“learning” the optimum tapvalues for an unknown chan-

nel. In that,case a procedure such as the Robbins-Monro

procedure is not applicable, and a compromise between

asmallersteady-statemean-squareerrorandashorter

adaptat ion time to channel changes is necessary.

There are a ,number of adaptation algorithms available,

in which th e exact details of the algorithm are somewhat

different,. A typical response of an adaptive receiver to a

step change in the channel characteristics when any of

these nlgorithms is used is shown in Fig. 6. The mean-

+--M k=- M

K



GEORGE et d.: ADAPTIVEECISION 287

square error at th e receiver outpu t is plotted as a func-

tion of the number of baud intervals after a step change

in the channel characterist,ics. It is a nonstationary ran-

dom variable, of course, since it is a function of the equal-

izer t ap values, which in turn are nonstat,ionary random

variables. Also shown in Fig. 6 is the, average of many

such adaptation curves. The twomost importantchar-

acteristics of such a curve are the "steady-state" mean-square error, and he "adaptation time," the time equired

to reach the steady-statemean-square error after a specific

change n the channelcharacteristics. .Theadaptation

curves tha t were obtained in a series of simulation studies

are discussed later in the paper, but some general obser-

vations may be made now.

First', since a cross correlat,ion is being measured, the

variance of the square of the signals involved contribute

significantly to the measurement error. Particularly when

binary signals are involved, there is a notable difference

between the input samples .(y( j ) and the output deci-

sions { e ( ) in this regard. In particular,

E [ { @ ( ) - E[@( ) ] ) 2 ] = 0 (32)

when

e ( j ) = A I

and

- K i Y 2 ( j ) - ~ ~ ~ 2 ~ ~ ~ 1 1 2 1

= 2{C "(i))Z + E"n"jj>I). (33)

(The additive noise samples n ( j ) are assumed to be

Gaussian in the calculation,) Certainly then in the case

of strong ntersymbol nterference, Cq2((i)s largeand

so @( ) is much less '!noisy" than y2( ) . Thus an esti-

mate of E[ e( j ) ^( j - m )]would usually involve less rror

than an estimate of E[e( ) y ( j f k ) ] .

Whether t'his implies that the decision feedback equal-

izer can adapt more rapidly or more closely to the per-

formance possible froma fixed optimum equalizer than

can the linear transversal equalizer, and hat t.he feedback

taps can adapt more easily than the orward t'aps, depends

on the sensitivity of the apadjustments.Thepartial

derivatives of ( 5 ) and (6 ) indicate this sensitivity. Since

the absolutesignal evelsare, of course, arbitrary, he

decisions e ( j ) are taken to be f and the average signalpower E [ y 2 ( ) ] s t'aken as unity. This effectively means

that the taps { a k ) and { b (1) ) are of the same order of

magnitude. This done, the sensit,ivityof the tap values

can be evaluated, giving:

= 2 (34)

= 2. (35)

The tap values are thereby shown to be equally sensitive

to adjustment, and this point combined with th at of the

previous paragraph implies tha t the feedback taps can be

adjusted more quickly and/or more accurately than the

forward t,aps or the taps of a transversal equalizer. Thus

the decision feedback equalizer would be expectedo have

abetteradaptation performance than he transversal

equalizer. This has also been observed experimentally, aswill be described.

The advantages of using the dross correlation between

the error and the decisions suggest t.he use of this same

measurement for adjustment of the t.ransversa1or forward

ta p values. Of course, the aps would not converge to

the correct value to minimize the error due t.o the addi-

tive noise and the intersymbol interference, but in some

cases a t least the taps converge to a value close t,o the

correct value. As these taps may be subject to less error

due to the ross correlat.ion measurement., improveddapt-

ive behavior can result,.

Suppose we specify the taps { a ( i ) by

E [ e ( j ) d ( j+ ) ] = 0, 1 = 0,1 , . . - ,N (36)

rather t,han by ( 5 ) . Then the tap values are the solution

to the equat'ions

N

a ( i ) z ( i- ) = 6(Z), 1 = 0,1,- * , N (37)i=O

rather t.han to (7) . Thus adjustment of the forward taps

by cross correlation between t'he error and the decisions

"forces zeros" in the overall ransmission characteristic.

If the equalizer had an infinite number of correctly spaced

taps, specified by ( 3 7 ) , the result would be an inverse

filter. In the limiting situation of no additive noise ahd a

similarly dealequalizer, an equalizeradjustedby the

minimummean-square errorapproach would alsoyield

an inverse filt'er. Consequently, it is not surprising that n

somehigh SNR situat.ionswhereeffectiveequalization

is being obt.ained, the two methods give similar results.

A potential difficulty with this "zero-forcil)g" algorithm

is that only as many system impulse response zeros can

beforcedas 'here are aps n he delay line,withone

additional ,ap eserved o orceaunit esponse at he

desired ime. The overallsystem mpulse esponsecan

become large both before andafter his nterval overwhich the response sforced to zero. In contrast, when

the equalizer is adjusted by the minimum output mean-

squareerrorapproach, .hemean-squarecontribution of

the tot.al system impulse response is minimized, not just

the responseover an ntervalas largeas the equalizer

delay line. Note, however, th at if the taps of the trans-

versal filter of the decision feedback equalizerare adjusted

by the zero-forcing algorithm, adjustment of the taps of

the feedback ilter will automatical1.ycancel any large

impulse response after the main pulse, without causing a

large impulse response at an even greater delay. This is

the basic deabehind the decision eedbackequalizer,

ba.sed on the assumption that the decisions in the feed-




ER -CONTROLLED

CHANNEL

Fig. 7. Hardware simulator.

back delay line are orrect. Thus only the system impulse

response before t.he area n which zeros are forced can

contribute to the output error. From this and from con-

siderations of the errorsssociatedwithmeasuring

E [ e ( j ) 8 ( + k ) ] and E [ e ( j ) y ( j + k ) ] , it is hypothe-sized that he decision feedbackequalizercan use bhe

cross correlation between the error and the decisions to

advantage for adjustment of both forward and feedback

taps. The experimental esults t,hatare described late r

substantia te t.his hypothesis.

The act,ual adaptation algorithm t.hat was used in t,he

experimental invest.igat,ion will now be discussed. AS

shown, the transversalor orward ta p gain houldbe

changed byanamountproportional”t0 a measure of

- E [ e ( j ) y ( + k ) ] or - E [ e ( j ) 8 ( + k ) ] , and the eed-

back ,ap byanamountproportional to a measure of

E [ e ( j ) 8 ( - nz)1.Actually, rather than taking a fixed

finite time average of these products and then changingthe tap values, the adaptatlion is done indirectly with an

algorit,hmsimilar to ha t developed byLucky [ a ] for

adaptation of the inear equalizer. The ap values are

changed in t.he following way.

1) An accumulator for the tap is set equal to zero.

2) Each t.ime a digit is processed, theroduct

e^( j )y( j+k) for theforwardtapa(k) ,or - -e^( j )8( j -m)

for the feedback tap b(m) is added to the accumulator;

Only t.he signs of e^ ( j ) y ( j + k ) and e^( j - m ) are used

in this calculation to simplify the equalizer synthesis.

3) If t.he accumulator contents exceed a threshold +V ,

then the .ap value is decreased byand step1 s repeated.

If the contents become less than -V , the tap value sincreased by A andstep I is epeated. If thecontents

remain between +V and -V , hen step 2 is repeated.

In t,he alternate procedurepreviously discussed, the

e ^ ( j ) y ( j+ k ) of step 2 are replaced by e ^ ( j ) 8 ( + k ) .

Both the transversal and decision feedback equalizer were

tested using each of,these adaptat ion algorithms.

The adap tive equalizers were evaluatedby observing

their ability t o adapt to an unknown but fixed channel,

rather than to a time-varying channel. This was done by

measuring the mean-square error at th e equalizer output

under the control of a PDP-5 digital computer was used

to do bhis. A block diagram of the simulator is .shown in

Fig. 7 . The t’ransmitt,edmessage was the pseudorandom

output of the m-sequence generator corresponding to the

poiynomiaIx31+ x28

+x27

+x24

+217

+x16

+x9

+x*

+1.

In some cases a time-invariant analog filter was used to

simulate the channel. The filter output was sampled. at

the baud rat,e after the additionf filtered Gaussian noise.

In other ests, a 32 tap 12-bit baud ate nonrecursive

digital filter was used to simulate he channel filter. I n

this case the additive noise was sampled at the baud rate

and henadded o he dispersed signal. In both cases,

the composite sampled signal was processed with a 7-bit

baud rate digital filter, as shown in Fig. 7. The sum of

the number of taps in the two nonrecursive filters could

be as great as eleven, with any division of taps between

th e two. These filter tap values were under direct com-

puter control.At he beginning of eachadapt,ation est,, all taps of

t,he decision feedbackequalizerexcept the ast forward

ta p were set to zero, so tha t the out put would be’ 0 if

there were no noise or intersymbol interference. The adapt-

ive transversal equalizer was tested in a similar way.

The digital computer was. used to change the tapvalues,

and took the sequences ( y ( j ) , (e^( j ) , and ( e ^ ( j )

directly as inputs. This method was used to avoid con-

st,ruction of adaptation circuitry for each tap. As a result,

only a few of the binarydigits that were processed by

the equalizer were used for adaptation processes. The

digits that were used are called “independentdigits”,

because the time between successive observations is long\compared o he timesover which theautocorrelation

functions of e ( j ) and y ( j ) are significant. A specified

number of these ndependentdigits,usually 100, were ’

processed according to the preceding algorithm to change

t.he taps. Then2000 digits were used to est imateE [ e 2 ( )1,without changing either the tap alues or theaccumulat,or

contents. Then 100 more samples were used for adap ta-

tion purposes, followed bynother measurement ofE[e2( j ) ] . This sequence continues until it is evident that

the equalizer has reached a “steady-state” mode of opera--as a. funct,ion of adaptat ion t,ime. A hardwaresimulator ion where t.he trend n mean-squareerror is no onger



GEORGE et d.:ADAPTIVE DECISION FEEDBACK EQUALIZER 289

TIME IN MULTIPLES OF l 39psec BAUD INTERVAL

Fig. 8. Impulse response of simulated telephone cable channel.

changingwith ime. The results of 50such adaptation

runs are then averaged to give a mean adaptation curve.

Both the signal samples { y ( j ) and the equalizer tap

values were quantized with a maximum accuracy of 7 bits.

(More will be said about quant ization accuracy require-

ment,s in Section IV. ) The least significant bit of the tap

gain values was changed during adaptation each time the

threshold +V or - was exceeded. Thus the adaptation

parameter A in these tests is ‘V 0.016.

Tests were carried ou t t,o determine whether the deci-

sion feedback equalizer can adapt bet ter than the linear

equalizer to an unknown channel, whether the results arevalid for a variety of channels, whether use of a learning

sequence is necessary or even advantageous, and whether

or not use of an estimate of E [ e ( ) e ( + k ) ] results in

better adapt.ation than an estimate of E [ e ( ) y ( + k ) ]

for the forward taps { a ( k ) . The channels that were

simulated in these tests included a channel with an expo-

nential mpulse response, a coaxial cable PCM channel,

and an audio-loaded telephone line.

One series of tests was made to compare the perform-

ances of the adaptive linear and decision feedback equal-

izers in an audio-loaded elephone cable system, and to

determine the advantage th at could be gained by using a

training sequence. The channel filter was a lumped-param-

eter filter designed by Bell Canada to simulate a15 000 ft

audio-loaded telephone cable and was terminated in 600

ohms. The impulse response of the filter is shown n Fig. 8.

Binary information was transmitted through this channel

at 7200 bit/s. Neither any intentional additive Gaussian

noise nor a filter matched to t,he isolated received pulse

were used in this series of tests. Because of the resulting

mismatch, choice of the third of 11 taps as the “main”

tap minimized the inear equalizer output mean-square

error. Similarly, it was found that the decision feedback

e,qualizer with 4 forward taps and 7 feedback taps made

the best use of the 11 available taps.Theadaptationthresholds were set a t f20 during this series of tests. It

0.3-

,

0.2-

0.1-

a0P

w 0.05.K

Waa25:

5 0.03.

I

W

0.02

0.01

UNKNOWN CHANNEL= SIMULATED 15,000

AUDIO-LOADED TELEPHONE LINE

DATA RATE = 7 2 0 0 B P S B IN AR Y

‘8

5

0 0 X.

OoX.

L I N E A R E O U A L I Z E R , N O T E S T S IG N AL

0 X *

X.

0 X =

0 /

L I N E A R E W A L I Z E R , W I T H T E S T S IG N AL

0

0

DECISIONFEEDBACK

E O U A L I Z E R , N O T E S T S IG N A L

nonoSJoooo

O 0 0 ~ O ~ooooooooo

dDECISIONFEEDBACK

E Q U A L I Z E R . W I T H T E S T S IG N AL

1 I 1 I I

500 I O 0 0 1500 2000 2 5 0 0NUMBER O F D I G I T S PR OC ESSED

Fig. 9. Adaptation curves with and without test sequence.

was found that adaptat ion based on the measurement of

E [ e ( j ) e ( + k )] resulted in a better performance than

measurement of E [ e ( j ) ( j + k )1. The mean-square

errors a t the equalizer outputs, using the former measure-

ment, are shown in Fig. 9 as a function of the number of

independentdigits that were processed. As shown, the

steady-state mean-square error of the decision feedback

equalizer is 5 dB b et ter t han that of the linear equalizer.This is consistent with the fixed equalizer tes ts tha t were





GEORGE et al.: ADAPTIVE DECISION FEEDBACK EQUALIZER 291

back case when E / N o = 13 dB and a large hresholdwas l o

used. I n allcasesamuchquicker adap tat ion could be

achieved by using e^(j ) 6 ( j + k ) I n all cases a minimum

product of adaptation ime and mean-squareerrorwas

achieved when V was 4.

Thusboth he experimental esults and he analysis

indicate that the decision feedback equalizer can be made

adaptive, and that its adaptiveerformance is bet ter thanthat of the linearqualizer. Estimates of either

E [ e ^ ( j ) y ( j+ k ) ] or E[;( j ) 6 ( j + k ) ] can be used to

modify the forward aps. The experimental esultsde-

scribedpreviously show tha t he at ter measurement is

\ better in many cases. However, the work of Hirsch and

1 Wolf [lo] indicates th at when other channelsare used

measurement of E[; ( j)6( j + k )3 cannot beused to make

the linear equalizer adaptive. Further investigation is re-

quired to determine which is the better measurement to

adapt the decision feedback equalizer to such channels.

IV. PRACTICAL CONSIDERATIONS

It has been shown previously that the performance of

the decision feedback equalizer is considerably bet ter than

that of the linear equalizer, both when the channel im-

pulse response is known and when it is not. This result is

particularly important when one realizes that thedecision

feedbackequalizer is no more complex than he linear

equalizer. For nstance, n he telephonecableexample

t.he decision feedback equalizer with 4 forward taps and

7 feedback taps outperformed the linearequalizer wit,h

11 taps. In both cases the inpu t signal and the tap values

were quantized o 7 bits. In fac t, the decision feedback

equalizer is potentially simpler, since the feedback delay

line can be a single bit shift register if the data s a binary

one.

It was determined romcomputersimulationstudies

that the decision feedback equalizer is no more sensitrive

to signalquantizationerrors or tap quantizat.ionerrors

than he inear equalizer,even hough it achieves its

superior performance by coherent subt,raction f th e inter-

symbol interference. This is consistent with the tap sensi-

tivity analysis of the previous ection, (34)and 35).

In he computer imulation study hematched filter

output g ( j ) and he equalizer tap values could be in-

dependentlyquantized oany specified accuracy. The

results of a typical test are shown in Fig. 12. In this testt,hechannel mpulse response was ATe-O.sr/T, he signal-

to-background noise ratio was 16.0 dB, the linear equal-

izer had .5 taps, and the decision feedback equalizer had

3 forward taps wit'h 8 feedbackaps.Two urves of

Fig. 12, one for each equalizer, show the error probability

as a function of the number of quantization bits when all

quantities requantizedwithhe same ccuracy. As

shown, the error probability sta rts to increase when the

number of quantization bits is reduced to 8. In contrast,

when the quantization of the signal was held a t 10 bits,

the tap gain quant ization of both equalizers could be re-

duced t o 6bits before any significant increase nerror

probability was observed.

,\

\

\

\\

\

\ \o \

\ a\

\\

.- \\"

\ \

\ \\ \\

\

\\

X LINEAREQUALIZER

0 DECISIONFEEOeACK EQUALIZER

10-

NUMBER OF QUANTIZATION BITS

10 14

Fig. 12. Effect of signal andapuantization on receiverperformance.

In a separate experiment, quantization of only the sig-

nal values j y ( j ) resulted in a performance very similar

to ha t achieved when all quantities were quantized

equally. It is believed that the reason for t,he 2-bit differ-

ence in quantization requirements is tha t the signal in-

cludes the additive noise and he ntersymbol interfer-

ence, and so the quantization error is a larger percentage

of the desired signal than of the total signal y (1).

Similar esults were observed when the coaxial cable

PCM channel was simulated. Over that channel a t 360

Mbit /s it was necessary to use 7-bit accuracy for the sig-

nal and 6-bit accuracy for the taps. At 450 Mbit/s the

linear equalizer could not effectively equalize the channel,even with as many as 21 taps and with no quantization

error in either the signal or the tap values. The decision

feedbackequalizerwith 5 forward taps and 6feedback

taps required 9-bit signal quant#ization accuracy and 7-bit

tap accuracy.

These results are directly applicable if a digital synthe-

sis method is used. They show that th e decision feedback

equalizer is no more sensitive to quantization inaccuracies

than the linear equalizer, and so is no more expensive

to construct. If an analog synthesis method is used, these

results indicate that the decision feedback equalizer is no

more sensitive to component naccuracies or signal dis-

tortion than the linear equalizer.




TABLE I

STEADY-STATEUTPUT NR s AS FUNCTIONF

NUMBERF TAPS

Number of Forward Taps

Feedback TapsNumber of

2 3 4

1 9.60. 7 11.12

11.011.43.34. 94. 2

3 11.94.56. 74~

11.94.35. 96. 011.8 14.7 16.0 16.111.8 14.9 16.1 16.2

7 11.78

14.911.74.8

The required number of equalizer taps was also exam-

ined. Computer simulation ests showed that; when the

channeladimplempulse response suchs or

both equalizers equalized the channel as well wit’h

a few transversal taps as with many, but that the ecision

feedback equalizer required several feedback taps to real-

ize its full potential, and as many as 10 or 12 a t very highrates. Note however, from Figs. 2 and 3, that the more

complex decision feedback equalizer could att ,ain a per-

formance not possible wit,h a inearequalizer wit.h any

number of taps. I n the more complex channel examples

the linear equalizer did not retain this advantage in sim-

p1icit.y. Computersimulation ests of the coaxial cable

PCB1 channel at 360 Mbit./s, wit.h a 20.0-dB signal to

background noise ratio, showed that the linear equalizer

required 9 taps to realize its full potenbial, and the deci-

sion feedbackequalizer equired4 orward tapsand 5

feedback taps.

A series of hardware simulation tests was carried out

to determine the numberof taps required by the adaptivedecision feedbackequalizer. I n these ests 450-Mbit8/s

transmissionover thePCRI channel a t high signal to

background noise ratio was simulated. The threshold V

was held a t 16 during these tests. The steady-state output

SNR in dB is shown as a function of the number of t aps

in Table I. As shown, 4 forward taps and 4 t.0 6 feedback

taps is a good compromise between better performance

and highercost. Use of more than 6 feedback taps de-

grades the performance, because the amount of quantiza-

tion noise and adaptat ion noise that the t.ap introduces is

more than the amount of intersymbol ,interference that is

removed.

From these experiment(a1 esults it, is concluded tha t thedecision feedback equalizer is a practical as well as a very

high performance receiver.

V. CONCLUSIONS

It has been shown that the decision feedback equalizer

can be used t o detect digital information t ha t has been

sent at high rates over an unknown or slowly varying

dispersive channel. The equalizer’s ability to combat inter-

symbol nterferencecaused by severalchannels was in-

vestigated experimentally. In each of the examples that

were investigated the digit error probability of the deci-

sion feedback equalizer was considerably less than that

of the linear equalizer. As well, at an y specified low error

probability t’he decision feedback equalizer allowed dat a

transmission at rates beyond that possible with the linear

equalizer. Two practicalalgorithms are described th at

make the decision feedback equalizeradaptive to unknown

or slowly varying channels. It was found experimentally

that thealgorithm based on t,he cross correlations between

theestimatederrorand heestimateddigits gave the

better performance, and that a training sequence was not

necessary foradaptation. Also, it was found that he

decision feedback equalizer is no more sensitive to quan-

tization errors than the linear equalizer. Because of t,hese

advantages, and because its performance is close to th at

of the much more complex Bayesian demodulator when

the channel is known, the decision feedbackequalizer

should be considered whenever inearmodulation ech-

niques are used to transmit digital information over dis-

persive linear channels at a high rate.

This is additionally verified in the theoretical portions

of the paper where it is shown tha t the idealized decision

feedback equalizer will always yield smaller mean-squareerror than the transversal equalizer. As well, theoretical

considerations indicate that the adaptive proper ties f the

decision feedback equalizer will t.end to be superior.

REFERENCES

pulses,” in Conf. Rec., 1965 IEE E In t. Conf. Communications,D. C. Coll and D. A. George, “A receiver for time-dispersed

R.. W. Lucky, “Techniques for adapt ive equalization of digitalcommunication svstems.” Bell Svst. Tech. J.,vol. 45. Feb.

pp. 753-758.

1966, pp. 255-268..I. G . Proakisand J. H. Miller. “An adaDtive receiver for. - ~~

digital signaling through channels with iitersymbolnter-ference,” IEEE Trans. Inform. Theory, vol. IT-15, July 1969,pp. 484-497.

transmission,” IE EE Trans. Commun. Technol., vol. COM-16,

R. A. Gonsalves, “Maximum-likelihood receiver for digital

June 1968, pp. 392-398.

digital signals,” ZEEE Trans. Inform. Theory (Corresp.), vol.R. R. Bowen, “Bayesian decision procedure for interfering

quences,” Ph.D. dissertation,CarletonUniv., Ottawa, Ont.,

IT-15, July 1969, pp. 506-507.- “Bayesiandetection of noisy time-dispersed pulse se-

Canada; Sept. 1969.K. Abend andB. D. Fritchman, Statistical detection forcommunication channels with intersvmbol interference.” Proc.ZEEE, vol. 58, May 1970, pp. 779-785.M. E. Austin, “Decision feedback qualizationor igitalcommunication over dispersivehannels,” M.I.T./R.L.E.Tech. Rep. 461, Aug. 11, 1967.

method,” Ann. Math. Statist., vol.,22, 1951, pp. 400-407.H. Robbinsnd S. Monro, “A stochastic approximation

D. Hirsoh and W. .J. Wolf. “A slmole adaDtlve eauahzer forefficient data t,ransmission,” IEEE krans. &rnmun. Technol.,vol. COM-18, Feb. 1970, pp. 5-12.

~ ~ ~ ~~ . . ~ ~

Donald A. George (SJ54-M’59) was orn

inGalt, Ont., Canada,on April 24, 1932.

He received the B.Eng. degree in engineering

physics from McGill University, Montreal,

P. Q ., Canada, n 1955, the M.S. degree in

electrical engineering from tanfo rd Uni-

versity,Stanford, Calif., in 1956, an d he

Sc.D. degree in electrical engineering from

Cambridge, in 1959.Massachusetts Institute of Technology, ’

From 1959 to 1962 hewas an Assistant

Professor of Electrical Engineering, Universi ty of New Brunswick,

I



IEEE TRANSACTIONS ON COMMUNICATION TECHNOLOGY,OL. cobs-19, N O . 3, JUNE 1971 293

Fredericton, Canada. Since then he has been a member of the

Facult,y of Engineering, Carleton University, O ttawa, Ont., Canada.While teaching, he has been a Consul tant to a number of organi-

zationsrincipally th e Defence Research Telecommunications

Establishment (now the CommunicationsResearch Cente r) nd

Canadian WestinghouseCompany, Ltd . Also, hepenthree

summers and a nine-month sabbatical period wit h the Communi-

cationsResearch Center.AtCarleton University, while being

concerned with he development of th e engineering program n

general, he has been particularly involved in building up graduate

activity in communications. His recent research activity has beenin the area of optimum and adap tive PAM systems and in signal

processing with small computers. At present, he is a Professor of

Engineering andDean of Engineering a t CarletonUniversity.

His research inter ests ren communication and information

theory, cybernetics and systems, and signal processing.

Robert R. Bowen (S'57-M'61) was born n

Peterborough, Ont.,Canada, on June 10,

1935. He received the B.Sc. degree in engi-

neering physics and he M.Sc. degree in

electrical engineering from Queen's Uni-

versity,Kingston, Ont., in 1958 an d 1960,

and t,he Ph.D. degree in electrical engineering

from Carleton University, Ottawa, Ont., in

1970.

In 1960 he joined the Defence Research

Telecommunications Establishment, which

has since become the Communications Research Center of the

Departmen t of Communications, Ottawa, Ont., and worked on

radar signal processing problems. In 1967 he returned to the Com-

munications Research Center, where he ontinuedhis work on

the transmission of da ta through dispersive media. More recently,

he and two colleagues have developed a computer anguage or

simulation of adaptive communication systems.

John R. Storey ("68) was born in Trelewis,

Wales, on September 19, 1926. He graduated

from Lewis School, Pengam, Wales.

After graduation he joined the Royal

Navy for a period of three years. In 1952

he joined Decca Radar, Ltd., Surrey,ngland,

working primarily on th e development of abaseband ommunication ystem. He emi-

grated oCanada n 1955 and joined the

Ferranti Packard Company where his main

interest was in H F communications using

meteor trial reflections. In 1957 he joined the Avro Aircraft Com-

pany,Malton,and was involved indata processing during he

flight trials of the Avro Arrow airc raft. He is now with the Com-

munications Research Center, Ottawa,Ont.,Canada, (formerly

the Defence Research Telecommunications Establishment) having

joined them n 1959. He has worked onprojects nvolved with

pulse compression techniquesor ionospheric sounding an d on

research in he field of adaptive receivers for da ta transmission.

He now heads a communication ngineering group currently working

on an auto mated ystem to measure noise in the H F communication

spectrum.

Multipath Intermodulation Associated with

Operation of FM-FDM Radio Relays in

Heavily Built Areas

DECIO ONGARO

Abstract-Microwave FM radio ink paths concerning heavily

built areas may be found to suffer from high amounts of inter-

modulation noise caused by multiple reflections on buildings and

reflectingobstacles lying alongside th e direction of propagation.

Little direct information maybe gained on these effects using

standard techniques for measuring transmission performance.

The limitations of those techniques are discussed and some addi-

tional one s are proposed allowing a moredirect nsight nto the

the IEEE 8ommunication Technology Group for publication afterPaperap roved by he Radio CommunicationCommittee of

presentation at he 1970 International Conference on Communi-cations, San Francisco, Calif., June 8-10. Manuscript receivedJuly 1, 1970; revised December 7, 1970.

The uthor is withheRadio

Communications DivisionofSocietd Italiana Telecomunicazioni, Siemens, Milan, Italy.

phenomenon. The esults obtained inmeasuremen ts on a eal

hop suffering from marked echo effects of this type a re reported

and discussed.

RI. INTRODUCTION

AD1 0 RELAY erminals re normallyocated in

densely populated areas where the conveyed nfor-

mationmust beutilized. It is widely known t ha t RF

interference is the main problem in such stations, espe-

cially when many routes converge to the same terminal.

The R F channel allocation plans regulating RF spectrum

utilization take this fact into full account. It is perhaps

less known th at additional roublesmay arise due t o

Documents

7.an Adaptive Decision Feedback Equalizer