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8/6/2019 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-
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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
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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
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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
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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
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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
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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-
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288 IEEE TRANSACTIONS ON COMMUNICATION TECHNOLOGY, JUNE 1971
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
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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
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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.
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292 IEEE TRANSACTIONS ON COMMUNICATION TECHNOLOGY, JUNE 1971
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
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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