Note: Descriptions are shown in the official language in which they were submitted.
PHF 80 519
The invention relates to an echo canceller con-
nected between two one-way transmit and receive paths
coupled to a two-way path and intended to cancel a vari-
able phase echo signal occurring in ~he receive path,
said echo canceller comprising an adaptive filter Eor
receiving the complex version of a signal -from the trans-
mit path and a difference circuit producing a difference
signal between two signals which are formed from the sig-
nal in the transmit path and the output signal of the
adap~ive filter, respectively.
An echo canceller is used in, for example, a
transceiver arrangement whose one-way transmit and receive
paths which together form a four-wire circuit are often
coupled by a circuit Xnown as hybrid junction in a manner
such that the arrangement has a two-wire access to the
exterior. It is known that when a connection is estab-
lished between two transceiver arrangements by their two-
wire access, a fraction of the signal transmitted by the
transmit path of an arrangement may be untimely produced
in the receive path of the same arrangement, owing to
imperfections of the hybrid coupler or owing to signal
reflections in the connection. An echo canceller has for
its object to automatically cancel this untimely signal or
echo signal appearing in the receive pathO The advantage
of this echo cancellation operation is that it enables a
simultaneous transmission into both directions between the
two transceiver arrangements intercoupled by their two-
wire access. The transceiver arrangements are, for
example, modems used for data transmission.
When the connection between the transceiver
arrangements is a two-wire transmission line, the echo
signal appearing in the receive path has the same fre-
quency as the signal transmitted by the transmit path and
has an invariable phase. The arrangements for cancelling
this type of echo signal, designated linear echo signal,
~'
PHF 80 519 2
are generally known. They comprise an adaptive -Eilter
which forms from a signal in the transmit path a simulated
echo signal which is subtracted from the signal appearing
in the receive path, in order to form a difference signal.
The coefficients of the adaptive filter are iteratively
controlled to minimize the mean square value oE the resi-
dual echo signal present in the difference signal.
However, it is not possible to solve the problem
of cancelling a variable phase echo signal in a satisfac-
tory manner by means of this convention echo canceller. Avariable phase echo signal results, for example, from a
frequency offset which may occur when the connection be-
tween two transceiver arrangements includes a section in
which the transmission is carried out by means of two car-
rier systems, each operating for only one of the twotransmission directions. If the frequencies used or the
modulation and demodulation in each carrier system are not
identical, a signal transmitted by the transmit path of a
transceiver arrangement may produce in the receive path of
this arrangement an echo signal which, having transited
the two carrier systems, may have a frequencv different
from the frequency of the transmitted signal and which con-
sequently has a time-varying phase.
An echo canceller for cancelling a variable
phase echo signal is disclosed in United States Patent
Specification No. 4,07~,83n. In this prior art echo can-
celler, use is made of a phase shifter provided at the in-
put of an adaptive filter and being controlled for shift-
ing the phase of the signal at the input of the filter
over an angle e~ual to a simulated phase of the echo sig-
nal in a manner such that at the output of the adaptive
filter a simulated echo signal is obtained with the same
phase as that of the echo signal. The simulated phase of
the echo signal is formed starting from the signal at the
output of the adaptive filter, so that the tapped delay
line o this filter is included in the control loop for
the simulated phase. The delay time of this tapped delay
line, determined by the duration of the impulse response
PHF 80 519 3
of the echo path, may be long and from this it follows
that this prior art echo canceller has a comparatively
slow response, which does not permit of -Eollowing the
rapid variations oE the phase of the echo signal. A fur-
ther disadvantage of this known echo canceller is that itcannot but result in complicated calculations in the adap-
tive filter, as the signal applied to this filter results
from a variable phase shift of the signal in the transmit
path. So, even in the case of a modem for baseband data
transmission, in which the adaptive filter for cancelling
a linear echo comprises only very simple circuits for
multiplication by 0 and l, it is necessary for cancelling
a variable phase echo in accordance with the concept of
this prior art echo canceller to use circuits for the
multiplication by the "complicated" numbers sin ~ and
cose ~, ~ representing the simulated phase of the echo
signal.
It is an object of the present invention to
avoid these disadvantages and to provide an echo canceller
having a rapid response as regards the variations of the
phase of the echo signal and avoiding in certain cases
complicated calculations in the adaptive filter.
A first embodiment of an echo canceller in
accordance with the invention comprises means for forming
a complex signal corresponding to the signal in the
receive path, phase shifting means to for change the phase
of said complex signal of the receive path over an angle
equal and opposite to a simulated phase of the echo sig-
nal, said difference signal resulting from the difference
between a signal supplied by said phase shifting means and
a signal supplied by the adaptive filter, the coefficients
of the adaptive filter and said simulated phase being con-
trolled together in an iterative way for minimizing the
mean square value of the residual echo signal present in
said difference signal.
A second embodiment of an echo canceller in
accordance with the invention comprises means in the adap-
tive filter for forming a complex signal at the output of
X
PHF 80 519 4
the filter, phase shifting means to change the phase of
the compl~x signal supplied by the adaptive filter over an
angle equal to a simulated phase of the echo signal, said
difference signal resulting from the difference be-tween a
signal from the receive path and a signal supplied by said
phase shifting means, the coefficients of the adaptive
filter and said simulated phase being controlled together
in an interative way for minimizing the mean square value
of the residual echo signal present in said diference
signal.
In the above two embodiments of the invention
the phase shifting operation for cancelling the echo is
not carried out at the input of the adaptive filter, but
either in the receive path or at the output of the adap-
tive filter, which results in an increased speed of theresponse of the echo canceller at phase changes of the
echo signal and facilitates simplification of the calcu-
lations in the adaptive filter.
As will appear hereinafter, depending on the
signals used to control the coefficients and the simulated
phase of the echo signal, a number of variations are pos-
sible which generally correspond to the two embodiments of
the invention.
Embodiments of the invention and their advan-
tages will I10W be further described, by way of non-limit-
ative example, with reference to the accompanying drawings,
in which:
Fig. 1 shows a block diagram of a transmission
system producing a variable phase echo signal;
Fig~ 2 and Fig. 3 show a block diagram of two
variants of the first embodiment of an echo canceller in
accordance with the invention, in which a complex differ-
ence signal is used;
Fig. 4 shows a block diagram of a second-order
filter suitable for use in the control loop of the simu-
lated phase of the echo signal;
Fig. 5 and Fig. 6 show a hlock diagram of two
PHF 80 519 5 19-2-1981
further variants of the -~irst embodirnen-t of the echo can-
celler in accordance wi-th the invention, in which a real
difference signal is used;
Fig. 77 Fig. 8 and Fig. 9 sllow a block diagram
of three variants of -the second embodimellt of -the echo can-
celler in accordance with -the invent-ion, in which a comple~
difference signal is used;
~ ig. 10 and Fig. 11 show a block diagram of two
further variants of the second embodiment of the echo can-
lO celler in accordance with the invention, in which a realdifferen^e signal is used.
~ ig. 1 shows by way o-f example the block diagram
of a data transmission system which may produce a variable
phase echo signal. A modem 1 comprises a transmit path 2
l5 including a modulator 3 recei~ing data from a -terminal (no-t
shown) and a receive path ~ including a receiver 5 supply-
ing data to this terminal. The output of modulator 3 and
the input of receiver 5 are coupled to a two-wire access
7 of the modem by means of a hybrid junction 6. A remo-te
~ modem 8 comprises the same elements, not shown in Fig. 1,
and also has a two-wire access 9. Irhen a connection is
established between these two modems 1 and 8, a fraction
of the signal transmitted by transmit path 2 may appear in
receive path L~ of modem 1 owing -to imperfections of hybrid
25 junction 6 and/or reflections of signals in the connection;
this untimely signal is denoted echo signal and has the
same frequency as the transmitted signal when the connec-
tion between the two modems is fully realized by means of
a two-wire transmission line~ In that event the echo sig-
30 nal has an invariable phase and is denoted linear echosignal. But, when the distance between the modems is large,
the connection often comprises a four-wire transmission
section with carrier systems. As shown in Fig. 1, this
section comprises at its ends two hybrid couplers 10 and
35 11 to change from a -two-wire to a four-wire connection.
At the ends of the path for one transmission direction
there are pro~ided a modulator ~l1 and a demodulator D1
util-izing carrier frequencies f1 and -f'1 At the ends of
:~8~6
PHF 80 519 6 19-2-1981
the path f`or the other transmission direction there are
provided a modulator M2 and a demodulator D2 utilizing
carrier ~requencies ~2 ar~d f ~ 2 When modu:l a tor 3 of moclem
transmi ts, it is possible -that in its receive path 4 an
5 echo signal occurs which is caused by imper:~ections o:~
hybrid coupler 11 and which has transited the carrier
systern Ml, Dl in one direction, and the car-rier system
M2 ~ J~2 in the other direction. Ir -the E`requencies -f` l, E` ' 1
and f2, f'2 are such -tha-t (f' ~ ~ (f'2 ~ f2) = ~ the
10 frequency of` the echo signal is the same as -the ~requency
of the signal transmitted by modulator 3, and we are
concerned wi-th an invariable phase linear echo signal. I~,
in contrast therewith, the f`requencies ~ l ~ f ' 1 and f 2, f ' 2
are such tha-t (f ' 1 ~ fl ) + (f ' 2 ~ ~2) does not equal 0,
15 the echo signal is subjected to a frequency offset of,
for example, some Hz and it has a time-varying phase. The
echo canceller in accordance with the invention is an
arrangement to be included in modem 1 for cancelling such
a variable phase echo signal occurring in receive path 4.
20 Let it be assumed hereinaf`-ter that no linear echo signal
occurs in this receive path 4.
Fig. 2 shows a block diagram o~ a first embod:i-
ment of` an echo canceller in accordance with the invention,
which embodiment corresponds to a struc-ture which will be
25 denoted structure I hereina~ter. Associated with this echo
canceller are the elements o f modem 1, sho~ already in
Fig. 1, which are given the same reference numerals. Let it
be assumed, by ~ay o~ e~iample, that this modem emplo~-s
phase modula-tion or phase and amplitude modulation of a
30 carrier for the data transmission and tha-t for forming the
modulated carrier signal in modulator 3 use is made of a
di gi t al m o dul at i on t e chni qua whi ch i s kno~lm as e cho m o du -
lation .
In the simplif`ied f`orm sho~vn, modulator 3 com-
35 prises an encoding circuit 12 receiving the da~ta to betransmittcd and procuding a pair of signals representative
of the ampl:itudes A(n) and -the phase changes ~D ~n) to be
assigned to the carrier as a f`unc-tion o:~ the data at in-
PHF go 519 7
stants nT determined by a generator 13 of the clock fre-
~uenty l/T, l/T being the modulation ra-te. In order to
take account of the phase changes ~ ~ of the (unmodulated)
carrier during each modulation interval T, an adder 14 is
used for forming at each instant nT the sum ~(n) ~
which is representative of the absolute phase ~ (n~ of the
modulated carrier to be transmitted. The two signals
representative of the amplitude A(n) and the absolute phase
~ (n) of the carrier are applied to a circuit 15 which
forms the real component A(n) . cos ~(n) and the imaginary
component A~n) . sin ~(n) of the complex signal having
amplitude A(n) and argument ~n). These two components
are applied to bandpass filters 16 and 17, whose output
signals are added together in an adder 18 for forming the
analog modulated carrier signal which is applied to the
transmit access of hybrid coupler 6.
In the echo canceller use is made of the complex
signal, also known as analytic signal, whose real and imag-
inary components are, in this example, available at the
output of circuit 15 and which is representative of the
amplitude A(n) and the absolute phase ~(n) of the carrier
to be transmitted at the instants nT. The complex signal
thus defined will be denoted complex signal D(n) herein-
after. For the event that the real and imaginary compon-
ents of this complex signal D(n) were not available in amodulator 3 of a different type, it will always be possible
to incorporate in the echo canceller circuits which form
these components from the actual data to be transmitted.
It should be noted that in the block diagram of
the echo canceller the connections represented by a double
line convey the two real and imaginary components of a
complex signal, but that for simplicity of the description
mention will only be made hereinafter of complex signals
conveyed by these connections. Likewise, it is obvious
that when complex signals are applied to processing cir-
cuits these processing operations will in practice be car-
ried out on their real and imaginary components which are
real signals and the processing operations carried out in
PHF 80 519 8
practice will generally not be further described as they
result from formulae which are known from complex number
systems.
Let it be assumed hereinafter, by way OI example,
that the two real and imaginary components of the comple~
signal D(n) produced by circuit 15 are analog signals sam-
pled at the instants nT. The samples forming the complex
signal D(n) are applied to an adaptive filter formed by a
transversal filter 19 and a control circuit 20~ which elab-
orates the complex coefficients used in filter 19. The im-
plementation of transversal filter 19 is not sho~, but it
is well-known that this filter comprises means for storing
a predetermined number of consecutive samples of the com-
plex signal D(n) applied to its input, calculation means
for weighting these consecutive samples with -the complex
coefficients supplied by circuit 20 and for forming the sum
of these weighted samples. Said sum constitutes the output
signal of the adaptive filter of the echo canceller. The
adaptive filter 19 is realized in accordance with analog
techniques, for example of the type known as CCD (Charge-
Coupled Device). It might alternatively be realized in
accordance with digital ~echniques which would imply an
analog-to-digital conversion of the samples of the complex
signal D(n).
The signal produced by transversal filter 19 is
applied to an input of a difference circuit 21. A signal
formed from the signal appearing at the receive access of
hybrid junction 6 is applied to the other input of this
difference circuit 21. The difference signal produced by
difference circuit 21 is applied to circuit 2~ for control-
ling the coefficients. In the echo cancellers intended to
cancel an invariable phase linear echo signal, the coeffi-
cients of transversal filter 19 are controlled in an inter-
ative way to minimize the mean square value of the residual
echo signal present in the difference signal. After the
convergence of the ecno canceller, the echo signal at the
input of receiver 5 connected to the output of difference
circuit 21 has been substantially cancelled.
The technique described in the above-mentioned
P~ 80 519 9 19-2~1981
United States Paten-t Specification No. ~,072,840 and per-
mittin2 cancellation of a variable phase echo signal con-
sis-ts in using a phase shifter connected -to the input of
transversal filter 19 for shifting the phase of the comple~
signal D(n), this phase shifter being controlled by the
d:if`ference signal and the output signal of -transversal fil-
ter 19. By simultaneously controlling the coefficients o~
the -transversal filter and the phase shift at -the input of
the transversal fil-ter so as to minimizc the mean square
lO value of the residual echo signal presen-t in -the difference
signal, i-t is possible to substantially cancel the variable
phase echo signal. ~owever, this kno~ technique has the
disadvantages mentioned above already, namely on the one
hand a slow response to changes in the phase of the echo
15 signal since transversal filter 19 is included in the con-
trol loop of -the phase shifter and on the other hand, in
the event of data transmission, the fact that -the calcula-
tions in transversal filter 19 becomes complica-ted due to
the variable phase shift carried out at -the inpu-t of said
20 filter.
The present invention obvia+es said disadvantages
by avoiding -the modification of the signal at the input of
the transversal filter for the cancellation of a variable
phase echo signal~
~5 According to the invention~ the echo cancellsr
comprises a circuit 22 connected to the receive access of
h~brid coupler 6 and comprising a direct path and a path
having a 90 phase shifter 23 for producing the real com-
ponent and the imaginary component of a complex signal,
30 respectively. From the point o~ view of functioning of the
echo canceller let it be assumed that the signal coming
from hybrid coupler 6 and applied to circuit 22 does not
con-tain any signal other than the echo signal (with vari-
able phase) produced by the signal transmitted by-modula-tor
35 3~ it is this case which enables simplification of the
reasoning and the calculations and which will be described
in greater detail hereinafter. The complex signal produced
by circult 22 then has the variable phase ~ of the echo
~HF 80 519 10
signal.
The complex signal produced by circuit 22 is
applied to a sample-and-hold circuit 24. Sampling is car-
ried out with a frequency fe supplied by clock generator
13 and having a value equal to a multiple of l/T so that
the Shannon theorem is satisfied with regard to the echo
signal. The instants te of this sampling are coupled to
the sampling moments nT of the complex signal D(n) by the
relation t = nT + rT/M, where M is a fixed integer, for
example equal to 6, and r is a variable integer varying
from 0 to ~M-l). Ti simplify the formulae for the calcu-
lations to be performed, only the variable n and not the
variable r will occur hereinafter, but it will be obvious
that the calculations described must be carried out for the
M values which the variable r may assume.
In a digital version of the echo canceller the
sampled signal produced by circuit 24 should be converted
into a digital form, while in the analog version, described
in Fig. 2, this signal is directly applied to a phase
shifter 25 which changes the phase ~ of the complex echo
signal applied to its input by an angle (-~ being a
simulated phase of the echo signal. To this end, phase
shifter 25 comprises a multiplying circuit 26 for complex
signals which receives on the one hand the complex echo
signal supplied by circuit 24 and on the other hand the
complex signal exp(-j0), supplied by a circuit 27 in the
form of the real and imaginary components cos ~ and -sin ~.
Circuit 27 is, for example, a memory containing discrete
values of cos ~ and -sin ~ and addressed by discrete values
of the simulated phase ~ of the echo signal. This simu-
lated phase is formed in a control circuit 28.
The phase-shifted complex echo signal produced
by phase shifter 25 is applied to one input of difference
circuit 21, the other input of which receives the complex
signal produced by transversal filter 19. The complex
difference signal produced by circuit 21 is the residual
echo signal, alternatively denoted error signal. It is on
the one hand applied to control circuit 20 for the coef~i-
~^~8~
PHF 80 519 11 19-2-1981
ciants of transversal fil-ter 19 and on the other hand to
control circuit 28 for the simulated phase of the echo
signal, which control circuit 2æ also receives the phase-
shif-ted complex echo signal produced by phase shi~-ter 25.
Hereinafter :it will bc demonstrated that by means of a
si.multaneous iterat-ive co~-trol of on -the one hand -the
coeffic:ients o:~ -transversal fil.ter 19 OIl the basis of the
error signal and on the o-ther hand the slmulated phase
on the basis of the error signal and the phase-shifted
lO echo signal :in order to minimize the mea.n square value of
the error si~lal, the untimely variable phase echo signal
at the outpu-t of difference circui-t 21 has been subs-tan-
tiall~ cancelled after a cer-tain number of consecutive
i-terations, Of -the comple~ signal produced by difference
15 circuit 21 (from which the echo signal has been removed i.n
the above-described manner) receiver 5 of -the modem only
uses the real component which has been filtered in a low-
pass filter 29.
The calculations to be performed out in the echo
20 canceller will now be mathematically formulated in order
to explain ho~i control circuit 2~0 for the filter coeffi-
cients and control circuit 28 for the slmulated phase are
implemented and ho~ the ~hole assembly of -the echo can-
celler f~unctions.
First of all the different quantities 9 signals
and notations used llereinafter wil.L be defined. At t.he
sampling moments nT:
~(n) is the phase of the echo signal,
0(n) is the simulated phase of the echo signal,
30 ~ f(n) is the comple~ echo signal applied to phase
shifter ~5,
~d(n) is the comple~ echo signal ~hose phase is shif-ted
over -0(n) by phase shifter ~5,
d(n) is the comple~ signal produced by transversal fil-
3~ ter 1~ and is a synthe-tic echo signal whose phase
is automatically shifted over -0~n),
e(n) is the coMple~ error signal produced by di_ference
ci~cui-t 21.
- - -
P:HF 80 519 12 19-2-1981
At an instant nT, transversal fil-ter 19 stores N
consecutive samples of the comple~ signal D(n) applied to
its inpu-t, it being possible to use the notation D(n-q)
for these samples, where q is a variable integer ~rom 0
to N~ using a vector notation these N samples D(n~q)
may be considered as the components of a vector D(n) so
that:
D(n)
D(n-1)
10 D(n) = .
D(n~N+1)
Likewise~ the N coefficients d of the transver-
sal filter may be considered as -the component of a vector
15 d so that:
~ d
d = .
dN_l ~
The t :ranspo se D(n) of -the vector D(n) is ~ritten
as:
D(n) = D(n), D(n-1) ... D(n-N~1)
The signal ~d(n) produced b~ transversal filter
19 is obtained from the convolution operation:
~ N-1
d(n) = ~ D(n-q) dq
q_
In vector notation this operation is ~ritten as:
d(n)=D(n) d (1)
In a similar manner the complex echo signal
~f(n~ may be described ~hich results from the application
of ~e signal D~n) to the pa-th of the variable phase echo
signal. If k is the imp~1lse response of this echo si~nal
35 path, a vector k can be defined havin~ as components the
values k of this impulse response at the instants qT. By
taking account of the variable phase 0(n) caused by the echo
signal path, the comple~ echo signal ~(n~ may be ~ritten as:
.. . . . . .
., ,.: . . .
~HF 80 519 13
f(n) = ~(n).~.exp j0(n) (2)
The phase shif-t -~ carried out on this echo sig-
nal by phase shifter 25 produces -the phase-shifted signal
~d(n), so that:
5 ~d(n) = D(n).k.exp j ~0(n) - ~(n~ (3)
When the formulae (1) and (3) are taken into
account, the error signal e(n) can be written as:
e(n) = D(n) ~k.exp j [0(n) - ~(n~
This error signal e(n), or residual echo signal,
will be cancelled if the following conditions are simul-tan-
eously satisfied:
rd = ~ exp-j ~O
~(n) = ~(n) + 0O (5)
where ~O is a constant.
It will now be demonstrated how in the echo can-
celler in accordance with the invention the coefficients
of transversal filter 19 and the simulated phase 0(n) are
controlled such that the two conditions (5) for cancelling
the echo signal are realized.
The control criterion is the minimization of the
mean square value of the complex error signal e(n), which
is written as E [¦e(n)3 2, where E is an operator which
indicates the mean value (or mathematical expectation) of
the subsequent quantity between brackets.
It is kno~ that if the algorithm of the gradient
is used to minimize said mean square value, the coeffici-
ents d and the simulated phase 0(n) must be controlled in
accordance with the recursion formulae:
~d(n + 1) = d(n) _ ~ ~ E e~n) 2 (6)
~(n + 1) = ~(n) 2~ ~E e(n)
In these formulae, d(n+l) and d(n) are the vectors
-
PHF 80 519 14 19-2-1981
which represent the coefficients ~ of transversal filter 19
at the instants (n~1)T and nT; ~ and ~ are coefficients
less than 1, which determine at each iteration the magni-tude
of the modifica-tion of the filter coefficients and the
simulated phase.
To use these recursi.on formulae (6) and (7), the
two partial derivatives -therein mus-t be calculatecl to ob-
tain simple processings of these signals. As calculations
of this type must be carried out several times in the follow-
ing description, the procedure to be followed will now bedescribed.
~ irstly, to compute the partial derivative in
formula (6):
~ E 7e~n)72
~ d(n)
the coefficient vector d is written as:
d(r~ n) ~ j b(~3
where ~a(n~ and b(n) are vectors whose componen-ts are -the
20 real parts and the imaginary parts of the comple~ coeffi-
cients of transversal filter 19, respectivelyO
IIereafter the complex colljugate of a comple~ quan-
tity is denoted by providing this comple~ quantity with an
asterisk as the inde~. As ¦e(n)¦~ = e(n) . e (n), it then
25 holds that:
~ ~ Ele(n)~~ = E¦e(n) ~,,e ln!~ ~ e~(n
I ~a(n) L a~ a(n~l
¦ ~ EIe(n)l = E7~e(n). e (n~ ~ e~(n),
L ~ b(n) L ~ b(n) ~ b(n)~
On the other hand it holds~ t~king account of
formula (4):
PHF 80 519 15 19-2-198-1
~e(n) = D~n)
~a(n)
~ = _j D(n)
¦ ~( ) = -D (n)
t = j D~(n)
By means of simple calculations it is possible to
10 derive therefrom:
_ -E~e(n)-D (n)+e (n).~(n)]= -2EI~ e~e(n)~D (n~
= E~j Le(n) .D (n)-e (n)-D(n)J] = -2E{~ mCe(n) D (n~
In these last formulae ~e and ~ m signi~y the
real part and the imaginary part of the subsequent complex
qua~tity between brac~ets.
By putting:
~ E I e (n?~ a :E le ( ~ . a E ¦ e ~n)~2
~ d(n) ~ a(n) 3 b(n)
the following result is obtained as regards the partial
derivative in the recursion formula (6):
~ E 1e(n~ = -2E ~e(n)-D (n)3 ~ )
It will now be demonstrated how the partial deri-
vative
_ E1e(n)1~
~ 0(n)
in the ~ormula (7) can be calculated. ~or this it holds
that:
E1e~n)l_ ~ e ~n) ~ e(n~1
= E e(n). ~ ~ e (n)
0(n) ~ 0(n) ~ ~n)
BIIF 80 519 16
On the other hand it holds, taken account of
formula (4):
J ~ ~(n) = _j D(n).k.exp j [~(n) - ~(r~
¦ ~ = +j D (n)-~ exp - j [~(n) - ~(n~
It can be easily seen that the two complex quan-
tities
a e(n) and ~ e (n)
~(n) ~0(n)
are the conjugates of each other and from this it follows
that:
a E I e (n) I = 2Er~ e Le (n) }
0(n) L ~(n)
= -2E {~m ~e(n).~ (n).k .exp - j[~(n)-~(n)~3
On the other hand it holds in accordance with
formula (2) that:
~ f(n) = D (n). ~ .exp - j 0(n)
By introducing this quantity Xf(n) into the
preceding formula the following result is obtained as
regards the partial derivative in formula (7):
e(n)l = -2E ~ m [e(n)~exp j ~(n)- f(n~ } (10)
By using the results of the formulae (9) and (10)
the recursion formulae (6) and (7) to be employed in the
echo canceller may finally be written as:
(n + 1) = d(n) + ~E ~e(n).D (n)~ (11)
~(n + 1) = ~(n) + ~ E ~ m ~(n).exp.j ~ f(n)]} (12)
By taking account of the random character of the
data to be transmitted, that is to say of the components
of the vector D(n), it can be demonstrated that when n tends
to infinity in these two recursion formulae (11) and (12),
DC
Pl~ 80 519 17 19-2-1981
the simulated phase 0(n) tends to the phase 0(n) of -the
echo signal, but for an additive constant 0 , ~here 0O is
the time average of -the phase 0(n) 7 while -the coefficients
d(n) of the -trans-versal fil-ter 19 tend to -the impulse res-
ponse k of the echo path~ but for a 1mll-tiplica-tive coe~
cient exp(- j00). As shown by formula (Ll), -it fol:Lo~s there-
~rom tha-t when n tends to in~ini-tive~ the error signal e(n)
that is to say the residual echo sig~lal~ tends -to zero. It
is a mat-ter of` course that when -the recursion formulae ( 11 )
10 and (12) are used, the residual echo signal is substan-tially
cancelled after a limited number of consecutive iterations.
In accordance with common practice, -the recursion
formulae (11) and (12) may be replaced by recursion formulae
which are simpler to implemen-t, it being possible to avoid
15 integrations for calculating mean val~es:
¦ d(n + 1) = d(n) + ~-e(n)-D (n) (13)
0(n + 1) = 0(n) +~ .~ mle(n).e~p j 0~n).~ f(n)~ (lL~)
l~here the coefficients ~ and ~ are very small ~ri-th respect
20 to 1 and de-termine the very small modification incrernents
of the fil-ter coefficients and the simulated phase at each
iterationO
~ or the simples-t implementation of the recursion
formula (14) it may be written in an equivalen-t form by
25 introducing the phase-shifted echo signal
~ d(n) = f(n).e~p-j 0(n)
Since it holds that:
~ d(n) = ~ f(n).e~p j0(n),
formula (14) can be simplified to:
0~r ~ (n) +~ ~ m[e(n)-~ d(n)] (15)
- Furthermore, it is possible -to write the recursion
formula ~14) in an alterna-tive, simple form by introducing
d(n) supplied by transversal filter 1~. To this end~ the
35 error signal e(n) in it~ equivalent e~pression (15) is
replaced by the e~pression e(n) = ~d(n) - 'd(n). By taking
account of the fact that -the quantity ~d(n) ~ d(n) is
a real quantity, the following recursion formula is finally
. .
~HF 80 519 18
obtained:
~(n + 1) = ~(n) ~ m [~d(n) ~ d( )] (16)
Applying the recursion formulae (13) and (15)
corresponds to a first variant, denoted variant 1, of the
structure I of the echo canceller in accoxdance with the
invention. Applying the recursion formula (13) and (16)
corresponds to variant 2 of the struc-ture I of said echo
canceller.
Fig. 2 shows the full block diagram of ~ariant 1.
Circuit 20 controls the complex coefficients of transversal
filter 19 in accordance with recursion formula (13). The
block diagram shown, which is identical for all coeffici-
ents, relates, for example, to the complex coefficient dq(n)
which at the instant nT has been multiplied in transversal
filter 19 ky the complex sample D(n-q) entering the filter
at a previous instant (n-q)T. As regards modifying this
coefficient dq(n), the formula (13) for obtaining the co-
efficient dq(n+l) to be employed in the filter at the
instant (n+l)T is written as:
dq(n + 1) = dq(n) + C~.e(n).D (n-q) (13A)
Control circuit 20 comprises for each coefficient
a circuit 30 which at each instant nT forms the complex
conjugate value n~ (n-q) of the complex sample D(n-q) stored
in filter 19. Circuit 30 comprises a simple circuit not
shown in Fig. 2, which changes the sign of the imaginary
part of D(n-q). A circuit 31 for multiplying complex sig-
nals produces the product e(n).D~(n-q) which is thereafter
multiplied by the coefficient cC by means of a multiplier
32. The modifying term C.e(n).D~(n-q) of the considered
coefficient is added by means of an adder 33 to the coef-
ficient dq(n) at the output of a delay circuit 3~ having a
time delay T for forming the coefficient dq(n+l) to be
employed in the filter at the instant (n+l)T.
The simulated phase is formed in control circuit
28 which implements the recursion formula (15). This con-
trol circuit 28 of the simulated phase comprises a circuit
35 which at each instant nT produces the comple~ conjugate
~HF 80 519 l9
value d(n) of the comple~ sample of -the phase-shifted
echo signal d(n) available at the output of phase shifter
25. A circuit 36 for multiplylng complex signals produces
the product e(n). ~d(n), of which - in a block 37 - only
the imaginary part is retained. The real signal supplied
by block 37 is applied to a multiplier 38 to be multiplied
by the coef~icient ~ . For reasons which will be explained
in detail hereinafter, this multiplier is included in a
block 39. The modifying term ~3 ~ m [e(n).~ ~d(n)] of the
simulated phase is added by means of an adder 40 to the
simulated phase ~(n) at the output of a delay circuit 41
having a time delay T for forming the simulated phase ~(n~l)
to be employed in phase shifter 25 at the instant (n+l)T.
As described in the foregoing~ after a certain
number of consecutive iterations the coefficients of the
transversal filter and the simulated phase substantially
attain values which effect the cancellation of the residual
echo signal e(n).
Fig. 3 shows the variant 2 of the structure I of
the echo canceller in accordance with the invention. Fig.
3 shows a portion of the elements of Figure 2 which have
been given the same reference numerals, so that only the
differences between the variants l and 2 are shown.
In Fig. 3, control circuit 20 for the coeffici-
ents of fllter l9 is not shown in detail as the use of the
recursion formula (13) makes this circuit exactly identical
to the circuit sho~m in Fig. 2. Control circuit 28 for the
simulated phase uses recursion formula (16) and therefore
differs from the circuit of Fig. 2 in that multiplying cir-
cuit 36 receives the simulated echo signal d(n) insteadof the error signal e(n), so that the product d(n).~d(n)
is formed. To allow for the sign assigned to the modifying
term of the simulated phase in formula (16), a circuit 42
is provided which changes the sign of the signal produced
by multiplier 38. After a certain number or consecutive
iterations, cancellation of the residual echo signal e(n)
is substantially achieved by means of the echo canceller in
accordance with variant 2 of Fig. 3.
PHY 80 519 20
In the echo canceller in accordance with the
invention which has been described so far the simulated
phase ~(n) i5 adjusted to the phase ~(n) of the echo signal
by means of a phase-locked loop formed by control circuit
28 connected between the input and the output of the phase
shifter 25 and receiving, in addition, either the error
signal e(n) for variant 1, or the signal d(n) at the out-
put of filter 19 for variant ~. In this loop, no delay is
introduced other than the unavoidable delay T determined by
circuit 41. From this it follows that the simulated phase
can follow the rapid phase variations of the echo signal
without a great deal of delay in order to contribute to
cancellation of the echo signal, the response time of the
phase-locked loop being substantially determined by the
value of the coefficient ~ which is applied to multiplier
38 and which must, however, remain comparatively small with
respect to 1 to avoid instabilities.
A person specialized in control techniques will
easily understand that in the phase-locked loop, circuit 38
for multiplying by the coefficient ~ acts as a first-order
loop filter, this loop filter being represented in a gen-
eral way by block 39. The signal applied to this loop
filter 39 is actually the deviation J ~ found be~ween the
phase of the echo signal and the simula-ted phase. It is
known that in such a phase-locked loop, using a first-
order filter, a residual value of the phase deviation J
subsists, even when the phase of the echo signal does not
change or does so only slowly. This phase deviation cr~
can be avoided by employing a loop filter 39 which is more
complex than a first-order filter.
This loop filter 39 may be, for example, a second
order filter having a block diagram as shown in Fig. 4. In
this filter 39, the phase deviation cr~ is applied to cir-
cuit 38 in order to be multiplied by the coefficient ~ and
to a further circuit a3 in order to be multiplied by a
different coefficient ~ which is less than 1. The product
Y.~ ~ is applied to an adder 44 which is connected to a
circuit 45 producing a delay T so as to form an accumulator.
PHF 80 519 21
~n adder 46 produces the sum of the product ~.~ 0 and
the accumulated products y.~ 0. this sum forming the out-
put signal of the second-order filter 39. When the phase
of the echo signal does not change or does so only slowly,
the residual value of the phase deviation ~ ~ is cancelled
by the branch 43~ a~, ~5 of the filter which always sup-
plies a signal unequal to zero.
Circuit 28 for controlling the simulated phase
can be realized in a slightly different way than the one
described in the foregoing with reference to Fig. 2 and
Fig. 3.
In Fig. 2 the phase control circui-t results from
the use of recursion formula (15), but as:
~m ~ (n). d(n~ m [e (n)- ~ d(
formula (15) may alternatively be written as:
~(n + 1) = ~(n) - ~ ~m [e (n).~ d(n~ (17)
To use this recursion formula (17) it is suffici-
ent in Fig. 2 to apply the phase-shifted echo signal d(n)
directly to one input of multiplying circuit 3~, to apply
the complex conjugate value e~(n) of the error signal e(n)
to the other input and, finally, to change the sign of the
signal supplied by filter 39.
In the same way, taking account of the equality
~m [d(n)- ~ d(n~ m ~ d( ) d
recursion formula (16) implemented in Fig. 3 may alter-
natively be written as:
~(n + 1) = ~(n) + ~ ~m ~ d(n). d(n~ (18)
The transformations to be carried out in Fig. 3
for using recursion formula (18) are obvious, siarting from
the foregoing.
For an echo canceller of the structure I described
so far~ that is to say comprising a phase shifter 25 for
shifting the phase of the complex echo signal, i-t is possible
to employ as a control criterion for the coefficients of
PHF 80 519 ,_2 19-2-1981
tlle transversal filter and the simula-ted phase o-f the echo
signal -the minimiza-tioIl of the mean square value of the
real component e (n~ of the comple~ error signa~ e(n) 7
instead of the comple~ error signal i-tself. Thls~ ~ ~
the aclvantage that a cer-tain number O:e calcula-tion circuits
can be simplified, but~ however, -this has -the disa~vantage
that the convergence period :is subject to some inc:rease.
I:~ the algorithm of the gradien-t i~ emp]oyed for
min:imizing the mean square value of -the real error signal
lO E [eR(n)~2, controlling the coefficients d of the -trans-
versal filter and the simulated phase 0(n) of -the echo
signal must be carried out in accordance with the recursion
formulae:
¦ d(n~1) = d(n) ~ ~ E ~ (n)~
~(n~ (n) - ~ E~e ~n)~~ (20)
~ ~(n)
By taking account of the fac-t that -the real
20 error signal e (n) is e~pressed as:
e (n~ = ~ ¦e~n) + e (n)]
the partial deriva-tives occurring in the formulae ~I9) and
(20~ can be calcula-ted in a manner which is similar to the
25 manner described in the foregoing for the complex error
signal e(n).
When all calcula-tions have been carried out, the
recursion formulae (19~ and (~O) - using the coefficients
d and ~ which are small rela-tive to 1 to avoid the cal-
30 culation of a mean value - may be written as follo~s:
d(n~1) = d(n) + ~.e (n)-~ (n) (21)
~(n*1) = 0(n) * ~-e (n) 7 ~ m ~ f(n) e~p j 0(n)~ (22)
~or tbe simpl~st wa~ of implementation of recur-
35 sion formula (22), said formula can be writ-ten in an equiT
~alent form by introducing the imaginary component ~ ~(n)
of the phase-shifted echo signal ~ d(n). This equivalen~t
form is:
PHF 80 519 23 l9-2-1981
0(n~ (n) - ~Oe (n)-~ d(n) (23)
In addition, the recursion formllla (22) can be
written in a different, simpler form by introducing the
real componen-t ~ d(n) of -thc comple~ signal ~ d(n~ at -the
OUtpllt of filter 19. To this end~ in -the equ:valent form
(23), the real error signal e (n) :is replaced by the e~-
pression
e (n) = d(n) ~ ~ d(n)
lO where ~ d(n) is -the real component o~ -the phase-shifted
echo signal. As the average value of the product f ~(n) .
~ d(n) ic equal to zero, the following recursion formula
is found:
0(n~1) = 0(n) ~ d(n) d(n) ~24)
A variant lbis ~hich uses the formula (21) and
(23) and ~hose block diagram is sho-~rn in Fig. S corresponds
to variant 1 of the echo canceller which uses the recursion
formulae (13) and (15) and whose block diagram is sho~vn in
20 Figure 2. Mainly the differences bet~een these two block
diagrams ~ill be sho~-n here~ the block diagrams having a
certain number of common elements ~hich are given the same
reference numerals.
In Fig. 5, phase shi~ter 25 produces the phase-
25 shifted echo signal d(n), of which only the rsal com-
ponent ~n) is applied to an input of difference circuit
21. The real component ~ d(n) of the signal for.med in
transversal filter 19 is applied to the other input of -this
difference circui-t. The real component eR(n) of -the error
30 signal is then obtained at the output o~ difference circui-t
2l. Circuit 20 for controlling the coe~ficients o~ filter
19 e-nploys the recursion formule (21). The block diagram
of this coefficiellt control circuit is identical to the
block diagram sho~n in ~ig. 2, but ~or the fact that multi-
35 plying circuit 31 receives the real error signal e (n)instead of the comple~ signa:L e(n)~ The coefficients used
in trans~ersal ~ilter l9 are comple~, but it should ~e
no-ted that, since filter 19 must only supply a real signal
PHF 80 519 24
~ d(n), only half of the calculations required Eor the
case of the echo canceller of Fig. 2 need be carried out in
this filter.
Circuit 28 for controlling the simulated phase of
the echo signal employs recursion formula (23) and conse-
quently processes only real signals. The imaginary compon-
ent d(n) of the phase-shi-fted echo signal is applied to
one input of multiplying circuit 36, the other input of
which receives the real component eR(n) of the error signal.
The real signal produced by multiplying circuit 36 is
applied to circuit 38 in order to be multiplied by the co-
efficient ~, said circuit 33 forming a first-order loop
filter. The sign of the signal produced by circuit 38 is
changed by circuit 42 and thereafter applied to the accumu-
lator formed by circuits 40 and ~1 and producing the simu-
lated phase ~tn) used in phase shifter 25.
The variant 1 bis of the echo canceller shown in
Fig. 5 has, compared to variant 1 shown in Fig. 2, the
obvious advantage that less calculations are required, par-
ticularly in transversal filter 19 which must only supplythe real component of the synthetic echo signal. A variant
which is derived from this variant 1 bis consists in the
use of the recursion formula:
~(n+l) = ~(n) -~ ~.eI(n). - d(n) (25)
for realizing control circuit 28.
It should be noted that this formula (25) results
from replacing, in formula (23), e (n) by e (n) and d(n)
by - ~ d(n). This replacement is correct as the components
~ (n) and (n) are equally characteristic, the one as
well as the other, for the phase shift -~(n) carried out in
phase shifter 25. It is easy to construct a block diagram
for the echo canceller which employs recursion formula (21)
for the control of the coefficients and recursion formula
(25) for the control of the simulated phase. It should
however, by noted that in this derived variant the advan-
tage of simplicity of the variant 1 bis of FigO 5 is lost
for the major part as then the real component e (n~ of the
~8~
PHF 80 519 25
error signal is required for the control of the coeffici-
ents and the imaginary component eI(n) is required for the
control of the simulated phase, which requires the calcu-
lation of the two real and imaginary componen-ts o the sig-
nal ~d(n) in transversal filter 19.
~ variant 2bis which employs formulae (21) and
(24) and whose block diagram is shown in Fig. 6 corresponds
to variant 2 of the echo canceller which employs recursion
formulae (13) and (16) and whose block diagram is shown in
Fig. 3.
In Fig. 6, circuit 20 for the control of the co-
efficients has not been shown in detail, as it is exactly
the same as the circuit of Fig. 5. The circuit diagram of
circuit 28 for the control of the simulated phase differs
]5 from the circuit of Fig. 5 in the fact that multiplying
circuit 36 receives the real component e d(n) of the output
signal of filter 19 instead of the real component e (n) of
the error signal, while on the other hand sign-inversing
circuit 42 has been omitted. These differences will become
evident when the formulae (23) and ~24) are compared. This
variant 2bis has the same advantages as variant 1 bis as
regards the reduction of the calculation volume, particu-
larly in filter 19.
A variant derived from the variant 2bis of Fig. 6
consists in the use of the following recursion formula for
realizing generator 28 of the simulated phase:
~(N+l) = ~(n) ~ ~ d(n). d(n) (26
For this derived variant both the real component and -the
imaginary component of the signal processed in filter 19
are required and the advantage furnished by variant 2bis
is largely lost.
So far different variants of the echo canceller
in accordance with the invention have been described which
are derived from one and the same structure I, which is
characterized by the fact that in all cases use is made
of a phase shifter 25 for changing the phase of the comple~
echo signal ~f(n) by an angle -~n), 0(n) being the simu-
D~
~8~
~F 80 519 26
lated phase of the echo signal, and by the fact that thisphase-shifted echo signal and the signal supplied by the
transversal filter are used to form the error signal for
the control of the echo canceller. A different structure
will now be described, designated structure II of the echo
canceller in accordance with the invention, in which a
phase shifter is used to change the phase of the signal
supplied by transversal filter 19 by an angle ~(n) and
this signal whose phase has been shifted thus, and the com-
plex echo signal (whose phase is not shifted) are used toform the error signal.
Fig. 7 shows a block diagram of the structure II
of the echo canceller in accordance with the invention. A
eertain number of elements of the preceding Figures are
deno-ted by the same reference numerals. The transversal
filter l9 receives the complex signal D(n) and supplies the
complex signal d(n)~ which is applied to a phase shifter
50 to be submitted therein to a phase shif-t over an angle
+~(n) equal to the simulated phase of the echo signal. To
this end, said phase shifter comprises a multiplying cir-
cuit 51 receiving the signal d(n) and the complex signal
exp j ~(n) supplied by a memory 52, which is read by means
of a simulated phase signal ~(n) received from a circuit 53
for controlling the simulated phase. The complex signal
~f(n) thus obtained is applied to one input of difference
circuit 21, the other input of which receives the co~plex
echo signal with variable phase ~f(n). As explained with
reference to Fig. 2, this complex signal ~f(n) is formed
by means of circuit 22 which produces the complex signal
corresponding to the real received signal originating from
hybrid junction 6 and by means of sample-and-hold circuit
.
The complex error signal e(n) produced by differ-
ence circuit 21 is used in a circuit 54 to control the co
efficients of transversal filter 19 and - together with
the signal f(n) - in circuit 53 to control the simulated
phase ~(n). This signal f(n) is obtained at the output
of phase shifter 50 and will be denoted echo copy signal
PHF 80 519 27 19-2-l98-l
hereinafter, as efforts are made to make this signal equal
to the echo signal ~f(n) for cancelling the residual echo
signal e(n).
The criterion used for the control of the coef-fi-
cien-ts of the transversal fil-ter and for the control of -the
simulated phase of the echo signal, is a:Lso here the mini-
mization of the mean square value of the error signal e(n).
I`he realization of this criterion by means of the algorithm
of the gradient results in the two recursion formulae (6)
lO and (7). On the other hand, employing the notatlons already
described in the foregoing~ -the following expressions can
be given for the signals occurring in Fig, 7:
(n) = D(n).d (27)
f~n) = D(n).k.exp j 0(n) (2~)
~(n) -- D~n).d.e~p j ~(n) (~)
e(n) = D(n) ¦ k.exp.j 0(n) - d.exp j p(n)~ (3O)
By using these expressions (27) to (3O) inclusive,
and by carrying out the calculations in accordance with
the method already described with reference to s-truc-ture I,
it can be demonstrated that the recursion formula (6)~used
for the control of the coefficients of transversal fil-ter
25 19, may be writ-ten as-
d(nT1) = d(n) * ~ .e(n).exp - j ~(n)-D (n) (31)
Likewise, it can be demonstrated that the recur-
sion formula (7)~ used for the control of the simulated
30 phase, may be written as:
0~n~1) = ~(n) ~ ~ ~ m¦e(n). f(n)] (32)
It can also be demonstrated thcat the recursion
formula ~7) may alternative1y be written as:
p(n*1) = ~(n) * ~ m ~f(n)- ~ ~f(n)~ (33)
Finally~ it can be demonstrated th~t the recursion
formula (7) may also be written as:
PHF 80 519 28
~n+l) = ~(n) + ~ ~ m ~(n).exp - j ~(n).~d(n)~ (34)
In these recursion formulae (31) -to (3~) inclu-
sive, the coefficients CX and ~ are small relative to 1,
so that it is not necessary to calculate the mean values.
The use of the recursion formulae (31) and (32)
corresponds to variant 1 of structure II of the echo can-
celler which has a certain similarity with variant 1 of
structure I, as in both cases the error signal e(n) occurs
in the modifying term of the simulated phase. To this end
the formulae (15) and (32) may be compared.
Fig. 7 shows the circuit diagram of this variant
1. Circuit 54 controls the coefficients of transversal
filter 19 in accordance with recursion formula (31). The
block diagram for the control of any coefficient dq(n)
employs the following recursion formula, which is derived
from formula (31):
dq(n+l) = dq(n) + O~.e(n).exp - j ~(n).D (n-q) (31A)
For forming the coefficient dq(n+l), circui-t 54
is provided with a multiplying circuit 55, which receives
the complex error signal e(n) and the complex signal exp -
j~(n) obtained at the output of a circuit 69. This circui~
69 produces the complex conjugate value of the signal
exp j ~(n) available at the output of memory 52. A circuit
56 produ-es the complex conjugate value D (n-q) of the sig-
nal D(n-q) and, by means of multiplying circuits 57 and 58,
the term cX.e(n).exp - j ~(n) . D~(n-q) is formed which, by
means of ~n adder 59, is added to the coefficient dq(n) at
the output of a delay circuit 60. In this way the coeffic-
ient d~(n+l) is formed which must be used in transversal
filter 19 at the instant (n+l)T.
The simulated phase is formed in control circuit
53 which employs recursion formula (32). This circuit 53
comprises a circuit 61 which forms the complex conjugate
value ~f(n) of the echo copy signal available at the out-
put of phase shifter 50. A multiplying circuit 62 pro-
duces the product e(n). ~f(n) r of which, by means of a
block 63, only the imaginary part is retained which is
' ~
s~
PH~ 80 519 29 19-2-1981
multiplied by the coefficien-t ~ by means of a mul-tiplying
circuit 64. The modifying term ~ 1I m~e(n). ~(n)~is added
by means of an adder 65 -to the simulated phase ~(n) at -the
outpu-t of a delay circui-t 66 in order to produce the Simu-
lated phase 0(n-~1) which must be used in phase shif-ter 50
at the ins-tant (n+-l)T. As demons-tra-ted in -the foregoing
with refererlce to s-tructure I, it is possible, for the same
reasons, to use a more com~le~ loop :filter 67, for e.~ample
a second-order filter in accordance with the block diagram
of Fig. 4 instead of the multiplying circui-t 64 which acts
as a first-order loop filter. This remark holds for all
-the varian-ts which are described hereinaf-ter.
A variant ~hich is derived from variaIlt 1 can be
obtained by taking account of the inequality
~ mLe(n)- f(n)] ~ m[e~~(n)- ~(n~
in formula (30). This results in the follo~.ring recursion
formula:
2D ~(n~ n) -~ mLe~(n). f(n)] (35)
In order -to use this recursion formula (35)
instead of (32) it is sufticient in -the block diagram of
Fig. 7 to apply the echo copy signal ~(n) directly to
one input of multiplying circui-t 62, -to apply the conjugated
25 value e (n) of the error signal -to the other input and,
finally, to change the sig~ of the signal supplied by filter
67.
The variallt 2 of the structure II of the echo
canceller in accordance ~ith the invention consists in -the
30 use of the recursion formulae (31) and (33). Th~ block
diagram of this Vari~lt ~ is sko~n in Fig. 8 in which the
elements having the same function as ln Fig. 7 are given
the same refQrence numerals~
In -this Fig 8~ circuit 54 is not sho~n in detail
35 since this circuit for the con-trol of the coefficient3 of
filter 19 employs formula (31) and is e-sactly identical to
the circuit sho~n ~n Fig. 7. Circuit 53 for the control of
the simulated phase ~(n) uses formula (33) and dif:fers from
PHF ~O 519 3O 19-2-1981
the circuit shown in Fig. 7 in that -the multiplying circuit
62 receives the echo signal ~(n) instead of the error
signal e(n).
A variant which is derived ~'rom varian-t 2 can
be obtalned by tak:ing account of the equali-ty
~ m ~~(n). ~f(n)~ m ~ ~f(n). ~(n)~
in fornlula (33). To control the simulated phase -the follow-
ing recursion formula is used in this derived varian-t ~:
~(n~ (n) -~ ~ m~ f(n)- ~ ~(n)~ (36)
The transformations to be carried out in the bloc~
dia~ram of Fig. 8 to enable the use of formula (36) will
be evident after the foregoing.
A variant 3 of structure II of the echo canceller
in accordance with the invention consists in the use of the
recursion ~ormulae (31) and (34). It should be noted -that
the same quan-ti-ty ed(n) = e(rl).e~p - j ~(n) app~a~`s in ~hese
two formulae, For variant 3 this results in the circuit
20 diagram shown in Fig. 9.
Circuit 5!~ for the control O:L the coefficients
and circuit 53 for -the control of -the simulated phase have
a circuit 7O in common which - by forming -the comple~ con-
jugate value of the signal e~p - j ~(n) availabe at the
25 output of memory 52 - produces the si~nal e~p - j ~(n) and
a multiplying circuit 71 ~rhich produces the product
ed(n) = e(n). e~p - j ~n~. For the sake of s-~plicity
these circuits 7O and 7-l are included in control circuit
53. The signal ed(n) is used in circuit 54 to control -the
30 coefficiellts by means of the circuits 56 to 6O, inclusive 9
which are connected in a similar manner as sho~n in Fig.
7. This signal ed~n~ is also applied to one input OL multi-
plying circuit 6~, the other input of which receives the
signal ~ d(n) produced in a circuit 7~ which is connected
35 to the OUtpllt of transversal ~il-ter 19. The output of multi-
plying circuit 6~ is connected to -the circuits 63 to 67~
inclusive, ~hich are connected in a similar manner as shown
in Fig~ 7.
PHF 80 519 31
In the recursion formula (34) the quantity
~m ~(n) exp - j ~(n). ~ d(n~
may be replaced by the quantity
- ~mre (n) exp j ~(n)- d( ~
This results in the following recursion formula:
~(n+l) = ~(n) - ~ ~m ~X(n).exp j ~(n). ~ d(n~ (37)
The use of this formula (37) forms a derived
variant of variant 3, whose block diagram can be easily
established starting from Fig. 9.
For an echo canceller having structure II, that
is to say an echo canceller comprising a phase shifter 50
to shift the complex signal supplied by filter l9 over a
phase angle +~(n), it is possible to use also the minimiz-
ation of the mean square value of the real component eR(n)
of the complex error signal e(n) as a criterion for the
control of the coefficients of filter 19 and the simulated
phase. This criterion can also be realized in accordance
with the gradient - algorithm which is expressed in the
general form by the recursion formulae (l9) and (20)~
When all computations have been carried out~ the
recursion formula (l9) for controlling the coefficients may
be written in the following form, where oC ~ 1:
~(n+l) = ~(n) + cC.eR(n).exp ~ j ~(n).~ (n) (38)
The recursion formula (20) used for the control
of the simulated phase may be brought to the following
form, where
~( +l) ~( ) ~ eR(n) I (n
A I
(n) is the imaginary component of the echo copy slgnal
f(n).
Recursion formula (20) may also be brought to the
following form:
~(n+l) = ~(n) - ~ . Rf(n). I(n) (40)
X
~F 80 519 32
~ f(n), the real component of ~he complex echo signal, is
actually the echo signal itself.
It should be noted that in all variants o-f struc-
ture II of the echo canceller, in which the real or ~he
imaginary component of the error signal is used, it is
always necessary to form in transversal filter l9 the two
real and imaginary components of the signal d(n), which
is a disadvantage compared with certain corresponding vari-
ants of structure I.
A variant lbis which uses the recursion formulae
(38) (39) and whose bloc~ diagram is shown in Fig. lO cor-
responds ~o varian~ l of structure II of the echo canceller
which uses the recursion formulae (31) and (32) and whose
block diagram is shown in Fig. 7.
In Fig. lO a signal designated f(n) and re-
sulting directly from sampling the echo signal at the re-
ceive access of hybrid junction 6 by circuit 24 is applied
to one input of difference circuit 21. The real component
Rf(n) of the echo copy signal produced by the phase
shifter 50 is applied to the other input of this difference
circuit 21. The real component eR(n) of the error signal
produced by difference circuit 21 is used in circuit 54 to
control the coefficients in accordance with the recursion
formula (38). The circuit diagram of this circuit 54 is
substantially identical to that of Fig. 7, the difference
being that multiplying circuit 55 receives at one input the
real signal e tn) instead of a complex signal e(n).
Circuit 53 for the control of the simulated phase
of the echo signal employs recursion formula 139) and con-
sequently processes only real signals. ~iultiplying circuit62 forms the product of the real component e (n) of the
error signal and the imaginary component f(n) of the
complex signal ~f~n) supplied by phase shifter 50. This
product is multiplied by the coeffi_ient ~ in circuit 6~,
its sign is thereafter changed in circuit 68 and it is
finally applied to accumulator 65, 66 which produces the
simulated phase used in phase shifter 50.
A variant derived from the variant lbis described
~HF 80 519 33
in the foregoing results from the subs-ti-tution in recursion
formula (39) of e (n). ~If(n) by -eI(n) ~R
results in the following recursion formula:
~(n+1) = ~(n) + ~ e (n). f(n) ~41)
In this derived variant lbis, use is made of
recursion formula (38) for the control of the coefficients
and recursion formula (41) for the control of the simulated
phase. The corresponding block diagram can be easily estab-
lished; this variant ~as the disadvantage that -the real
component of the error signal must be formed for the con-
trol of the coe~ficients and the imaginary component
thereof for the control of the simulated phase.
A variant 2bis which uses the recursion formula
(38) and (40) and whose block diagram is shown in Figure 11
corresponds to variant 2 of structure II of the echo can-
celler which uses the recursion formulae (31) and (33) and
whose block diagram is shown in Fig~ 8.
In Figure 11, circuit 54 for the control of the
coefficients is not shown in detail as it is exactly iden-
tical to the circuit of Fig. 10. The block diagram of cir-
cuit 53 for the control of the simulated phase differs from
that of Figure 10 in that the multiplying circuit 62
receives the echo signal Rf(n) instead of the real error
signal e (n).
A variant derived from the variant 2bis described
in the foregoing results from the substitution in recursion
formula (40) of f(n). I~n) by - I (n) ~ R (n) Thi
results in the following recursion formula:
~(n+l) = ~(n) ~ J3~ If(n). Rf(n) (42)
In this derived variant 2bis the recursion for-
mulae (38) and (42) are used. The corresponding block
diagram is easy to establish; this variant has the disad-
vantage that a circuit 22 is re~uired ~or forming the com-
ples echo signal whose real component ~ Rf(n) is necessary
for forming the real error signal e~(n) used in formula (38),
and whose imaginary component If(n) is used in formula
PHF 80 519 34 19-2-1981
(~2).
A variant 3bis which uses -the *ormula (38) ~or -the
control of the coe-~ficients and the ~ollowing recursion
-~ormula ~or -the control o~ -the simulated phase:
~(n~1~ = 0(n) ~ mLe (n) e~p - j 0(n) d(n)~ 3)
corresponds to the variant 3 described in -the ~oregoing
which results from the use of the recursion ~ormulae (31)
and (34)-
With the aid o~ the preceding block diag:rams the
block diagranl of this variant 3-bis can be easil-y established.
In the -foregoing a certain number of variants of
the echo canceller in accordance 1rith the inven-tion have
been described, each o~ these variants being based Oll the
15 use o~ recursion ~ormulae for the control of the coe~
cients and of the simulated phase. It is obvious that by
drafting equivalent forms o~ several of the above-mentioned
recursion ~ormulae many other variants can be found ~ithout
departing -from the scope of the invention.
On the other hand, one skilled in the art will
easily understand that the echo canceller in accordance
with -the invention is not onlv suitable ~or use in data
transmission but also ~or the transmission ol teiepholle
signals, where the same problem o~ a variable phase echo
25 may be encountered.
