Adaptive echo canceller with AGC for transmission systems

An adaptive echo canceller for a full duplex transmission system comprises a cascade arrangement of an adaptive digital filter and an automatic gain control device. The AGC device receives the output signal from the adaptive digital filter and delivers the estimate of the echo signal to the receive line for subtraction. It has a multiplier receiving the output signal and a signal representative of the multiplication factor from a gain adaptation circuit. A separate gain change circuit is connected to receive the output signal from the adaptive digital filter and simultaneously modifies the tap coefficients of said filter and the multiplication factor of the AGC device in opposite directions for maintaining the output of the adaptive digital filter in a predetermined range.

BACKGROUND AND SUMMARY OF THE INVENTION 
The invention relates to the field of simultaneous two-way transmission of 
information on a same communication channel, that is duplex data 
transmission. It more particularly relates to an echo canceller for such a 
system, of the type having an adaptive digital filter. 
Before the state of the prior art is considered and the invention is 
summarized, it may be useful to give some indications regarding duplex 
transmission of data on a common communication channel and to outline the 
problems which are involved. 
Referring to FIG. 1, a system for simultaneous two-way communication 
between two remote stations A and B on a single communication channel 10, 
for instance a two-wire telephone circuit, is schematized. The data to be 
transmitted consist of a sequence of symbols which are typically 
quantified, which may represent data signals as well as speech signals. 
When the useful signals a and b from stations A and B are transmitted in 
the same frequency range, the signal r which is received by receiver 12 at 
station A includes the useful signal b sent by transmitter 11 of the 
remote station B, and an additive noise x: 
EQU r=b+x (1) 
The noise x may frequently have power much greater than that of the useful 
signal b. It comprises an echo of signal a transmitted by source 11 at 
station A, although differential transformers 15 are provided at both ends 
of the transmission channel 10. That phenomenom is indicated in FIG. 1, 
where transmission from B toward A is indicated in full line, while 
transmission from A toward B is indicated in dash-dot lines. 
Since the echo signal b may prevent correct recovery of signal b by 
receiver 12 at station A, its action should be cancelled. There exists a 
number of approaches for cancellation of the echo. Reference may for 
instance be had to the following documents for finding examples: Mueller, 
"A New Digital Echo Canceller for Two-wire Full Duplex Data Transmission", 
IEEE Transaction on Communications 24, No. 9, 1976, pp. 956-962; French 
Pat. No. 2,377,734; Weinstein, "A Passband Data Driven Echo Canceller For 
Full Duplex Transmission on Two-wire Circuits", IEEE Transaction on 
Communications, 25, No. 7, 1977, pp. 654-666; Falconer et al "Adaptive 
Echo Cancellation/AGC Structures for Two-wire Full Duplex Data 
Transmission", The Bell System Journal, Vol. 58 (1979), pp. 1593-1616; 
U.S. Pat. No. 3,780,233 (Campanella et al). 
As a general rule, it has been proposed to locate an echo canceller (which 
will be referred to in the following by the abreviation ECC) in the 
receive line. That ECC is an adaptive digital filter 13 whose transfer 
function may be represented with a vector H which, from a sequence A of 
successive symbols a.sub.k (where k indicates the serial number of the 
symbol) transmitted by source 11 of station A, delivers a linear 
estimation: 
EQU y=H.multidot.A (2) 
That estimation y may be considered as a reconstruction of the actual echo 
x. The reconstructed echo is applied to a subtractor 14 which also 
receives the signal r arriving to station A from the far end on line 10. 
The difference between the two signals is applied to the receiver 12. 
The echo x may generally be considered as comprising a close echo x.sub.p 
due to the lack of adaptation of the differential transformer 15 of 
station A and a remote echo x.sub.L due to reflections of the signal a 
transmitted from A toward B, reflections which are due to lack of 
impedance adaptation in the communication channel 10: 
EQU x=x.sub.p +x.sub.L ( 3) 
The two echo components have different features. The close echo is much 
more powerful than the remote echo. And the features of the two echo 
components and the parameters of the useful signal exhibit large 
variations depending upon the communication channel which is considered. 
It is important to note that the power of echo x is quite variable and its 
value is unknown. Under actual conditions, the only available indication 
is the fact that the value is lower than a predetermined maximum level. 
The power of the useful signal b is also quite variable and the only 
available indication is the fact that it is higher than a predetermined 
minimum level. Last, the remote echo x.sub.L is fequently affected with a 
phase shift, due to phase jitter and a frequency shift in the 
communication channel, while the close echo is typically not subject to 
phase shift. 
When the ECC consists of an adaptive digital filter of conventional type, 
it must comprise a large number n of bits on each tap coefficient for the 
correction to be satisfactory, even if there is no phase shift of the 
remote echo. Most prior art ECCs typically have twenty bits per tap 
coefficient, with the consequence that they are complex and of high cost. 
The need for a large number of bits is particularly due to the broad 
dynamic range of the echo and the useful signal. 
It is an object of this invention to provide an echo canceller for data 
communication systems which makes it possible to substantially decrease 
the number n of bits of each coefficient, without detrimentally affecting 
the performances, particularly the acceptable dynamic range of the echo 
and useful signal. 
When the remote echo exhibits a phase shift, there is another problem which 
is not overcome in the prior art. As will be more apparent in the 
following, the ECCs of the prior art cannot operate properly when the echo 
has a phase shift, unless the power of the echo which is not in phase is 
known. The performance is detrimentally affected when the power of the 
echo which exhibits a phase shift increases. 
It is another object of the invention to provide an echo canceller which is 
more effective than the prior art ECCs when an echo exhibiting a phase 
shift is present. 
According to an aspect of the invention, there is provided an echo 
canceller for a full duplex communication system between two remote 
stations, comprising an adaptive digital filter and automatic gain control 
means located downstream of said filter in the communication path, and 
means for delivering the value of the gain of said automatic gain control 
means to said filter as an input signal thereof. 
In other words, the adaptive digital filter is "looped" on the AGC means, 
since the gain of the AGC means is fed back to the adaptive filter as an 
input signal which cooperates in determining the vector of the 
coefficients of the filter. 
Means controlled by the output signal of the adaptive filter will be 
provided for adjusting the coefficients of the latter for maintaining the 
power or amplitude level of said output signal in a predetermined range. 
Such means simultaneously modify the coefficients of the filter and the 
gain of the AGC means, in opposite directions. 
The invention will be better understood from the following description of 
particular embodiments of the invention and a comparison with the prior 
art.

DETAILED DESCRIPTION OF TICULAR EMBODIMENTS 
Before the invention is described, the structure and operation of an ECC 
according to the prior art will be described. A more complete description 
may be found in the documents identified above, whose contents are 
included in the present specification by way of reference. 
Referring to FIG. 2, there are illustrated source 11 and receiver 12 of 
station A. The signal a sent by transmitter 11 is sampled by a component 
which is schematically represented as a switch 20, which is closed at 
intervals .DELTA.. The ECC 13 uses N successive samples to evolve an 
estimated echo: 
EQU N=K+L+1 (4) 
The successive samples are made simultaneously available by K+L delay 
elements 16 and their values are: 
##EQU1## 
When signal a is a data signal, .DELTA. corresponds to the transmission 
period. When a is an analog signal, the sampling may be made by any known 
method. However, Shannon sampling will typically be used, for instance 
with .DELTA..perspectiveto.125 .mu.S for a speech signal. 
The N available successive samples are combined for generating vector 
A.sub.k which represents the signal as processed by the digital filter at 
time k.DELTA., just after sample a.sub.k has been delivered by transmitter 
11. The echo y is reconstructed from such samples by associating a 
specific coefficient h.sub.-k, . . . h.sub.O, . . . , h.sub.L to each of 
them, and then summing the products. The N coefficients are delivered by 
an adaptation circuit to individual multipliers 17 (or a single 
time-shared multiplier) and constitute a vector H which may change in 
accordance with an adaptive algorithm of the type: 
EQU H.sub.k+1 =H.sub.k +.mu.f (e.sub.k, A.sub.k, 100.sub.k) (6) 
In formula (6), e.sub.k is a difference which is representative of the 
residual echo after compensation. In the approach of FIGS. 1 and 2: 
EQU e.sub.k =r.sub.k -y.sub.k (7) 
e.sub.k may be designated as a "clean signal". It consists of the useful 
signal of transmitter B and the residual echo. It is the difference 
between signal r.sub.k received at time k.DELTA. and echo y.sub.k 
estimated by the ECC at that time: 
EQU y.sub.k =H.sub.k.sup.T .multidot.A.sub.k (8) 
Again in formula (6), .phi..sub.k designates an estimation of the phase 
shift of the echo. .phi..sub.k is to be considered only when the echo has 
a phase shift. Such a phase shift occurs when the echo is remote. In 
certain cases, it will not be necessary to take it into account. 
.phi..sub.k may be delivered by a manually adjustable circuit (FIG. 2). 
Last, coefficient .mu. of formula (6) is a predetermined positive constant 
value, which constitutes an incrementation step. 
In the prior art situation of an ECC for eliminating the close echoes, 
which exhibit no phase shift, in a data transmission system, formula (6) 
may be simplified and becomes the conventional gradient algorithm: 
EQU H.sub.k+1 =H.sub.k +.mu.(r.sub.k -y.sub.k)A.sub.k (9) 
The transmitted signal is frequently used for modulation of two carrier 
waves having a 90.degree. phase difference (QAM). In that case, which is 
for instance described in French Certificate of Addition 2,394,938, a is a 
complex signal; A.sub.k and H.sub.k are also complex. The received signal 
r.sub.k is complex if the receiver 12 has means for obtaining two 
components with a 90.degree. phase difference (phase splitter in pass-band 
transmission, demodulation on two carriers with a 90.degree. phase 
difference if in base band). If the values are complex, the simplified 
adaptation algorithm (9) may be written: 
EQU H.sub.k+1 =H.sub.k +.mu.(r.sub.k -y.sub.k)A.sub.k * (10). 
In the opposite case (reception system which restitutes only a real 
component r.sub.k) the estimated real echo is: 
EQU y'.sub.k =Re{H.sub.k .multidot.Ak} (8bis) 
And the adaptation algorithm may be written: 
EQU H.sub.k+1 =H.sub.k +.mu.(r.sub.k -y'.sub.k)A.sub.k * (10bis) 
In formulae (10) and (10bis), A.sub.k * designates the parameter which is 
conjugated of A.sub.k and in formula (10) Re designates the real part. 
The residual echo which is actually present after compensation by such a 
conventional ECC may be computed. The power of the residual echo is given 
by: 
EQU R=.mu..multidot.N.multidot.S.multidot.E(.vertline.a.sub.k 
.vertline..sup.2)/2 (11) 
in which S designates the power of the useful signal. 
Since signal a is typically 1: 
EQU E(.vertline.a.sub.k .vertline..sup.2)=2 (12) 
The incrementation step is selected to provide a fixed level of residual 
noise due to echo for the receiver at station A, that is 
EQU .mu.N=.alpha. (constant) (13) 
In most cases: 
EQU .alpha.=2.sup.-6 (14) 
for obtaining a signal/noise ratio which has a usual value, of about 18 db, 
in receiver 12 of station A. Then the incrementation step is: 
EQU .mu.=.alpha./N (15) 
For an ECC which has about 64 coefficients, that is a number of 
coefficients which is usual in systems for transmission of data at a rate 
of 2400 bits/sec., in full duplex, the incrementation step is 
.mu.=2.sup.-12. 
A calculation indicates that the LSB 2.sup.-Bmin of the binary word h.sup.r 
which represents the real (or imaginary) part of one of the coefficients 
of the ECC is related to the incrementation step .mu. and to the power S 
of the useful signal by a relation which may be written: 
EQU .mu..sqroot.2 .sqroot.S.gtoreq.2.sup.-Bmin (16) 
if r.sub.k is complex and is: 
EQU .mu..sqroot.S.gtoreq.2.sup.-Bmin (16bis) 
if r.sub.k is real. 
The number of bits of the binary word h.sub.r should be such that the MSB 
2.sup.Bmax can represent the maximum value of the echo, and consequently 
that number is selected for fulfilling the condition: 
EQU 2.sup.Bmax .gtoreq..sqroot.Pmax (17) 
It is then possible to represent instantaneous echo power values which 
exceed 4 P.sup.max, when all bits of the word h.sub.r are equal to 1. 
Taking into account the sign bit, the total number n of bits representing 
h.sub.r should be at least: 
EQU n=1/2 log.sub.2 (Pmax/Smin)+1.5+log.sub.2 (1/.mu.) (18) 
If actual digital values are introduced into formula (18), it is found that 
the ECC according to the prior art should have from 20 to 22 bits per 
coefficient, when Pmax=0 dBm and Smin=-42 dBm, that is when Pmax and Smin 
have typical values. 
It is further to be noted that there is a degradation of the theoretical 
efficiency of such ECCs when the useful signal level decreases. 
As indicated above, it is an object of the invention to permit a reduction 
in the number n of bits representing the coefficients. It is an other 
object to increase the immunity of the ECC to the phase shift of the echo, 
which phase shift is particularly important when the remote echo echo is 
substantial. For making apparent the detrimental action of such an echo on 
the operation of a conventional ECC, a short description will be given of 
the approach for compensating the phase shift in such an ECC, with 
reference to FIG. 3. On FIG. 3, those components which are in addition to 
those of FIG. 2 for compensating phase shift are indicated with strong 
lines. 
Referring to FIG. 3, the digital filter 21, which includes components 16, 
17 and 19 of FIG. 2 and delivers an estimated echo y.sub.k whose amplitude 
has been reconstructed, is in series relation with a downstream component 
22 for providing a phase shift exp(i.phi..sub.k). 
Phase .phi..sub.k is elaborated by a loop controlled by the phase shift 
between the estimated echo z.sub.k which is delivered by the phase shifter 
22 and the received signal r.sub.k. Operation of that phase loop may for 
instance be written as: 
EQU .phi..sub.k+1 =.phi..sub.k +.lambda.I.sub.m [(r.sub.k -z.sub.k)]z.sub.k * 
(19) 
where: 
EQU z.sub.k =y.sub.k exp (i.phi..sub.k) (20) 
In formula (19), Im is the imaginary part of the complex number. 
As a general rule, the loop will consist of a complex multiplier 22 and a 
circuit 23 for adaptation of .phi..sub.k. Circuit 23 has two inputs 24, 
25, which respectively receive e.sub.k and z.sub.k. 
In formula (19), .phi. is the positive incrementation step, which must be 
decreased when the power of the echo increases, since it must fulfil the 
condition: 
EQU .lambda.=.lambda..sub.0 /E(.vertline.y.sub.k 
.vertline..sup.2)=.lambda..sub.0 /2P (21) 
where .lambda..sub.0 is a constant value which is conditioned by the gain 
of the loop. 
That calculation indicates that the incrementation step cannot be defined 
unless the echo power P is known. As a consequence, an ECC having means 
for correcting the phase of a substantial echo cannot operate correctly 
unless the power P of the echo is known. In most situations, the condition 
is not fulfilled and the efficiency of the ECCs according to the prior art 
is detrimentally affected when the power of the component of the echo 
which has a phase shift increases. 
A first important difference between the invention and the prior art 
consists in that filter 21 having a single vector H defined by 
coefficients h is substituted with: 
an "upstream" standardized vector F which is such that application of 
vector F to signal a regulates the amplitude at a value which is 
approximately fixed, for instance equal to 1, 
and a "downstream" single multiplication factor g which is variable and 
positive and may be considered as being an AGC gain. 
F and g should be adaptive. 
An approximative amplitude regulation may be sufficient, with a tolerable 
variation range which may be in a ratio of from 1 to 2. That possibility 
is most important, since it results in a possible reduction of the number 
of bits representing each coefficient of F. 
In other words, the signal is subjected to two successive processing steps, 
the upstream processing step being symbolized by vector F and being looped 
on the downstream processing step g. 
Referring to FIG. 4, a preferred (but not exclusive) embodiment of the 
invention will now be described. For more clarity, those components of 
FIG. 4 which are in addition to those necessary in FIG. 2 are indicated in 
strong lines. The common components are designated by the same reference 
numerals. 
The circuit component which introduces vector F consists of a conventional 
echo canceller 21 (which may include the delay elements 16, multipliers 17 
and summation circuit 19 of FIG. 2) associated with a circuit 18 which 
delivers a vector F.sub.k corresponding to each sample a.sub.k. Circuit 18 
will be defined in more detail in the following. Suffices it to note for 
the time that circuit 18 is controlled for the output signal a.sub.k of 
ECC 21 to have a power level which is approximately fixed, for instance 
approximately equal to 1. 
A "downstream" AGC circuit is located between the ECC 21 and the adder 14. 
That AGC circuit comprises a multiplier 26 which receives the output 
signal v.sub.k from the "upstream" component (ECC 21) and which delivers 
an output signal y.sub.k to adder 14. The multiplication factor g.sub.k 
for a sample v.sub.k is determined by a gain adapting circuit 27. The 
adder 14 again delivers the clean signal e.sub.k. With the above notation, 
the signals satisfy the relations: 
EQU e.sub.k =r.sub.k -y.sub.k (22) 
EQU v.sub.k =F.sub.k .multidot.A.sub.k (23) 
EQU y.sub.k =g.sub.k .multidot.v.sub.k (24) 
Formulae (22) and (23) are respectively similar to formulae (7) and (8) of 
a conventional ECC. 
However, control of the adaptive circuit 18 will now be effected non only 
responsive to the useful signal e.sub.k (as in prior art systems), but 
also responsive to: 
the loop feed back signal g.sub.k delivered by circuit 27, 
a signal for approximative amplitude regulation delivered by a circuit 28 
which has a symetrical action on the adaptive circuit 18 and the gain 
adapting circuit 27. 
As an example, it will be assumed that the approximative amplitude 
regulation is for standardizing the real part v.sub.k.sup.1 (and/or the 
imaginary part v.sub.k.sup.2) of v.sub.k according to the condition: 
EQU 0.5.ltoreq.Ampl (v.sub.k.sup.1)&lt;1. 
Such a regulation may be effected quite simply. In the embodiment 
schematically illustrated in FIG. 5, circuit 28 has a test device 29 which 
determines the first significant bit 2.sup.p of .vertline.v.sub.k.sup.1 
.vertline. which is not equal to zero. That circuit does not make the 
determination on the instantaneous value, but on an average value of 
v.sup.1 taking into account adjacent time periods having a predetermined 
duration. The test device 29 consequently determines the integer p which 
corresponds to the first significant bit of v for each value v.sub.k, that 
is the value of p which fulfils the condition: 
EQU 2.sup.p .ltoreq.E(.vertline.v.sub.k.sup.1 .vertline.)&lt;2.sup.p+1 (25) 
The amplitude regulation, with an approximation which corresponds to a 
multiplication factor of 2, may be made by a circuit 30 for adjustment of 
the coefficients of F.sub.k and of gain g.sub.k by applying multiplication 
factors to them. Since the circuits use binary digits, a multiplication is 
carried out by sending a bit shift order symetrically on two outputs 31 
and 32. For instance, a multiplication by a factor of 2.sup.-(p+1) is 
necessary for power regulation, the bit shift orders delivered on outputs 
31 and 32 would be such that: 
EQU F.sub.k.sup.1 =F.sub.k .multidot.2.sup.-(p+1) (26) 
EQU g.sub.k.sup.1 =g.sub.k .multidot.2.sup.p+1 (27) 
It is readily apparent that the estimated echo y.sub.k is unchanged, while 
echo v.sub.k is regulated for approximatively keeping an amplitude value 
equal to 1. 
A similar approach could be used for controlling the average power E 
(.vertline.v.sub.k.sup.1 .vertline..sup.2). However, regulation is then 
with an approximation on two bits, that is of the type: 
EQU 1/4.ltoreq.P (v.sub.k ')&lt;1 (28) 
While operation could be represented by a single algorithm (Formula 10) in 
a conventional ECC, the apparatus of the invention is controlled by two 
algorithms, which respectively correspond to the ECC 21 and to the 
multiplier 26: 
EQU F.sub.k+1 =F.sub.k +(.beta./g.sub.k)e.sub.k A.sub.k * (29) 
EQU g.sub.k+1 =g.sub.k +.nu.Re{e.sub.k v.sub.k *} (30) 
In the formulae .beta. and .nu. are two incrementation steps having 
positive predetermined values. 
Algorithm (29) is the same as algorithm (10) corresponding to a 
conventional ECC, except that the incrementation step .beta./g.sub.k 
incorporates the value of the gain downstream of the ECC. 
In a first embodiment, circuit 18 is designed to take into account the 
effective gain g.sub.k for each sample. However, since that approach 
requires a considerable amount of computing time due to the number of 
divisions which are involved, it may be preferable to consider the first 
significant bit of g.sub.k which is different from zero. For that 
determination, the average value is computed on predetermined periods 
overlapping the sample numbered k. That determination of the average value 
may be made in the same way as that of v.sub.k.sup.1. 
According to that approach, there is determined the integer n which is such 
that: 
EQU 2.sup.m .ltoreq.E(g.sub.k)&lt;2.sup.m+1 (31) 
And algorithm (29) may be written: 
EQU F.sub.k+1 =F.sub.k +(.beta./2.sup.m)e.sub.k A.sub.k * (29bis) 
That simplified approach results in a considerable gain in the computation 
time, since the division by g.sub.k consists of a shift by one or more 
binary positions. It will be shown that the simplification has no 
substantial influence on the performance of the device. 
Gain g.sub.k as determined represents the amplitude value of the echo. As a 
consequence, the power P in formula (28) is: 
EQU 2.sup.m .perspectiveto..sqroot.P (32) 
Before a quite important advantage of the invention, namely the reduction 
in the number of bits necessary for each coefficient is emphasized, it may 
be useful to mention an apparent shortcoming, which however has no true 
importance, particularly since there is a complete freedom to adopt a 
compromise between a maximum adaptation speed and the suppression of any 
echo additional to that of a conventional ECC. 
Due to the cascade arrangement of two components, the power R' of the 
residual echo is not as given by formula (11), but the sum of two 
components: 
EQU R'=R.sub.F +R.sub.g (33) 
R.sub.F designates the contribution of the ECC 21. In the situation of a 
unitary signal corresponding to formula (12), R.sub.F can be written as: 
EQU R.sub.F =.beta.NS (34) 
The contribution R.sub.g is always positive. It is due to the adaptative 
AGC. The degradation due to the separation of a conventional ECC into two 
components may be expressed as: 
EQU .delta.=R.sub.g /R.sub.F 
.delta. may be computed easily and it appears that it is a function of 
.nu./.beta.: 
EQU .delta.=1/2N.multidot..nu./.beta. (35) 
It is essential to keep in mind that such a degradation does not 
automatically reflect performances lower than that of the single ECC of 
FIGS. 1 and 2, but only the effect of the cascade arrangement of two 
adaptive components. 
Degradation .delta. is an increasing function of .nu./.beta.. It will 
always be possible to maintain it at a low value, for instance: 
EQU .delta..ltoreq.0.25 (36) 
(that degradation corresponds to a loss of 1 dB only on the attenuation of 
the echo). 
From that selection, the condition to be fulfilled for a negligible 
degradation may be written: 
EQU (.nu./.beta.).sub.opt .ltoreq.N/2 (37) 
For an ECC having 55 coefficients: 
EQU (.nu./.beta.).sub.opt .ltoreq.27 (38) 
The power R' of the residual echo reflects the behaviour of the device in 
static condition. It is however essential to consider the dynamic 
behaviour, for which a maximum value of .nu./.beta. is quite preferable, 
since it corresponds to a maximum speed of convergence of the device. A 
comparison between the dynamic behaviour of a conventional ECC as shown in 
FIGS. 1 and 2 and the behaviour of a device according to the invention 
indicates that the two devices have the same convergence speed if: 
EQU .nu./.beta.=2N/(N=2)&lt;&lt;27 (39) 
As soon as .nu./.beta. has a value which is higher than that given by 
formula (39), the device according to the invention has an adaptation 
speed which is increased as compared with that of the prior art devices, 
at the cost of a small amount of increase of the residual echo, of about 1 
dB. 
On the other hand, if the primary objective is to avoid any supplemental 
residual echo as compared with a prior art ECC (i.e. if the two residual 
echoes as given by formulae (33) and (11) should be equal), it is 
sufficient to select an appropriate value of .beta.. If for instance N=55: 
EQU .beta.=4/5.mu. (40) 
In short, it will be appreciated that the invention always provides a 
reduction in the number of bits necessary for representing each 
coefficient and in addition makes it possible to reach an increased 
adaptation speed. 
That possibility appears from a line of reasoning similar to that which 
resulted into formula (17). That line of reasoning indicates that the 
first significant bit of the word f.sup.r representing the real (or 
imaginary) part of one of the coefficients of the ECC fulfils the 
condition: 
EQU 2.sup.B.sbsp.F max&gt;(maximum power of v.sub.k.sup.1) (41) 
Since that power is regulated and has a value which is close to 1, formula 
(41) may be written: 
EQU B.sub.max.sup.F =0 (42) 
The first or least significant bit is related to the incrementation step 
.beta./2.sup.m, which appears in formula (29), by a formula similar to 
formula (16). A line of reasoning similar to that already given for a 
conventional ECC indicates that the total number n' of bits of f.sup.r is: 
EQU n'=1/2 log.sub.2 (P/S).sub.max +1.5+log.sub.2 (1/.beta.) (43) 
If formulae (43) and (18) are compared, it is found that the difference 
n-n' between the number of bits of a conventional ECC and the number of 
bits in a device according to the invention is: 
EQU n-n'=1/2 log .beta./.mu.+1/2 log (Pmax/Smin)=1/2 log (P/S).sub.max (44) 
Referring to the above examples, where Pmax=0 dBm, Smin=-42 dBm and 
(P/S).sub.max =16 dB, with .beta./.mu.=0.794, the difference is 4 bits: 
the device as a whole is considerably less complex. 
That advantage remains if an echo phase shift should be compensated and a 
further advantage consists in improved immunity. The device may then be as 
shown in FIG. 6, where the components already shown in FIG. 4 have been 
designated by the same reference number. Compensation of the phase shift 
.phi..sub.k takes place after amplitude regulation and before automatic 
gain control. In the embodiment of FIG. 6, that compensation is achieved 
by locating a multiplier 22.sub.1 between components 21 and 26, so that 
the multiplier receives the reconstructed echo v.sub.k. The multiplication 
factor of the complex multiplier which constitutes the phase shift circuit 
is determined by a phase adaptation circuit 23.sub.1 with two inputs. A 
first input 24.sub.1 receives the clean signal e.sub.k and the other input 
25.sub.1 receives the output signal of multiplier 26. 
In such an arrangement, the incrementation step .lambda. of the phase 
correction loop is independent from the echo power P, since signal v.sub.k 
received by the multiplier 22.sub.1 is regulated and its power variations 
are in a range of from 1 to 4 (for the complex signal). 
As a consequence, the efficiency of the ECC is not detrimentally affected 
when there is an increase of the power of that echo which exhibits a phase 
shift and this is a definite advantage on the prior art ECCs. 
There is no need to describe the internal arrangement of the various 
components of the device. They consist of digital logic circuits having a 
construction which is conventional in datacommunication. The elements 
which are in addition to those present in conventional ECCs have a 
construction which is much simpler thn that of the prior art ECCs. The 
main difference between the adaptation circuit 18 of FIGS. 4 and 6 and 
that of a conventional ECC resides in the provision of a supplemental 
circuit for up and down shifting of the bits of all coefficients by one 
position, depending upon the signals received from circuit 28, for 
achieving modifications in a ratio of 2/1 and 1/2. 
In short, the ECC according to the invention, which combines a conventional 
adaptive filter with an AGC device, retains the advantageous properties of 
the prior art devices as regards datacommunication. The elaborated 
computing device consisting of the adaptive filter directly handles the 
binary signals consisting of the local data. However, the echo canceller 
according to the invention has a less number of bits per coefficient than 
the prior art ECCs and it is much less sensitive to echoes exhibiting a 
phase shift. 
Those skilled in the art will appreciate that numerous embodiments and 
numerous variations are possible. The invention may be used in a system 
operating in passband as well as in the base band system which was more 
particularly considered above, with the usual modifications to be made in 
the reception system.