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Claims  |
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We claim:
1. In a OAM or phase modulation data transmission system for transmission
of local data a.sub.k from a local station to a remote station over a
transmission medium exhibiting an echo and simultaneous transmission of
far end data d.sub.k over said medium from said remote station, whereby
said local station receives a far end data signal y.sub.k including said
far end data d.sub.k and said echo,
an adaptative echo suppressor located at said local station and comprising:
an adaptive digital filter connected to receive the local data a.sub.k and
a clean signal e.sub.k derived from the far end data signal and
substantially free of said echo and arranged to deliver on an output an
estimation .sigma..sub.k of the actual echo of the local data by
multiplying a vector of coefficients C.sub.k with the local data a.sub.k,
said vector having an adaptation algorithm:
C.sub.k+1 =C.sub.k +.mu.a.sub.k *.f(e.sub.k)
wherein .mu. is a predetermined incrementation step, a.sub.k * is a
conjugated value of the local data a.sub.k and f is a predetermined
function of e.sub.k, and
subtractor means having an input connected to receive said far end data
signal y.sub.k from said transmission medium and a subtractive input
connected to receive said estimation .sigma..sub.k from said digital
filter,
wherein said digital filter is provided with means for rendering it only
responsive to a vectorial component of e.sub.k which is orthogonal to the
far end data.
2. Echo suppressor according to claim 1, wherein the function f uses the
sign of said vectorial component of e.sub.k which is orthogonal to the far
end data signal.
3. In a QAM or phase modulation data transmission system for transmission
of local data from a local station to a remote station over a transmission
medium exhibiting an echo and simultaneous transmission of far end data
signal y.sub.k including said far end data d.sub.k and said echo, said far
end data being distributed between points having different phases among a
finite plurality of predetermined phases specific to the modulation,
an adaptive echo suppressor located at said local station and comprising:
an adaptive digital filter connected to receive the local data a.sub.k and
a phase shifted clean signal e.sub.k derived from the far end data signal
and substantially free of said echo and arranged to deliver on an output
an estimation .sigma..sub.k of the actual echo of the local data by
multiplying a vector of coefficients C.sub.k with the local data a.sub.k,
said vector having an adaptation algorithm:
C.sub.k+1 =C.sub.k +.mu.a.sub.k *.f(e.sub.k)
wherein .mu. is a predetermined incrementation step, a.sub.k * is a
conjugated value of the local data a.sub.k and f is a predetermined
function of e.sub.k,
subtractor means having an input connected to receive said far end data
signal y.sub.k from said transmisson medium and a subtractive input
connected to receive said estimation .sigma..sub.k from said digital
filter, and
adaptive phase correction means connected in series between the
transmission medium and said subtractor and arranged for phase shifting
all complex far end data d.sub.k by the same angle .phi..sub.k which is
selected so that all those of the far end data d.sub.k which have at least
one of said predetermined phases are rendered either (i) purely real, or
(ii) purely imaginary and devoid of real component, before those data are
applied to the subtractor means, said same angle .phi..sub.k being the sum
of a predetermined angle .lambda. related to said one of the predetermined
phases and not greater than .pi./4 and of a slowly variable phase shift
.theta. introduced by the transmission medium.
4. Echo suppressor according to claim 3, characterized in that, for data
brought back along axes, the function f is the sign of e.sub.k.
5. Echo suppressor according to claim 3, wherein the phase correction means
includes a first order digital phaselock loop, placed between the output
of said subtractor means and a multiplier receiving data coming from said
transmission medium.
6. In a OAM or phase modulation data transmission system for transmission
of local data a.sub.k from a local station to a remote station over a
transmission medium exhibiting an echo and simultaneous transmission of
far end data d.sub.k over said medium from said remote station, whereby
said local station receives a far end data signal y.sub.k including said
far end data d.sub.k and said echo,
an adaptive echo suppressor located at said local station and comprising:
an adaptive digital filter connected to receive the local data a.sub.k and
a phase-shifted clean signal e.sub.k derived from the far end data signal
and substantially free of said echo and arranged to deliver on an output
an estimation .sigma..sub.k of the actual echo of the local data by
multiplying a vector of coefficients C.sub.k with the local data a.sub.k,
said vector having an adaptation algorithm:
C.sub.k+1 =C.sub.k +.mu.a.sub.k *.f(e.sub.k)
wherein .mu. is a predetermined incrementation step, a.sub.k * is a
conjugated value of the local data a.sub.k and f is a predetermined
function of e.sub.k,
subtractor mans having an input connected to receive said far end data
signal y.sub.k from said transmission medium and a subtractive input
connected to receive said estimation .sigma..sub.k from said digital
filter, and
adaptive phase correction means connected in series between the
transmission medium and said subtractor and arranged for phase shifting
all complex far end data d.sub.k by the same angle .phi..sub.k which is
selected so that at least some of the far end data d.sub.k are rendered
either (i) purely real, or (ii) purely imaginary and entirely devoid of a
real component, before the data are applied to the subtractor means, said
same angle .phi..sub.k being the sum of a predetermined angle .xi.
characteristic of the nature of the far end data and not greater than
.pi./4, and of a slowly variable phase shift .theta. introduced by the
transmission medium,
wherein the adaptive phase correction means includes a first order digital
phase-lock loop, connected between the output of said subtractor and a
multiplier receiving data coming from said transmission medium,
said loop including further means for determining said same angle phase
shift from the real and the imaginary components of the complex signal
delivered at an output of said subtractor means, said further means
operating according to the algorithm:
.phi.k+1=.phi.k+.gamma.f.sub.1 (.PSI..sub.k)
wherein .phi..sub.k is said same angle of phase shift, .gamma. is a
positive adaptation parameter, f.sub.1 is a predetermined function and
.PSI..sub.k is an angle, formed by (i) e.sub.k and (ii) one of an
imaginary axis and a real axis, selected to be the smaller angle necessary
to render at least some of the far end data purely real or purely
imaginary.
7. Echo suppressor according to claim 6, characterized in that f.sub.1 is
proportional to .PSI..sub.k.
8. Echo suppressor according to claim 7, characterized in that .gamma. has
a value inversely proportional to .sqroot.S, S being the power of far end
data.
9. In a QAM or phase modulation data transmission system for transmission
of local data a.sub.k from a local station to a remote station over
transmission medium exhibiting an echo and simultaneous transmission of
far end data d.sub.k over said medium from said remote station, whereby
said local station receives a far end data signal y.sub.k including said
far end data d.sub.k and said echo, said far end data being distributed
between points having different phases among a finite plurality of
predetermined phases specific to the modulation,
an adaptive echo suppressor located at said local station and conprising:
an adaptive digital filter connected to receive the local data a.sub.k and
a phase-shifted clean signal e.sub.k derived from the far end data signal
and substantially free of said echo and arranged to deliver an an output
an estimation .sigma..sub.k of the actual echo of the local data by
multiplying a vector of coefficients C.sub.k with the local data a.sub.k,
said vector having an adaptation algorithm:
C.sub.k+1 =C.sub.k +.mu.a.sub.k *.f(e.sub.k)
wherein .mu. is a predetermined incrementation step, a.sub.k * is a
conjugated value of the local data a.sub.k and f is a predetermined
function of e.sub.k,
subtractor means having an input connected to receive said far end data
signal y.sub.k from said transmission medium and a subtractive input
connected to receive said estimation .sigma..sub.k from said digital
filter, and
phase correction means having: a multiplier connected in series relation
between the transmission medium and said subtractor, having a first input
connected to receive the far end data signal from said transmission
medium, a second input connected to receive a signal representing an angle
of phase shift and an output connected to said subtractor means; and phase
lock loop means having an input connected to receive the output of said
subtractor and an output connected to deliver said signal representing
said angle of phase shift to said multiplier, said phase lock loop means
being so arranged that said angle of phase shift is such as to render all
those far end data which have at least one phase of said plurality of
predetermined phases either (i) purely real, or (ii) purely imaginary
without a real component, before those data are applied to the subtractor
means, said angle of phase shift being the sum of a predetermined angle
.xi. related to said one of the predetermined phases and not greater than
.pi./4 and of a slowly variable phase shift .theta. introduced by the
transmission medium. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
1. Technical Field
The invention covers simultaneous bidirectional (duplex) data transmission
field, and especially QAM or phase modulation, over a same media. The
specific subject is an echo suppressor for such a system, of the type
including an adaptive digital filter designed to provide an estimate of
.sigma..sub.k (the effective echo) and whose adaptation algorithm of
vector C of coefficients has the form:
C.sub.k+1 =C.sub.k +.mu.a.sub.k *.f(e.sub.k)
wherein .mu. and f are a determined incrementation step and a predetermined
function;
2. Description of the Prior Art
Before presenting the state of the prior art and the contribution of the
invention, it may be useful to recall some information related to data
bidirectional transmission over a same medium and the relevant problems.
FIG. 1 shows the schematic diagram of a simultaneous bidirectional
transmission system between two remote terminals A and B, over a same
transmission medium 10 that may be for example a two-wire telephone line.
The information to be transmitted consists of a sequence of symbols,
generally quantified, that may represent data signals as well as speech
signals, when useful signals a and d coming from terminals A and B are
transmitted within the same bandwidth, signal y received in receiver 12 of
terminal A includes the useful signal d (remote data) generated by
transmitter 11 of remote terminal B, lost however in additive noise:
y:d+n+.sigma.' (1)
The noise is often of a higher level than useful signal d, it includes
additive line noise n and the echo .sigma.' of signal a (local data) sent
by terminal A, and this in spite of the presence of differential
transformers 15 at both ends of the transmission media 10. This phenomenon
is schematically illustrated in FIG. 1 where transmission from B to A is
shown in solid lines, whereas transmission from A to B is shown in dashed
lines. The preponderant part of this noise is generally echo .sigma.',
which derives from local data through the unknown "echo filter" C.sub.o :
.sigma.'.sub.k =C.sub.o.a.sub.k.
It is necessary to cancel, or at least attenuate the action of the echo
which would prevent the recovery of signal d in receiver 12 of terminal A.
Many echo suppression techniques have been proposed. The most common
solution has been to insert at each station an adaptive digital filter 13,
so-called "echo canceller", with a transfer function represented by a
vector of coefficients C.sub.k, which from a sequence of successive
symbols a.sub.k (k indicating the symbol sequential number) transmitted by
source 11 in station A, sequence obviously available in station A,
provides a linear estimation
.sigma..sub.k =C.sub.k .multidot.a.sub.k ( 2).
The estimation is called recovered echo or estimation of true echo
.sigma.'. This recovered echo is sent to substractor 14 that receives also
the signal y sent to station A through line 10. The difference e.sub.k
between the two signals
e.sub.k =y.sub.k -.sigma..sub.k ( 3)
is applied to receiver 12.
The power of echo .sigma..sub.k ', is much variable, as well as the power
of useful signal d.sub.k.
The data used is, as a rule, complex (case of phase modulation and
modulation with two carriers in quadrature. In this case the adaptation
algorithm used typically has the following form:
C.sub.k+1 =C.sub.k +.mu..a.sub.k *.f(e.sub.k) (4)
wherein .mu. and f are respectively an incrementation step and a
predetermined function.
This formula assumes, as a representation of residual echo er.sub.k, the
"clean" signal
e.sub.k =tr.sub.k +d.sub.k +n.sub.k
wherein er.sub.k =(C.sub.o -C.sub.k).a.sub.k.
Most of the time, when the echo does not exhibit a significant phase shift,
the function f adopted is the gradient of the quadratic error, so that the
algorithm (4) becomes:
C.sub.k+1 =C.sub.k +.mu.(y.sub.k -.sigma..sub.k)a.sub.k * (5).
The shortcoming of the above solution is to require a complex filter, with
a great number of bits for each coefficient--namely about twenty--and
heavy computation.
Therefore it has been envisioned to use the sign of e.sub.k =y.sub.k
-.sigma..sub.k as a function, instead of the gradient itself, in order to
simplify the implantation. But it is found that this algorithm cannot
ensure a full convergence of the adaptation.
Actually this algorithm is written as:
C.sub.k+1 =C.sub.k +.mu..a.sub.k *.sign e.sub.k ( 6)
wherein
sign.(e.sub.k)=1/.sqroot.2[signe.sub.k.sup.r +i signe.sub.k.sup.i ](7)
e.sub.k.sup.r and e.sub.k.sup.i being respectively the real and imaginary
components of e.sub.k.
To obtain convergence, e.sub.k must have the same sign as the residual echo
er.sub.k. However, as soon as the adaptation is sufficient to have the
level of er.sub.k lower than the remote data level d.sub.k, the sign
identity condition is not satisfied anymore and the echo residue
convergence is interrupted (T.A.C.M; CLAASEN, W. F. G. MECKLENBRAUKER,
"Comparison of the convergence of two algorithms for adaptive FIR digital
filters", TEEE Trans. ASSP, Vol. 29, No. 3, June 1981, pp. 670-678).
This difficulty is shown in FIG. 2 where is illustrated the case with
opposite signs of the real components of residual echo er.sub.k and of the
difference e.sub.k between the recovered echo .sigma..sub.k and the
received signal d.sub.k.
Other solutions have been used to solve this problem. For example it has
been proposed to insert a forced noise signal b.sub.k, with a kown level
close to the level of remote data d.sub.k, in order to compensate for the
presence of the data (FIG. 1). However, this adjunction significantly
increases the system complexity (N. HOLTE, S. STUEFLOTTEN, "A new digital
echo canceler for two-wire subscriber lines"; IEEE Trans. on
Communications, Vol. COM-29, No. 11, Nov. 1981, pp. 1573-1581).
SUMMARY OF THE INVENTION
The object of the present invention is to provide an echo suppressor that
has better performances than existing algorithms and significantly better
than the conventional gradient algorithm. To accomplish the objective, the
invention uses a completely different approach and starts from the
observation that, when the remote data d.sub.k are along one of the axes
(along the imaginary axis, in the case of FIG. 3), the component of the
clean signal e.sub.k in quadrature with data d.sub.k (along the real axis
in FIG. 3) is equal to the corresponding component of residual echo
er.sub.k : by using only this significant quadrature component of residual
echo er.sub.k, the convergence will be improved. And, accordingly, the
invention proposes--when the data are not along the axes--to accomplish
the adaptation of the algorithm by means of the only component of the
clean signal that is in quadrature with the remote data d.sub.k : it can
be said that the projection principle is used.
The invention proposes accordingly an echo suppressor in conformity with
claim 1.
The invention will be better understood upon reading the forthcoming
description of a particular embodiment, given as a non limitating example.
The description refers to the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1, already mentioned, is a schematic diagram of a data transmission
system according to the prior state of the art, with terminals equipped
with an echo suppressor.
FIGS. 2 and 3 are interpretation geometrical diagrams, showing the residual
echo er for a complex data (FIG. 2) and for a purely imaginary data (FIG.
3).
FIG. 4 is a diagram showing the noise reduction in the case of the sign
algorithm (solid line SI curve) and in the case of the algorithm according
to the invention (dashed line curve) versus the incrementation step .mu..
FIG. 5 is a diagram showing the representative graphs of the difference
between the binary length of the coefficients with algorithm EE, SI, SI'
and SURAX and with the SIGNIF algorithm for S/N=20 dB, versus -R/S.
FIG. 6 shows the general implementation of the algorithm operating with the
adaptation loop of phase .theta..sub.k, the loop allowing for the
determination of .xi..sub.k and the adaptation of the echo suppressor
coefficients.
FIG. 7 is a graph showing how .xi..sub.k +.theta..sub.k is selected.
FIG. 8 is a graph showing the direction in which the phase compensation
loop must rotate e.sub.k to bring it back on one of the axes.
FIG. 9 illustrates the phase .theta..sub.k adaptation algorithm in the
general case.
FIGS. 10A and 10B are two equivalent schematics reflecting the digital
phase .xi..sub.k determination mode in the QAM 16 points diagram case.
FIG. 11 shows the echo suppressor coefficients adaptation according to one
of the operation modes of the invention.
FIG. 12, similar to a portion of FIG. 1, shows the principle of the echo
suppressor phase compensation loop, for a graph with data on the
diaganols.
FIGS. 13A and 13B are respectively four and sixteen points graphs with
points on the diagonals, that is for which .xi..sub.k is equal to .pi./4.
FIG. 14 is a detailed diagram of the phase adaptation loop according to a
particular embodiment illustrated in FIG. 12.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
In order that the invention may be compared with the previous state of the
art, the structure and operation of the known echo suppressor using the
gradient algorithm (5) will first be described.
Referring to FIG. 1, the signal coming from transmitter 11 in station A is
sampled by component 20 shown as a switch closed at intervals .DELTA..
Echo suppressor 13 includes a filter using N successive samples for
providing an evaluation .sigma..sub.k of the echo from K+L+1 delay
elements:
##EQU1##
The N samples are combined to generate a vector a.sub.k that represents the
signal applied to the digital filter at time k.DELTA., just after supply
of a.sub.K by transmitter 11. Estimated echo .sigma..sub.k is assessed by
multiplying samples k-L through k+K by coefficients h.sub.-k through
h.sub.L, and performing the sum of the products. Vector C.sub.k of N
coefficients is generated by the adaptation algorithm (5). In the
presentation of the invention, the case with the data on one axis will be
presented first, then the case where the data are located anywhere.
CASE OF DATA ON ONE AXIS
The following notation is used:
##EQU2##
A=power of near data a.sub.k B=Power of remote data d.sub.k
R=power of residual echo er.sub.k.
In order to simplify, the power of in-line noise n.sub.k is assumed to be
negligible, a hypothesis that is often fulfilled and which in any event
does not change the results.
On the other hand, it will be assumed that sequences {a.sub.k } and
{d.sub.k } are representing centered random variables, taking discrete
values with equal probabilities.
With above notations, it can be written that the clean signal e.sub.r at
time k is:
e.sub.k =(er.sub.k.sup.r d.sub.k.sup.r)+i(er.sub.k.sup.k.sbsp.i
+d.sub.k.sup.i).
If the remote data are on the axis (FIG. 3), that is real or imaginary, one
of their components is zero. If, for example, d.sub.k is imaginary, that
is d.sub.k.sup.r =0, the real part of e.sub.k is equal to the real part of
echo residue er.sub.k, except for the line noise, and the increment of the
gradient algorithm (5) becomes, from formula (8):
##EQU3##
The formula is similar when d.sub.k is real.
In the forthcoming comparison, the gradient algorithm (9) will be called
ONAX when the remote data is on one of the axes.
This algorithm ONAX can be transformed according to the projection
principle, into a simplified algorithm SIGNID by using only the
significant data contained in (e.sub.k): it is sufficient to delete in
formulas (8) and (9) the portion of the increment affected by d.sub.k,
that shows as a noise. In the case where d.sub.k.sup.r =0, formula (9 bis)
is obtained where the remote data do not appear anymore.
##EQU4##
In complex form, those formulas expressing algorithm SIGNID can be
written:
##EQU5##
One of the objects is to reduce the complexity of the algorithms; this
simplification can be accomplished by considering only the sign of the
significant applicable component. Algorithms ONAX and SIGNID respectively
generate algorithms that will be respectively called SURAX and SIGNIF it
will be shown how those two latter algorithms by using the "sign" function
eliminate the shortcomings of the forementioned sign SI algorithms--given
by formula (6)--and SI'--applicable to the addition of forced noise.
CASE OF DATA NOT ON AXES
If the remote data d.sub.k is not on an axis, it is, according to the
invention, brought back on the axis by a rotation .phi..sub.k (in order to
remain in a fixed reference frame). Thus:
d.sub.k =d.sub.k exp (i.phi..sub.k)
wherein d.sub.k has one null component (real or imaginary).
This rotation transforms the gradient algorithm increment into:
##EQU6##
wherein e.sub.k.sup.r and n.sub.k being respectively the result by
rotation .phi..sub.k of: er.sub.k and n.sub.k.
If, for example, data d.sub.k has been brought back on imaginary axis oy by
rotation, whereby d.sub.k.sup.r =0, the following formula is obtained:
e.sub.k =(er.sub.k.sup.r +ier.sub.k.sup.i)+id.sub.k.sup.i +(n.sub.k.sup.r
+in.sub.k.sup.i).
The projection principle application yields the following increment:
.DELTA.'(C.sub.k exp i.phi.)=a.sub.k.sup.r (er.sub.k.sup.r
+n.sub.k.sup.r)-ia.sub.k.sup.i (er.sub.k.sup.r +n.sub.k.sup.r)
with data d.sub.k rotated to Ox axis, that is such that d.sub.k.sup.i =U,
the result would be:
##EQU7##
The resulting algorithm is now written
##EQU8##
The manner that the data can be brought on one axis will be described
later with reference to FIG. 7. The performances of the various algorithms
and in particular the power of residual echo er may be computed and
compared. This comparison was performed between residues R.sub.E ;
R.sub.SI ; R.sub.SI' ; R.sub.ON ; R.sub.SD ; R.sub.GEN ; R.sub.SU ;
R.sub.SIG for the algorithms: E=gradient, according to formula (5)
SI=sign, according to formula (6)
SI'=sign with insertion of forced noise
ONAX=gradient, with data along one axis according to formula (9 bis)
SIGNID=ONAX considering the significant component only
GEN=data previously brought back along one axis, then using the significant
component
SURAX=sign of SI, in the particular case where the data are along one axis
SIGNIF=SURAX, considering the significant component only.
In the representative case of a Gaussian residue, and without line noise,
the residues are given in the following table:
TABLE I
______________________________________
Algorithm Gaussian residue
______________________________________
(E) and (ONAX)
##STR1## (10)
(SI)
##STR2## (11)
(SI')
##STR3## (12)
(SURAX)
##STR4## (13)
(SIGNIF)
##STR5## (14)
______________________________________
It may be observed that in addition algorithms SIGNID and GEN have a null
limit residue. Actually, for those two algorithms, the residue value, with
line noise is:
R SIGNID=RGEN=.mu.NAB/(2-.mu.Na).
The remote data power has no effect. This result is a great advantage. It
is maintained for all algorithms using the projection principle: the
adaptation is accomplished by using the "clean" signal component that is
orthogonal to the remote data, and only the remote data.
In both following comparisons, only simplified forms of SURAX and SIGNIF
have been taken into account in order to simplify, not ONAX, SIGNID and
GEN.
Table I shows that algorithms SURAX and SIGNIF have performances superior
to the sign SI conventional algorithm and that R.sub.SIG does not depend
on power 5 of remote data; At last, regardless of R and .mu., R.sub.SIG is
smaller than R.sub.SU for S/R>2, which is applicable to acceptable
performances, the gain of SIGNIF in relation to SURAX is of 3 to 6 dB.
The advantage of SIGNIF versus 5 is much greater. With a Gaussian residue,
the ration R.sub.S /R.sub.SIG is exp (S/R.sub.SI) with no noise. The ratio
is close to 7 to the value previously considered, S/R=2, and rapidly rises
with S/R, that is when echo suppression is improving.
It can be seen from equations (10) and (13) that parameter .mu. used in
SIGNIF is not as small as necessary in algorithm SI. Actually .mu. is
multiplied by the factor exp (5/2R) by using SIGNIF, whereas the same echo
residue is obtained.
As indicated above, one of the advantages of SIGNIF is not to depend on
remote data power S, so that there is no saturation of R at level S. This
advantage is even more obvious if, not the Gaussian residus are
considered, but the binary echo residues. For SI, residue R.sub.SI
decreases as .mu..sup.2 when R>S, but this decrement stops taking place
for R=S, as shown in FIG. 4. Conversely for SIGNIF, the decrement as a
function of .mu..sup.2 continues and a forced noise becomes unnecessary.
If it is recalled that for algorithm (E) the decrement is as .mu., it is
found a great advantage of SIGNIF versus E, a higher value of .mu.,
accelerating the convergence.
Furthermore, a comparison of formulas (10) and (14) shows that, for
S>.mu.NA.pi./4, which is a hypothesis that is practically always verified,
we have R.sub.E .gtoreq.R.sub.SIG : in other words, SIGNIF algorithm has
better performances than E when .mu. is small, that is has the value that
must be selected at the end of convergence, when R/S is small.
Moreover, in evaluating the complexity of computation by E and SIGNIF
algorithms in finite precision, as we are going to do it herein, it is
noted that the drawback of having .mu..sub.SIG <.mu..sub.E for higher
values of -R/S is only apparent since the word lengths required for the
echo suppressor coefficients are smaller for the SIGNIF algorithm.
The minimum number of bits b necessary to represent a component of the echo
suppressor filter 13, depends on the searched residual echo R and the
algorithm used. The computation indicates that the smallest b providing
convergence fulfills the condition:
##EQU9##
Starting from the hypothesis that er.sub.k is a Gaussian variable, the
smallest bit weight expression can be derived from (15) by replacing .mu.
by the value that it must have to get the same echo residue er. The result
is the following table when B is supposed to be null:
TABLE II
__________________________________________________________________________
Least significant bit
to guarantee the
Algorithm
.mu. at predetermined er
convergence :b
__________________________________________________________________________
(E)
##STR6##
##STR7##
(SI)
##STR8##
##STR9##
(SI')
##STR10##
##STR11##
(SURAX)
##STR12##
##STR13##
(SIGNIF)
##STR14##
##STR15##
__________________________________________________________________________
The comparison between SIGNIF and SURAX (for which the least significant
bits are called b.sub.SIG and b.sub.SU) in Table II above indicates that:
##EQU10##
This quantity is between -0.5 bit and +0.5 bit, but for a good echo
suppression, implying R<<S, the algorithm SIGNIF contributes to a gain of
0.5 bit over SURAX. Computation taking the noise in consideration shows
that it would be equivalent in the case of forced noise B=S.
Comparison between the results in Table II for algorithms SI and SIGNIF
shows that:
##EQU11##
Thus b.sub.SIG is less than b.sub.SI in all useful cases, and the
difference is large if the system operates satisfactorily, that is if R/S
is small. This point is very important since one of the drawbacks of (SI)
versus (E) is the great accuracy required for the binary representation of
the coefficients. It can be seen that (SIGNIF) eliminates the drawbacks of
(SI).
Last, if binary lengths of E and SIGNIF are compared, we find:
##EQU12##
meaning that the SIGNIF binary length is greater than E's for all values
of R/S; actually inequality (17) is not satisfied since the noise in E is
the line noise, which is low. It may be concluded that b.sub.E >b.sub.SIG
as soon as:
##EQU13##
In actual cases, the desired residue level is always less than the level
determined in (18) so that algorithm SIGNIF requires less bits than
algorithm E proper. A more elaborate computation, taking the noise into
account, indicates that the difference
##EQU14##
for a medium quality of echo suppression, that is when both algorithms
yield:
R.perspectiveto.B.
For a very high signal-to-noise ratio, that is R<<B, the difference is:
##EQU15##
From this point, it is possible to determine the saving in number of bits
of SIGNIF as compared to E for predetermined S/N value:
##EQU16##
FIG. 5 shows the binary word length saving accomplished with algorithm
SIGNIF versus algorithms SI, SURAX, SI' and E. The saving is shown in
relation to R/S (quality of echo suppression) for a line signal/noise
ratio S/N of 20 dB.
Considering that, as for the conventional sign algorithm, SIGNIF uses sign
(e.sub.k) and not e.sub.k during coefficient adaptation process, this
additional average reduction of 2 bits versus algorithm E, puts algorithm
SIGNIF in better place among the possible echo adaptive suppression
algorithms.
Computation steps (filtering by convolution C.sub.k.sup.T.a.sub.k and
adaptation) are also simpler for SIGNIF than for E. The computation
complexity can be assessed according to the number of required single
multiplications and additions: those figures depend on the algorithm as
well as on the length of the used binary words.
The evaluation shows that for each component of two multiplications and a
large number of additions are saved by substituting SIGNIF to SI.
A great number of multiplications and additions are saved by substituting
SIGNIF for E.
The only obligation with SIGNIF is to detect a threshold on each step in
order to determine which of data d.sub.k.sup.r and d.sub.k.sup.i is zero.
However this operation must be performed anyway by the receiver with a
decision device if it is not done in the echo suppressor. Therefore it is
not a complication.
For a representative case with a N=16 taps filter, a power S=10.sup.-1 of
signal, ratio R/S=-18.5 dB, the computation savings, by using SIGNIF
instead of E, are 36%. Moreover, this percentage hardly decreases when the
signal magnitude .sqroot.S decreases. Actually for small values of S, the
input analog/digital converter has to be more accurate. For example, if
the input signal decreases down to S=-42 dBm, the converter requires 12
bits, and the saving is 35%.
Refering to FIGS. 6, 7 (where indexes are not marked for the sake of
clarity) and 8, the way of performing the rotation to be carried out and
an embodiment of an echo suppressor that includes means capable of using
the projection principle implementing a phase follower algorithm that
simultaneously works with GEN. The elements of FIG. 6 corresponding to
those in FIG. 1 are designated with the same reference numbers.
Before describing the echo suppressor, its function and operating mode have
to be determined. Phase correction .phi..sub.k to be performed may be
broken down in two parts
.phi..sub.k =.theta..sub.k +.xi..sub.k (20 bis).
In this formula, .theta..sub.k is an analog parameter, corresponding to the
phase shift (jitter, drift) contributed by the transmission line; angle
.theta..sub.k varies slowly in relation to .xi..sub.k, as will be observed
hereunder. If d.sub.k is the transmitted or remote data, the phase shift
caused by the line results for example into received data d.sub.k '
contained in received signal y.sub.k) being of the form
d'.sub.k =d.sub.k exp (-i.theta..sub.k ').
It is necessary to estimate .theta..sub.k from .theta..sub.k '. It is the
function of the phase adaptation algorithm that will thus perform
synchronization of the carrier.
In this same (20 bis) formula, .xi..sub.k is a random discrete value,
characteristic of transmitted data d.sub.k ; it can be defined as:
.xi..sub.k =(Od.sub.k, axis closest to Od.sub.k).
Yielding .vertline..xi..sub.k .vertline..gtoreq..pi./4; when the two
components of d have equal modulus, it is possible to arbitrarily select
.xi..sub.k =.pi./4 rather than -.pi./4: It will be so for points on the
graph diagonals (all points for the 4 point graph of FIG. 13A, eight out
of sixteen points in FIG. 13B).
The system will also have to evaluate .xi..sub.k.
To do so, .theta..sub.k has to be evaluted (assuming that .xi..sub.k is
found, that is the steady operation mode is established). The "clean"
signal e.sub.k has been rotated by phase angle .phi..sub.k and has become
e.sub.k :
e.sub.k =e.sub.k exp (i.phi..sub.k).
This signal e.sub.k provides modified data d.sub.k :
d.sub.k =d.sub.k exp [i(.phi..sub.k -.theta..sub.k ')]=d'.sub.k exp
(i.phi..sub.k)
Data d.sub.k will be located in the neighbourhood of one axis if angle
.phi..sub.k has been judiciously selected. If the value of .phi..sub.k is
not right (that is if .theta. is not the correct estimation of .theta.'),
even if the echo suppressor operates satisfactorily, d.sub.k will not be
on an axis.
Signal e.sub.k is a representation of phase shift residue (.phi..sub.k
-.xi..sub.k -.theta..sub.k '), by angle:
.phi..sub.k =(Oe.sub.k, axis closest to Oe.sub.k).
It is therefore possible to proceed with .theta..sub.k phase shifting by
installing an adaptive algorithm operating as a first order digital
phase-lock loop, that has to automatically track the proper value of
.theta..sub.k by means of the error signal .psi..sub.k (shown in FIG. 7)
through the following recurrence formula:
.theta..sub.k+1 =.theta..sub.k +.gamma.f.sub.1 (.psi..sub.k) (21)
wherein .gamma. is a positive adaptation parameter, and f.sub.1 a suitably
selected function.
The phase adaptation algorithm (21) may be written more accurately by
considering the four zones A1-A4 bounded by the two bisectors. (FIG. 8).
If, for example e.sub.k is in zone A4, the axis closest to axis Oe.sub.k
is Ox, so that the data rotated d.sub.k has to be along axis Ox;
Angle .psi. is such that
tan .psi..sub.k =-e.sub.k.sup.i /e.sub.k.sup.r for e.sub.k .epsilon.A4 (22)
and modified data d.sub.k must be brought by rotation on Ox. With this
rotation, the modulus of d.sub.k (or e.sub.k) remains constant and the
optimum value is obtained when the imaginary component d.sub.k.sup.i (or
e.sub.k.sup.i) is made maximum. Therefore, when e.sub.k is in A4 zone,
variable .theta..sub.k can be set by the gradient algorithm. With
notations of FIGS. 7 and 8, the algorithm can be written in the following
general form:
##EQU17##
For small values of error angle .psi..sub.k, the first formula (23) may be
written, using the value given by (22):
.phi..sub.k+1 =.phi..sub.k +.gamma..psi..sub.k .vertline.e.sub.k.sup.i
.vertline., e.sub.k .epsilon.A1UA3 (24)
and since e.sub.k and d.sub.k are hardly different, by replacing (d.sub.k)
by a mean value .sqroot.S, algorithm (24) can be approximated as:
.phi..sub.k+1 =.phi..sub.k +.gamma..sqroot.S.psi..sub.k (25).
Under the latter form, it can be observed that it is advantageous to give
.gamma. a value inversely proportional to .sqroot.S. When S can be
evaluated, the parameter .gamma. may be initially set, otherwise, it may
be given a larger value and an adaptation algorithm will be provided which
gradually decreases it down to the optimum value.
Turning back to algorithm (23), it can be seen that it outlines how the
imaginary component e.sub.k.sup.i tends to be maximized (or minimized)
when e.sub.k is located in zone A1 (or A3): for A2 and A4 the mechanism is
similar.
It is interesting to note that, even without line generated interferences,
the receiver has to synchronize the carriers, that is the demodulator
phase with the useful signal phase: here, this task is automatically
performed by algorithm .theta..sub.k, that is substituted to an element of
the receiver.
In other words, the function required from the echo suppressor, that
consists in modifying data d.sub.k ' in order to rotated them in the
direction of axes, does not involve additional burden, as compared to
usual echo suppression algorithms.
Once phase .theta..sub.k adaptation performed, the system is stabilized,
and signal .epsilon..sub.k is obtained (FIGS. 6 and 7)
.epsilon..sub.k =e.sub.k.exp (i.theta..sub.k)
or
.epsilon..sub.k =er.sub.k.exp (i.theta..sub.k)+S.sub.k
with
S.sub.k =d.sub.k exp [i(.theta..sub.k -.theta..sub.k ')].
The echo residue being small and shift .theta..sub.k ' well compensated by
.theta..sub.k, signal .epsilon..sub.k enables to detect transmitted data
d.sub.k, that is to perform the evaluation of angle .xi..sub.k.
FIG. 6 (using the same notations as FIG. 1) shows in a simplified
presentation the general configuration of an adaptation echo suppressor of
phase O operating according to this principle. It includes, in addition to
the components shown in FIG. 1, a phase adaptation loop 54, and a loop 56
for generating .xi..sub.k.
Phase .theta..sub.k adaptation loop 54 can have, in all cases, the general
configuration illustrated in FIG. 9, with the same configuration as loop
22 in FIG. 14, which need therefore not to be described here. Loop 56 may
have:
the configuration shown in FIGS. 10A or 10B in the case of 16 points graphs
(FIG . 13B),
the configuration shown in FIG. 11 in the case of SIGNIF algorithm
application, by formula (26) that will be mentioned later.
FIG. 10A illustrates the components required to determine .xi. by
application of formula
##EQU18##
where a=sign/.epsilon..sup.r -2/.sign/.epsilon..sup.1 -2/ and b and c are
as defined later applicable to the case taking into account the 16 points
of FIG. 13B graph (used for transmission at 9600 bauds) with:
##EQU19##
The group of so determined cases is in agreement with all points of the
graph. For example, for points on the diagonal, corresponding to:
[.vertline.d.sup.1 .vertline.>2et.vertline.d.sup.r .vertline.>2]
or
[.vertline.d.sup.i .vertline.<2et.vertline.d.sup.r .vertline.<2]
yielding:
.xi..sub.k =.pi./4.
Conversely for points B1, B2, B3, B4:
[.vertline.d.sup.i .vertline.>2et.vertline.d.sup.r .vertline.<2]
and in this case:
.xi..sub.k =sig(d.sup.1).sig(d.sup.r)Arct1/3.
A similar result is found for the four remaining points.
The circuit in FIG. 10A provides adaptation for all points, hence rapid
convergence. It includes two channels, one for .epsilon..sup.r, the other
for .epsilon..sup.i and including each a circuit 62a or 62b adding -2 to
the output of 60a and 60b and a circuit 64a or 64b determining the sign.
The sign product is performed in 66, in order to generate a and 1-a. In
parallel, c is generated by threshold detector 70 with .epsilon..sup.r and
.epsilon..sup.i as inputs.
In the case of the eight points on the diagonals, computation is performed
in a single amplifier 72 with the following gain:
##EQU20##
For the other eight points, compu | | |
