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FIELD OF THE INVENTION
The present invention relates generally to the transmission of data and, in
particular, to the transmission of data over voice-band telephone channels
using modems.
BACKGROUND OF THE INVENTION
Present telephone networks are evolving toward the almost exclusive use of
digital carrier systems. At the heart of such systems are non-linear
analog-to-digital (A/D) converters which encode analog voice and modem
signals for digital transmission. A common D4 channel bank, for example,
uses 64 kilo-bit per second (KBPS) pulse code modulation (PCM). Similarly,
many systems designed for voice transmission use 32 KBPS adaptive
differential PCM, or ADPCM.
It is desirable to be able to use the full capacity of a channel in
transmitting data over the voice-band telephone network using analog
modems. Non-linearities in such systems, however, serve as a limit on the
maximum bit rate that analog modems can obtain while still maintaining a
commercially acceptable error rate. This limitation is primarily due to
the multiplicative effect that the non-linearities have on signals
transmitted through the channel, such as PCM quantization noise, and on
intermodulation distortion.
One technique and system for improving the performance of data transmission
via a transmission channel in the presence of multiplicative noise is
disclosed in U.S. Pat. No. 5,265,127, entitled "Non-linear Encoder and
Decoder For Information Transmission Through Non-linear Channels," which
is assigned to the assignee of the present invention and which is
incorporated by reference herein. FIGS. 1 and 2 are, respectively, block
diagrams of the modem transmitter and modem receiver disclosed in the
aforementioned patent. The invention disclosed in the above-referenced
patent uses a signal constellation which is arrived at by starting with a
base constellation whose signal points and whose geometry are selected in
accordance with conventional criteria. The base constellation is warped by
adjusting the positions of its signal points according to a warp function
which models the inverse of a non-linear characteristic of the
transmission channel and which is known a priori. The warped signal points
are then transmitted to a receiver where the inverse of the warp function
is applied to the received signal points prior to processing them in a
Viterbi decoder. As a result, the amount of distortion to the transmitted
signal points due to the non-linear characteristic of the channel is
reduced, and, in particular, the amount of distortion for points near the
perimeter of the signal constellation is reduced. The Viterbi decoder can
then use the standard, unmodified Viterbi decoding algorithm. One
embodiment of the non-linear encoder has been incorporated into the V.34
modem standard and the V.32 Terbo standard.
The warp function typically depends upon the magnitude of the transmitted
signal. Another independent factor in the warp function is a warp factor g
which is selected as a function of the degree to which it is desired to
warp or compress the overall base constellation prior to transmission. The
desired degree of warping depends, in turn, upon the non-linear component
of the transmission channel. A particular value of the warp factor g
depends upon the application and may be pre-set in the transmitter and
receiver based upon the expected characteristics of the channel. It is
desirable, however, to be able to adapt the warp factor g to account for
changes in the non-linear characteristics of the channel that may occur
over time.
SUMMARY OF THE INVENTION
The present invention discloses a data recovery apparatus for recovering
data from a sequence of warped signal points received from a transmitter
via a non-linear transmission channel, where each of the warped signal
points is related to a respective signal point of a predetermined base
constellation in accordance with a warp function having a warp factor as
an independent variable. The apparatus comprises components for unwarping
each of the received signal points using substantially an inverse of the
warp function. It further comprises components for computing the ratio of
the average dispersion of unwarped signal points related to outer signal
points of the constellation and the average dispersion of unwarped signal
points to related inner signal points of the constellation. The apparatus
also has components for updating the value of the warp factor used by the
unwarping components according to the ratio computed by the computing
components. In addition, the apparatus comprises components for
communicating the updated value of the warp factor to the transmitter.
Other features and advantages of the present invention will be readily
apparent by reference to the following detailed description and
accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of a known modem transmitter.
FIG. 2 is a block diagram of known modem receiver.
FIG. 3 is a flow diagram showing the basic steps according to one
embodiment of the method of the present invention.
FIG. 4 is a block diagram of a system embodying the principles of the
present invention.
DETAILED DESCRIPTION OF THE PRESENT INVENTION
FIG. 3 is a flow diagram showing the basic steps in the method of the
present invention. As shown in step 100, a sequence of warped signal
points is transmitted via a transmission channel having a non-linear
component. The warped signal points may be generated by an encoder in a
transmitter modem, where each of the warped signal points is related to a
respective signal point of a predetermined base constellation according to
a warp function, as described more fully in U.S. Pat. No. 5,265,127
referred to above. For example, the in-phase and quadrature-phase values
of each signal point may be multiplied by a warp multiplier w generated in
accordance with the selected warp function.
The warp function is selected to model the inverse of the non-linear
component of the transmission channel. For example, in the case of a PCM
system, the non-linear component is typically the .mu.-law characteristic,
a logarithmic function of the magnitude of the signal being transmitted.
An inverse logarithmic function, or an exponential function, of the
magnitude of the transmitted signal would, therefore, be used to warp the
constellation. A series approximation to the exponential inverse of the
u-law characteristic conveniently may be used as the warp function. Thus,
for a PCM system, the warp multiplier w would be generated in accordance
with the warp function
w=1+(8192P.sub.t +2731P.sub.t.sup.2 +683P.sub.t.sup.3 +173P.sub.t.sup.4
+23P.sub.t.sup.5 +3P.sub.t.sup.6)/16384,
where P.sub.t =p.sub.t /g, p.sub.t is the magnitude of the signal, and g is
the warp factor. It should be understood, however, that in its broadest
aspects the present invention is not limited to any particular warp
function, and the above warp function is intended to be merely exemplary.
Next, as shown in step 105, the sequence of warped signal points is
received by a receiver. Once the sequence of warped signal points is
received, each signal point is unwarped as shown in step 110. The step of
unwarping is performed by applying substantially an inverse of the warp
function to each received signal point in a known fashion. Next, as shown
in step 120, the dispersion of the received signal points about a sequence
of expected signal points is calculated for the unwarped inner and outer
points of the constellation, respectively. The sequence of expected signal
points represents an approximation to the ideal signal points that would
be received if there were no distortion caused by the channel. Once the
dispersion is calculated for the inner and outer signal points, the
difference in the amount of dispersion or distortion that occurs for the
outer and inner signal points is calculated as shown in step 130. Next, as
shown in step 140, the value of the warp factor g is adapted according to
the amount of dispersion to minimize the effects of the channel
non-linearity upon the dispersion. The adapted value of the warp factor is
communicated to the encoder, as shown in step 150. Finally, as shown in
step 160, the transmitter and receiver are adjusted to use the adapted
value of the warp factor for warping and unwarping, respectively, a
subsequent sequence of signal points.
FIG. 4 is a block diagram of a system 200 embodying the principles of the
present invention. A transmitted line signal including warped signal
points is received in a modem receiver 202 from a channel 201 having a
non-linear component. In conventional fashion, the received line signal is
applied sequentially to a receiver filter 203 and a demodulator/equalizer
205. The output of the demodulator 205 represents a best estimate of the
in-phase and quadrature-phase components of the transmitted signal points.
The in-phase and quadrature-phase components are preferably unwarped in the
manner described in U.S. Pat. No. 5,265,127 referred to above by
multiplying them by an unwarp multiplier W in a multiplier 215. The unwarp
multiplier W is generated by a non-linear decoder 210, which provides the
multiplier W on lead 212 to the multiplier 215. As more fully described in
the above-mentioned patent, the non-linear decoder generates the unwarp
multiplier W according to substantially the inverse of the warp function
which depends upon the magnitude of the received signal as well as the
value of the warp factor g. The magnitude of the received signal may be
calculated in the decoder 210 based upon the values of the in-phase and
quadrature-phase components received from the demodulator 205 via lead
207. The value of the warp factor g may be received by the non-linear
decoder 210 via lead 262 as will be described more fully below.
The unwarped in-phase and quadrature-phase values from the output of the
multiplier 215 are applied to a slicer 220 via lead 217. The slicer 220
determines for each unwarped signal point the in-phase and
quadrature-phase values of an expected or ideal signal point that would be
received if there were no distortion caused by the channel. One output of
the slicer 220 may be sent via lead 221 to a Viterbi decoder for further
processing and decoding. The components of FIG. 4 described above are more
fully described in U.S. Pat. No. 5,265,127 referenced above.
The technique of the present invention assumes that, in an ideal situation,
there would be approximately no difference in the amount of dispersion or
distortion between signal points at the center and the perimeter of the
constellation. According to the principles of the present invention, the
unwarped in-phase and quadrature-phase values from the output of the
multiplier 215 are also sent to one input of a comparator 225 via lead
218. A second input of the comparator 225 receives the ideal in-phase and
quadrature-phase values from the slicer 220 via lead 222. The comparator
225 calculates a quantity which represents the distance between the signal
point corresponding to the unwarped in-phase and quadrature-phase values
received on lead 218 and the expected signal point corresponding to the
values received on lead 222. The quantity calculated by the comparator 225
may be represented, for example, in the form of a voltage signal, which
corresponds to an error signal or distortion that results from the
non-linear characteristic of the channel.
In a preferred embodiment, the normalized radial component of the
dispersion or distortion is calculated. The real part of the ideal signal
point on lead 222 is multiplied by the real part of the output of the
comparator 225, and the imaginary part of the ideal signal point on lead
222 is multiplied by the imaginary part of the output of the comparator
225. The two products are then added together, and the sum of the products
is divided by the magnitude of the signal on lead 222. A processor 226,
which receives as inputs the ideal signal point on lead 222 and the output
of the comparator 225, may be used for performing these multiplying,
adding and dividing functions.
The output of the comparator 225 or, in the preferred embodiment, the
normalized radial component from the processor 226, is sent to a switch
227. If the signal point is represented by an outer point on the perimeter
of the constellation, the switch 227 sends the output of the comparator
225 to an outer point integrator 230 via lead 228. Similarly, if the
signal point is represented by an inner point at the center of the
constellation, then the switch 227 sends the output of the comparator 225
to an inner point integrator 231 via lead 229. In one embodiment, the
switch 227 may distinguish between inner and outer points, for example,
according to the power of the signal on lead 222, because signals
represented by inner points are transmitted at a relatively low power,
whereas signals represented by outer points are transmitted at a
relatively high power. If the V.34 modem standard is used, then the ring
index M.sub.i,j,k, known from the shaping by rings technique, may be used
to distinguish between inner and outer points. The shaping by rings
technique is described more fully in U.S. Pat. No. 5,115,453, assigned to
the assignee of the present invention and incorporated by reference
herein. In the embodiment utilizing the V.34 standard, the ring index
would be taken from lead 221. Inner points would be represented by a ring
index having the lowest values, and outer points would be represented by a
ring index having the highest values.
The integrators 230 and 231 calculate the logarithmic value of the average
power of the signal errors of the outer and inner signal points,
respectively, accumulated over a statistically significant period of time.
The period over which the signal points are accumulated depends, in part,
on the size of the constellation. For voice band-width applications,
however, this period typically may range from several seconds to several
minutes. Other applications may require shorter or longer periods. The
integrators 230 and 231 thus calculate an average dispersion about the
sequence of expected signal points for two sets of unwarped signal points
corresponding, respectively, to outer and inner signal points of the
constellation.
The values calculated by the integrators 230 and 231 serve as inputs to
another comparator 235 which computes the difference between the values
calculated by the integrators 230 and 231 by subtracting the value
calculated by the integrator 231 from the value calculated by the
integrator 230. The value computed by the comparator 235 thus represents,
on a logarithmic scale, the ratio of the average power of the outer point
signal errors to the average power of the inner point signal errors.
Furthermore, this ratio provides an indication of whether the present
amount of warping or compression is appropriate, too small, or excessive.
If, for example, the amount of compression currently being used were
ideal, then the ratio obtained at the output of the comparator 235 would
be equal to zero. It should be noted, however, that in cases using Trellis
coding, the ideal value may be slightly negative. The negative value
results because there are more signal constellation points on the
perimeter of a circular constellation than in the center of the
constellation.
The value computed by the comparator 235 is sent to a first conversion
table 240, which may be, for example, a read-only or read-write memory
unit. In the presently preferred embodiment, the first conversion table
240 converts each value provided to it by the comparator 235 to an integer
value based upon a linear or an approximately linear scale by quantizing
the output of the comparator 235. Integer values ranging, for example,
from -15 to +15 may be conveniently used, although other ranges of integer
values may also be employed. Each integer value, therefore, corresponds to
a particular range of values for the logarithmic ratio of the outer to
inner signal error power. Conveniently, a value of zero at the output of
the comparator 235 may, for example, be converted to the integer zero,
representing no change in the amount of warping or compression desired.
Use of the conversion table 240 serves to limit the number of discrete
warp values, resulting in less data that must be sent to a remote
transmitter 300 which encoded and transmitted the signals received by the
receiver 202 via the channel 201.
The integer value obtained from the first conversion table is then sent,
via lead 241, to an adder 245 which adds this integer value to an integer
value stored in a memory unit 250. The integer value stored in the memory
unit 250 may be received by the adder 245 via lead 255 and corresponds to
the warp factor g that is currently being used by the transmitter 300 and
receiver 202, as will be further explained below. The sum obtained from
the adder 245 corresponds to a warp factor g that represents the total
amount of warping or compression that would result in approximately no
dispersion between the outer and inner signal points after transmission by
the transmitter 300 and unwarping by the decoder 202. The adder 245, as
well as the comparators 225 and 235, may be implemented, for example,
using commercially available AT&T DSP-16A signal processors. This device
can also perform the functions performed by the multiplier 215 and the
component 226. The aforementioned processor also has conditional branches
and memory pointer registers to implement switching functions, such the
switching function performed by the switch 227.
In the preferred embodiment of the present invention as shown in FIG. 2, a
new or updated warp factor g that corresponds to the sum obtained from the
adder 245 is not automatically used. Rather a determination is made
whether a change in the value of the warp factor g is warranted. The
integer value obtained from the first conversion table 240 is thus sent
via lead 246 to a gate 247 which may also be implemented, for example, by
an AT&T DSP-16A processor. The gate 247 also receives as inputs a
predetermined threshold value (THR) and the sum obtained from the adder
245. If the integer value received from the first conversion table 240 is
greater than the threshold value (THR), then the gate 247 allows the sum
obtained from the adder 245 to pass to the memory unit 250 where it is
stored and where it replaces the previously stored value. The threshold
value (THR) may be selected to represent a significant change in
throughput and to minimize unnecessary changes to the warp factor g that
would otherwise be caused by ambient variations in the integrators 230 and
231.
The integer value currently stored in the memory unit 250 is then sent via
lead 257 to a second conversion table 260 which also may be a read-only or
a read-write memory unit. The conversion table 260, which may be generated
experimentally, converts the value received from the memory unit 250 to a
corresponding warp factor g. The warp factor g obtained from the
conversion table 260 is the new or updated warp factor that is sent to the
non-linear decoder 210 via lead 262.
The new or updated warp factor g is also sent to a remote encoder 280 which
generated the warped signal points and which forms a component of the
transmitter 300. The transmitter 300 may be, for example, the modem
transmitter shown in FIG. 1 which is more fully described in U.S. Pat. No.
5,265,127, referred to above. The updated warp factor may be sent, for
example, via conventional diagnostic channel communications between the
two modems represented by line 270. The methods described in the V.32bis
or V.34 modem standards may be used to transfer this information and to
synchronize the encoder 280 and decoder 210 so that the decoder 210 uses
the same value of the warp factor g to unwarp received signal points as
the encoder 280 used to warp the same signal points. In the V.34 modem,
for example, the updated value of the warp factor may be sent in the MP
sequence in the same manner used to transfer precoder coefficients. In
accordance with the principles of the present invention, the encoder 280
is connected to a conversion table 290 that is identical to the second
conversion table 260. The conversion table 290 allows the encoder 280 to
adjust or update automatically the value of the warp factor that will be
used to warp a subsequent sequence of signal points.
It may be noted that the current V.34 standard uses a warp factor, as
defined therein, with a value of either 0.3125 or zero. According to the
principles of the present invention, the warp factor may take on a range
of values from zero to one. Values greater than one are also possible,
although a more complex encoder would be required.
Furthermore, it should be noted that certain modems, such as the AT&T
Paradyne 3400 series modems, use different outer points for different data
rates. The contents of the first look up table 240, therefore, may be
different for different data rates. It should also be noted that an
adjustment to the value of the warp factor g may result in changes to the
total average power due to the non-linearities in the channel. Preferably,
therefore, the gain of the signals is adjusted at the transmitting encoder
to compensate for such changes so as to maintain an approximately constant
average power. One such gain correction factor is described more fully in
W. Betts, "Nonlinear Encoding by Surface Expansion," Int'l Conf. on Data
Transmission, Publication No. 356 (Sep. 1992), which is incorporated
herein by reference. This publication describes a gain correction factor
for use in the transmitter when the warp function is a series
approximation to the hyperbolic sine function.
The principles of the present invention may also be used to determine
whether signal distortion is related to the distance from the
constellation center in a non-linear manner and to adjust the value of the
warp factor accordingly. In particular, a plurality of integrators,
similar to the integrators 230, 231, would be used to measure the average
dispersion for multiple sets of signal points where each set of signal
points is defined by its distance from the center of the constellation. As
before, the comparator 235 would be used to compute the difference between
the average dispersion for pairs of signal point sets. For example, the
comparator 235 would compute the difference between the average dispersion
of the inner-most points on the constellation and the average dispersion
of each other set of signal points. The values thus computed by the
comparator 235 would be sent to the conversion table 240 which would
provide an output indicative of the change in the amount of warping
desired. The contents of the table 240 may be experimentally determined so
as to discriminate between first, second, third or higher order harmonics
in the distortion and so as to provide an optimal output indicative of the
change in the amount of warping desired. It should be noted that in this
situation, the relationship between the inputs and output of the table 240
will often be non-linear. The output of the table 240 would then be used
as described above to update the value of the warp factor g whenever a
threshold value is met.
It should also be noted that although the conversion tables 240, 260 and
290 may conveniently be implemented as memory units, they may also be
implemented by other means, such as a processor which performs the
conversion according to an experimentally determined equation. Integrated
circuits may also suitably be used to perform specified functions of the
system 200. It will be appreciated, therefore, that, although the present
invention has been described with reference to specific embodiments, other
arrangements within the spirit and scope of present invention will be
readily apparent to persons of ordinary skill in the art. The present
invention is, therefore, limited only by the appended claims.
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