U.S. patent application number 12/766693 was filed with the patent office on 2010-08-19 for frequency-domain equalization of the fiber optic channel.
This patent application is currently assigned to MENARA NETWORKS, INC.. Invention is credited to Salam ELAHMADI, Siraj Nour ELAHMADI.
Application Number | 20100209115 12/766693 |
Document ID | / |
Family ID | 40295466 |
Filed Date | 2010-08-19 |
United States Patent
Application |
20100209115 |
Kind Code |
A1 |
ELAHMADI; Salam ; et
al. |
August 19, 2010 |
Frequency-Domain Equalization of the Fiber Optic Channel
Abstract
Systems and methods for frequency-domain compensation in optical
communication systems. In pre-equalization embodiments, the
transmitter transforms the data stream into a frequency domain
signal and applies a compensation filter before transforming it
back into a pre-distorted time domain signal. As the pre-distorted
time domain signal propagates through the optical channel, optical
dispersion effects counter the pre-distortion, producing an
equalized signal at the channel output. In post-equalization
embodiments, the receiver transforms the received signal into a
frequency domain signal and applies a compensation filter before
transforming it back into an equalized time domain signal.
Pre-equalization may prove less expensive due to the square-law
characteristic of photodetectors employed by most receivers.
Inventors: |
ELAHMADI; Salam; (Dallas,
TX) ; ELAHMADI; Siraj Nour; (Dallas, TX) |
Correspondence
Address: |
KRUEGER ISELIN LLP (SC)
P O BOX 1906
CYPRESS
TX
77410-1906
US
|
Assignee: |
MENARA NETWORKS, INC.
Dallas
TX
|
Family ID: |
40295466 |
Appl. No.: |
12/766693 |
Filed: |
April 23, 2010 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
11829806 |
Jul 27, 2007 |
|
|
|
12766693 |
|
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Current U.S.
Class: |
398/147 ;
398/193 |
Current CPC
Class: |
H04B 10/25137
20130101 |
Class at
Publication: |
398/147 ;
398/193 |
International
Class: |
H04B 10/12 20060101
H04B010/12 |
Claims
1. A method for countering dispersion caused by a fiber optic
medium, the method comprising: transforming a time-domain data
block into a frequency-domain data block; acting on the
frequency-domain data block with an inverse dispersion function to
create a corrected frequency-domain data block; converting the
corrected frequency-domain data block into a corrected time-domain
signal; and modulating an optical beam with the corrected
time-domain signal.
2. The method of claim 1, wherein said converting includes:
transforming the corrected frequency-domain data block into a
corrected time-domain data block; forming a serial data stream from
the corrected time-domain data block; and performing digital to
analog conversion to convert the serial data stream into the
corrected time-domain signal.
3. The method of claim 2, wherein said forming includes overlapping
each of the corrected time-domain data blocks by L-1 samples, so
that the last L-1 samples of each block is added to the first L-1
samples of a subsequent block, where L is a predetermined
integer.
4. The method of claim 1, wherein the inverse dispersion function
is expressible with a frequency dependence in the form of
exp(-j.beta..sub.2.omega..sup.2L/2), where exp( ) is the
exponential function, j is the square root of (-1), .beta..sub.2 is
a group velocity dispersion parameter, .omega. is frequency, and L
is an effective length of a fiber channel that carries said optical
beam.
5.-9. (canceled)
10. An optical modulator that comprises: a complex multiplier that
applies a compensation filter to frequency-domain data blocks to
produce compensated frequency-domain data blocks; an inverse
frequency transform module that transforms the compensated
frequency-domain data blocks into compensated time-domain data
blocks; a conversion module that forms a compensated transmit
signal from the compensated time-domain data blocks; and an
electrical-to-optical converter that produces an optical beam
modulated with the transmit signal.
11. The modulator of claim 10, further comprising: a frequency
transform module that converts time-domain data blocks into the
frequency-domain data blocks.
12. The modulator of claim 11, wherein the time-domain data blocks
are zero-padded with a predetermined number of zeros.
13. The modulator of claim 10, wherein the conversion module
overlaps compensated time-domain data blocks by a predetermined
number of samples, and serializes the summed compensated
time-domain data blocks to produce a transmit data stream, wherein
the transmit signal is the analog form of the transmit data
stream.
14. The modulator of claim 10, wherein the inverse frequency
transform module implements an inverse fast Fourier transform.
15. The modulator of claim 10, wherein the compensation filter
compensates for optical dispersion effects of the channel.
16.-19. (canceled)
Description
BACKGROUND
[0001] Optical communications systems transfer vast amounts of
information over substantial distances using optical transmissions,
typically through a fiber optic cable or similar optical medium.
Transmissions through an optical medium degrade over distance in a
different manner than electrical transmissions. Typically,
dispersion of the optical signal is a substantial limitation on the
length of the fiber optic channel before conversion to electrical
signals is required for regeneration of the communicated data
signal. Thus, for extreme distances, a series of transmitters and
receivers (or transceivers) are linked by sections of fiber optic
cable. The communications signal is converted back to electrical
signals and regenerated, e.g., amplified, in electrical form.
[0002] Optical dispersion causes pulse broadening that impairs
receiver performance, particularly when the transmitted optical
signal is detected using square-law detection. If the pulses
broaden too much, then the symbols used to encode the
communications signals "overlap," producing
intersymbol-interference.
[0003] A representation of a basic optical communications system is
shown in prior art FIG. 1A. An input signal X(t) 105 to be sent
over the optical channel is received at a transmitter 150 and
modulated onto an optical beam 155. The optical beam 155 has a
frequency domain representation X(.omega.) which is modified by
dispersion response of the channel D(.omega.) 170. At the output of
the channel, a receiver 185 receives a channel output beam 175
(having a frequency domain representation
Y(.omega.)=D(.omega.)X(.omega.)). The ideal receiver 185 converts
the output beam into a electrical receive signal 190. If the system
were unaffected by dispersion (and other noise sources), the
received signal Y(t) 190 would be recognized as the transmitted
signal X(t) 105.
[0004] The most common method to address dispersion impairments in
fiber optic transmission is the use of dispersion compensation
modules (DCM). A DCM is a specially-designed optical filter that
compensates the pulse-spreading effect, but is costly, bulky, and
lossy.
[0005] An example of how a DCM may be used is shown in the optical
communications system in prior art FIG. 1B. Somewhere along the
signal path, one or more DCMs 160 act on the optical signal
X(.omega.) 155 with a correction function C(.omega.) to create a
corrected signal X'(.omega.) 165. The channel still creates
dispersion in the optical beam as represented by dispersion block
D(.omega.) 170. The correction function C(.omega.) for the DCM 160
is chosen so that C(.omega.) cancels out as much of the channel
dispersion D(.omega.) 170 as possible. When the signal reaches the
receiver 185, the output signal Y(.omega.) 180 now has the
frequency representation given by
Y(.omega.)=D(.omega.)C(.omega.)X(.omega.). If the correction
function C(.omega.) has been chosen correctly, then the product
D(.omega.)C(.omega.) is independent of w, making Y(t) simply an
attenuated and time-shifted version of X(t). Such a compensation
function can be difficult to achieve in the optical domain.
SUMMARY
[0006] There are disclosed herein various systems, transmitters,
receivers, transceivers, and methods employing frequency-domain
equalization of the fiber optic channel. In some embodiments, an
electrical time domain signal is converted to the frequency domain,
such as by Fourier transform and then the frequency domain signal
is acted up by a correction function, such as by complex
multiplication, to form a corrected frequency domain signal. The
corrected frequency domain signal is then converted back to the
time domain before being transmitted over the optical
communications channel. In other embodiments, an optical receive
signal is converted to an electrical receive signal and transformed
into the frequency domain. A frequency domain filter is applied to
compensate for dispersion effects. Thereafter the signal may be
converted back into the time domain and demodulated.
BRIEF DESCRIPTION OF THE DRAWINGS
[0007] A better understanding of the various disclosed embodiments
can be obtained when the following detailed description is
considered in conjunction with the following drawings, in
which:
[0008] FIG. 1A is a block diagram of a prior art optical
communications system;
[0009] FIG. 1B is a block diagram of a prior art optical
communications system with a dispersion correction module;
[0010] FIG. 2 is a block diagram of an optical communications
system according to various embodiments of the present
invention;
[0011] FIG. 3 is a block diagram of a transmitter according to
various embodiments of the present invention;
[0012] FIG. 4 is a block diagram of a receiver according to various
embodiments of the present invention; and
[0013] FIG. 5 is a flowchart of a method of frequency domain
equalization according to various embodiments of the present
invention.
[0014] While the invention is susceptible to various modifications
and alternative forms, specific embodiments thereof are shown by
way of example in the drawings and will herein be described in
detail. It should be understood, however, that the drawings and
detailed description thereto are not intended to limit the
invention to the particular form disclosed, but on the contrary,
the intention is to cover all modifications, equivalents and
alternatives falling within the scope of the present invention as
defined by the appended claims.
DETAILED DESCRIPTION
[0015] As used herein, dispersion is a general term including the
group velocity dispersion, chromatic dispersion, and other similar
phenomena that creates a nonlinear, frequency-dependent phase
distortion. Described herein are various invention embodiments that
counter dispersion effects in the frequency domain. The dispersion
compensation may be implemented at the transmitter
(pre-equalization), at the receiver (post-equalization), or at a
transceiver (pre- and/or post-equalization). Embodiments of the
present invention may eliminate the need for DCMs in ultra
long-haul systems, those with reach >1000 km. This simplifies
the network architecture and results in significant cost saving.
Many embodiments of the present invention can be implemented in an
integrated circuit.
[0016] Ignoring nonlinear effects, a signal that has traveled a
distance z in an optical fiber or other optical channel is
mathematically described by equation (1), where A(0,w) is the
Fourier transform of the transmitted signal A(0,t) (for time t,
launched at z=0) and .beta..sub.2 is the group velocity dispersion
(GVD) parameter of the optical channel:
A ( z , t ) = 1 2 .pi. .intg. ~ - .infin. .infin. A ( 0 , .omega. )
exp ( 2 .beta. 2 .omega. 2 z - .omega. t ) .omega. ( 1 )
##EQU00001##
In the frequency domain, equation (1) becomes
A(z,.omega.)=A(0,.omega.)H(z,.omega.), (2)
where the fiber channel transfer function H(z,w) is
H ( z , .omega. ) = exp ( 2 .beta. 2 .omega. 2 z ) . ( 3 )
##EQU00002##
[0017] The transmitted signal can be recovered by inverse
filtering, i.e.,
A(0,.omega.)=A(z,.omega.)H.sup.-1(z,.omega.), (4)
where the inverse filter transfer function H.sup.-1(z,w) is
H - 1 ( z , .omega. ) = exp ( - 2 .beta. 2 .omega. 2 z ) . ( 5 )
##EQU00003##
Note that depending on the specific model used, the GVD parameter
.beta..sub.2 may be a constant or a function of frequency or other
variable.
[0018] Determining the GVD parameter .beta..sub.2, and thus the
filter transfer function, may be performed as is known in the art.
One method of determining the GVD parameter .beta..sub.2 would be
to transmit a training signal over the optical channel and
calculate the filter transfer function based on the received
version of the training signal. The GVD parameter .beta..sub.2 may
be determined at the physical setup of the optical channel and/or
the electrical setup of the optical channel. The GVD parameter
.beta..sub.2 may also be re-determined periodically or before a
given transmission. Because the GVD parameter is expected to change
very slowly or not at all, it should be unnecessary to make
frequent measurements or adjustments to account for changes in this
parameter.
[0019] FIG. 2 shows a generalized block diagram of an optical
communications system in accordance with some embodiments of the
present invention. The input signal X(t) 105 is received by a
frequency domain equalization module 220. In the frequency domain
equalization module 220, a frequency domain transform module, 210
accepts the input signal X(t) 105 and transforms the input signal
into the frequency domain as X(.omega.) 215. The frequency domain
transform module 210 may be implemented as a fast Fourier transform
(FFT) module, though other digital Fourier transform
implementations are know and may be used. The transform module 210
operates on complex-valued data blocks of at least length N+L-1,
where N is the block size and L is the length of the inverse or
correction filter transfer function. At the input to the transform
module 210, N real (for single phase signaling) or complex (for
in-phase and quadrature phase signaling) data symbols are padded
with at least L-1 zeros, resulting in at least an N+L-1 point
frequency domain signal X(.omega.) 215.
[0020] The frequency domain signal X(.omega.) 215 is acted upon by
a frequency domain correction filter C(.omega.) 230, resulting in
an equalized signal {tilde over (X)}(.omega.) 235. In the frequency
domain, this filtering operation consists of multiplying each
frequency coefficient by a corresponding filter coefficient. A time
domain transform module, shown here including an inverse FFT (iFFT)
module, 240 receives the equalized signal {tilde over (X)}(.omega.)
235 and transforms it to the time domain. The time domain transform
module 240 produces blocks containing at least N+L-1 complex valued
time samples. The last L-1 samples of each block overlap with the
first L-1 samples of the subsequent block. Thus, the equalization
module 220 includes an overlap-and-add unit that adds each of the
last L-1 samples of each block with a corresponding one of the
first L-1 samples of a subsequent block, thereby producing an
equalized time domain signal {tilde over (X)}(t) 245 that is
pre-corrected for the effects of dispersion during the optical
transmission. As an alternative to the overlap-and-add approach,
the frequency transform may be applied to N-sample input blocks
that overlap by L-1 samples, and the last L-1 samples from each
output block may be discarded. The resulting equalized time domain
signal 245 will be the same.
[0021] The equalized time domain signal {tilde over (X)}(t) 245 is
then sent over the optical channel by the transmitter 150.
Transmitter 150 includes a two-dimensional (I&Q) optical
modulator, sometimes called an I&Q electrical-to-optical
converter, or "I&Q E/O". Ideally, the spectrum of the optical
signal 255 matches the equalized signal {tilde over (X)}'(.omega.)
235. As the signal travels along the optical channel, it is subject
to dispersion, shown here as D(.omega.) 170. At the input of the
receiver 185, the received signal is now
Y(.omega.)=D(.omega.){tilde over (X)}'(.omega.) 280. In the time
domain, the received signal Y(t) 290 should ideally be a
time-delayed version of the input signal X(t), assuming that the
pre-equalization in the frequency domain using correction signal
C(.omega.) 230 properly corrects for the dispersion.
[0022] FIG. 3 provides additional detail regarding some transmitter
module implementations. A transmitter 300 receives the input signal
X(t) 105. In the example of FIG. 3, the input signal X(t) 105 is a
serial digital data signal. The serial input signal X(t) 105 is
parallelized by a demultiplexer 305 into N-sample blocks of digital
data (each sample may represent one or more data bits, and in some
embodiments, may be complex-valued). In other embodiments, the
input signal 105 is a parallel data signal that does not need to be
parallelized, so the demultiplexer 305 need not be present.
[0023] An N'-FFT block 310 receives the N-sample blocks of digital
data and pads each block with zeros, such as from a zero padding
unit 315, to create N'-sample blocks of digital data. The number of
padded zeros is preferably L-1 as described above. Block 310
applies an N'-point fast-Fourier transform (FFT) to each N'-bit
block producing an N'-point real part block (I) and an N'-point
imaginary part block (Q). The N'-point real part block (I) and the
N'-point imaginary part block (Q) are provided to a complex
multiplier 320 that multiplies each complex data point with a
corresponding complex-valued filter coefficient. The filter
coefficients implement a correction filter C(.omega.) 330 designed
to compensate for channel dispersion effects. The N'-point products
of the complex multiplication are output to an N'-point inverse FFT
block 340.
[0024] The N'-point inverse FFT block 340 produces an N'-sample
block of complex values, represented by in-phase output I and
quadrature phase output Q. The overlap add unit 345 receives
N'-sample blocks of data "overlaps" them by adding the last L-1
samples of each block with corresponding ones of the first L-1
samples of the next block, resulting in N-sample blocks of output
data. The overlap add unit 345 produces an N-sample in-phase output
block I and an N-sample quadrature-phase output block Q. The I and
Q output blocks are separately serialized by a multiplexer 350 to
form two serial streams.
[0025] The pre-equalized serial data streams are separately
converted from digital to analog form by the digital-to-analog
converters (DACs) 360A and 360B. The DACs 360A and 360B provide the
analog I and Q signals to a two dimensional electrical-to-optical
converter 370 that generates a pre-compensated optical signal.
[0026] The modulated light is launched into a fiber channel and
travels over an uncompensated line to a receiver. In multi-span
lines, the junction between spans may be bridged by optical
amplifiers. In some embodiments, the junction is bridged only by
optical amplifiers. Optical-to-electrical conversion is then
performed after N amplified spans. In other embodiments, the
junction between spans may be bridged by a transceiver. At the end
of each fiber span, the received light is converted into electrical
signal using a standard square-law optical-to-electrical converter
(O/E) device, such as PIN photodiode-based receiver or and
avalanche photodiode-(APD-) based receiver, which are known in the
art. In both embodiments, the output of the O/E device is applied
to a standard clock & data recovery device (CDR), which is
known in the art. The CDR output produces the recovered signal,
Y(t). Transceivers include a transmitter configured to re-modulate
the data into an optical signal that traverses the next span. Each
transmitter may include a frequency-domain pre-equalizer as
described above.
[0027] As an alternative to performing frequency domain
pre-equalization in the transmitter, frequency domain
post-equalization may be performed in the receiver. FIG. 4 shows an
illustrative receiver implemented in accordance with some
embodiments of the invention. The receiver 400 receives the
transmitted data signal 401 with a linear (or linearized) receiver,
which may be configured to operate as a coherent receiver based on
a clock signal 402 If no clock signal is available from the
transmitter, it may be reconstructed from the receive signal or
derived in the digital domain. The in-phase and quadrature
components of the electrical receive signal are digitized by
analog-to-digital converters 410B and 410A, respectively. A
demultiplexer 415 converts the digital in-phase and quadrature
signals from serial to parallel blocks.
[0028] In switching from pre-equalization to post-equalization, it
becomes desirable for the transmitter to add a "cyclic prefix" to
each block of data. A cyclic prefix is a copy of the last L-1
samples in a data block prefixed to the beginning of the data block
to create an N+L-1 sample data block, where L is the length of the
channel response. N may be chosen to be significantly larger than L
to minimize the overhead created by these prefixes. The effect of
these channel prefixes is to cause the linear convolution of the
channel response to mimic the effect of circular convolution in the
digital domain. At the receiver, the demultiplexer discards the
cyclic prefix from each data block, but the intersymbol
interference created by the presence of the cyclic prefix remains
in the N-sample blocks presented to the frequency domain transform
block 420.
[0029] A N-point fast-Fourier transform (FFT) is applied at the
N-FFT block 420 to each (complex-valued) N-sample block producing
an N-point block of complex-valued frequency domain coefficients,
as represented by a real part block (I) and an N-point imaginary
part block (Q). A complex multiplier 425 multiplies each complex
valued frequency domain coefficient by a corresponding
complex-valued filter coefficient from a correction filter
C(.omega.) 430. An inverse Fourier transform block 440 converts the
resulting products into an complex-valued N-sample data block in
the time domain. A multiplexer 450 serializes and interleaves the
in-phase (I) and quadrature-phase components to reconstruct the
transmitted data stream 495.
[0030] FIG. 5 is a flowchart of an illustrative method for
equalizing an optical channel in the frequency domain. In block
510, a transmitter converts serial digital data into a plurality of
parallel digital blocks. The incoming data may already be parallel,
in which case, the transmitter need only divide the data into the
plurality of blocks. If the incoming data is analog, then the
transmitter additionally converts the incoming analog data to
digital form using a standard encoding.
[0031] In block 520, the transmitter transforms the plurality of
parallel digital data blocks from the time domain to the frequency
domain. In block 530, the transmitter applies an inverse dispersion
filter to the frequency domain data blocks create a corrected
frequency domain signal. The inverse dispersion filter will
typically include the form given in equation (5) above. If the
inverse dispersion filter is implemented to correct for more than
linear dispersion, the form of the inverse dispersion function may
be more complex than the right side of equation (5). In various
embodiments, acting on the frequency domain data sets includes
element-by-element multiplication by the inverse dispersion
function. In some cases, the multiplication will involve both real
and/or imaginary numbers (i.e., generally speaking, complex
multiplication).
[0032] In block 540, the transmitter transforms the
frequency-domain data blocks into the time domain. In block 550,
the transmitter converts the plurality of parallel data blocks to
one or more serial data streams. In some embodiments, the serial
form is of two separate serial data streams, I and Q. In block 560,
the transmitter converts the serial data stream(s) from digital
form to analog form. Finally, in block 570, the transmitter
optionally transmits the analog signal from block 560 over the
optical channel by modulating an optical beam.
[0033] Numerous variations and modifications will become apparent
to those skilled in the art once the above disclosure is fully
appreciated. For example, the method shown in FIG. 5, when taken in
conjunction with the preceding description, is understood to also
disclose a post-equalization method used by a receiver in
accordance with some embodiments of the present invention. The
following claims are interpreted to embrace all such variations and
modifications.
* * * * *