U.S. patent application number 10/914989 was filed with the patent office on 2006-02-16 for adaptive optical equalization for chromatic and/or polarization mode dispersion compensation.
Invention is credited to Young-Kai Chen, Ut-Va Koc, Andreas Leven.
Application Number | 20060034618 10/914989 |
Document ID | / |
Family ID | 35800077 |
Filed Date | 2006-02-16 |
United States Patent
Application |
20060034618 |
Kind Code |
A1 |
Chen; Young-Kai ; et
al. |
February 16, 2006 |
Adaptive optical equalization for chromatic and/or polarization
mode dispersion compensation
Abstract
An adaptive optical parallel equalizer architecture is based on
a controllable optical modulator device to realize an optical FIR
(finite-impulse-response) filter including a plurality of
coefficient taps in order to have independent control of each
optical FIR filter coefficient. A unique adaptive opto-electronic
LMS (least mean squares) process is utilized to generate an
electronic error signal utilized to control the plurality of
parallel tap coefficients of the optical parallel equalizer. The
electronic error signal is used as the optimization criterion
because the electronic signal after photo-detection is needed to
achieve any measurable performance in terms of bit error rate
(BER). In a specific embodiment, the controllable optical parallel
FIR filter is realized by employing an optical vector modulator.
The optical vector modulator is realized by splitting a supplied
input optical signal into a plurality of parallel similar optical
signals, controllably adjusting the phase and/or amplitude of each
of the plurality of optical signals and delaying the resulting
optical signals in a prescribed manner relative to one another.
Then, the "delayed" signals are combined to yield the optical
signal comprising the vector modulated input optical signal to be
transmitted as an output. In one particular embodiment, both the
phase and amplitude is adjusted of each of the plurality of
parallel optical signals, and the error control signals for
effecting the adjustments are generated in response to the optical
modulator optical output signal utilizing the unique
Opto-Electronic LMS process.
Inventors: |
Chen; Young-Kai; (Berkeley
Heights, NJ) ; Koc; Ut-Va; (Bridgewater, NJ) ;
Leven; Andreas; (Gillette, NJ) |
Correspondence
Address: |
Thomas Stafford
4173 Rotherham Court
Palm Harbor
FL
34685
US
|
Family ID: |
35800077 |
Appl. No.: |
10/914989 |
Filed: |
August 10, 2004 |
Current U.S.
Class: |
398/198 |
Current CPC
Class: |
H04B 10/2569 20130101;
H04B 10/2513 20130101 |
Class at
Publication: |
398/198 |
International
Class: |
H04B 10/04 20060101
H04B010/04 |
Claims
1. Apparatus for use in an adaptive optical equalizer comprising: a
controllable optical modulator having an input and an output, and
being coupled to receive an incoming optical signal and configured
to generate an output optical signal by phase modulation and/or
amplitude modulation of the received optical signal, said
controllable optical modulator including a plurality of similar
optical signals in a corresponding plurality of optical paths, each
of said parallel optical paths including an opto-electronic
controller responsive to electronic control signals for effecting
said phase modulation and/or amplitude modulation of said optical
signal being transported in said optical path; and a control signal
generator responsive to an optical output signal from said output
of said controllable modulator for generating said electronic
control signals in accordance with predetermined criteria.
2. The apparatus as defined in claim 1 wherein said controllable
optical modulator comprises arrayed waveguide gratings.
3. The apparatus as defined in claim 1 wherein said control signal
generator is configured to update said adjustable control signals
at a predetermined sampling rate.
4. The apparatus as defined in claim 1 wherein said controllable
optical modulator is configured to operate as a controllable
optical finite impulse response (FIR) filter.
5. The apparatus as defined in claim 4 wherein said FIR filter
includes a plurality of parallel adjustable taps.
6. The apparatus as defined in claim 1 wherein said controllable
optical modulator is configured to operate as a controllable
optical vector modulator.
7. The apparatus as defined in claim 6 wherein said controllable
optical vector modulator includes an optical splitter having an
input and a plurality of outputs for splitting said received
optical signal into a plurality of similar optical signals which
are supplied on a one-to-one basis to said plurality of optical
vector modulator output ports, an optical combiner having a
plurality of inputs and an output and a plurality of controllable
waveguides coupling predetermined ones of said optical splitter
outputs to said optical combiner input ports, and wherein said
opto-electronic control signals are supplied to control at least
one of said plurality of controllable waveguides.
8. The apparatus as defined in claim 1 wherein said predetermined
criteria includes an opto-electronic least means square (LMS)
process.
9. The apparatus as defined in claim 8 wherein said control signal
generator includes an optical detector having prescribed
characteristics and being responsive to said received optical
signal for generating a version of said received optical signal and
apparatus utilizing said version of said received optical signal in
accordance with said opto-electronic LMS process to generate
amplitude and/or phase adjustment values for each tap of said
controllable optical modulator.
10. The apparatus as defined in claim 9 further including an
interferometer supplied with said optical input signal to and said
optical output signal from said optical vector modulator, a
differential amplifier supplied with electronic versions of outputs
from said interferometer for generating a difference signal, said
difference signal being supplied to said utilization apparatus to
be employed in said opto-electronic LMS process to generate said
amplitude and/or phase adjustment values.
11. The apparatus as defined in claim 9 wherein said optical
detector includes a photodiode for generating a current version of
said received optical, and said signal utilization apparatus
includes an amplifier for generating a voltage version of said
current signal, a slicer for generating a sliced version of said
voltage signal in accordance with a supplied adjustable threshold
level, an algebraic combiner supplied with said voltage signal and
an output from said slicer for generating an error signal and a
control signal generator responsive to said error signal for
generating said amplitude and/or phase adjustment signals in
accordance with said opto-electronic LMS process.
12. A method for use in an adaptive optical equalizer including a
controllable optical modulator comprising the steps of: adaptively
controlling said controllable optical modulator to modulate a
supplied optical signal to generate an equalized optical output
signal; converting, in accordance with predetermined first
criteria, said equalized optical output signal to an electronic
signal version; utilizing said electronic signal version to
generate, in accordance with second predetermined criteria,
amplitude and/or phase control signals; feeding back said control
signals to adaptively control said controllable optical modulator;
and employing each control signal to adjust the amplitude and/or
phase of a corresponding optical signal propagating on a
corresponding optical waveguide of a parallel array of waveguides
of said controllable optical modulator.
13. The method as defined in.claim 12 wherein said controllable
optical modulator is configured to operate as a controllable
optical finite impulse response (FIR) filter, and wherein said
parallel array of waveguides form parallel optical taps of said
controllable optical FIR filter.
14. The method as defined in claim 12 wherein said controllable
optical modulator is configured to operate as a controllable
optical vector modulator.
15. The method as defined in claim 14 wherein in operation of said
controllable optical vector modulator a supplied optical signal is
split into a plurality of similar optical signals corresponding in
number to a number of said parallel waveguides in said array, said
plurality of similar optical signals being supplied on a one-to-one
basis to said plurality of optical waveguides, in response to said
control signals adjusting the amplitude and/or phase of said
optical signals being transported in said optical waveguides,
optically combining said adjusted optical signals from said
plurality of optical waveguides to generate said equalized optical
output signal.
16. The method as defined in claim 1 wherein said second
predetermine criteria includes use of an opto-electronic least
means square (LMS) process.
17. The method as defined in claim 16 wherein said control signals
are generated by optical detecting said output optical signal from
said controllable optical modulator to generate an electronic
signal version, and processing said electronic signal version in
accordance with said opto-electronic LMS process to generate said
amplitude and/or phase control signals.
18. The method as defined in claim 17 further including the steps
of generating sum and difference optical signals of an optical
signal supplied to the input of said controllable optical modulator
and said optical output signal generated by said controllable
optical modulator, converting said sum and difference optical
signals into electronic versions, differentially amplifying said
sum and difference signal versions to generate a difference signal,
utilizing said difference signal in said opto-electronic LMS
process for generating said amplitude and/or phase adjustment
control signals.
19. The method as defined in claim 17 wherein said optical
detecting includes utilizing a photodiode to convert said output
signal from said controllable optical modulator to an electronic
signal having predetermined characteristics, converting said photo
diode output signal into a voltage electronic signal, slicing said
voltage signal in accordance with a supplied threshold level,
algebraically combining said voltage signal and a sliced version of
said voltage signal to generate an error signal and utilizing said
error signal in said opto-electronic LMS process for generating
said amplitude and/or phase adjustment control signals.
20. The method as defined in claim 12 wherein said controllable
optical modulator comprises arrayed waveguide gratings.
Description
TECHNICAL FIELD
[0001] This invention relates to optical transmission systems and,
more particularly, to optical equalization.
BACKGROUND OF THE INVENTION
[0002] Intersymbol interference (ISI) is a problem commonly
encountered in high-speed fiber-optic communication systems. This
ISI problem can introduce bit errors and thus degrade the system
performance and reliability. It is typically caused by two major
impairment sources: chromatic dispersion (sometimes called group
velocity dispersion or GVD) and polarization mode dispersion (PMD).
Another source of transmission impairments is optical noise.
[0003] In a fiber-optic link, a number of optical amplifiers are
employed to strengthen the optical signal, but at the same time add
in incoherent amplified spontaneous emission (ASE) noise (commonly
called optical noise).
[0004] Because of the frequency-dependent propagation constant in
optical fibers, different spectral components of a pulse travel at
slightly different velocities, resulting in pulse broadening in the
optical domain. Two parameters are commonly used to characterize
first-order and second-order chromatic dispersion (GVD) of a fiber:
a dispersion parameter, in ps/km/nm, and a dispersion slope
parameter, in ps/km/nm.sup.2. GVD of any order is linear in the
optical domain but becomes nonlinear after square-law
photo-detection. Usually chromatic dispersion is static and can be
effectively compensated by a dispersion compensation module (DCM)
comprised of specialty fibers and other passive components.
However, a DCM is usually expensive and may add unwanted latency in
the optical link that causes a drop in the network quality of
service (QoS). It is also possible that residual chromatic
dispersion remains even after employing a DCM in the optical ink,
and is desirably compensated for by an equalizer. Therefore, for
the purpose of evaluating the performance of an adaptive equalizer,
the first-order chromatic dispersion is specified in terms of ps/nm
without explicitly specifying the fiber type and transmission
distance.
[0005] Polarization mode dispersion (PMD) is caused by different
travelling speeds of two orthogonal polarization modes due to fiber
birefringence. Fiber birefringence originates from non-circularity
of the fiber core and can also be induced by stress, bending,
vibration, and so on. Thus, PMD is dynamic in nature and drifts
slowly over time. PMD can be modeled as dispersion along randomly
concatenated birefringent fiber segments through mode coupling
between neighboring sections. Differential group delay (DGD) is the
parameter used to characterize the PMD-induced pulse broadening and
follows a Maxwellian distribution. As a result of this variability,
the PMD of a fiber is usually characterized by the mean DGD
parameter in terms of ps/sqrt(km). In addition, PMD is
frequency-dependent. First-order PMD is the frequency-independent
component of this frequency-dependent PMD. Second-order (or
higher-order) PMD is frequency-dependent and has an effect similar
to chromatic dispersion on pulse broadening.
[0006] To evaluate the performance of an equalizer, the
instantaneous DGD is used instead to describe the delay between the
fast and slow orthogonal polarization modes (in particular, the
principal states of polarization or PSPs of a fiber). In the
worst-case scenario, the input power is split equally between these
two orthogonal polarization modes, i.e., the power-splitting
ratio=0.5. The performance against the first-order instantaneous
DGD (frequency-independent dispersion component) in ps is essential
in evaluating the effectiveness of a dispersion compensator. Since
these two polarization modes are orthogonal to each other, the
photo-current I(t) at the photo-detector is proportional to the
summation of the optical power in each polarization. Thus,
first-order PMD creates linear ISI at the output of the
photo-detector.
[0007] Optical equalizers have been used in attempts at
compensating for these impairments. The most common form of these
equalizers is a cascaded structure, which tends to have less
flexibility in control of filter parameters.
[0008] In controlling these optical equalizers, usually
non-adaptive equalization approaches-are used, but it has been
shown that adaptive control algorithms provide good performance
improvement. One such adaptive scheme is to monitor the frequency
component(s) of the electronic signal. Other adaptive approaches
involve nonlinear least squares optimization of criteria such as
minimum mean-square-error (MSE), minimization of ISI, or
maximization of eye openings. This requires the use of the modified
Gauss-Newton or Levenberg-Marquardt methods, which are iterative
and incapable of tracking fast change of channel condition.
SUMMARY OF THE INVENTION
[0009] These and other problems and limitations of prior known
optical equalization arrangements are overcome in applicants'
unique invention by employing a parallel adaptive equalizer
architecture based on a controllable optical modulator device to
realize an optical FIR (finite-impulse-response) filter including a
plurality of parallel coefficient taps in order to have independent
control of each optical filter coefficient.
[0010] Additionally, a unique adaptive opto-electronic LMS (least
mean squares) process is utilized to generate an electronic error
signal utilized to control the plurality of parallel tap
coefficients of the parallel optical equalizer. The electronic
error signal is used as the optimization criterion to generate
control signals to adapt the adaptive optical equalizer because the
electronic signal after photo-detection is needed to achieve any
measurable performance in terms of bit error rate (BER).
[0011] In a specific embodiment of the invention, the controllable
optical parallel FIR filter is realized by employing an optical
vector modulator. The optical vector modulator is realized by
splitting a supplied input optical signal into a plurality of
similar parallel optical signals, controllably adjusting the phase
and/amplitude of each of the plurality of optical signals and
delaying the resulting optical signals in a prescribed manner
relative to one another. Then, the "delayed" signals are combined
to yield the signal comprising the vector modulated input optical
signal to be transmitted as an output. Wherein a signal can be
"delayed" by a zero (0) delay interval.
[0012] In one particular embodiment, both the phase and amplitude
is adjusted of each of the plurality of parallel optical signals,
and the error control signals for effecting the adjustments are
generated in response to the optical modulator output signal
utilizing the unique Opto-Electronic LMS process.
BRIEF DESCRIPTION OF THE DRAWING
[0013] FIG. 1 shows, in simplified block diagram form, one
embodiment of the invention;
[0014] FIG. 2 shows, in simplified block diagram form, details of a
controllable optical modulator that may be employed in the practice
of the invention of the invention; and
[0015] FIG. 3 illustrates, in simplified block diagram form,
details of another embodiment of the invention.
DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION
[0016] FIG. 1 shows, in simplified block diagram form, one
embodiment of the invention. Specifically, shown is optical light
input terminal to which an optical input signal from an optical
channel is supplied. Exemplary optical carrier signals to be
processed have optical frequencies of about 2.3.times.10.sup.14
Hertz to about 1.8.times.10.sup.14 Hertz, i.e., a wavelength of
about 1.3 microns to about 1.7 microns. In one example, an optical
carrier signal having a wavelengti of approximately 1.55 micronns,
i.e., a frequency of 1.93.times.10.sup.14 Hertz is supplied via
input terminal 101 to controllable optical modulator 102. Also
supplied to controllable optical modulator 102, via circuit path
112, is error signal e(k), which is used to phase and/or amplitude
modulated, i.e., vector modulate the supplied optical signal from
input terminal 101 to generate the desire transport signal at
output terminal 103. As indicated above, controllable optical
modulator 102 is essentially a controllable optical FIR filter. One
embodiment of an optical FIR filter that may be advantageously
employed as controllable optical modulator 102 in the embodiment of
the invention of FIG. 1 is shown in FIG. 2 and described below. As
indicated above, other embodiments for optical modulator 102 may
also be equally employed in practicing the invention. One such
embodiment is an array of optical waveguide gratings.
[0017] For a received optical signal E(t) supplied to controllable
modulator 102 via input terminal 101 the output optical signal
E.sub.o (t) from controllable modulator 102 at output terminal 103
is E O .function. ( t ) = i = 1 n .times. .alpha. i .times. e j
.times. .times. .theta. i .times. E .function. ( t - .tau. i ) = i
= 1 n .times. c i .times. E .function. ( t - .tau. i ) , ( 1 )
##EQU1## where n is the number of taps for the optical equalizer,
.alpha..sub.i is amplitude parameter, .theta..sub.i and
c.sub.i=.alpha..sub.ie.sup.j.sup..theta., is the i.sup.th filter
coefficient. In one embodiment, for a tap delay of 1/f.sub.s,
.tau..sub.i=(i-1)/f.sub.s for i=1, . . . , n. The optical output
signal E.sub.o(t) from controllable modulator 102 is transported to
an optical receiver and therein to photodiode 104. As is well
known, photodiode 104 is a square-law detector and generates a
current |q(k)|.sup.2 in response to detection of E.sub.o(t).
Transimpedance amplifier 105 converts the current from photodiode
104 to a voltage signal, in well known fashion. The electronic
voltage signal from transimpedance amplifier 105 is supplied to
slicer unit 106 and to a negative input of algebraic combiner,
i.e., algebraic adder 108. An automatic threshold control signal is
also supplied to slicer unit 106. The threshold control is such as
to slice the voltage signal from transimpedance amplifier 105 in
such a manner to realize a desired output level from slicer 106.
The output from slicer 106 is the desired compensated received data
signal {circumflex over (d)} (k) and is supplied as an output from
the receiver and to a positive input to algebraic adder 108. The
error signal output from alegbraic combiner 108 is supplied to WUD
({overscore (.alpha.)}, {overscore (.theta.)}) unit 109, where the
electronic control signal amplitude ({overscore (.alpha.)}) and
phase ({overscore (.theta.)}) values are generated, in accordance
with an aspect of the invention, utilizing the unique
opto-electronic LMS process. The amplitude ({overscore (.alpha.)})
values and phase ({overscore (.theta.)}) values are supplied via
circuit path 110 to adjust the tap coefficients in controllable
modulator 102. Note that although a single circuit path 110 is
shown, it will be understood that as many circuit paths are
included equal to the number of controllable taps or legs included
in controllable optical modulator 102. In this example, there may
be N such circuit paths. Again, the values of ({overscore
(.alpha.)}) and ({overscore (.theta.)}), in this embodiment of the
invention, are generated in accordance with the unique
opto-electronic LMS process. It is further noted that when only the
amplitude of the received optical signal is modulated only the
amplitude adjustment values ({overscore (.alpha.)}) are supplied
from unit 109 to controllable optical modulator 102. Similarly,
when only the phase of the received optical signal is being
modulated only the phase adjustment values ({overscore (.theta.)})
are supplied from unit 109 to controllable optical modulator 102.
Finally, when both the amplitude and phase of the received optical
signal are being modulated both the amplitude adjustment values
({overscore (.alpha.)}) and the phase adjustment values ({overscore
(.theta.)}) are supplied from unit 109 to controllable optical
modulator 102.
[0018] Not shown in the above embodiment is the typical clock data
recovery circuitry (CDR). Just before the CDR, an uncompensated
detected signal may contain a certain amount of ISI induced by
optical impairments along the optical path, such as GVD and PMD. To
remove the ISI present in the electronic signal before recovering
the bit stream, a coefficient-updating process is employed, in
accordance with the invention, to control controllable optical
modulator 102. Operating in the optical domain, this process,
however, minimizes the electronic error between the compensated
signal and the desired signal in the mean square sense in a similar
fashion to the least-mean-square (LMS) algorithm for pure
electronic equalization.
[0019] Thus, the ISI elimination process in this invention utilizes
a unique opto-electronic LMS process.
[0020] FIG. 2 shows, in simplified block diagram form, details of
one optical vector modulator that may be utilized as controllable
optical modulator 102 employed in FIG. 1 in the embodiment of the
invention. The optical vector modulator 102 is based on the summing
of multiple optical tapped delay lines. The principle of operation
is as follows: The to be phase-shifted and/or to be
amplitude-modulated input optical signal E(t) is an optical
carrier. Input optical signal E(t) is supplied to optical vector
modulator 102 via input terminal 101 where it is split via input
multimode interference (MMI) coupler 201 into a plurality of
similar branches. Input MMI 102 is essentially a power splitter.
Each of the plurality of branches is equipped with an amplitude
and/or phase modulator 202-1 through 202-N to adjust the amplitude
and/or phase of the input optical carrier E(t). In this example,
not to be construed as limiting the scope of the invention, both
the amplitude and phase is adjusted in each branch of the optical
vector modulator. Each of the amplitude and phase modulators 202-1
through 202-N is followed by an optical delay line, namely, delay
units 203-1 through 203-N, respectively. The delays in each of the
modulator branches including phase modulators 202-1 through 202-N
are generated by delay units 203-1 through 203-N respectively. Each
of these delay lines in delay units 203-1 through 203-N changes the
phase of the sub-carrier of the optical signal from amplitude and
phase modulators 201-1 through 201-N, respectively, by a fixed
amount. For example, the delay line in unit 203-1 provides a delay
of .tau., delay unit 203-2 provides a delay of 2 .tau. and delay
unit 203-N provides a delay of N .tau.. Typically, a delay .tau. of
1/(N* carrier frequency) is required. In an embodiment in, which
delay unit 203-1 supplies a zero (0) delay interval, delay unit
203-2 supplies a delay of .tau. and so on until delay unit 203-N
supplies a delay of .tau.(N-1). Thus, if the carrier frequency is
40 GHz, the delay range should be 0, . . . , 25 picoseconds (ps).
Delay .tau. can be equal to one (1) bit period, i.e., T=25 ps for
the instance of 40 Gbps. Therefore, the delay range is 0, . . . ,
.tau.(N-1). Alternatively, delay .tau. can be a fraction of a bit
period, for example, T/2=12.5 ps. for 40 Gbps. Thus, for the
example that .tau.=/2=12.5 ps., the delay range is 0, . . . ,
(N-1)* 12.5 ps. Another MMI 204 coupler, which is for example a
power combiner, combines all of the amplitude and phase adjusted,
and delayed optical signals from all branches to produce a
modulated output optical signal at output 106, which will interfere
constructively or destructively depending on the summing optical
phases from all tributary branches. Therefore, by interfering
signals with different carrier phase, the phase and the amplitude
of the carrier of the summing signal can be set to an arbitrary
state. These interfered optical carriers will produce microwave
phasors with prescribed amplitude and phase at the remote optical
detector, namely, photodiode 104 of FIGS. 1 and 3.
[0021] The amplitude and phase modulator 202 of each branch can be
fabricated, for example, in a material system with linear
electro-optic effect, as InP, GaAs or LiNbO.sub.3. The effective
refractive index of an optical waveguide changes in proportion to
the applied electrical field perpendicular to this waveguide. A
high frequency distributed electrical waveguide is engineered to
co-propagate with the optical wave with matched propagating
velocity to deliver the local electrical field with high modulation
bandwidth. The different branches will delay the optical signal by
a different length of time. This results in different sub-carrier
phases at the outputs of these delay lines in units 203. In the
combiner 204, these different output signals that interfere
constructively have a different carrier phase due to the different
time delays these signals experienced. The carrier of the signal
after the MMI coupler, i.e., power combiner 204, is the sum of all
carriers of the signals that interfere constructively.
[0022] FIG. 3 shows, in simplified form, details of another
embodiment of the invention. The embodiment of the invention
illustrated in FIG. 3 is similar to that shown in FIG. 1 except it
specifically employed the optical vector modulator shown in FIG. 2
for controllable optical modulator 102 of FIG. 1., and that it
employs interferometer 113 (FIG. 3) for generating a signal
employed in the opto-electronic LMS process. Thus, elements similar
to those shown in FIG. 1 have been similarly numbered and will not
be described again in detail.
[0023] In the embodiment of FIG. 3 an optical interferometer 113 is
supplied via optical path 111 with the optical signal supplied via
input 101 to optical vector modulator 102, and via optical path 112
with the output optical signal at output 103 of optical vector
modulator 102. As is well known, optical interferometer 113 in
response to the supplied optical signals develops optical output
signals, which are representative of the sum and difference of the
supplied optical signals from controllable optical modulator 102.
These sum and difference signals are supplied to photodiodes 114
and 115. Photodiodes 114 and 115 generate electronic signals which
are supplied to differential amplifier 116, which generates a
correlated signal of the optical vector modulator 102, i.e., the
optical FIR filter, input signal and output q*(k)r(k+i) signal, as
described below in relation to Equation (5) which is supplied to
WUD ({overscore (.alpha.)}, {overscore (.theta.)}) unit 109. The
"*" denotes the complex conjugate.
[0024] Operation of this embodiment of the invention, is described
for an incoming optical signal E(t) of a single polarization is
sampled at a sampling rate f.sub.s=1T.sub.s equal to or being a
multiple of the bit rate f.sub.b. When f.sub.s=f.sub.b,
controllable optical modulator 102 (which is essentially a FIR
filter having a plurality of parallel legs) is synchronous (SYN).
On the other hand, when f.sub.s is a multiple of the bit rate
f.sub.b, controllable optical modulator 102 is said to be
fractionally spaced (FS). Denote the sampled data vector as {right
arrow over (r)}(k)=[r(k+L) . . . r(k-L)].sup.T, where
r(k)=E(kT.sub.s) and the superscript T denote a transpose function.
The controllable optical modulator 102 coefficient vector of a
length N=2L+1 is denoted as {right arrow over (c)}(k)=[c.sub.-L(k),
. . . , c.sub.i(k), . .. ,C.sub.L(k)].sup.T, where the coefficient
indices are rearranged to i=-L, . . . ,L to center the middle tap
of controllable optical modulator 102 for the sake of "easy"
mathematical manipulation. It should be noted that {right arrow
over (c)}(k) is complex in general. The output of controllable
optical modulator 102 is then q(k){right arrow over (=)}{right
arrow over (c)}.sup.H(k){right arrow over
(r)}.sup.H(k)=.SIGMA..sub.i=-L.sup.Lc.sub.i*(k)r(k-i). Here the
superscript H implies conjugate transpose and H=T* implies complex
conjugate transpose Then, photodetector 104 (FIG. 1, FIG. 3)
converts the optical output signal q(k) from controllable optical
modulator 102 to an electronic signal, namely,
|q(k)|.sup.2=q(k)q*(k)={right arrow over (c)}.sub.H(k)R(k){right
arrow over (c)}.sup.H(k), where R(k)={right arrow over
(r)}(k){right arrow over (r)}.sup.H(k). It can be shown that R(k)
is a Hermitian matrix and, therefore, can be diagonalized by a
unitary matrix.
[0025] Error signal e(k) is generated in conjunction with the
output from TIA 105 |q(k)|.sup.2 and the output from slicer 106
{circumflex over (d)}(k) being supplied to the negative and
positive inputs, respectively, of algebraic combiner, i.e., adder,
108 (FIG. 1, FIG. 3), namely, e(k)={circumflex over
(d)}(k)-|q(k)|.sup.2. It is noted that {circumflex over (d)}(k) is
generated during normal operation of the invention and is the
desired output. It is further noted that although not specifically
shown here, it is well known that a training sequence can be
employed to train controllable optical modulator 102 of FIG. 1 and
optical vector modulator 102 of FIG. 3 or any other arrangement
that may be employed to realize the desired FIR filter
function.
[0026] The unique opto-electronic LMS process tends to minimize
deterministically the cost function defined here as
J(k)=|e(k)|.sup.2. Therefore, taking a step in the negative
gradient direction for minimizing the cost function, the
opto-electronic LMS process determines the optimized {right arrow
over (c)} recursively as follows: c .fwdarw. .function. ( k + 1 ) =
c .fwdarw. .function. ( k ) - .beta. 4 .times. .gradient. c .times.
{ | e .function. ( k ) | } , ( 2 ) ##EQU2## where .beta. is a
preset step size and .gradient.c{[e(k)].sup.2} is the gradient of
the cost function. In this example,
.gradient.c{[e(k)].sup.2}=2e(k).gradient.c{e(k)}=-2e(k).gradient-
.c{{right arrow over (c)}.sup.H(k)R(k){right arrow over (c)}(k)}.
Since it can be shown that .gradient.c{{right arrow over
(c)}.sup.H(k)R(k){right arrow over (c)}(k)}=2R(k){right arrow over
(c)}(k), the opto-electronic LMS process updates the FIR
coefficients in the manner that follows: c .fwdarw. .function. ( k
+ 1 ) = c .fwdarw. .function. ( k ) + .beta. .times. .times. e
.function. ( k ) .times. R .function. ( k ) .times. c .fwdarw.
.function. ( k ) = c .fwdarw. .function. ( k ) + .beta. .times.
.times. e .function. ( k ) .times. q * .function. ( k ) .times. r
.fwdarw. .function. ( k ) . ( 3 ) ( 4 ) ##EQU3## Thus, the i.sup.th
FIR filter coefficient is updated as follows:
c.sub.i(k+1)=c.sub.i(k)+.beta.e(k)q*(k)r(k+i). (5) The additional
product term q* (k) results directly from the square-law detection
via photodetector 104 converting the optical signal output from
controllable modulator (optical vector modulator) 102 to an
electronic signal. In other words, the inner product q*(k)r(k-i)
between the un-equalized and equalized signals is used for the
adjustment of the coefficients of controllable optical modulator
102. Alternatively, in equation (3), the sole information required
for optical equalization is the optical input correlation matrix R,
since the FIR filter coefficients {right arrow over (c)} are
already known. To obtain the correlated signal of q(k) and r(k-i),
interferometer 113 (FIG. 3) is employed. To this end, the optical
input signal E(t) to and the optical output signal E.sub.0(t) from
controllable optical modulator 102 (optical vector modulator
(FIG.3)) are supplied to first and second inputs, respectively, of
optical interferometer 1 13. In known fashion, optical
interferometer 113 generates optical signals at its outputs, which
are representative of the sum and difference of the supplied
optical signals from optical vector modulator 102. These optical
sum and difference signals are supplied to photodiodes 114 and 115,
respectively. Photodetectors 114 and 115, which are photodiodes,
convert the optical output from optical interferometer 113 to
electronic signals. These electronic signals are supplied to
differential amplifier 116 that generates a difference signal,
which is supplied to WUD({overscore (.alpha.)},{overscore
(.theta.)}) 109 for use in generating the amplitude and phase
control signals {overscore (.alpha.)},{overscore (.theta.)},
respectively, for each leg, i.e., tap, of optical vector modulator
102.
[0027] The above discussion assumes a polarized incoming optical
signal E(t) and, thus, leads to a single-polarization
opto-electronic LMS process, which can effectively mitigate
GVD-induced ISI. However, for the instance of first-order PMD, two
orthogonal polarizations and involved, namely, E.sub.V(t) and
E.sub.H(t) representing the optical signals of vertical and
horizontal polarizations, respectively. In consideration of both
the vertical and horizontal polarizations, the electronic output
from photodiode 104 is
|q(k)|.sup.2=|q.sub.V(k)|.sub.2+|q.sub.H(k)|.sup.2, where
q.sub.V(k)={right arrow over (c)}.sup.H(k){right arrow over
(r)}.sub.V(k) and q.sub.H(k)={right arrow over (c)}.sup.H(k){right
arrow over (r)}.sub.H(k) under the assumption of the optical FIR
filter, i.e., optical vector modulator 102, of FIG. 3, being
insensitive to polarization, i.e., {right arrow over
(c)}.sub.V={right arrow over (c)}.sub.H={right arrow over (c)}.
Hence, q(k)={right arrow over
(c)}.sup.H(k)[R.sub.V(k)+R.sub.H(k)]{right arrow over (c)}(k) and
.gradient.c{[e(k)].sup.2}=2e(k).gradient.c{e(k)}=-4e(k)[R.sub.V(k)+R.sub.-
H(k)]{right arrow over (c)}(k). Thus, the opto-electronic LMS
process tap weight-date procedure becomes: c .fwdarw. .function. (
k + 1 ) = c .fwdarw. .function. ( k ) + .beta. .times. .times. e
.function. ( k ) .function. [ R V .function. ( k ) + R H .function.
( k ) ] .times. c .fwdarw. .function. ( k ) = c .fwdarw. .function.
( k ) + .beta. .times. .times. e .function. ( k ) .function. [ q V
* .function. ( k ) .times. r .fwdarw. V .function. ( k ) + q H *
.function. ( k ) .times. r .fwdarw. H .function. ( k ) ] ( 6 ) ( 7
) ##EQU4## In scalar form, the i.sup.th FIR filter tap coefficient
is updated as follows:
c.sub.i(k+1)=c.sub.i(k)+.beta.e(k)[q*.sub.V(k)r.sub.V(k-i)+q*.sub.H(k)r.s-
ub.H(k-i)}. (8) If we denote {right arrow over
(q)}(k)={q.sub.V(k),q.sub.H(k)}.sup.T,{right arrow over
(u)}(k-i)=[r.sub.V(k-i),r.sub.H(k-i)}.sup.T, then,
c.sub.i(k+1)=c.sub.i(k)+.beta.e(k){right arrow over
(q)}.sup.H(k){right arrow over (u)}(k-i). (9 Here {right arrow over
(q)}.sup.H(k){right arrow over (u)}(k-i)=.parallel.{right arrow
over (q)}(k).parallel..parallel.(k-i).parallel..parallel.cos
(.theta..sub.q,u), where .parallel.{right arrow over (q)}.parallel.
is the Euclidean norm of {right arrow over (q)} and .theta..sub.q,n
is the angle between {right arrow over (q)} and {right arrow over
(u)}. In both equations (5) and (9), the knowledge of the inner
product of the input {right arrow over (u)} and the equalized
{right arrow over (q)} is required for the optimization of the
optical FIR filter coefficients. Note that once the values for all
c.sub.i are known, the corresponding values for {right arrow over
(.alpha.)}.sub.i and {right arrow over (.theta.)}.sub.i are readily
generated, since c.sub.i=.alpha..sub.ie.sup.j.theta..sub.i, as
shown in Equation (1) above.
[0028] The above-described embodiments are, of course, merely
illustrative of the principles of the invention. Indeed, numerous
other methods or apparatus may be devised by those skilled in the
art without departing from the spirit and scope of the invention.
Specifically, other arrangements may be equally employed for
realizing the controllable optical FIR filter.
* * * * *