Adaptive optical equalization for chromatic and/or polarization mode dispersion compensation
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.
This invention relates to optical transmission systems and, more particularly, to optical equalization.
BACKGROUND OF THE INVENTIONIntersymbol 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.
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).
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/nm2. 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.
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.
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.
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.
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 INVENTIONThese 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.
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).
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.
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
For a received optical signal E(t) supplied to controllable modulator 102 via input terminal 101 the output optical signal Eo (t) from controllable modulator 102 at output terminal 103 is
where n is the number of taps for the optical equalizer, αi is amplitude parameter, θi and ci=αiej
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.
Thus, the ISI elimination process in this invention utilizes a unique opto-electronic LMS process.
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 LiNbO3. 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.
In the embodiment of
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 ƒs=1Ts equal to or being a multiple of the bit rate ƒb. When ƒs=ƒb, controllable optical modulator 102 (which is essentially a FIR filter having a plurality of parallel legs) is synchronous (SYN). On the other hand, when ƒs is a multiple of the bit rate ƒb, 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)]T, where r(k)=E(kTs) 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−L(k), . . . , ci(k), . .. ,CL(k)]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)}H(k){right arrow over (r)}H(k)=Σi=−LLci*(k)r(k−i). Here the superscript H implies conjugate transpose and H=T* implies complex conjugate transpose Then, photodetector 104 (
Error signal e(k) is generated in conjunction with the output from TIA 105 |q(k)|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 (
The unique opto-electronic LMS process tends to minimize deterministically the cost function defined here as J(k)=|e(k)|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:
where β is a preset step size and ∇c{[e(k)]2} is the gradient of the cost function. In this example, ∇c{[e(k)]2}=2e(k)∇c{e(k)}=−2e(k)∇c{{right arrow over (c)}H(k)R(k){right arrow over (c)}(k)}. Since it can be shown that ∇c{{right arrow over (c)}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:
Thus, the ith FIR filter coefficient is updated as follows:
ci(k+1)=ci(k)+βe(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 (
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, EV(t) and EH(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)|2=|qV(k)|2+|qH(k)|2, where qV(k)={right arrow over (c)}H(k){right arrow over (r)}V(k) and qH(k)={right arrow over (c)}H(k){right arrow over (r)}H(k) under the assumption of the optical FIR filter, i.e., optical vector modulator 102, of
In scalar form, the ith FIR filter tap coefficient is updated as follows:
ci(k+1)=ci(k)+βe(k)[q*V(k)rV(k−i)+q*H(k)rH(k−i)}. (8)
If we denote
{right arrow over (q)}(k)={qV(k),qH(k)}T,{right arrow over (u)}(k−i)=[rV(k−i),rH(k−i)}T,
then,
ci(k+1)=ci(k)+βe(k){right arrow over (q)}H(k){right arrow over (u)}(k−i). (9
Here
{right arrow over (q)}H(k){right arrow over (u)}(k−i)=∥{right arrow over (q)}(k)∥∥(k−i)∥∥cos (θq,u),
where ∥{right arrow over (q)}∥ is the Euclidean norm of {right arrow over (q)} and θq,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 ci are known, the corresponding values for {right arrow over (α)}i and {right arrow over (θ)}i are readily generated, since ci=αiejθ
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.
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.
Type: Application
Filed: Aug 10, 2004
Publication Date: Feb 16, 2006
Inventors: Young-Kai Chen (Berkeley Heights, NJ), Ut-Va Koc (Bridgewater, NJ), Andreas Leven (Gillette, NJ)
Application Number: 10/914,989
International Classification: H04B 10/04 (20060101);