In Software defined elastic optical networks, modulation format and constellation size may be flexibly modified. As a result, digital signal processing (DSP) algorithm should be compatible with different modulation schemes or readily reconfigurable at the optical coherent receiver. Therefore we propose a novel cascaded adaptive blind equalizers based on decision-directed modified least mean square (DD-MLMS) algorithm for polarization separation and carrier phase recovery. The algorithm is square quadrature amplitude modulation (QAM) independent so that it could be applied in the elastic optical systems. The 28 Gbaud polarization multiplexing quadrature phase shift keying (PM-QPSK) and PM-16QAM back-to-back transmission is demonstrated. The results show that the performance is very close to the general algorithm but with a benefit of the reduced operation complexity. We transmit the 8×240 Gb/s PM-16QAM wavelength division multiplexing (WDM) signal over 1200 km standard single mode fiber (SSMF) based on the proposed blind equalization with a bit error ratio (BER) less than 2×10−2.
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1. A decision-directed modified least mean square (DD-MLMS) method comprising:
receiving an mqam modulated data signal comprising a plurality of symbols; and
equalizing the data signal using an adaptive finite impulse response (FIR) filter having multiple tap coefficients,
wherein the tap coefficients are adaptively updated using a DD-MLMS algorithm and a cost function according to earlier symbol character information,
wherein the filter tap coefficients updating equation is w(n)=w(n−1)+μe(n)x(n)*, where w(n) is the adaptive FIR filter, μ is a convergence parameter, e(n) is a complex error vector, x(n) is the received data signal, and [·]* stands for conjugation operation;
wherein each of the symbols is determined as a decision symbol that is a shortest distance away from a respective mqam constellation point, and the DD-MLMS algorithm tries to force the equalized signal to reside on the decision point, whereby carrier phase offset is blindly compensated.
6. A decision-directed modified least square mean (DD-MLMS) system comprising:
a filter adapted to receive an mqam modulated data signal comprising a plurality of symbols, and equalize the data signal using an adaptive finite impulse response (FIR) filter having multiple tap coefficients,
wherein the tap coefficients are adaptively updated using a DD-MLMS algorithm and a cost function according to earlier symbol character information,
wherein the filter tap coefficients updating equation is w(n)=w(n−1)+μe(n)x(n)*, where w(n) is the adaptive FIR filter, μ is a convergence parameter, e(n) is a complex error vector, x(n) is the received data signal, and [·]* stands for conjugation operation;
wherein each of the symbols is determined as a decision symbol that is a shortest distance away from a respective mqam constellation point, and the DD-MLMS algorithm tries to force the equalized signal to reside on the decision point, whereby carrier phase offset is blindly compensated.
3. The method of
4. The method of
reserving amplitude error information and phase error information; and
using the amplitude error information and the phase error information in calculating separately, and then combining, errors of a real signal part and an imaginary signal part.
5. The method of
8. The system of
9. The system of
reserve amplitude error information and phase error information; and
use the amplitude error information and the phase error information to calculate separately, and then combine, errors of a real signal part and an imaginary signal part.
10. The system of
11. The system of
a plurality of cascaded adaptive blind equalizers comprising multiple finite impulse response (FIR) filters for polarization separation and multiple finite impulse response filters for carrier phase recovery,
wherein, in operation, the finite impulse response filters are adaptively updated by using a pre-convergence method followed by DD-MLMS for precise feedback control.
13. The system of
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This Application claims the benefit of U.S. Provisional Application 61/757,991 filed on Jan. 29, 2013, the entirety of which is incorporated herein by reference.
For 100 Gb/s and beyond optical transmission systems, the flexible and adaptive bandwidth, known as elastic bandwidth, enables to efficiently distribute data according to the needed capacity and transmission length. Consequently the software defined elastic optical networks are becoming more and more attractive and important at present [1]-[4]. In this software defined networking (SDN), modulation format and constellation size may be flexibly modified. In that case, digital signal processing (DSP) must be compatible with different modulation schemes or readily reconfigurable at the receiver. Polarization multiplexing quadrature phase shift keying (PM-QPSK) is proposed and commercially available for 100-Gb/s optical transmission system [5]. Polarization multiplexing 16-ary quadrature amplitude modulation (PM-16QAM) [6] and higher-level QAM (e.g., 36QAM) [7], [8] are proposed for beyond 100-Gb/s optical transmission system. Therefore, it is quite important to discuss the DSP compatibility for the mQAM signal especially for QPSK and 16QAM in the future elastic optical networks.
Recently, lots of algorithms have been proposed to recover the distorted signal. The static filter is used for chromatic dispersion (CD) compensation [9]. The filter parameters are dependent on the residual CD and have no relation with modulation format. The constant modulus algorithm (CMA) is well accepted to separate the two polarization components. It is proved efficient to adapt the finite impulse response (FIR) tap weights for the QPSK and m-ary phase shift keying (mPSK) signal which has constant modulus. However, CMA is not well compatible with 16QAM because high order QAM no longer presents constant symbol amplitude and equalized signal error cannot approach to zero. Instead, radius directed equalization (RDE) algorithm is proposed [10], but it needs changing with the number of radius of the constellation. For carrier recovery, Viterbi and Viterbi algorithm is useful to QPSK signal [11], while feed forward estimation is more hardware efficient for mQAM signal [12]. The common problem is that the algorithm needs re-configuration and re-initialization so they are not flexible for the dynamic modulation format deployment.
The decision-directed least radius distance (DD-LRD) algorithm for blind equalization is proposed [13], which is also named phase independent decision-directed least mean square (DD-LMS) [14]. But it is unrelated to carrier phase so that cannot be applied for carrier recovery. Although conventional DD-LMS algorithm is compatible with all kinds of modulation formats, it is too sensitive to phase error. Generally, it should be combined with CMA or RDE for pre-convergence. In this paper, we propose a novel decision-directed modified least mean square (DD-MLMS) algorithm which is suitable for square-QAM signal. Besides, carrier phase is blindly recovered simultaneously because phase error is reserved in the cost function. Low complex cascaded DD-MLMS based adaptive equalizers are applied for polarization separation and carrier phase recovery in the flexible square-QAM coherent optical systems for the elastic optical networks.
The accompanying drawings are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification. The drawings illustrate disclosed embodiments and/or aspects and, together with the description, serve to explain the principles of the invention, the scope of which is determined by the claims.
It is to be understood that the figures and descriptions provided herein may have been simplified to illustrate elements that are relevant for a clear understanding of the present invention, while eliminating, for the purpose of clarity, other elements found in typical algorithms on flexible square-QAM coherent detection systems and methods. Those of ordinary skill in the art may recognize that other elements and/or steps may be desirable and/or necessary to implement the devices, systems, and methods described herein. However, because such elements and steps are well known in the art, and because they do not facilitate a better understanding of the present invention, a discussion of such elements and steps may not be provided herein. The present disclosure is deemed to inherently include all such elements, variations, and modifications to the disclosed elements and methods that would be known to those of ordinary skill in the pertinent art of optical network operation.
We may model the fiber optics channel simply by a unitary 2×2 matrix considering CD, polarization mode dispersion (PMD) and carrier phase as shown in (1),
where hcd is the fiber transfer function under dispersion. 2θ and ø are the azimuth and elevation rotation angles, respectively. φx and φy are the carrier phase offset. With respect to (1), we can recover the signal with the digital FIR equalizer.
As we know, adaptive FIR filter is a popular blind equalizer for intersymbol interference (ISI) mitigation, polarization separation, and carrier phase tracking. The equalizer coefficients will be updated adaptively using a cost function according to a priori knowledge of the symbol character.
er(n)=(|{circumflex over (d)}r(n)|2−|yr(n)|2)×sgn[yr(n)] (2)
ei(n)=(|{circumflex over (d)}i(n)|2−|yi(n)|2×sgn(yi(n)) (3)
e(n)=er(n)+j·ei(n) (4)
where the signum function is defined as sgn(x)=x/|x|. The error functions of real part and imaginary part are then combined together, which is expressed as a complex error vector as shown in (4).
The filter tap weights updating equation is shown in (5).
w(n)=w(n−1)+μe(n)×(n)* (5)
where w(n) is the adaptive FIR filter, and μ is the convergence parameter. [·]* stands for conjugation operation.
Since real part and imaginary part of the equalizer output are estimated respectively, the DD-MLMS algorithm tries to force the equalized signal to reside on the decision point. In addition, the error function includes both amplitude and phase information of the equalized signal. As a result, carrier phase offset is also blindly compensated.
In order to realize polarization separation and carrier phase recovery which is transparent to mQAM modulation format in the elastic optical networks, we propose cascaded DD-MLMS based adaptive equalizers.
Numerical simulation is done in order to evaluate the performance of our proposed algorithm. We take 16QAM signal as an example. The initial carrier phase offset is 45°. The inset constellations in
The received signal is resampled to 2 times of the symbol rate by cubic interpolation with square timing method [15]. As described in section II, cascaded FIR equalizers are used to blindly recover the signal. Four 9-tap T/2-spaced adaptive butterfly FIR filters are applied for polarization demultiplexing. Afterward two 9-tap T-spaced adaptive FIR filters are applied for carrier recovery. The filters' weights are first updated by CMA for pre-convergence. The final adaptation is switched to DD-MLMS for precise feedback control. Frequency offset is compensated based on the fast Fourier transform (FFT) method [16] which is also modulation format independent. Finally, the signal is detected for data bit error ratio (BER) measurement. As a comparison, DD-LRD scheme together with general carrier phase estimation (CPE) (Viterbi-and-Viterbi algorithm for QPSK signal and feed forward estimation algorithm for 16QAM signal) is also evaluated.
The measured BERs of QPSK and 16QAM signals as a function of OSNR are shown in
We carry out 8×240 Gb/s PM-16QAM wavelength division multiplexing (WDM) transmission experiment over different length standard single mode fibers (SSMF). The spectrum of the signal is shown in
The final symbol decision is constellation dependent right now. In order to realize the practical and really full blind DSP to unknown received signals, we must figure out this problem. One of the methods is that we can estimate the signal format by the statistics after pre-equalization such as CMA. This issue will be studied in the future.
We propose a novel cascaded adaptive equalizers based on DD-MLMS algorithm for the future elastic optical networks. The DSP is compatible with square-QAM signal. So it could be deployed in the flexible mQAM modulation format coherent optical systems. We demonstrate the 28 Gbaud dual polarization QPSK signal and 16QAM signal back-to-back transmission. The results show that the performance is very close but the complexity is much reduced compared to the general algorithm. The 8 channel WDM 240 Gb/s/ch PM-16QAM signal transmission with different fiber length is demonstrated. The transmission length can achieve 1200 km with a BER less than 2×10−2 based on the proposed blind equalization.
Although the invention has been described and illustrated in exemplary forms with a certain degree of particularity, it is noted that the description and illustrations have been made by way of example only. Numerous changes in the details of construction and combination and arrangement of parts and steps may be made. Accordingly, such changes are intended to be included in the invention, the scope of which is defined by the claims.
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9912500, | Nov 04 2013 | ZTE Corporation | Adaptive pre-equalization in optical communications |
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