Maximum-likelihood sequence estimation in dispersive optical channels (original) (raw)
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Latin American applied research Pesquisa aplicada latino americana = InvestigacioĢn aplicada latinoamericana
Maximum likelihood sequence estimation (MLSE) has been proposed in earlier literature to combat the effects of nonlinear dispersion in intensity modulation/direct detection (IM/DD) optical channels. In this paper, we develop a theory of the bit error rate (BER) of MLSE-based IM/DD receivers operating in the presence of nonlinear dispersion and amplified spontaneous emission (ASE) noise. We focus on long haul or metro links spanning several hundred kilometers of single mode fibers with optical amplifiers. Numerical results show a close agreement between the predictions of the theory and computer simulations.
Maximum likelihood sequence estimation receivers for DWDM lightwave systems
IEEE Global Telecommunications Conference, 2004. GLOBECOM '04., 2004
As the spacing between channels in dense wavelength division multiplexed (DWDM) links decreases and their number increases, nonlinear coupling effects such as four wave mixing (FWM) and cross-phase modulation (CPM) become more important. These impairments, combined with chromatic dispersion (CD), polarization mode dispersion (PMD), and amplified spontaneous emission (ASE) noise ultimately limit the maximum reach of the links. A receiver robust to these impairments would increase the maximum possible length of links without regeneration, reduce the number of required compensation elements such as dispersion compensation fibers (DCF) and optical amplifiers, and simplify link provisioning by making its fine tuning less critical and labor intensive.
Journal of Lightwave Technology, 2000
This paper thoroughly investigates the maximumlikelihood sequence detection (MLSD) receiver for the optical ON-OFF keying (OOK) channel in the presence of both polarization mode dispersion and group velocity dispersion (GVD). A reliable method is provided for computing the relevant performance for any possible value of the system parameters, with no constraint on the sampling rate. With one sample per bit time, a practically exact expression of the statistics of the received samples is found, and therefore the performance of a synchronous MLSD receiver is evaluated and compared with that of other electronic techniques such as combined feedforward and decision-feedback equalizers (FFE and DFE). It is also shown that the ultimate performance of electronic processing can be obtained by sampling the received signal at twice the bit rate. An approximate accurate closed-form expression of the receiver metrics is also identified, allowing for the implementation of a practically optimal MLSD receiver.
Long-Haul Optically Uncompensated IMDD Transmission With MLSE Using the M-Method
IEEE Photonics Technology Letters, 2000
Recent experimental evidence with off-line processing has shown that intensity-modulation direct-dectection receivers using maximum-likelihood sequence estimation (MLSE) can successfully operate over a very long distance without any optical dispersion compensation. One hurdle towards the actual exploitation of the technology is the required complexity of the processor, which grows exponentially with distance. In this letter, we investigate the use of a complexity-reduction algorithm originally proposed for nonoptical communications, called the M-method. We show by simulation that over 400 and 700 km of G.652 fiber, at 10.7 Gb/s, the M-method allows us to operate with virtually no excess penalty with respect to conventional MLSE, while keeping track of only 32 and 128 trellis states, respectively, out of optimum full-fledged trellises requiring 512 and 8192 states, respectively. We investigate the robustness of the algorithm versus limited analog-digital resolution and confirm its effectiveness by testing it over experimental data at 10 Gb/s over 1040 km.
Channel Estimation Algorithms for MLSD in Optical Communication Systems
IEEE Photonics Technology Letters, 2000
Maximum likelihood sequence detection represents the most efficient technique in the electrical domain to combat fiber impairments such as polarization-mode dispersion and group-velocity dispersion. In order to successfully apply this technique, it is mandatory to estimate some key channel parameters needed by the Viterbi processor. We propose a simple and effective solution based on the least-mean-square algorithm to perform such an estimation.
Maximum-Likelihood Sequence Estimation for Optical Phase-Shift Keyed Modulation Formats
IEEE/OSA Journal of Lightwave Technology, 2009
Electronic chromatic dispersion compensation employing maximum-likelihood sequence estimation (MLSE) has recently been the topic of extensive research and a range of commercial products. It is well known that MLSE provides a considerable benefit for amplitude modulated modulation formats such as ON-OFF keying (OOK) and optical duobinary. However, when applied to optical phase modulation formats, such as differential phase-shift keying (DPSK) and differential quadrature phase-shift keying (DQPSK), it has been shown that the benefit is only marginal. This paper investigates joint-decision MLSE (JD-MLSE) detection applied to 10.7-Gb/s DPSK. It demonstrates that a JD-MLSE using the constructive and destructive components preserves the 3-dB optical signal-to-noise ratio (OSNR) advantage of DPSK over OOK in dispersion-limited optical systems. Furthermore, we demonstrate that the use of a shortened MZDI with MLSE for the 10.7-Gb/s DPSK modulation can equalize an accumulated chromatic dispersion of 4000 ps/nm.
State-complexity reduction in MLSD receivers for direct-detection optical communications
2007
We investigate the impact of state-complexity reduction on the performance of maximum likelihood sequence detection (MLSD) receivers for direct-photodetection long-haul optical communication systems affected by uncompensated chromatic dispersion (CD). We directly compare two possible approaches: (i) detection through a simple "brute-force" state-complexity reduction strategy and (ii) a more structured reduced-state sequence detection (RSSD) strategy. The performance of both state-complexity reduction techniques is evaluated considering two realistic optical transmission schemes, based on on-off keying (OOK) and optical duobinary modulation (ODBM), respectively. The detection algorithms are characterized considering the impact of the timing offset, the quantization scheme, and the amount of uncompensated CD. As one would expect, for a given number of states in MLSD receivers, the schemes based on RSSD exhibit better performance with respect to those based on simple brute-force state-complexity reduction. However, we show that MLSD schemes based on the use of brute-force state-complexity reduction are characterized by a better complexity/performance trade-off for low/medium CD values, whereas RSSD is the best choice for high CD values.
Journal of Lightwave Technology, 2000
In this paper, we propose new closed-form approximations to the probability-density function (pdf) of the received signal in intensity-modulation/direct-detection (IM/DD) optical channels. These approximations greatly simplify the problem of channel estimation. This is an important problem in the implementation of maximum-likelihood sequence-estimation (MLSE) receivers for electronic dispersion compensation (EDC) of optical fibers, which has been a topic of great interest in recent years. The approximations proposed here are also useful in the analysis of the error rate of these receivers. It is well known that noise in IM/DD optical channels is strongly non-Gaussian and signal dependent. Except in the simplest situations, the pdf of the signal corrupted by noise does not have a closed-form expression. This leads to difficulties in the calculation of the probability of error on these channels and, more importantly, in the implementation of receivers that exploit knowledge of the signal pdf to minimize the error rate, for example, those based on MLSE techniques. To limit the complexity of channel estimation (an important requirement in real-time adaptive EDC receivers), it is important that the functional form assumed for the pdf be as simple as possible, while providing a good match with the actual statistical properties of the channel. In this paper, we introduce a new generic functional form for the pdf that accurately models the behavior of the received signal. Based on this expression, we introduce a channel-estimation approach that dramatically simplifies the analysis and design of MLSE receivers for IM/DD channels. Simulations show an excellent agreement between the results based on the approximations proposed here and the exact expressions for the pdf.
Assessing the Noise Statistics in Common Optical Transmission Systems
IEEE Photonics Technology Letters, 2000
We experimentally investigate the probability density function (pdf) of sampled bits in common intensity-modulated direct-detection systems in linear and nonlinear regime, both single-channel and wavelength-division-multiplexed. To this aim, we use a recirculating fiber loop and selectively obtain the sample pdf for the various bits in a given sequence, which allows separating the intersymbol interference (ISI) effects. Our measurements confirm a recent theoretical simplified model, suggesting that, under the above conditions, a generalized analytic form is a good approximation of the true pdf, provided that a pattern-dependent effective noise density and noiseless signal value are assumed: all the pdfs estimated from the experimental data are indeed well fitted by this analytic form. Moreover, when nonlinear effects become dominating, the analytic form is still fitting properly the data histograms, showing, however, that the effective noise density increases. In the above regime, we clearly observe that ISI also affects the increase of the effective noise density.