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Register a new userCarrier Phase Estimation in Dispersion-Unmanaged Optical Transmission Systems
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Tianhua Xu
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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The study on carrier phase estimation (CPE) approaches, involving a one-tap normalized least-mean-square (NLMS) algorithm, a block-wise average algorithm, and a Viterbi-Viterbi algorithm has been carried out in the long-haul high-capacity dispersion-unmanaged coherent optical systems. The close-form expressions and analytical predictions for bit-error-rate behaviors in these CPE methods have been analyzed by considering both the laser phase noise and the equalization enhanced phase noise. It is found that the Viterbi-Viterbi algorithm outperforms the one-tap NLMS and the block-wise average algorithms for a small phase noise variance (or effective phase noise variance), while the three CPE methods converge to a similar performance for a large phase noise variance (or effective phase noise variance). In addition, the differences between the three CPE approaches become smaller for higher-level modulation formats.
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Using coherent optical detection and digital signal processing, laser phase noise and equalization enhanced phase noise can be effectively mitigated using the feed-forward and feed-back carrier phase recovery approaches. In this paper, theoretical analyses of feed-back and feed-forward carrier phase recovery methods have been carried out in the long-haul high-speed n-level phase shift keying (n-PSK) optical fiber communication systems, involving a one-tap normalized least-mean-square (LMS) algorithm, a block-wise average algorithm, and a Viterbi-Viterbi algorithm. The analytical expressions for evaluating the estimated carrier phase and for predicting the bit-error-rate (BER) performance (such as the BER floors) have been presented and discussed in the n-PSK coherent optical transmission systems by considering both the laser phase noise and the equalization enhanced phase noise. The results indicate that the Viterbi-Viterbi carrier phase recovery algorithm outperforms the one-tap normalized LMS and the block-wise average algorithms for small phase noise variance (or effective phase noise variance), while the one-tap normalized LMS algorithm shows a better performance than the other two algorithms for large phase noise variance (or effective phase noise variance). In addition, the one-tap normalized LMS algorithm is more sensitive to the level of modulation formats.
The performance of long-haul coherent optical fiber transmission system is significantly affected by the equalization enhanced phase noise (EEPN), due to the interaction between the electronic dispersion compensation (EDC) and the laser phase noise. In this paper, we present a comprehensive study on different chromatic dispersion (CD) compensation and carrier phase recovery (CPR) approaches, in the n-level phase shift keying (n-PSK) and the n-level quadrature amplitude modulation (n-QAM) coherent optical transmission systems, considering the impacts of EEPN. Four CD compensation methods are considered: the time-domain equalization (TDE), the frequency-domain equalization (FDE), the least mean square (LMS) adaptive equalization are applied for EDC, and the dispersion compensating fiber (DCF) is employed for optical dispersion compensation (ODC). Meanwhile, three carrier phase recovery methods are also involved: a one-tap normalized least mean square (NLMS) algorithm, a block-wise average (BWA) algorithm, and a Viterbi-Viterbi (VV) algorithm. Numerical simulations have been carried out in a 28-Gbaud dual-polarization quadrature phase shift keying (DP-QPSK) coherent transmission system, and the results indicate that the origin of EEPN depends on the choice of chromatic dispersion compensation methods, and the effects of EEPN also behave moderately different in accordance to different carrier phase recovery scenarios.
We consider least squares estimators of carrier phase and amplitude from a noisy communications signal that contains both pilot signals, known to the receiver, and data signals, unknown to the receiver. We focus on signaling constellations that have symbols evenly distributed on the complex unit circle, i.e., M-ary phase shift keying. We show, under reasonably mild conditions on the distribution of the noise, that the least squares estimator of carrier phase is strongly consistent and asymptotically normally distributed. However, the amplitude estimator is not consistent, but converges to a positive real number that is a function of the true carrier amplitude, the noise distribution and the size of the constellation. Our theoretical results can also be applied to the case where no pilot symbols exist, i.e., noncoherent detection. The results of Monte Carlo simulations are provided and these agree with the theoretical results.
Spectrum sensing and direction of arrival (DOA) estimation have been thoroughly investigated, both separately and as a joint task. Estimating the support of a set of signals and their DOAs is crucial to many signal processing applications, such as Cognitive Radio (CR). A challenging scenario, faced by CRs, is that of multiband signals, composed of several narrowband transmissions spread over a wide spectrum each with unknown carrier frequencies and DOAs. The Nyquist rate of such signals is high and constitutes a bottleneck both in the analog and digital domains. To alleviate the sampling rate issue, several sub-Nyquist sampling methods, such as multicoset sampling or the modulated wideband converter (MWC), have been proposed in the context of spectrum sensing. In this work, we first suggest an alternative sub-Nyquist sampling and signal reconstruction method to the MWC, based on a uniform linear array (ULA). We then extend our approach to joint spectrum sensing and DOA estimation and propose the CompreSsed CArrier and DOA Estimation (CaSCADE) system, composed of an L-shaped array with two ULAs. In both cases, we derive perfect recovery conditions of the signal parameters (carrier frequencies and DOAs if relevant) and the signal itself and provide two reconstruction algorithms, one based on the ESPRIT method and the second on compressed sensing techniques. Both our joint carriers and DOAs recovery algorithms overcome the well-known pairing issue between the two parameters. Simulations demonstrate that our alternative spectrum sensing system outperforms the MWC in terms of recovery error and design complexity and show joint carrier frequencies and DOAs from our CaSCADE systems sub-Nyquist samples.
Multiple carrier-frequency offsets (CFO) arise in a distributed antenna system, where data are transmitted simultaneously from multiple antennas. In such systems the received signal contains multiple CFOs due to mismatch between the local oscillators of transmitters and receiver. This results in a time-varying rotation of the data constellation, which needs to be compensated for at the receiver before symbol recovery. This paper proposes a new approach for blind CFO estimation and symbol recovery. The received base-band signal is over-sampled, and its polyphase components are used to formulate a virtual Multiple-Input Multiple-Output (MIMO) problem. By applying blind MIMO system estimation techniques, the system response is estimated and used to subsequently transform the multiple CFOs estimation problem into many independent single CFO estimation problems. Furthermore, an initial estimate of the CFO is obtained from the phase of the MIMO system response. The Cramer-Rao Lower bound is also derived, and the large sample performance of the proposed estimator is compared to the bound.
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