Low complexity carrier phase estimation for m-QAM optical communication systems

A linewidth tolerant and low complexity carrier phase estimation algorithm is proposed by using phase linear interpolation. The performance of proposed phase linear interpolation based CPE algorithm can achieve comparable performance to the sliding window based algorithms, while the hardware complexity is reduced by a factor of 40.

Quantum computers are expected to perform full-configuration interaction calculations with less computational resources compared to classical ones, thanks to the use of quantum phase estimation (QPE) algorithms. However, only a limited number of QPE-based quantum chemical calculations have been reported even for numerical simulations on a classical computer, and the practical workflow for the QPE computation has not yet been established. In this paper, we report the QPE simulations of the electronic ground and the π-π* excited singlet state of benzene and its chloro- and nitro-derivatives as the representative industrially important systems, with the aid of GPGPU acceleration of quantum circuit simulations. We adopted the pseudo-natural orbitals obtained from the MP2 calculation as the basis for the wave function expansion, the CISD calculation within the active space to find the main electronic configurations to be included in the input wave function of the excited state, and the technique to reduce the truncation error of the calculated total energies. The proposed computational workflow is easily applicable to other molecules and can be a standard approach for performing QPE-based quantum chemical calculations of practical molecules.

Two novel low-complexity multistage digital feed-forward carrier phase estimation algorithms for 64-ary quadrature amplitude modulation (QAM) are proposed and analyzed by numerical simulations. The first stage is composed of a Viterbi and Viterbi block, based on either the standard quadrature phase shift keying (QPSK) partitioning algorithm using only Class-1 symbols or a modified QPSK partitioning scheme utilizing both Class-1 and outer most triangle-edge symbols. The second stage applies the Viterbi and Viterbi algorithm after a 64-QAM-to-QPSK transformation, while the subsequent stages iterate a maximum likelihood estimation algorithm for phase estimation. All proposed techniques are characterized by a high tolerance to laser phase noise: with an optical signal-to-noise ratio penalty of 1 dB at bit error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> , the proposed schemes can tolerate a linewidth times symbol duration product (Δv·T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ) equal to 5.6 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> and 7.1 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> , respectively. At 32 Gbaud, all of the above linewidth requirements can be met using commercial tunable lasers. The proposed schemes achieve a similar linewidth tolerance with a reduced implementation complexity with respect to algorithms based on the blind phase search method.

To improve the spatial density and quality of measurement points in multitemporal interferometric synthetic aperture radar, distributed scatterers (DSs) should be processed. An essential procedure in DS interferometry is phase estimation, which reconstructs a consistent phase series from all available interferograms. Influenced by the well-known suboptimality of coherence estimation, the performance of the state-of-the-art phase estimation algorithms is severely degraded. Previous research has addressed this problem by introducing the coherence bias correction technique. However, the precision of phase estimation is still insufficient because of the limited correction capabilities. In this paper, a modified phase estimation approach is proposed. Particularly, by incorporating the information on both interferometric coherence and the number of looks, a significant bias correction to each element of the coherence magnitude matrix is achieved. The bias-corrected coherence matrix is combined with advanced statistically homogeneous pixel selection and time series phase optimization algorithms to obtain the optimal phase series. Both the simulated and Sentinel-1 real data sets are used to demonstrate the superiority of this proposed approach over the traditional phase estimation algorithms. Specifically, the coherence bias can be corrected with considerable accuracy by the proposed scheme. The mean bias of coherence magnitude is reduced by more than 29%, and the standard deviation is reduced by more than 18% over the existing bias correction method. The proposed approach achieves higher accuracy than the current methods over the reconstructed phase series, including smoother interferometric phases and fewer outliers.

As spatial division multiplexed transmission systems employing few mode fibers (FMFs) rely heavily on digital signal processing (DSP), the impact of computational complexity should be considered. A key DSP process block is the carrier phase estimation (CPE), which consists of a phase estimator and digital phase locked loop (DPLL) per output. In this letter, a low complexity phase estimator is proposed, and the common-mode laser frequency offset is exploited to reduce the number of DPLLs. The combination of a low complexity CPE and single DPLL is experimentally demonstrated for a 28 GBd six-channel transmission over a 41.7-km FMF, carrying up to 32 quadrature amplitude modulation. Thereby, the nonlinear tolerances for the proposed CPE scheme are shown to perform similarly as the more computationally complex conventional CPE scheme.

In this paper, we propose a novel pilot-aided phase and channel estimation algorithm for coherent mode-division multiplexing multiple-input multiple-output free-space optical communication system. This algorithm enables the implementation of advanced multiple-input multiple-output decoders, leading to a significantly better bit error rate performance. This algorithm also supports phase-asynchronous light sources at each transmit and receive channel, significantly reducing the hardware requirements. Moreover, it has low computational complexity and Cramér-Rao lower bound approaching estimation performance. In our proof-of-concept experiment, we employed 10 decorrelated channels to achieve a record-high 689.2 Gbit/s/wavelength line rate in strong turbulence, verifying the feasibility of our phase and channel estimation algorithm.

Direct application of the phase estimation algorithm to find the eigenvalues of the Hamiltonians

We propose a novel two-stage carrier phase estimation (CPE) algorithm for 64-ary quadrature amplitude modulation (64-QAM) coherent optical systems. It makes use of a new quadrature phase shift keying partitioning (QPSK-partitioning) approach and an enhanced maximum likelihood (ML) detection. 36/64 of the 64-QAM symbols are statistically employed by the modified QPSK-partitioning approach to estimate phase noise in the first stage. The proposed enhanced ML detection is used in the second stage to improve linewidth tolerance performance. The simulation results show that, our proposed VVPE <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c1&amp;c2</sup> + EML algorithm can achieve much higher linewidth tolerance performance than the modified V&V + MLE algorithm at high laser linewidth level. A combined laser linewidth symbol duration product as high as 5.6 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> is achieved by the proposed two-stage CPE algorithm at a target BER of 1 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> with 1 dB SNR sensitivity penalty.

Quantum phase estimation algorithm (PEA) is one of the most important algorithms in early studies of quantum computation. However, we find that the PEA is not an unbiased estimation, which prevents the estimation error from achieving an arbitrarily small level. In this paper, we propose an unbiased phase estimation algorithm (UPEA) based on the original PEA. We also show that a maximum likelihood estimation (MLE) post-processing step applied on UPEA has a smaller mean absolute error than MLE applied on PEA. In the end, we apply UPEA to quantum counting, and use an additional correction step to make the quantum counting algorithm unbiased.

Quantum computing is carried out based on the working principles of quantum mechanics. Current $2$-dimensional quantum computing techniques face major problems such as noise and information capacity. As such, high-dimensional quantum computing is leveraged to solve these problems. This study attempts to approximate the pi number through the multi-global and single-global Quantum Phase Estimation (QPE) algorithms in high-dimension. This study reveals that pi can be calculated by using fewer quantum resources in high dimension with at least equal or higher precision than that obtained by $2$-dimensional QPE. In addition, when the number of qudits or the number of dimensions is kept constant, the multi-global QPE in high dimensions yields at least equal or better results than the single-global QPE. All calculations performed in this study are implemented on Cirq.

A differentially coherent receiver which uses the Viterbi algorithm is presented. This receiver compensates for intersymbol interference (ISI) and avoids noise enhancement. A phase estimate which takes into account the presence of inherent ISI in the signal is derived. This phase estimate is then used in the decision metric of a coherent receiver. The resulting decision rule can be implemented using the Viterbi algorithm. The complexity of the resulting receiver increases with the duration of observation used by the implicit phases estimator. A simple four-state Viterbi receiver with good performance is obtained when the phase estimate is based on one observable. Simulation results are given. >

A dynamic programming algorithm, developed in [1]-[4] for obtaining the joint estimate of carrier phase and data, is applied to multi h continuous phase modulation. A MAP estimator detects data and jointly tracks carrier phase consisting of a normal random walk phase jitter process. Monte Carlo computer simulations are used to evaluate the probability of error performance for two receivers employed in demodulation of multi- h CPM signals. A simplified algorithm is proposed which yields up to a tenfold reduction in computation time at the expense of less than 1 dB in signal-to-noise ratio at the error rates computed, and for suitable ranges of phase jitter increments variance.

Quantum phase estimation algorithm (PEA) has been successfully adapted as a sub frame of many other algorithms applied to a wide variety of applications in different fields. However, the requirement of a good approximate eigenvector given as an input to the algorithm hinders the application of the algorithm to the problems where we do not have any prior knowledge about the eigenvector. In this paper, we show that the principal eigenvalue of an irreducible non-negative operator can be determined by using an equal superposition initial state in the PEA. This removes the necessity of the existence of an initial good approximate eigenvector. Moreover, we show that the success probability of the algorithm is related to the closeness of the operator to a stochastic matrix. Therefore, we draw an estimate for the success probability by using the variance of the column sums of the operator. This provides a priori information which can be used to know the success probability of the algorithm beforehand for the non-negative matrices and apply the algorithm only in cases when the estimated probability is reasonably high. Finally, we discuss the possible applications and show the results for random symmetric matrices and 3-local Hamiltonians with non-negative off-diagonal elements.

Making use of the general physical model of the Mach-Zehnder interferometer with photon loss which is a fundamental physical issue, we investigate the continuous-variable quantum phase estimation based on machine learning approach, and an efficient recursive Bayesian estimation algorithm for Gaussian states phase estimation has been proposed. With the proposed algorithm, the performance of the phase estimation may be improved distinguishably. For example, the physical limits (i.e., the standard quantum limit and Heisenberg limit) for the phase estimation precision may be reached in more efficient ways especially in the situation of the prior information being employed, the range for the estimated phase parameter can be extended from [0, π/2] to [0, 2π] compared with the conventional approach, and influences of the photon losses on the output parameter estimation precision may be suppressed dramatically in terms of saturating the lossy bound. In addition, the proposed algorithm can be extended to the time-variable or multi-parameter estimation framework.

The Cramer-Rao lower bound (CRLB) and minimum mean-square error (MMSE) lower bound on the variance of phase estimation in CDMA receivers in AWGN and slow and fast Rayleigh fading conditions are presented. The bounds are useful as benchmark information for implementation of channel estimator algorithms needed for coherent combining in CDMA receivers. Analytical results indicate that increasing the signal-to-noise ratio or/and averaging period for phase estimation improves the performance. Hence, the phase error can be reduced to avoid significant degradation in bit error rate of the system. However, for fast fading there is a high error floor on the phase estimation (about 50 degrees of rms phase error) regardless of how high the signal-to-noise ratio is made. This presents a challenge of achieving acceptable bit error rate performance for users who are moving at very fast speeds.