A feedforward pilot-symbols-aided carrier-phase recovery scheme is described. The approach relies on pilot symbols that are time-division multiplexed with the transmitted data. In the scheme, an initial coarse estimation of the optical carrier phase, exploiting the knowledge of pilot symbols, is followed by a fine nondata-aided, or blind, estimation. The main advantage of the proposed solution is that of avoiding the phase- ambiguity problem after a cycle slip. The overhead and the impact on the performance of pilot symbols are investigated for long-haul transmission of 100-Gb/s polarization-multiplexed quadrature phase-shift keying wavelength-division-multiplexing signals in different scenarios. For homogeneous transmission, the proposed scheme outperforms blind carrier recovery with differential decoding.

The paper deals with carrier recovery based on pilot symbols in single-carrier systems. The system model considered in the paper includes the channel additive white noise and the phase noise that affects the local oscillators used for up/down-conversion. Wiener's method is used to determine the optimal filter in estimation of phase noise assuming that a sequence of equally spaced pilot symbols is available. Our analysis allows to capture the cyclostationary performance of the estimate, a phenomenon that is not considered in the previous literature. In the paper, closed-form formulas for the transfer function of the optimal filter and for the mean-square phase error are derived for the case where the phase noise is modelled as random phase walk. For this case, a suboptimal filter is proposed. Numerical results are presented to substantiate the analysis.

The information rate transferred through the Additive White Gaussian Noise (AWGN) channel affected by discrete-time multiplicative Wiener's phase noise is computed in the paper. Upper and lower bounds based on quantization of the phase space and trellis representation of phase noise memory are proposed. The results presented in the paper show that both the upper bound and the lower bound converge to the actual information rate as the number of quantizer's bins increases, the convergence of the lower bound being faster. The analysis presented in the paper allows for pilot symbols being considered. From the one hand, the insertion of pilot symbols penalizes the net symbol rate, thus subtracting space to information transmission, while, from the other hand, they bring information on channel state. The balance between what is lost and what is gained is computed in the paper.

An empirical phase noise channel model suitable for performance evaluation of high spectrally efficient modulations in 100G long-haul coherent optical transmission systems using polarization-division multiplexed and wavelength-division multiplexing channels is presented. The derivation of the model is worked out by exploiting the similarity between the power spectral density of the carrier extracted from the analysis of propagation measurements and the Lorentzian spectrum that is usually adopted to describe instabilities of semiconductor lasers. The proposed channel model is characterized by only two parameters: the linewidth of the carrier and the signal-to-noise ratio. We show that in the case of quadrature phase-shift keying transmission a good agreement exists between quantitative measures of performance extracted by processing experimental data and those obtained from simulations based on the use of the empirical model.

The constrained capacity of the additive white Gaussian noise channel affected by Wiener phase noise is investigated in the letter. Evaluation of channel capacity based on quantization of the phase space and trellis representation of the memory is proposed. The results presented in the letter show that quantization of the phase into 128 bins is adequate to accurately evaluate the capacity at signal-to-noise ratio lower than 30 dB.

The discrete-time phase-locked loop (PLL) operating at the steady state is considered in this paper. Phase noise, which always affects oscillators, is modeled as a stationary random waveform and optimization of the loop filter is worked out in the light of Wiener's theory. Delay in the loop, which may affect the numerical implementation of the PLL, is considered. The main results and novelties of this paper are the optimal loop filter and the minimum mean-square error (MSE) that can be achieved for a given spectrum of phase noise and for a given delay in the loop. Closed-form expressions for the loop filter and for the MSE are given for the case where the phase noise is characterized as a second-order disturbance. Application of these results to carrier recovery based on the Costas loop is presented in this paper.