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Enhanced equalization phase noise (EEPN), generated from the uncompensated dispersion experienced by laser phase noises, can cause serious damage to the transmission quality of optical fiber systems. In this work, the performance of a wideband Nyquist-spaced long-haul nonlinear optical fiber communication systems suffering from EEPN is investigated and discussed through split-step numerical simulations and analytical models based on the perturbation analysis, in the cases of digital nonlinearity compensation (NLC) and electronic dispersion compensation (EDC). The efficiency and the accuracy of the analytical models were validated via simulations, considering the different symbol rates and modulation formats. The performance of the C-band transmission was comprehensively studied based on the model. Our results reveal that the growth of symbol rates and transmission distances aggravates the distortions in the C-band system.

An X-band low-phase noise planar oscillator employing the substrate integrated waveguide (SIW) active resonator is demonstrated. By compensating the losses in the SIW cavity with an active feedback loop, the Q-factor of the SIW active resonator is greatly improved. The measured results show a loaded Q-factor of 1569 and unloaded Q-factor of 8782, which is very high among other planar resonators. A simplified generalised phase noise condition and its optimisation approach are proposed for the low-phase noise oscillator design. To validate the proposed optimisation approach, experimental prototypes of oscillators using different design parameters and resonators are fabricated. The measured results show that the optimised SIW active resonator oscillator possesses low-phase noise of −109.2 dBc/Hz at 100 kHz at X-band, which is 17 and 9 dB better than the microstrip resonator oscillator and SIW passive resonator oscillator, and is comparable with the dielectric resonator oscillator measured in this study.

We consider the phase noise filtering problem for Interferometric Synthetic Aperture Radar （InSAR） using a total variation regularized complex linear least squares formulation. Although the original formulation is convex, solving it directly with the standard CVX package is time consuming due to the large problem size. In this paper, we introduce the effective and efficient alternating direction method of multipliers （ADMM） to solve the equivalent well-defined complex formulation for the real and imaginary parts of the optimization variables. Both the iteration complexity and the computational complexity of the ADMM are established in the forms of theorems for our InSAR phase noise problem. Simulation results based on simulated and measured data show that this new InSAR phase noise reduction method not only is 3 orders of magnitude faster than the standard CVX solver, but also has a much better performance than the several existing phase filtering methods.

This article shows the design of two different low phase noise (LPN) planar X-band frequency oscillators using two various microstrip filters (MFs). These two MFs act as a frequency stabilization part in the loop of the microwave oscillator. The first one, the modified Jerusalem MF (MJ-MF), is based on the Jerusalem scheme. The second one, the complementary modified Jerusalem MF (CMJ-MF), is complementary of the MJ-MF. Finally, by employing the branchline coupler, the LPN MF oscillator is achieved. The MJ-MF (narrowband filter) LPN X-band oscillator operates at 8.17 GHz and denotes a phase noise (PN) of −161 dBc/Hz at 1-MHz frequency offset. The CMJ-MF (wideband filter) LPN X-band oscillator operates at 8.14 GHz and mentions a PN of −157 dBc/Hz at 1-MHz frequency offset.

Laser phase noise is a critical factor that limits the range and performance of coherent lidar systems, especially in high-resolution applications such as inverse synthetic aperture lidar (ISAL), which demands stringent coherence. The effective suppression of laser phase noise is essential to enable high-resolution imaging over long distances. This paper presents a phase noise compensation technique utilizing dual reference channels (DRCs) based on concatenated generated phase (CGP) principles. The proposed method uses two reference channels with different delay lengths: a long-delay channel for coarse phase noise compensation and a short-delay channel for fine adjustments. We performed ISAL imaging experiments on stationary and rotating targets using a seed laser with a 3.41 MHz linewidth, achieving round-trip distances exceeding 110 times the laser coherence length. Imaging quality closely matched a 100 Hz narrow linewidth laser, approaching theoretical resolution limits. Compared to prior methods based on residual error linear estimation, the DRC method enhances compensation speed tenfold while maintaining accuracy. These results highlight the efficacy of the proposed DRC method in mitigating laser phase noise, significantly improving ISAL imaging performance.

SAR interferometry (InSAR) provides a framework for extracting high-resolution topographic information and detecting surface deformation. By analyzing the phase difference between radar acquisitions obtained at different times, one can characterize landscape geometry and surface changes. However, inherent phase noise often compromises the reliability of the resulting interferometric products. Consequently, there is a sustained need for spatial filtering techniques that suppress noise while preserving structural integrity and resolution. This work addresses the challenge of filtering the unwrapped phase, a process traditionally reliant on accurate coherence images to identify reliable pixels. We evaluate three statistically based spatial filters for phase noise reduction. The Enhanced Lee filter, which utilizes spatial adaptation and a physically grounded probability model, serves as the baseline for comparison. We examine the Gierull model, which improves computational efficiency by restricting the parameter space. To further reduce execution time, we propose and evaluate two empirical alternatives: the truncated wrapped normal (TcN) and the truncated wrapped Cauchy (TcC) distributions. Results indicate that these empirical models significantly reduce computational demand without degrading the quality of the filtered phase. We assess performance using a simulated dataset for objective validation alongside InSAR imagery of La Cumbre volcano, Los Alamos, and Robledo volcano. While the proposed models demonstrate significant gains in computational efficiency compared to current methods, we identify numerical integration as a primary bottleneck in the filtering process; this challenge warrants further investigation. Our results indicate that empirical statistical models provide a viable path for accelerated InSAR processing with accuracy equivalent to traditional, computationally intensive approaches.

The future generations of communication technologies envision the transmission of signals across the millimeter wave and sub-THz spectrums. However, the characteristics of the propagation channel at such high frequencies differ from what is observed in the conventional low-frequency spectrum with for instance, the apparition of stronger phase noise (PN) induced by the Radio Frequency (RF) transceivers and more especially by the oscillators. That is why there is growing interest in evaluating and adapting the 5G new radio (5G-NR) physical layer to the presence of PN. This article is dedicated to the study of discrete Fourier transform-spread-Orthogonal Frequency Division Multiplexing (DFT-s-OFDM) under uncorrelated Gaussian PN (GPN) impairments. We show that the presence of GPN induces two distortions: (i) a frequency-dependent random rotation of data, namely the subcarrier phase error (SPE) and (ii) a frequency-dependent intercarrier interference (ICI) that are analytically expressed. Then, we investigate the design of the adapted and optimal detection criterion according to the baseband model we derived in this paper. We demonstrate that (i) the proposed polar detector outperforms the conventional Euclidean detector and (ii) contrary to legacy OFDM, DFT-s-OFDM is a promising solution when strong GPN is involved.

The article examines the necessity of establishing a primary working standard for the unit of relative phase noise in order to ensure metrological traceability of phase noise measurements at low levels. The relevance of creating such a standard consists in the increased requirements for short-term frequency stability of modern signal generators and highly stable crystal oscillators, which is characterized by a relative phase noise level. It is noted that under available verification procedures, the error of phase noise measurements is determined via sinusoidal phase modulation, which does not cover low levels of phase noise. The presence of additional unaccounted sources of error in measuring phase noise in the low-level range has been experimentally demonstrated, which is additionally confirmed in various publications. A phase noise calibrator was developed on the basis of the additive white Gaussian noise method to be used as part of the primary working standard (i.e., to reproduce the unit within low levels of phase noise). In order to disseminate the unit of relative phase noise, it is proposed to use a comparator in the form of a phase noise analyzer within the local hierarchy scheme. In this case, the values of relative phase noise reproduced by the calibrator are close to the measured values due to the possibility of adjusting the level of additive white Gaussian noise. This approach enabled a two- to threefold reduction in the error due to measuring relative phase noise as compared to the normalized error of phase noise analyzers and ensured the reliability of low phase noise estimation within a small value range.

This paper proposed an adaptive bandwidth Phase-Locked Loop (PLL) that integrates integer-N and fractional-N switching for energy-efficient RF synthesis in IoT and mobile applications. The architecture exploits wide-bandwidth integer-N mode for rapid lock acquisition, then seamlessly transitions to narrow-bandwidth fractional-N mode for high-resolution synthesis and noise optimization. The architecture features a bandwidth-reconfigurable loop filter with intelligent switching control that monitors phase error dynamics. A novel adaptive digital noise filter mitigates ΔΣ quantization noise, replacing conventional synchronous delay lines. The multi-loop structure incorporates a high-resolution digital phase detector to enhance frequency accuracy and minimize jitter across both operating modes. With 180 nm CMOS technology, the PLL consumes 13.2 mW, while achieving −119 dBc/Hz in-band phase noise and 1 psrms integrated jitter. With an operating frequency range at 2.9–3.2 GHz from a 1.8 V supply, the circuit achieves a worst case fractional spur of −62.7 dBc, which corresponds to a figure of merit (FOM) of −228.8 dB. Lock time improvements of 70% are demonstrated compared to single-mode implementations, making it suitable for high-precision, low-power wireless communication systems requiring agile frequency synthesis.

Fiber interferometers are widely used in precision measurement fields such as seismic observation, gravitational-wave detection, and aerospace guidance. However, phase noise in the Hz–kHz range has become an important factor limiting further improvement in measurement accuracy. In this work, a solid-core photonic crystal fiber (PCF) and a hollow-core photonic bandgap fiber (HC-PBGF) were introduced into the sensing arms of a fiber interferometer to reduce phase noise in this frequency range. Theoretical analysis showed that, compared with a conventional solid-core fiber, the PCF and the 19-cell HC-PBGF used in this study could reduce the phase noise by approximately 3 dB and 7 dB, respectively. The experimental results agreed well with the theoretical predictions, confirming that both fibers can effectively suppress high-frequency phase noise, with HC-PBGF showing superior noise reduction performance. This work provides a feasible approach for improving the performance of fiber interferometers in precision measurement.