Phase Noise Mitigation Research Articles

Amplified squeezed states: analyzing loss and phase noise

Abstract Phase-sensitive amplification of squeezed states is a technique to mitigate high detection loss, which is especially attractive at 2μm wavelengths. We derived an analytical model proving that amplified squeezed states can mitigate phase noise significantly. Our model discloses two practical parameters: the effective measurable squeezing and the effective detection efficiency of amplified squeezed states. A realistic case study includes the dynamics of the gain-dependent impedance matching conditions of the amplifier. Our results recommend operating the optical parametric amplifier at high gains because of the signal-to-noise ratio’s robustness to phase noise. Amplified squeezed states are relevant in proposed gravitational wave detectors and interesting for applications in quantum systems degraded by the output coupling loss in optical waveguides.

Hybrid algorithm for initial phase calibration of optical phased array.

The synthesis of laser coherence and the accuracy of beam scanning, which are based on an optical phased array (OPA), are severely constrained by phase noise. This limitation hampers their applications in various fields. Currently, the most widely utilized calibration method is adaptive optics, which can effectively mitigate phase noise and enhance the quality of the output beam. However, because of the multiple array elements of the OPA and the large optimization range for each element, the adaptive optimization method experiences slow convergence and a high risk of falling into local optima. We propose a narrowing search range algorithm that can quickly reduce phase noise by narrowing the search range of the optimal value. After initial optimization, the SPGD algorithm was used. This study was verified through simulations and experiments utilizing the OPA of various array elements. These findings indicate that the hybrid algorithm expedites the calibration process, requires simple experimental equipment, and can be broadly utilized.

A design of a high‐resolution frequency modulated continuous wave radar for drone detection based on spurious phase noise and discrete clutter reduction

AbstractThe authors deal with the problem of the design and manufacture of a high‐resolution FMCW radar for drone detection and classification. The difficulties of the problem are discrete clutter reduction and spurious phase noise mitigation. The discrete clutter is due to the reflected signals from land vehicles, birds etc., while the spurious phase noise is inherent in the radar signal due to the phase‐locked loop component and leakage between the transmitting and receiving paths. Both spurious phase noise and clutter will increase the system noise level and hence reduce the probability of detection of small targets such as drones and induce false alarms on the radar screen. In order to reduce discrete clutter, the authors propose a method to separate a drone from discrete clutter based on the design of the radar system parameters for a drone and its propeller detection, target's Doppler dispersion and moving characteristics. For spur mitigation, a method that focuses on the design of the isolation coefficient between transmitting and receiving paths to decrease the power of spurs below the minimum power requirement at the input of the analogue‐to‐digital converter is introduced. The results were applied by the authors to the development and manufacture of a radar with the given specifications for drone detection and classification. Different laboratory and field tests show that the spurs are mitigated and the drones are separated from discrete clutter with a range and accuracy better than the one recently published.

On the design of low phase noise and flat spectrum optical parametric frequency comb

Optical frequency combs (OFCs) have become increasingly pervasive in recent years, with their advantageous frequency coherence properties enabling significant developments in numerous fields, such as optical communications, spectroscopy, and microwave signal processing. Recent interest in OFC development emphasizes minimizing and mitigating phase noise of individual comb lines for high-quality signal generation, processing, and detection. Cavity-less electro-optic combs and parametric combs are attractive sources for these applications in that they permit flat spectra, tunable tone spacing, and robustness to temperature variations. Although previous research has demonstrated broadband parametric OFC generation, the scaling of the phase noise has not been systematically investigated. Here, we demonstrate a 25 GHz-spacing cavity-less parametric OFC generator and investigate the interaction between electronic and optical noise sources that affect its phase noise and linewidth. In addition, we study the optimal design of a nonlinear amplified loop mirror based pulse shaper with a focus on the impact of pump power on the signal-to-pedestal power ratio, which ultimately influences the spectral flatness and the optical signal-to-noise ratio (OSNR) after the parametric expansion. Notably, we design the OFC using all polarization-maintaining (PM) components, demonstrating the performance of PM highly nonlinear fibers in parametric comb generation. This results in a PM cavity-less comb with <9 dB power variation over 110 nm, >0 dBm power per tone, <10 kHz linewidth, and >23 dB OSNR. These characteristics make it highly desirable for application in communication and signal processing.

On the Nonlinear Shaping Gain With Probabilistic Shaping and Carrier Phase Recovery

The performance of different probabilistic amplitude shaping (PAS)techniques in the nonlinear regime is investigated, highlighting its dependence on the PAS block length and the interaction with carrier phase recovery (CPR). Different PAS implementations are considered, based on different distribution matching (DM) techniques—namely, sphere shaping, shell mapping with different number of shells, and constant composition DM—and amplitude-to-symbol maps. When CPR is not included, PAS with optimal block length provides a nonlinear shaping gain with respect to a linearly optimized PAS (with infinite block length); among the considered DM techniques, the largest gain is obtained with sphere shaping. On the other hand, the nonlinear shaping gain becomes smaller, or completely vanishes, when CPR is included, meaning that in this case all the considered implementations achieve a similar performance for a sufficiently long block length. Similar results are obtained in different link configurations ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1\times 180$</tex-math></inline-formula> km, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$15\times 80$</tex-math></inline-formula> km, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$27\times 80$</tex-math></inline-formula> km single-mode-fiber links), and also including laser phase noise, except when in-line dispersion compensation is used. Furthermore, we define a new metric, the nonlinear phase noise (NPN) metric, which is based on the frequency resolved logarithmic perturbation models and explains the interaction of CPR and PAS. We show that the NPN metric is highly correlated with the performance of the system. Our results suggest that, in general, the optimization of PAS in the nonlinear regime should always account for the presence of a CPR algorithm. In this case, the reduction of the rate loss (obtained by using sphere shaping and increasing the DM block length) turns out to be more important than the mitigation of the nonlinear phase noise (obtained by using constant-energy DMs and reducing the block length), the latter being already granted by the CPR algorithm.

Phase noise mitigation in photonics-based radio frequency multiplication.

Two photonics-based radio frequency multiplication schemes for the generation of high-frequency carriers with low phase noise are proposed and experimentally demonstrated. With respect to conventional frequency multiplication schemes, the first scheme induces a selective cancelation of phase noise at periodic frequency-offset values, whereas the second scheme provides a uniform 3-dB mitigation of phase noise. The two schemes are experimentally demonstrated for the generation of a 110-GHz carrier by sixfold multiplication of an 18.3-GHz carrier. In both cases, the experimental results confirm the phase noise reduction predicted by theory.

Phase rearrangement shell mapping in single-span nonlinear optical fiber communication system

The importance of single-span systems is emphasized by the fact that they currently constitute the fastest growing section of the fiber communication markets. In such systems, the correlation time of the nonlinear phase noise is too short to allow the nonlinear phase-noise mitigation such as adaptive phase-recovery or equalization, while it is sufficient for the shaping approaches. The multi-dimensional (MD) coded-modulation based standard shell mapping (SM) algorithm can realize signal shaping and mitigate the nonlinear phase noise in single-span optical fiber transmissions. However, the standard SM algorithm has poor performance resulted from the decoding penalty in two-dimensional (2D) decoding with a low signal-to-noise (SNR) ratio. In this paper, we propose a phase rearrangement shell mapping (PRSM) algorithm to improve the 2D decoding performance by rearranging the constellation sequence in order of signal phase for each shell. This proposed technique is verified through the simulation of a 5 × 70-GBaud 4D/8D modulated signal in a 5-channel wavelength division multiplexing (WDM) system after a single span transmission of 100-km standard single mode fiber (SSMF). We also conduct an experiment to verify the performance of 3 × 45-GBaud 4D/8D-16QAM with PRSM algorithm after unrepeated transmission of 100-km SSMF. The simulation and experimental results show that the Q2 factor gain of PRSM-4D/8D-16QAM is about 0.2∼0.3 dB compared with standard SM-4D/8D-16QAM using 2D decoding. There is about 1.6-dB or 1.8-dB launch optical power (LOP) dynamic range improvement by PRSM compared with standard SM for 4D/8D-16QAM, respectively.

Phase noise mitigation of the microwave-to-photonic conversion process using feedback on the laser current

The generation and transfer of ultra-stable microwave signals are of paramount importance in numerous applications spanning from radar systems to communications and metrology. We demonstrate residual phase noise mitigation at 10 GHz of a directly modulated laser system through active control of the laser bias current. The latter is tuned to a finely selected point, where the current-to-phase dependence, measured at several microwave power and frequency values, is maximized. A residual phase noise of − 113 d B r a d 2 / H z at 1 Hz offset frequency from a 10 GHz carrier, with a fractional frequency stability of 1.2 × 10 − 16 at 1 s and below 10 − 19 at 10 5 s , is measured. These performances are compliant with the transfer of the most stable microwave signals available to date, obtained with cryogenic sapphire oscillators or combs locked to cavity-stabilized lasers. This approach is of interest for the distribution of ultra-stable microwave signals in a very simple photonic configuration.

OFDM Radar and Communication Joint System Using Opto-Electronic Oscillator With Phase Noise Degradation Analysis and Mitigation

Orthogonal frequency division multiplexing (OFDM) signal is a superior dual-functional waveform for the integration of radar sensing and communication in intelligent transportation. But the sensitivity to phase noise is a serious issue introducing interference and causing performance degradation during demodulation. In this paper, we explore the essential mechanism of the action and generation of phase noise through theoretical analysis, where the OFDM demodulation process and power spectrum density (PSD) of phase noise is discussed in the frequency domain, and draw the conclusion that high-speed phase jitter will cause unrecoverable deterioration of OFDM demodulation. Therefore, a photonics-aided radar and communication integrated system based on Optoelectronic oscillator (OEO) is proposed. The positive feedback oscillation with long energy storage time make the phase noise pattern of OEO just suitable to against the phase noise sensitivity of OFDM. A proof-of-concept experiment is demonstrated at 24 GHz with 2 GHz bandwidth to verify the radar sensing and communication function. A two-dimensional radar imaging with a range resolution of 0.075 m and velocity resolution of 4.4 km/h, a communication capacity of 6.4 Gbps is obtained. A quantitative performance comparison is also carried out. By using an ordinary microwave source and OEO separately, the demodulation constellation and error vector magnitude (EVM) under different subcarrier spacing is measured and compared. The result is corresponding to our analysis with the EVM decreasing from 12.5% to 4.7% under subcarrier spacing of 125 kHz.

Optimization of 16-QAM and 32-QAM Constellations for Mitigating Impairments of Phase Noise in Millimeter-Wave Receivers

In this paper, two optimized circular quadrature amplitude modulations (C-16QAM and C-32QAM) are proposed to mitigate phase noise in millimeter-wave receivers. A six-port direct conversion receiver in a short range wireless link test bench is used to validate the concept. Those modulation techniques are performed through the optimization of both, Euclidean distance between symbols and the gap between the concentric rings of the symbol constellation. The numerical simulations and experimental results show that the proposed constellation schemes can achieve lower bit error rate (BER) compared to the typical squares 16-QAM and 32-QAM, and other C-16QAM and C-32QAM modulations, reported in the literature.

Phase noise mitigation by a realistic optical parametric oscillator

We address the exploitation of an optical parametric oscillator (OPO) in the task of mitigating, at least partially, phase noise produced by phase diffusion. In particular, we analyze two scenarios where phase diffusion is typically present. The first one is the measurement of the phase of a noisy optical field, while the second involves a quantum estimation scheme of a phase shift imposed on a noisy probe. In both cases, we prove that an OPO may lead to a partial or full compensation of the noise.

Mitigation of time-series InSAR turbulent atmospheric phase noise: A review

Synthetic Aperture Radar (SAR) interferometry is one of the most powerful remote sensing tools for ground deformation detection. However, tropospheric delay greatly limits the measurement accuracy of the InSAR technique. While vertically stratified tropospheric delays have been extensively investigated and well tackled, turbulent tropospheric phase noise still remains an intractable issue. In recent years, great efforts have been made to reduce the influence of turbulent atmospheric delay. This contribution is intended to provide a systematic review of the progress achieved in this field. First, it introduces the physical characteristics of atmospheric signals in interferograms. Then, a review of the main mitigation algorithms proposed in the literature is provided. In addition, the strengths and weaknesses of each approach are analyzed to provide guidance for choosing a suitable method accordingly. Finally, suggestions for resolving the challenging issues and an outlook for future research are given.

Artificial Neural Network Symbol Estimator With Enhanced Robustness to Nonlinear Phase Noise

This letter reports a novel approach for nonlinear phase noise mitigation, based on artificial neural networks (ANNs) tailored to classification applications and a pre-processing stage of feature engineering. Starting with a set of proof-of-concept simulations, we verify that the proposed system can achieve optimal performance for the additive white Gaussian noise (AWGN) channel. Then, considering a dispersion-less channel with strong nonlinear phase noise (NLPN) distortion, we demonstrate a Q-factor increase of 0.4dB, comparing with standard carrier-phase estimation (CPE) followed by minimum distance detection. Finally, simulating the propagation of 64Gbaud PM-16QAM over standard single mode fiber (SSMF), we verify that the ANN-based solution is effective on wavelength-division multiplexing (WDM) transmission conditions, enabling to increase the maximum signal reach by approximately 1 fiber span over the legacy CPE-enabled NLPN compensation.

Mitigation of nonlinear phase noise in single-channel coherent 16-QAM systems employing logistic regression

We propose and analyze a classifier based on logistic regression (LR) to mitigate the impact of nonlinear phase noise (NPN) caused by Kerr-induced self-phase-modulation in digital coherent systems with single-channel unrepeated links. Simulation results reveal that the proposed approach reduces the bit error ratio (BER) in a 100-km-long 16 quadrature amplitude modulation (16-QAM) system operating at 56-Gbps. Thus, the BER is reduced from 6.88 × 10−4 when using maximum likelihood to 4.27 × 10−4 after applying the LR-based classification, representing an increase of 0.36 dB in the effective Q-factor. This performance enhancement is achieved with only 624 operations per symbol, which can be easily parallelized into 16 lines of 39 operations.

Mitigation of phase noise and Doppler-induced frequency offsets in coherent random amplitude modulated continuous-wave LiDAR

We present a detailed analysis of techniques to mitigate the effects of phase noise and Doppler-induced frequency offsets in coherent random amplitude modulated continuous-wave (RAMCW) LiDAR. The analysis focuses specifically on a technique which uses coherent dual-quadrature detection to enable a sum of squares calculation to remove the input signal's dependence on carrier phase and frequency. This increases the correlation bandwidth of the matched-template filter to the bandwidth of the acquisition system, whilst also supporting the simultaneous measurement of relative radial velocity with unambiguous direction-of-travel. A combination of simulations and experiments demonstrate the sum of squares technique's ability to measure distance with consistently high SNR, more than 15 dB better than alternative techniques whilst operating in the presence of otherwise catastrophic phase noise and large frequency offsets. In principle, the technique is able to mitigate any sources of phase noise and frequency offsets common to the two orthogonal outputs of a coherent dual-quadrature receiver including laser frequency noise, speckle-induced phase noise, and Doppler frequency shifts due to accelerations.

Mitigation of Phase Noise and Nonlinearities for High Capacity Radio-over-Fiber Links

Radio-over-fiber (RoF) links successfully provide high data rates and bandwidth capacity with a low complexity system architecture, as compared to its counterpart digital-RoF. In addition, the compound of quadrature amplitude modulation (QAM) and orthogonal frequency division multiplexed (OFDM) modulation schemes further enhance the process of these achievements. However, high data rates and bandwidth-capacity-supported RoF links face nonlinearities (NLs), linear distortions (LDs), and phase noise challenges that degrade the reliability of communication networks (CNs). Therefore, in this paper, to suppress NLs, LDs, and phase noise, next generation cloud radio access networks (CRANs) are investigated using RoF links and wavelength division multiplexing (WDM) methodology based on 16, 32, and 64 QAM-OFDM modulation schemes. The receiver of the proposed framework is designed, applying an improved digital signal processing (DSP) system that includes overlap frequency domain equalization (OFDE), a synchronization process, and time domain equalization (TDE). Theoretical and simulation models are organized for estimating the proposed RoF link with the aid of different values of transmission ranges, input power, output power, bit rate, bits per symbol, channel spacing, and the number of users. The fitness of the model matches that of existing approaches.

Accurate Estimation of Chromatic Dispersion for Non-Degenerate Phase-Sensitive Amplification

A phase-sensitive amplifier (PSA) has the potential of low-noise optical amplification and nonlinear phase noise mitigation. For PSA operation, the chromatic dispersion (CD) that causes gain ripple must be compensated before amplification. We propose an accurate CD estimation method for non-degenerate PSAs (ND-PSAs). We experimentally demonstrated its effectiveness by using periodically poled LiNbO3 waveguides as amplification mediums. We first modified the conventional formula for the gain spectrum under residual CD conditions to be applicable to ND-PSAs by considering phase locking. We then experimentally described the effect of passband narrowing due to the gain ripple on the signal quality using a probabilistically shaped 64QAM signal. Furthermore, we applied the modified formula to CD estimation and compensation. As a result, accurate CD estimation on the sub-ps/nm order and gain-flattened spectrum over 3.5 THz were demonstrated with our method. We also propose a method for estimating residual CD from the gain variation among wavelength division multiplexing (WDM) channels. The possibility of adaptive compensation for CD was shown by carrying out WDM amplification.

Design of Time-Frequency Packed WDM Superchannel Transmission Systems

We consider time and frequency-packing (TFP) wavelength division-multiplexing (WDM) superchannel systems for longhaul optical fiber communication. Employing very high baud rates in conjunction with higher-order modulation formats is challenging due to practical constraints. TFP superchannels therefore become an attractive choice to facilitate high data rates with improved spectral efficiency. However, TFP introduces inter-symbol interference (ISI) and/or inter-carrier interference (ICI) that necessitate efficient interference handling techniques. Moreover, phase noise (PN) due to wide laser linewidth (LLW) may cause significant signal distortion in WDM transmission, and the presence of ISI and ICI in TFP systems further complicates carrier phase recovery (CPR). In this article, we propose a spectrally efficient TFP superchannel design equipped with powerful interference cancellation and PN mitigation techniques, targeting Terabit-per-second (Tbps) data rates. First, we propose a joint ISI and ICI channel estimation algorithm coupled with polarization-recovery and a coarse PN cancellation method. Second, we investigate two iterative CPR algorithms to mitigate the distortion due to the residual PN. Third, a combination of successive and parallel interference cancellation methods for ICI mitigation is investigated in tandem with turbo ISI equalization. The effectiveness of the proposed algorithms is demonstrated through computer simulations of a coded TFP superchannel system in the presence of linear fiber impairments, targeting a throughput of 1.2 Tbps. Numerical results suggest that the proposed TFP design offers more than 2 dB performance gains and as high as 960 km transmission distance improvement over existing competitive super-Nyquist designs. Simulation results also indicate that the proposed design exhibits excellent tolerance to high LLWs and aggressive optical filtering stemming from cascaded reconfigurable optical add-drop multiplexers in the fiber link.

Pilot-Free Common Phase Error Estimation for CO-OFDM With Improved Spectral Efficiency

We propose an improved pilot free phase noise mitigation algorithm for CO-OFDM systems using weighted multi-level QPSK partitioning and Kalman filtering. Through extensive Monte Carlo simulations, we demonstrate an improvement in spectral efficiency of $>$ 6% in case of 200 Gbps single channel and 1 Tbps multi channel 16QAM CO-OFDM transmission with blind carrier phase estimation. We also experimentally demonstrate the performance of the proposed algorithm against the standard pilot aided algorithm for the transmission of 120 Gbps 16QAM CO-OFDM at different noise levels.

Phase Noise Cancelation Based on Polarization Modulation for Massive MIMO-OFDM Systems

In massive multiple-input multiple-output (MIMO) systems, phase noise introduced by oscillators can cause severe performance loss. It leads to common phase error and intercarrier interference in massive MIMO-OFDM uplink. To solve the issue, a novel phase noise cancelation scheme based on polarization modulation for the massive MIMO-OFDM system is proposed. We first introduce the polarization modulation (PM) exploited in massive MIMO-OFDM uplink. Then, by exploiting the zero-forcing detection, we analyze the asymptotically ICI and the distribution of the transformed noise under different XPD values. Furthermore, we demonstrate that phase noise can be asymptotically canceled and only the transformed additive white Gaussian noise exists as the number of antennas at the base station is very large. Moreover, we derive the instantaneous signal-to-noise ratio (SNR) on each subcarrier and analyze the ergodic capacity. To increase the ergodic capacity performance further, a joint modulation scheme combining the PM and 2PSK is proposed and the ergodic capacity performance of the joint modulation is discussed. The simulation results show that the proposed scheme can effectively mitigate phase noise and achieve a higher ergodic capacity.