Phase Noise Cancellation Research Articles

Earthquake source inversion by integrated fiber-optic sensing

We present an earthquake source inversion using a single time series produced by integrated fiber-optic sensing in a phase noise cancellation (PNC) system used for frequency metrology. Operating on a 123 km long fiber between Bern and Basel (Switzerland), the PNC system recorded the Mw3.9 Mulhouse earthquake that occurred on 10 September 2022 around 10 km north-west of the northern fiber end. A generalised least-squares inversion in the 4 - 13 s period band constrains the components of a double-couple moment tensor with an uncertainty that corresponds to around 0.2 moment magnitude units, nearly independent of prior information. Uncertainties for hypocenter location and original time are more variable, ranging between 4 - 20 km and 0.1 - 1 s, respectively, depending on whether injected prior information is realistic or almost absent. This work is a proof of concept that quantifies the resolvability of earthquake source properties under specific conditions using a single-channel stand-alone integrated (non-distributed) fiber-optic measurement. It thereby constitutes a step towards the integration of long-range phase-transmission fiber-optic sensors into existing seismic networks in order to fill significant seismic data gaps, especially in the oceans.

Phase noise cancellation for digital holographic microscopy based on compressed sensing iterative adaptive sparse dictionary

Digital holographic microscopy (DHM), like other digital imaging techniques, will introduce severe coherent noise, which is called random noise, due to the high coherence of the required light source and the measurement experimental environment. Random noise seriously affects the accuracy of DHM surface topography measurements. To overcome this problem, this paper proposes a DHM phase noise cancellation method based on compressed sensing (CS) iterative adaptive sparse dictionary. The holographic image is first acquired using the proposed recording method. Then a sparse dictionary more suitable for the sample is trained by dictionary learning to sparsely encode the holographic image. Finally, reconstruction is performed using the improved orthogonal matching pursuit (IOMP), which can obtain almost noise-free holographic images. The experimental results show that the reconstructed phase peak signal-to-noise ratio (PSNR) is 33.2871, which is improved by 65.01 %. The sample feature similarity is 0.9553, which is improved by 45.41 %. The proposed method can also be used with different learning modes and learning objects. On top of the original results, the reconstructed phase PSNR was able to continue to improve by 5.99 % and its reconstruction time was also accelerated by 29.57 %.

Optical frequency dissemination via 103-km urban fiber link with remote passive phase stabilization.

In this paper, we propose a technique for a fiber-based optical frequency dissemination system with remote passive phase noise cancellation. At the remote site, a 1×2 fiber pigtailed acousto-optic modulator (AOM) with two diffraction order outputs (0 and -1 order) is employed as the phase-compensated device, the undesired phase noise of fiber link introduced by environmental perturbations are passively canceled at remote sites. Different from other existing schemes, the proposed technique harnesses the benefits of remote radio frequency (RF) independence and low-temperature sensitivity in this noise-suppression configuration. Consequently, the system noise floor of the proposed optical frequency dissemination system achieves 9.44 × 10-21 without requiring a precise remote RF reference, and the phase-temperature coefficient is reduced to about 2 fs/K. A real-world experiment is conducted over a noisy round-trip 103 km urban fiber link. After being passively compensated, we demonstrate a fractional frequency instability of 1.57 × 10-14 at the integration time of 1 s and scales down to 3.96 × 10-20 at 10,000 s in terms of modified Allan deviation. The frequency uncertainty of the retrieved light after transferring through this noise-compensated fiber link relative to that of the input light achieves 1.80 × 10-18. This work demonstrates the system's capability to disseminate the ultra-stable optical frequency standards and is a significant step towards realizing multi-node dissemination of the state-of-the-art optical clock signal with remote noise compensation via a tree-like topology fiber network.

A Quadrature Balanced N-Path Receiver for Frequency Division Duplex With Thermal and Phase Noise Cancellation Under Antenna VSWR

A Quadrature Balanced <i>N</i>-Path Receiver for Frequency Division Duplex With Thermal and Phase Noise Cancellation Under Antenna VSWR

Coherent optical frequency transfer via 972-km fiber link

We demonstrate coherent optical frequency dissemination over a distance of 972 km by cascading two spans where the phase noise is passively compensated for. Instead of employing a phase discriminator and a phase locking loop in the conventional active phase control scheme, the passive phase noise cancellation is realized by feeding double-trip beat-note frequency to the driver of the acoustic optical modulator at the local site. This passive scheme exhibits fine robustness and reliability, making it suitable for long-distance and noisy fiber links. An optical regeneration station is used in the link for signal amplification and cascaded transmission. The phase noise cancellation and transfer instability of the 972-km link is investigated, and transfer instability of 1.1 × 10−19 at 104 s is achieved. This work provides a promising method for realizing optical frequency distribution over thousands of kilometers by using fiber links.

Long-range fiber-optic earthquake sensing by active phase noise cancellation

We present a long-range fiber-optic environmental deformation sensor based on active phase noise cancellation (PNC) in metrological frequency dissemination. PNC sensing exploits recordings of a compensation frequency that is commonly discarded. Without the need for dedicated measurement devices, it operates synchronously with metrological services, suggesting that existing phase-stabilized metrological networks can be co-used effortlessly as environmental sensors. The compatibility of PNC sensing with inline amplification enables the interrogation of cables with lengths beyond 1000 km, making it a potential contributor to earthquake detection and early warning in the oceans. Using spectral-element wavefield simulations that accurately account for complex cable geometry, we compare observed and computed recordings of the compensation frequency for a magnitude 3.9 earthquake in south-eastern France and a 123 km fiber link between Bern and Basel, Switzerland. The match in both phase and amplitude indicates that PNC sensing can be used quantitatively, for example, in earthquake detection and characterization.

Photonic millimeter-wave transfer with balanced dual-heterodyne phase noise detection and cancellation.

We report on the realization of long-haul and high-precision millimeter-wave (mm-wave) transfer through a fiber-optic link based on balanced dual-heterodyne phase noise detection. The balanced dual-heterodyne detection is achieved by detecting the fiber phase noise superimposed two intermediate frequency (IF) signals without requiring a local synchronization signal and its output is used to compensate the fiber-induced phase noise by actuating the frequency of the one optical carrier. The proposed scheme can effectively get rid of the effect of the local reference, largely simplifying the configuration at the local site. Additionally, we model and experimentally study the noise contribution coming from the out-of-band, which can be effectively suppressed to the below of the system noise floor with a fractional frequency instability of 1.9 × 10-17 at 10,000 s by designing and implementing a high-precision temperature control module with a peak-to-peak temperature fluctuation of no more than 0.002 K. We experimentally demonstrate that a 100 GHz mm-wave signal to be transmitted over a 150 km fiber-optic link can achieve the fractional frequency instabilities of less than 3.4 × 10-14 at 1 s and 3.5 × 10-17 at 10,000 s.

Suppression of laser phase noise by using updated common arm locking

The space-borne gravitational wave (GW) detectors, e.g., LISA, TianQin, TaiJi, are designed to measure the GW in the low-frequency regime (0.1 mHz to 1 Hz). The arm length mismatches in the flying constellation prevent exact laser phase noise cancellation. For a typical Michelson interferometric design such as LISA, the two arms will differ by a few percent and the uncanceled fluctuation from the ultra-stable laser is about 5 orders larger than the sensitivity goal in the science band (0.1 mHz to 1 Hz). In this work, we try to resolve this discrepancy in real time by using an arm locking technique. Unlike the analysis in previous literatures, we use the subtraction of one closed loop phase meter output from another one at the main spacecraft to cancel the laser phase noise further. We find that, with a careful design of the arm locking controller, the laser phase noise can be suppressed below the level of secondary noises in most parts of the science band. We point out that since the nulls always exist in the presence the GW transfer function of Michelson interferometer, there is no need to move the nulls to outside the science band by using a complicated arm locking sensor. Then, a study on the Doppler frequency pulling for the system has been carried out, and the result suggests that the pulling rate can meet the requirement. Finally, a good agreement between the time-series simulation in Simulink and theoretical result indicates the feasibility of this scheme. Therefore, the suppression of laser phase noise can possibly be realized in real time with prestabilization and updated common arm locking techniques. Our work can provide a back-up strategy for the implementation of arm locking in future space-borne GW detectors.

Joint Cancellation of Phase Noise and Clipping Noise for OFDM

The problem of high peak-to-average power ratio (PAPR) and phase noise (PHN) weighs heavily against the performance of orthogonal frequency division multiplexing (OFDM). They can cause out-of-band radiation and signal distortion. The clipping method is efficient to reduce the high PAPR. This paper studies the problem of data detection under PHN for clipped OFDM. An optimization function is established over PHN and data. After that, the variational message passing theory is applied to calculate the key parameters of the simplified posterior distribution of unknown parameters. Theoretical analysis and simulation results demonstrate the effectiveness and merit of the proposed algorithm.

Improved Phase Noise Cancellation Technology for Auxiliary Reference Interferometer Demodulation Scheme

In an unbalanced interferometer, the phase noise level is positively related to the optical path length difference (OPD) and the wavelength instability of the light source. The effective current solution for reducing phase noise is to use an auxiliary reference interferometer to measure the phase noise signal. However, this method requires that all interferometers have the same OPD, otherwise the phase modulation depth of different interferometers with the same light source will be different and the noise reduction effect will be severely reduced. It is difficult to provide interferometers with precisely the same OPD in practical. In this paper, an improved phase-generated carrier (PGC) demodulation technique for phase noise cancellation that does not require strictly equal OPDs of interferometers is proposed. Combining an auxiliary reference interferometer scheme with an ellipse fitting algorithm (EFA) can eliminate the effect of different phase modulation depths due to different OPDs, and phase modulation depth drift on demodulation results, significantly reducing harmonic distortion. The additional phase modulation signal ensures the correct calculation of small signals by the EFA, while the OPDs of the interferometers are evaluated in real time to achieve constant phase noise cancellation capability under different OPD. Experimental results show that the proposed technique achieves a highly stable phase demodulation result with a maximum phase noise reduction of about 9dB and a minimum THD of -74.59 dB in interferometers with non-strict equal OPD.

Coherent-detection radio-over-fiber link with high spectral efficiency based on digital phase noise cancellation.

A radio-over-fiber (RoF) link with high spectral efficiency using digital phase cancellation is proposed and experimentally verified. The link can be utilized to transmit four microwave vector signals. The four microwave vector signals are modulated on optical signals by using a dual-polarization dual-parallel Mach-Zehnder modulator at the transmitter. The optical signals subsequently pass through a spool of single-mode fiber (SMF) and are sent into a coherent receiver. A digital signal processing (DSP) algorithm is proposed to eliminate the phase noise and frequency difference caused by two free-running lasers at transmitter and receiver. Two 16-quadrature amplitude modulation (16-QAM) vector signals at 6GHz and another two 16-QAM vector signals at 7GHz transmit over a 10-km SMF and are successfully recovered after a DSP algorithm. In order to evaluate the transmission performance of the RoF link, error vector magnitudes and bit error rates are also estimated.

Supply-Noise-Desensitized Techniques for Low Jitter RO-Based PLL Achieving ≤1.6 ps RMS Jitter Within Full-Spectrum Supply Interference

This paper presents a supply-noise-robust PLL that achieves low-jitter performance within full-spectrum supply interference. A digital-regulated supply noise cancellation (DSNC) scheme suppresses the large amplitude supply noise within an adequate range for a supply-noise-insensitive (SNI) VCO. It ensures that the low pushing factor SNI-VCO only induces a decent amount of phase noise falling within the effective correction range of the phase noise cancellation (PNC). A sample-and-isolate-based (S/I)-PNC cascaded at the VCO output enables a wider correction range for a fine supply noise and phase noise suppression. Fabricated in 28-nm CMOS with an area of 0.088 mm2, the proposed PLL consumes 6.65 mW from a 1 V supply at 4 GHz output. With 20 mVpp supply interference, the prototype obtains a maximum >37 dB output spur reduction at 5 MHz and maintains ≤1.6 ps RMS jitter in the worst case. The suppression performance degrades less than 10% within −20 °C to 80 °C operation temperature.

A Microwave Photonic Link With Quadrupled Capacity Based on Coherent Detection and Digital Phase Noise Cancellation

A microwave photonic link (MPL) with quadrupled capacity based on coherent detection and digital phase noise cancellation is proposed and experimentally demonstrated. At the transmitter, a continuous-wave (CW) light wave is intensity modulated by four independent microwave vector signals with two having an identical center microwave frequency at a dual-parallel Mach-Zehnder modulator (DPMZM) consisting of two dual-drive MZMs (DEMZMs) with the sub-DEMEMs biased at the quadrature transmission point. Four intensity-modulated optical signals are generated and transmitted over a single-mode fiber (SMF) to a coherent receiver. To perform coherent detection, a second CW laser source as a local oscillator (LO) is also applied to the coherent receiver. To recover the microwave vector signals, a novel digital phase noise cancellation algorithm is developed and applied to eliminate the joint phase noise from the transmitter laser source and the LO laser source as well as the unstable offset frequency between the two laser sources. A theoretical analysis is performed to show the recovery of the microwave vector signals which is verified by an experiment. For four independent 16 quadrature amplitude modulation (16-QAM) microwave vector signals with a symbol rate of 0.5 GSymbol/s, error-free transmission over a 9-km SMF is achieved when the received optical power at the coherent receiver is higher than −18 dBm with forward error correction (FEC).

All-Passive Cascaded Optical Frequency Transfer

We for the first time present an all-passive cascaded optical frequency transfer technique over a fiber link, in which the phase noise of the each fiber link introduced by environmental perturbation and the laser repeater station are simultaneously compensated by using passive phase noise cancellation. The laser repeater station consisting of a cavity-stabilized laser is employed as a regenerative amplifier with a 45 dB optical gain. We demonstrate a cascaded optical frequency transfer with two 100 km spooled fiber links and one laser repeater station, illustrating an instability of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4.8\times 10^{-15}$ </tex-math></inline-formula> at the integration of 1 s and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4.9\times 10^{-19}$ </tex-math></inline-formula> at 10,000 s improved by a factor of 2 compared to the single-span 200 km fiber link. Dividing the whole fiber link into sub-sections could significantly improve the bandwidth of the phase noise compensation. Additionally, all-passive phase noise cancellation has the advantage of avoiding the servo bumps in the transferred light relative to the conventional active technique. The proposed technique provides a promising solution for high-performance and robust long-distance optical frequency transfer.

A 1–2-GHz Quadrature Balanced N-Path Receiver for Frequency Division Duplex Systems

The implementation of fully integrated frequency division duplexing (FDD) transceivers imposes many challenges, such as receiver (RX) desensitization by the transceiver (TX), reciprocal mixing, and sensitivity, to antenna voltage standing wave ratio (VSWR) variations. Here, we present the quadrature balanced N-path receiver (QBNR) architecture. The QBNR is composed of a quadrature hybrid and two identical mixers, presenting a short circuit and 50- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula> matching in the TX and RX bands, respectively. The TX power reflects at the mixers and reconstructs in-phase at the antenna, while the RX signal from the antenna can be reconstructed in phase at the baseband RX port. This architecture provides wideband FDD functionality while providing TX noise and local oscillator phase noise cancelation and antenna VSWR tunable compensation. Our implementation measurement results for an equalized configuration show more than 55-dB TX to RX isolation at frequencies of 1–2 GHz and for antenna VSWR of 2:1, with 3-dB TX loss and 4-dB RX loss, RX IP <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1 dB</sub> of 5 dBm and TX IP <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1 dB</sub> of 16 dBm, and receiver <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${B_{1\,\text {dB}}}$ </tex-math></inline-formula> of 10 dBm.

Coherent UD-WDM RoF Fronthaul Network With D-EML Transmitter and Phase-Noise Robust Receiver

This work proposes and tests a simplified coherent uplink architecture for ultra-dense coherent analog mobile Fronthaul with phase noise cancellation based on single sideband modulation of a dual-EML. Results show optical channel spacings of only 1.5 GHz and error-free signal recovery with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \nu $ </tex-math></inline-formula> Tb = 1.2% and 3% with reaching power as low as −46dBm for 100 Mbit/s and −38 dBm for 1 Gbit/s using QPSK modulation.

A High Spectral Efficiency Radio Over Fiber Link Based on Coherent Detection and Digital Phase Noise Cancellation

An approach to transmitting two independent microwave vector signals on a single optical carrier with one polarization state based on coherent detection and digital phase noise cancellation is proposed and experimentally demonstrated. At the transmitter, two independent microwave vector signals are modulated on an optical carrier via a dual-drive Mach-Zehnder modulator (DD-MZM). The modulated optical signals are transmitted over a single-mode fiber (SMF) and sent to a coherent receiver. At the receiver, the optical signals are detected where a local oscillator (LO) optical wave generated by a second free-running laser source is also applied. To recover the two microwave vector signals, a novel digital signal processing (DSP) algorithm is developed and applied to eliminate the joint phase noise terms from the transmitter and the LO laser sources as well as the unstable offset frequency between the two laser sources. An experiment is performed. The transmission of two independent 16 quadrature amplitude modulation (16-QAM) microwave vector signals at 4 GHz with a symbol rate of 1 GSymb/s over a 9-km SMF is demonstrated. The transmission performance in terms of error vector magnitudes (EVMs) and bit error rates (BERs) is also evaluated.

Adaptive Phase Noise Cancellation Technique for Fiber-Optic Interferometric Sensors

The optical source phase noise is one of the main factors influencing the noise performance of fiber-optic interferometric measurement systems. The phase noise is directly proportional to the optical path length difference of the interferometer and wavelength instability of the optical source. Conventional phase noise suppression techniques involve the use of highly stable optical sources and reduction of path length differences of sensing interferometers. However, such methods are not always appropriate for all interferometric configurations. Alternative phase noise suppression techniques suggest the use of an auxiliary reference interferometer for independent measurements of the phase noise. In this case, the phase noise signal can be directly subtracted from the sensor signal. But equal path length differences are required for all interferometers in the measurement system. In this paper, an adaptive phase noise cancellation technique for fiber-optic interferometric sensors is presented. The proposed technique is based on the real-time evaluation of optical path length differences for all interferometers in the measurement system. This approach doesn't require identical path length differences and takes into account their variations caused by environmental conditions. Thus, the optical source phase noise can be independently measured by the reference interferometer and subtracted from the sensor signal with the required attenuation. The results of experimental investigations of the proposed technique for two types of interferometric schemes are presented. It is shown that the proposed technique demonstrates the phase noise reduction up to 30 dB in the frequency range up to 500 Hz.

High-Resolution Optical Vector Analysis With Enhanced Sensitivity

High-resolution and high-sensitivity optical vector analysis (OVA) is highly desired by many applications, such as optical sensors and photonic integrated circuits (PICs). However, it is difficult to achieve high resolution and high sensitivity simultaneously. Here, we propose and experimentally demonstrate a high sensitivity OVA using coherent detection to achieve the complex frequency responses (including magnitude and phase responses) of a device under test (DUT). Carrier phase noise (CPN) cancellation is employed to eliminate the carrier phase fluctuation induced by the coherent detection. In an experiment, the frequency responses of a fiber Bragg grating (FBG) is accurately measured by the proposed method when the probe light is suppressed by ~18 dB. As a comparison, the method using coherent detection without CPN cancellation can only achieve the magnitude response, and the method using direct detection cannot obtain an effective measurement. The influence of the linewidth and time delay on the measurement is discussed. The proposed OVA provides a stable, high resolution, high sensitivity and low cost approach for characterizing optical devices with arbitrary response, especially for optical devices with large loss or bandpass response.

Branching Optical Frequency Transfer With Enhanced Post Automatic Phase Noise Cancellation

We present a technique for coherence transfer of laser light through a branching fiber link, where the optical phase noise induced by environmental perturbations via the fiber link is passively compensated by remote users without the requirements of any active servo components. At each remote site, an acousto-optic modulator (AOM) is simultaneously taken as a frequency distinguisher for distinguishing its unique frequency from other sites' and as an optical actuator for compensating the phase noise coming from the optical fiber. With this configuration, we incorporate a long outside loop path consisting of a fiber-pigtailed AOM into the loop, enabling the significant reduction of the outside loop phase noise in the passive way. To further address the residual out-of-loop phase noise coming from the interferometer and the two-way optical frequency comparison setup, we design a low-noise active temperature stabilization system. Measurements with a back-to-back system show that the stability in our stabilization system is $2\times10^{-16}$ at 1 s, reaching $2\times10^{-20}$ after 10,000 s. Adopting these techniques, we demonstrate transfer of a laser light through a branching fiber network with 50 km and 145 km two fiber links. After being compensated for the 145 km fiber link, the relative frequency instability is $3.4\times10^{-15}$ at the 1 s averaging time and scales down to $3.7\times10^{-19}$ at the 10,000 s averaging time. This proposed technique is suitable for the simultaneous transfer of an optical signal to a number of independent users within a local area.