Phase Noise Estimation Research Articles

Parallel indirect time-of-flight ranging using on-chip dual-frequency combs

The significant advancements in autonomous vehicle applications demand detection solutions capable of swiftly recognizing and classifying objects amidst rapidly changing and low-visibility conditions. Light detection and ranging (LiDAR) has emerged as a robust solution, overcoming challenges associated with camera imaging, particularly in adverse weather conditions or low illumination. Rapid object recognition is crucial in dynamic environments, but the speed of conventional LiDARs is often constrained by the 2D scanning of the laser beam across the entire scene. In this study, we introduce a parallelization approach for the indirect time-of-flight (iToF) ranging technique. This method enables efficient and high-speed formation of 1D clouds, offering the potential to have extended range capabilities without being constrained by the laser coherence length. The application potential spans mid-range autonomous vehicles ranging to high-resolution imaging. It utilizes dual-frequency combs with slightly different repetition rates. The method leverages the topology of the target object to influence the phase of the beating signal between the comb lines in the RF domain. This approach enables parallel ranging in one direction, confining the scanning process to a single dimension, and offers the potential for high-speed LiDAR systems. A tri-comb approach will be discussed that can provide an extended unambiguous range without compromising the resolution due to the range–resolution trade-off in iToF techniques. The study starts by explaining the technique for parallel detection of distance and velocity. It then presents a theoretical estimation of phase noise for dual combs, followed by an analysis of distance and velocity detection limits, illustrating their maximum and minimum extents. Finally, a study on the mutual interference conditions between two similar LiDAR systems is presented, demonstrating the feasibility of designing simultaneously operating LiDARs to avoid mutual interference.

Phase Noise Compensation Algorithm for Space-Borne Azimuth Multi-Channel SAR.

Azimuth multi-channel synthetic aperture radar (SAR) has always been an important technical means to achieve high-resolution wide-swath (HRWS) SAR imaging. However, in the space-borne azimuth multi-channel SAR system, random phase noise will be produced during the operation of each channel receiver. The phase noise of each channel is superimposed on the SAR echo signal of the corresponding channel, which will cause the phase imbalance between the channels and lead to the generation of false targets. In view of the above problems, this paper proposes a random phase noise compensation method for space-borne azimuth multi-channel SAR. This method performs feature decomposition by calculating the covariance matrix of the echo signal and converts the random phase noise estimation into the optimal solution of the cost function. Considering that the phase noise in the receiver has frequency-dependent and time-varying characteristics, this method calculates the phase noise estimation value corresponding to each range-frequency point in the range direction and obtains the phase noise estimation value by expectation in the azimuth direction. The proposed random phase noise compensation method can suppress false targets well and make the radar present a well-focused SAR image. Finally, the usefulness of the suggested method is verified by simulation experiments.

Phase Noise Effects on OFDM Chirp Communication Systems: Characteristics and Compensation

Orthogonal frequency-division multiplexing (OFDM) chirp waveforms are an attractive candidate to be a dual-function signal scheme for the joint radar and communication systems. OFDM chirp signals can not only be employed to transmit communication data through classic phase modulation, but also can perform radar detection by applying linear frequency modulation for subcarriers. However, the performance of the OFDM chirp communication system under the phase noise environment still remains uninvestigated. This paper tries to discuss the influence of phase noise on OFDM chirp communication systems and proposes effective phase noise estimation and compensation methods. We find that the phase noise effect on OFDM chirp communication systems consists of a common phase error (CPE) and an inter-carrier interference (ICI). If not compensated, the performance of the dual-function systems can be seriously degraded. In particular, an exact expression for the signal-plus-interference to noise ratio (SINR) for the OFDM chirp communication system is derived and some critical parameters are analyzed to exhibit the phase noise effects on system performance. Moreover, two low-complexity estimation approaches, maximum likelihood (ML) and linear minimum mean square error (LMMSE), as well as two compensation approaches, the de-correlation and cancellation algorithms, are respectively utilized to eliminate the phase noise impairment. Finally, the phase noise effects and the effectiveness of the compensation approach are verified by extensive numerical results.

Phase noise of signal generators with multichannel digital synthesizers

Wide use of a direct digital synthesizer (DDS) and digital to analog converters (DAC) in digital antenna arrays permits for fast modulation parameters variations and beam positioning, and also improves the quality of beam forming due to high accuracy of signal generation. However, any systematic and random phase deviations of array channels not only lead to distortion of radiation pattern but also cause deterioration of signal processing at receiver end. Phase noise is one of critical parameters of such systems. Traditional theory and empirical methods assumes small or zero phase deviation of phase of channel output signal when combining these signals. We have proposed the model in which coupling of AM and PM noise persists for any arbitrary phase deviation of channels in multistage circuits comprising multichannel digital synthesizers. Absolute phase noise measurements of combined DACs outputs for zero phase offset and antiphase modes with two values of DAC output signal amplitude difference permit for estimation of residual phase noise of DAC and clock receiving and distribution circuitry and demonstrate good compliance of results of calculation.

Modeling, Estimation, and Applications of Phase Noise in Wireless Communications: A Survey

Modeling, Estimation, and Applications of Phase Noise in Wireless Communications: A Survey

Integrating key generation and distribution with the quantum noise stream cipher system without compromising the transmission performance

We propose and experimentally demonstrate a secure quantum noise stream cipher transmission system that integrates key generation and distribution. At the stage of carrier phase recovery, the estimated phase noise is used to generate randomness keys without additional equipment. Based on direct sequence spread spectrum technology, we integrate the distributed keys with quantum noise stream cipher signals. The key distribution and encryption transmission can be completed simultaneously without occupying additional bandwidth or time slots. By changing the position of distributed keys in the encryption base, the BER performance of QAM/QNSC signals cannot be affected by the keys. Experimental results demonstrate that the 54.5 Mbps key distribution and 31 Gbps encryption transmission without OSNR penalty can be achieved simultaneously over a 120 km standard single-mode fiber.

Partially decoupled polarization demultiplexing and phase noise equalizer for Alamouti code-based simplified coherent systems.

Alamouti space-time block code (STBC) combined with a simple heterodyne coherent receiver can realize polarization-insensitive phase-diversity detection to reduce the cost. In the receiver, a joint equalizer has been used for STBC's polarization demultiplexing and phase tracking. However, the joint equalizer requires two different step size parameters to update the tap weight coefficients for polarization demultiplexing and the phase noise estimation. This leads to the search process being complex so requiring more iterations for convergence. In this paper, we propose a partially decoupled equalizer that consists of a polarization and phase decoupled equalizer (PPDE) and a pilot-aided blind phase search (P-BPS) algorithm to accelerate the convergence and improve the phase noise tolerance. By theoretically calculating the phase noise, the PPDE can achieve polarization demultiplexing with only one single step size parameter, thus suppressing the searching space and greatly reducing the iterations required for convergence. In the carrier phase recovery stage, the P-BPS algorithm can effectively improve the phase noise tolerance and solve the cyclic slip problem of BPS. We conduct numerical simulations and an experiment to transmit a quadrature phase-shift keying (QPSK) signal. The results demonstrate that the number of iterations required for PPDE convergence is only half of that of the joint equalizer while maintaining polarization-insensitive characteristics in large phase noise. Meanwhile, the achievable linewidth tolerance of P-BPS is increased by three times compared with DD-LMS.

Parametric Test of the Sentinel 1A Persistent Scatterer- and Small Baseline Subset-Interferogram Synthetic Aperture Radar Processing Using the Stanford Method for Persistent Scatterers for Practical Landslide Monitoring

The landslide monitoring method that uses the Sentinel 1A Interferogram Synthetic Aperture Radar (InSAR) through the Stanford Method for Persistent Scatterers (StaMPS) method is a complimentary but complex procedure without exact guidelines. Hence, this paper delivered a parametric test by examining the optimal settings of the Sentinel 1A Persistent Scatterer (PS)- and Small Baseline Subset (SBAS)-InSAR using the StaMPS compared to the Global Navigation Satellite Systems (GNSS) in landslide cases. This study first revealed parameters with the suggested values, such as amplitude dispersion used to describe amplitude stability, ranging from 0.47 to 0.48 for PS and equal to or more than 0.6 for SBAS in WuWanZai, Ali Mt. The study further examined the suggested values for other factors, including the following: unwrap grid size to re-estimate the size of the grid; unwrap gold n win as the Goldstein filtering window to reduce the noise; and unwrap time win as the smoothing window (in days) for estimating phase noise distributions between neighboring pixels. Furthermore, the study substantiated the recommended settings in the Woda and Shadong landslide cases with the GNSS, inferring that the SBAS has adequate feasibility in practical landslide monitoring.

How Does Ambient Temperature Fluctuation Influence the Short-Term Frequency Stability of OCXO?

Short-term frequency stability (STFS) is one of the most important specification of oven-controlled crystal oscillators (OCXOs). Although numerous studies have investigated factors that influence STFS, research on the impact of ambient temperature fluctuation is rare. This work investigates the relationship between the ambient temperature fluctuation and the STFS by introducing a model of the OCXO's short-term frequency-temperature characteristic (STFTC), which considers the transient thermal response of the quartz resonator, the thermal structure, and the oven control system. According to the model, an electrical-thermal co-simulation is adopted to determine the temperature rejection ratio of the oven control system and estimates the phase noise and Allan deviation (ADEV) that caused by fluctuations in ambient temperature. As a verification, a 10-MHz single-oven oscillator is designed. From the measured results, the estimated phase noise near the carrier agrees well with the measured results, and it can be seen that only when the temperature fluctuation is less than 10 mK at 1-100 s, the oscillator can maintain the characteristics of flicker frequency noise at the offset frequency from 10 mHz to 1 Hz, and the ADEV is possible to reach at the order of E -13 in 100 s. Thus, the model proposed in this study effectively predicts the impact of ambient temperature fluctuation on the STFS of an OCXO.

End-to-End Optimization of Constellation Shaping for Wiener Phase Noise Channels With a Differentiable Blind Phase Search

As the demand for higher data throughput in coherent optical communication systems increases, we need to find ways to increase capacity in existing and future optical communication links. To address the demand for higher spectral efficiencies, we apply end-to-end optimization for joint geometric and probabilistic constellation shaping in the presence of Wiener phase noise and carrier phase estimation. Our approach follows state-of-the-art bitwise auto-encoders, which require a differentiable implementation of all operations between transmitter and receiver, including the DSP algorithms. In this work, we show how to modify the ubiquitous blind phase search (BPS) algorithm, a popular carrier phase estimation algorithm, to make it differentiable and include it in the end-to-end constellation shaping. By leveraging joint geometric and probabilistic constellation shaping, we are able to obtain a robust and pilot-free modulation scheme improving the performance of 64-ary communication systems by at least 0.1 bit/symbol compared to square QAM constellations with neural demappers and by 0.05 bit/symbol compared to previously presented approaches applying only geometric constellation shaping.

Physical-layer encryption and authentication scheme based on SKGD and 4D hyper-chaos.

In this paper, a scheme to realize encryption and digital identity authentication at the same time is proposed for enhancing the physical-layer security of point-to-point optical links (PPOL). Exploiting identity code encrypted by the key as authentication information effectively resists passive eavesdropping attacks in fingerprint authentication. The proposed scheme theoretically realizes secure key generation and distribution (SKGD) by phase noise estimation of the optical channel and the generation of identity codes with good randomness and unpredictability by the four-dimensional (4D) hyper-chaotic system. The local laser, erbium doped fiber amplifier (EDFA), and public channel provide the entropy source of uniqueness and randomness to extract symmetric key sequences for legitimate partners. The simulation conducted in a quadrature phase shift keying (QPSK) PPOL system over 100km standard single mode fiber verify successfully that 0.95Gbit/s error-free SKGD. The unpredictability and high sensitivity to the initial value and control parameters of the 4D hyper-chaotic system provide a huge space of ~10125 for identity codes, which is sufficient to resist exhaustive attack. With the proposed scheme, the security level of key and identity can be increased markedly.

Gaussian blur aided blind phase search algorithm in low SNR QAM transmission system

Probabilistic constellation shaping (PCS) reduces the required SNR compared with the uniform distribution system to achieve the same mutual information (MI). However, severe amplified spontaneous emission (ASE) noise degenerates the performance of the conventional blind phase search (BPS) algorithm, showing an unpleasant MI penalty and reducing the shaping gain. In this paper, we reveal that the MI impairment comes from the misjudgment of phase noise estimation by the conventional BPS algorithm interfered by severe ASE noise. To cope with this problem, we propose a Gaussian blur-aided BPS (GBA-BPS) algorithm by introducing an unequal weight filter with an efficient solution of variance configuration into the conventional BPS. Details about why the GBA-BPS algorithm outperforms the conventional BPS algorithm are elaborated based on the spectrum analysis of the phase noise estimated by both schemes. Evaluated on a 50-GBaud PCS-64QAM system, the proposed GBA-BPS algorithm with a 31-tap filter effectively mitigates the misjudgment of phase noise estimation, achieving a maximum MI gain of 0.5 and 0.25 bits/symbol compared with conventional BPS when the SNR is 16 dB and 18 dB respectively. The proposed GBA-BPS is a significant improvement over conventional BPS and it is more suitable for carrier phase recovery in low SNR systems.

Auxiliary Variable-Aided Hybrid Message Passing for Joint Channel, Phase Noise Estimation and Detection for Multi-User MIMO Systems

This paper considers a multi-user multiple-input multiple-output (MU-MIMO) system with independent phase noise (PN) at user terminals (UTs) due to non-synchronous noisy local oscillators. The conventional factor graph of MU-MIMO involves an observation factor with multiple high-dimensional variables in the form of multiplication and summation. In this work, the MU-MIMO factor graph is represented by introducing auxiliary variables, which enables the decomposition of the observation factor into several simpler sub-factors and then use different message passing techniques to obtain approximate marginals. Specifically, belief propagation and expectation propagation (BP-EP) are used for the linear factors for random walk process, modulation and coding, while mean field (MF) is used for non-linear factor in exponential form. To reduce the computational complexity, the non-Gaussian MF messages are approximated to be Gaussian by using the second order Taylor expansion at its belief obtained in the previous iteration. The proposed receiver has a quadratic computational complexity per symbol per iteration. Simulation results show that the performance of the proposed receiver is better than existing methods and is close to the matched filter bound (MFB) in terms of the bit error rate (BER).

Sensing Integrated DFT-Spread OFDM Waveform and Deep Learning-Powered Receiver Design for Terahertz Integrated Sensing and Communication Systems

Terahertz (THz) communications are envisioned as a key technology of next-generation wireless systems due to its ultra-broad bandwidth. One step forward, THz integrated sensing and communication (ISAC) system can realize both unprecedented data rates and millimeter-level accurate sensing. However, THz ISAC meets stringent challenges on waveform and receiver design to fully exploit the peculiarities of THz channel and transceivers. In this work, a sensing integrated discrete Fourier transform spread orthogonal frequency division multiplexing (SI-DFT-s-OFDM) system is proposed for THz ISAC, which can provide lower peak-to-average power ratio than OFDM and is adaptive to flexible delay spread of the THz channel. Without compromising communication capabilities, the proposed SI-DFT-s-OFDM realizes millimeter-level range estimation and decimeter-per-second-level velocity estimation accuracy. In addition, the bit error rate (BER) performance is improved by 5 dB gain at the 10°3 BER level compared with OFDM. At the receiver, a deep learning based ISAC receiver with two neural networks is developed to recover transmitted data and estimate target range and velocity, while mitigating the imperfections and non-linearities of THz systems. Extensive simulation results demonstrate that the proposed deep learning methods can realize mutually enhanced performance for communication and sensing, and is robust against Doppler effects, phase noise and multi-target estimation.

Multi-Level Phase Noise Model for CO-OFDM Spatial-Division Multiplexed Transmission

Spatial division multiplexed (SDM) transmission systems with coherence communication technology have become an important issue in meeting the demands for the capacity of fiber. However, research on the phase noise from lasers is mainly focused on single-channel systems or single-carrier SDM systems. In this paper, a phase noise model comprising common laser phase noise, in addition to the core phase drifts induced by the SDM, is introduced and analyzed for a coherence orthogonal frequency-division multiplexing (CO-OFDM) spatial-division multiplexed transmission (SDM) system. Based on the phase noise model, the applicability of the blind phase search algorithm and the pilot-aided phase estimation algorithm is discussed and demonstrated via simulation. The results show that these two algorithms can work well when considering combined laser linewidths with core phase drifts for CO-OFDM 7-core multi-core fiber (MCF). The results mean that with the SDM phase noise model, phase noise estimation in other cores can be transferred from one core to lower the complexity with the help of the model. This research provides a proper application of the phase noise analysis of large-capacity optical communication based on a weak-coupled MCF.

245Gb/s P2MP Mobile Fronthaul Downstream Transmission Using Code-Division Multiplexing and Self-Homodyne Coherent Technologies

We have proposed and experimentally demonstrated a high-speed and point-to-multipoint (P2MP) mobile fronthaul (MFH) downstream system based on the code-division multiplexing (CDM) and self-homodyne coherent (SHC) technologies. We find that compared with the traditional 16-ary quadrature amplitude modulation (16-QAM) signal transmission, the change of phase noise between two demultiplexed symbols is much larger in the CDM-16QAM signal transmission because it is the accumulation of phase noise change of n multiplexed symbols. Therefore, a low-complexity pilot sequence-assisted phase noise estimation algorithm is proposed and designed to compensate for the phase noise caused by fiber mismatch length, which makes it possible to use a low-cost distributed feedback (DFB) laser. Besides, the spread signal's distribution in the frequency domain of each code sequence is different, leading to different transmission performances between different remote radio units (RRUs). A power optimization scheme is proposed to balance the transmission performances of different RRUs by multiplying each channel's signal by a normalized weight factor at the transmitter. The experimental results show that the proposed system could successfully support the transmission of 245 Gb/s 16QAM signal from baseband unit (BBU) to 7 RRUs (each RRU could have 2 antennas to transmit signals at 2 polarizations) over 10 km standard single-mode fiber (SSMF). The measured worst bit error rate (BER) value of 14 channels is 1.77e-3 which is below the hard-decision forward error correction (HD-FEC) threshold (3.8e-3).

Pattern search and compressed sensing based phase noise and channel estimation for mmWave massive MIMO-OFDM systems

Phase noise (PN) can seriously affect the performance of millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems, especially when orthogonal frequency division multiplexing (OFDM) is employed. This paper studies the PN effect on mmWave massive MIMO-OFDM systems, and proposes a time variant training mode to save training time. In addition, an iterative channel and PN estimation method is proposed, which can estimate the PN with pattern search and estimate the channel with compressed sensing, and can converge according to the residual of the received signal. Moreover, the error vector magnitude and the computational complexity are analyzed. Finally, our simulation results demonstrate that by employing the proposed method, the performance of the mmWave massive MIMO-OFDM system can be improved.

Beyond a 107 range-resolution-1 product in an OFDR based on a periodic phase noise estimation method.

We present and demonstrate a method based on a periodic phase noise estimation in an optical frequency domain reflectometry (OFDR) capable of a beyond 107 range-resolution-1 product (RRP) for the first time, which corresponds to 2.5 × improvement compared with the state-of-the-art. The moving average filter is employed to suppress the amplification of noise in the derivation process. Further, with the help of a third-order Taylor expansion, this method provides a highly precise estimation of periodic phase noise, which is the main factor impacting the performance of OFDR systems with medium-to-long measurement range combined with a submillimeter spatial resolution. A spatial resolution within 535 μm over the measurement range of 8 km is obtained. The proposed method offers a promising technique for fiber network monitoring and sensing applications.

Low complexity blind detection in OFDM systems with phase noise

Phase noise is one of the major impairments that degrade the performance of orthogonal frequency division multiplexing (OFDM) systems. When an OFDM system works at high-order modulation or high carrier frequency, phase noise's impairments cannot be ignored. Existing phase noise estimation algorithms either require a large number of pilots or have high computation complexity. In this paper, we propose a low complexity blind data detector based on the maximum a posteriori (MAP) criterion. With prior knowledge of slow time-varying property of phase noise, a simplified iterative phase noise estimation and data detection algorithm is developed. Compared to existing algorithms, the proposed algorithm does not require pilot data transmission, and achieves satisfactory performance with low computation complexity. Simulation results validate the effectiveness of proposed algorithm.

Polarization Attack on Continuous-Variable Quantum Key Distribution with a Local Local Oscillator.

The estimation of phase noise of continuous-variable quantum key distribution protocol with a local local oscillator (LLO CVQKD), as a major process in quantifying the secret key rate, is closely relevant to the intensity of the phase reference. However, the transmission of the phase reference through the insecure quantum channel is prone to be exploited by the eavesdropper (Eve) to mount attacks. Here, we introduce a polarization attack scheme against the phase reference. Presently, in a practical LLO CVQKD system, only part of the phase reference pulses are measured to compensate for the polarization drift of the quantum signal pulses in a compensation cycle due to the limited polarization measurement rate, while the other part of the phase reference pulses are not measured. We show that Eve can control the phase noise by manipulating the polarization direction of the unmeasured phase reference to hide her attack on the quantum signal. Simulations show that Eve can obtain partial or total key rates information shared between Alice and Bob as the transmission distance increases. Improving the polarization measurement rate to 100% or monitoring the phase reference intensity in real-time is of great importance to protect the LLO CVQKD from polarization attack.