Presence Of Phase Noise Research Articles

Uncertainty of the initial phase estimation of a sinewave in the presence of phase noise, additive noise or jitter

This paper presents the derivation of a simple analytical expression for the precision of the initial phase estimates obtained through a least-squares procedure. That expression depends on number of samples, phase noise standard deviation and additive noise standard deviation. This study is applicable to the estimates obtained through the sine fitting algorithm with known frequency and to the Discrete Fourier Transform algorithm. The analytical expression supplied was verified using a Monte Carlo simulation with numerically created data. The non-ideal phenomena treated in this work is the presence of jitter in the sampling instant, phase noise in the oscillator and additive noise in the system both of which must be normally distributed with a known value of standard deviation. It is useful information for an engineer in order to choose the proper number of samples to acquire to achieve a desired level of precision on the estimates made and thus carry out an efficient data acquisition with no unnecessary samples thus optimizing the test duration.

Study of the Bias of the Initial Phase Estimation of a Sinewave of Known Frequency in the Presence of Phase Noise.

The estimation of the parameters of a sinusoidal signal is of paramount importance in various applications in the fields of sensors, signal processing, parameter estimation, and device characterization, among others. The presence, in the measurement system, of non-ideal phenomena such as additive noise in the signals, phase noise in the stimulus generation, jitter in the sampling system, frequency error in the experimental setup, among others, leads to increased uncertainty and bias in the estimated quantities obtained by least squares methods and those derived from them. Therefore, from a metrological point of view, it is important to be able to theoretically predict and quantify those uncertainties in order to properly design the measurement system and its parameters, such as the number of samples to acquire or the stimulus signal amplitude to use to minimize the uncertainty in the estimated values. Previous works have shown that the presence of these non-ideal phenomena leads to increased uncertainty and bias in the estimation of the sinewave amplitude. The present work complements this knowledge by focusing specifically on the effect of phase noise and sampling jitter in the bias of the initial phase estimation of a sinusoidal signal of known frequency (three‑parameter sine fitting procedure). A theoretical derivation of the bias of initial phase estimation that takes into consideration the presence of phase noise in the sinewave is presented. Since a Taylor series approximation was used where only the first term was retained, it was necessary to validate the analytical derivations with numerical simulations using a Monte Carlo type of procedure. This process was applied to different conditions regarding the phase noise standard deviation, initial phase value, and number of samples. It is concluded that, in most scenarios, initial phase estimation using sine fitting is unbiased in the presence of phase noise or jitter. It is shown, however, that in cases of extremely high phase noise standard deviation and a very low number of samples, a bias occurs.

SDR implementation of a light deep learning model based CNN for joint spectrum sensing and AMC

Automatic modulation classification (AMC) aims to blindly recognize the modulation type of a received signal in wireless systems. It is also a critical component of non-cooperative communication systems after the detection of the presence of a signal. In this paper, we introduce a robust approach, termed DET-AMC (joint Detection and Automatic Modulation Classification), employing Convolutional Neural Networks (CNNs) trained via transfer learning methodology. The main advantage of our approach is its ability to handle a wide range of modulation types, including 10 different schemes generated in Gnuradio and their detection using the same model. Through extensive experimentation, we evaluate the performance of our light CNN-based DET-AMC method across varying signal-to-noise ratio (SNR) levels, as well as in the presence of phase noise and frequency offset. We find that the CNN’s learned features, obtained through transfer learning, exhibit robustness, particularly in low SNR and various challenging conditions, leading to accurate modulation classification. In general, our approach outperforms existing methods by using the effectiveness of deep learning in capturing relevant discriminative features. Additionally, our model offers a robust solution for join detection and AMC by achieving an accurate probability of detection and modulation classification without the need for manual feature engineering or the consideration of frequency offset, phase noise or noise estimation. Our model achieves 100% accuracy for synthetic and real data at an SNR equal to -10 dB for detection, and 100% and 98% for classification of synthetic and real signals at −4 dB, respectively.

A robust hybrid receiver for binary phase-shift keying discrimination in the presence of phase noise

We address the problem of coherent state discrimination in the presence of phase diffusion. We investigate the role of the HYbrid Near-Optimum Receiver (HYNORE) we proposed in [J. Opt. Soc. Am. B 40 (2023) 705] in the task of mitigating the noise impact. We prove the HYNORE to be a robust receiver, outperforming the Displacement Photon-Number-Resolving (DPNR) receiver and beating the standard quantum limit in particular regimes. We introduce the maximum tolerable phase noise [Formula: see text]max as a figure of merit for the receiver robustness and show that HYNORE increases its value with respect to the DPNR receiver.

Characterization of Orthogonal Chirp Division Multiplexing and Performance Evaluation at THz Frequencies in the Presence of Phase Noise

Characterization of Orthogonal Chirp Division Multiplexing and Performance Evaluation at THz Frequencies in the Presence of Phase Noise

A Novel CNN-Based Channel Estimation Algorithm in the Presence of Phase Noise and CFO

A Novel CNN-Based Channel Estimation Algorithm in the Presence of Phase Noise and CFO

A U-Net Approach for InSAR Phase Unwrapping and Denoising

The interferometric synthetic aperture radar (InSAR) imaging technique computes relative distances or surface maps by measuring the absolute phase differences of returned radar signals. The measured phase difference is wrapped in a 2π cycle due to the wave nature of light. Hence, the proper multiple of 2π must be added back during restoration and this process is known as phase unwrapping. The noise and discontinuity present in the wrapped signals pose challenges for error-free unwrapping procedures. Separate denoising and unwrapping algorithms lead to the introduction of additional errors from excessive filtering and changes in the statistical nature of the signal. This can be avoided by joint unwrapping and denoising procedures. In recent years, research efforts have been made using deep-learning-based frameworks, which can learn the complex relationship between the wrapped phase, coherence, and amplitude images to perform better unwrapping than traditional signal processing methods. This research falls predominantly into segmentation- and regression-based unwrapping procedures. The regression-based methods have poor performance while segmentation-based frameworks, like the conventional U-Net, rely on a wrap count estimation strategy with very poor noise immunity. In this paper, we present a two-stage phase unwrapping deep neural network framework based on U-Net, which can jointly unwrap and denoise InSAR phase images. The experimental results demonstrate that our approach outperforms related work in the presence of phase noise and discontinuities with a root mean square error (RMSE) of an order of magnitude lower than the others. Our framework exhibits better noise immunity, with a low average RMSE of 0.11.

Inter-Numerology Interference in Mixed Numerology OFDM Systems in Time-Varying Fading Channels With Phase Noise

Mixed numerology has been adopted in the orthogonal frequency division multiplexing-based physical layer of 5G new radio (NR) to serve diverse use cases and services. Since the subcarriers of different numerologies have different bandwidths and symbol durations, they interfere with each other despite being centered at different frequencies. We analyze the inter-numerology interference (INI) encountered by these systems in wideband time-varying channels in the presence of phase noise. We derive novel expressions for the fading-averaged INI power at each subcarrier as a function of the channel’s power delay profile. These lead to insightful, tight bounds for the bandwidth-averaged INI power, which bring out the combined impact of Doppler spread and phase noise. Our comprehensive approach applies to the entire family of numerologies of 5G NR, and accounts for partial subcarrier loading, guard bands, and non-line-of-sight and line-of-sight channels. Our results show that INI affects high-rate modulation and coding schemes (MCSs). To mitigate its impact, we propose a novel statistical square root power allocation scheme that exploits the variation in the average INI powers across the subcarriers. It achieves a lower block error rate than uniform power allocation, which is used in 5G NR.

An Improved AoA Estimation Algorithm for BLE System in the Presence of Phase Noise

Location-based service (LBS) provides users with personalized experience. With the latest Bluetooth low energy (BLE) technology, switched antenna array and constant tone extension (CTE) are introduced enabling angle of arrival (AoA) estimation for improved positioning accuracy. However, phase noise may significantly degrade the AoA estimation performance. Such impairment and its mitigation method are not well discussed in existing literature. In this paper, we theoretically analyze the performance degradation of AoA estimation caused by phase noise in BLE system. Based on the specific antenna switching pattern, an improved multiple signal classification (MUSIC) algorithm is proposed. We further propose an expectation maximization MUSIC (EM-MUSIC) algorithm to improve the AoA estimation accuracy by estimating the phase noise with extended Kalman filter. Simulation results show that at typical SNR level, the proposed algorithm can reduce the estimation error by more than 55% compared with existing algorithms. The proposed EM-MUSIC algorithm can greatly improve the positioning accuracy and is ideal for LBS.

Photon statistics and quantum phase distribution for coherent optical links in the presence of phase noise from both the laser source and the RF oscillator, and dispersion

A model of photon statistics and quantum phase distribution is analyzed for coherent optical communication links in the presence of quantum phase noise, dispersion and phase noise of the radio-frequency (RF) oscillator using an in-line optical amplifier. The quantum analysis of a dual drive Mach–Zehnder modulator and the quantum transfer function for an optical field mode across an in-line amplifier is performed by taking into account both the quantum and the classical phase noises. The resulting photon statistics are compared with the semiclassical model. We analyze the quantum phase distribution by considering the Wigner quasiprobability distribution for a coherent optical link. Here, we investigate the broadening of the quantum phase distribution due to quantum phase noise of the laser, the dispersive optical fiber, the phase noise of the RF oscillator and the inevitable noise coefficient of the optical amplifier for arbitrary amplified spontaneous emission (ASE) field modes. We analytically investigate the quantum analog to the bit error rate (BER) as a function of the laser’s linewidth, the linewidth of the RF oscillator and chromatic dispersion. The results of quantum models are compared with the semiclassical model. Quantum treatment of both the BER and variance is found to agree with prior results for a single-mode ASE field in the absence of phase noise but deviate when the effect of phase noise is considered. Including phase noise effects in the amplitude in the semiclassical treatment of the BER yields a new semiclassical expression that agrees with quantum expressions of machine precision for single-mode ASE fields.

ИССЛЕДОВАНИЕ ВЛИЯНИЯ ФАЗОВЫХ ШУМОВ МОДУЛЯТОРОВ ЦИФРОВЫХ СИГНАЛОВ НА ВЕРОЯТНОСТНЫЕ ХАРАКТЕРИСТИК ПРИ ИХ ПРИЕМЕ

The results of studies of the distorting effect for phase noise of digital signal modulators, generated by short-term instability of clock generators, on the degradation of probabilistic characteristics (bit error probability) when receiving digital signals with two-dimensional "constellations" (signals with multi-position phase shift keying and signals with amplitude-phase shift keying) are presented. Research is carried out for two models of phase noises with parameters of their power with uniform and normal laws of phase density distribution. Numerical estimates of energy losses are given, obtained by theoretical calculation and computer simulation of the algorithm for receiving digital signals using the considered models of phase noise with respect to additive white Gaussian channel noise. It is shown that the energy losses calculated using the analytical relation for these signals are fairly approximate estimates in relation to the simulation results. It is also shown that for signals with 2-position phase shift keying and for amplitude-phase keying with a keying order equal to 8, in the presence of phase noise with specified powers and distribution density laws, the bit error probabilities are practically equivalent to the theoretical values of the bit error probabilities for channel with additive white Gaussian noise - in this case, the energy loss is almost equal to 0. Signals with 8-position phase-shift keying are most susceptible to the distorting effect of phase noise - for the considered phase noise power parameter, the energy loss exceeds 1.5 dB. The method of reducing energy losses when receiving the considered series of digital signals is based on the use of clock generators with a decrease in the power of phase noise

Monostatic Sensing With OFDM Under Phase Noise: From Mitigation to Exploitation

We consider the problem of monostatic radar sensing with orthogonal frequency-division multiplexing (OFDM) joint radar-communications (JRC) systems in the presence of phase noise (PN) caused by oscillator imperfections. We begin by providing a rigorous statistical characterization of PN in the radar receiver over multiple OFDM symbols for free-running oscillators (FROs) and phase-locked loops (PLLs). Based on the delay-dependent PN covariance matrix, we derive the hybrid maximum-likelihood (ML)/maximum a-posteriori (MAP) estimator of the deterministic delay-Doppler parameters and the random PN, resulting in a challenging high-dimensional nonlinear optimization problem. To circumvent the nonlinearity of PN, we then develop an iterated small angle approximation (ISAA) algorithm that progressively refines delay-Doppler-PN estimates via closed-form updates of PN as a function of delay-Doppler at each iteration. Moreover, unlike existing approaches where PN is considered to be purely an impairment that has to be mitigated, we propose to exploit PN for resolving range ambiguity by capitalizing on its delay-dependent statistics (i.e., the range correlation effect), through the formulation of a parametric Toeplitz-block Toeplitz covariance matrix reconstruction problem. Simulation results indicate quick convergence of ISAA to the hybrid Cramér-Rao bound (CRB), as well as its remarkable performance gains over state-of-the-art benchmarks, for both FROs and PLLs under various operating conditions, while showing that the detrimental effect of PN can be turned into an advantage for sensing.

Copula-Based Modeling of RIS-Assisted Communications: Outage Probability Analysis

Statistical characterization of the signal-to-noise ratio (SNR) of reconfigurable intelligent surface (RIS)-assisted communications in the presence of phase noise is an important open issue. In this letter, we exploit the concept of copula modeling to capture the non-standard dependence features that appear due to the presence of discrete phase noise. In particular, we consider the outage probability of RIS systems in Rayleigh fading channels and provide joint distributions to characterize the dependencies due to the use of finite resolution phase shifters at the RIS. Numerical assessments confirm the validity of closed-form expressions of the outage probability and motivate the use of bivariate copula for further RIS studies.

Learning-Based Channel Estimation and Phase Noise Compensation in Doubly-Selective Channels

In this letter, we propose a learning based channel estimation scheme for orthogonal frequency division multiplexing (OFDM) systems in the presence of phase noise in doubly-selective fading channels. Two-dimensional (2D) convolutional neural networks (CNNs) are employed for effective training and tracking of channel variation in both frequency as well as time domain. The proposed network learns and estimates the channel coefficients in the entire time-frequency (TF) grid based on pilots sparsely populated in the TF grid. In order to make the network robust to phase noise (PN) impairment, a novel training scheme where the training data is rotated by random phases before being fed to the network is employed. Further, using the estimated channel coefficients, a simple and effective PN estimation and compensation scheme is devised. Numerical results demonstrate that the proposed network and PN compensation scheme achieve robust OFDM performance in the presence of phase noise.

Performance Evaluation and Diversity Analysis of RIS-Assisted Communications Over Generalized Fading Channels in the Presence of Phase Noise

In this paper, we develop a unified theoretical framework for analyzing the outage performance of reconfigurable intelligent surfaces (RISs)-assisted communication systems over generalized fading channels and in the presence of phase noise. Fox&#x2019;s H function theory is then utilized to derive the outage probability for various channel fading and phase noise distributions in closed-form. We further conduct an asymptotic outage analysis to obtain insightful findings. In particular, we present the maximum diversity order achievable over such channels and demonstrate the performance variation in comparison to conventional Rayleigh channels. Then, based on upper bounds and lower bounds, we propose a design criteria for RISs to achieve the maximum diversity order in the presence of phase noise. More specifically, we show that if the absolute difference between pairs of phase errors is less than <inline-formula> <tex-math notation="LaTeX">$\pi /2$ </tex-math></inline-formula>, RIS-assisted communications achieve the full diversity order over independent fading channels, even in the presence of phase noise. The theoretical frameworks and findings are validated with the aid of Monte Carlo simulations.

Neural Network Nonlinear Equalizer in Long-Distance Coherent Optical Transmission Systems

Recently, neural network (NN) nonlinear equalizers which are expected to reduce computational complexity have attracted attention as fiber nonlinear compensation methods for coherent optical transmission systems. However, these fiber nonlinear compensation methods have problems that training of NN is not easy for long-distance transmission systems because of accumulated phase noise. In this letter, we propose a training method of NN nonlinear equalizer using the target outputs including phase noise which is produced by received signals. The phase noise is estimated by the inverse modulation of received signals and filtering. The estimated phase noise is added to transmitter signals, and the target outputs are obtained. The target outputs allow training of NN in long-distance coherent optical transmission systems. Since the NN trained by this proposed method compensates only for fiber nonlinearities, the phase locked loop (PLL) is placed after the NN to compensate for phase noise. The performances are evaluated by the simulation of 32 Gbaud 16QAM 4000 km long-distance coherent optical transmission. These results indicate that the proposed training method is effective in training NN nonlinear equalizer in long-distance coherent optical transmission in the presence of phase noise.

Performance of free-space optical systems in the presence of receiver imperfections

We present a review of papers considering the subcarrier intensity modulation free-space optical (FSO) communication systems in the presence of phase noise. This phase noise is a consequence of imperfect reference signal extraction in electrical domain after photodetector. We illustrate the effects of this phenomenon on the system symbol-error rate performance. The examples show that receiver imperfections, presented through phase noise, can degrade the FSO system performance to a large extent.

Full-Duplex Transceiver Design in the Presence of Phase Noise and Performance Analysis

Phase noise introduced by oscillators shows significant impacts on full-duplex (FD) transceivers, even for the architecture in which the transmitter and receiver share the same oscillator. In this paper, an FD transceiver design is proposed to mitigate the phase noise contained in the multipath self-interference (SI) components. This design is featured by deploying two receive chains whose oscillator signals are originated from the transmit oscillator signal but with different delays. To work with the proposed design, an SI cancellation algorithm is developed, where the phase noise contained in the multipath SI components are extracted by dividing the two received signals. The cancellation capabilities of the proposed transceiver, as well as two typical conventional transceivers, are derived in closed-forms. The impacts of oscillator delay adjustment errors and SI channel estimation errors on the cancellation capability are also analyzed to reveal guidelines for FD transceiver designs. Simulation results show that the proposed transceiver design can expand the transmission power and relax the requirement for the analog canceller, which shows advantages in the long-range communication with high transmission power, or in the scenario where analog cancellations are not applicable.

Bit Error Probability of MQAM in the Presence of Phase Noise

In Gray coded rectangular and square quadrature amplitude modulation (QAM), for each bit, the bit decision boundaries are distributed only along one dimension. Consequently, the exact calculation of bit error probability (BEP) of rectangular and square QAM in the additive white Gaussian noise (AWGN) channel results in simple one-dimensional (1-D) error/Q-functions. This is while the symbol decision boundaries involve two dimensions. This paper presents exact and general expressions for the BEP of Gray coded M -ary rectangular and square QAM in the presence of phase noise in the AWGN as well as flat-fading channels. In doing so, we first derive exact expressions for the BEP of MQAM in the presence of a fixed phase error. The expression will be a weighted sum of 1-D complementary error functions for the AWGN channel. For the flat-fading channels, these formulas consist of only single integrals or simple functions. We then integrate the formulas across noise distribution, to derive the average BEP expression of Gray coded MQAM in the presence of random phase error. Moreover, we provide an exact expression for the bit error floor (BEF) of MQAM in the presence of phase noise in the AWGN and fading channels. The exact expressions include numerous terms for higher order MQAM. Considering the most dominant terms of the exact expressions, we also propose simpler expressions. Simulation results validate the accuracy of the proposed exact expressions for arbitrary levels of input SNR. Moreover, the results show very good performance for the approximate expressions.

Joint MAP channel estimation and data detection for OFDM in presence of phase noise from free running and phase locked loop oscillator

This paper addresses a computationally compact and statistically optimal joint Maximum a Posteriori (MAP) algorithm for channel estimation and data detection in the presence of Phase Noise (PHN) in iterative Orthogonal Frequency Division Multiplexing (OFDM) receivers used for high speed and high spectral efficient wireless communication systems. The MAP cost function for joint estimation and detection is derived and optimized further with the proposed cyclic gradient descent optimization algorithm. The proposed joint estimation and detection algorithm relaxes the restriction of small PHN assumptions and utilizes the prior statistical knowledge of PHN spectral components to produce a statistically optimal solution. The frequency-domain estimation of Channel Transfer Function (CTF) in frequency selective fading makes the method simpler, compared with the estimation of Channel Impulse Response (CIR) in the time domain. Two different time-varying PHN models, produced by Free Running Oscillator (FRO) and Phase-Locked Loop (PLL) oscillator, are presented and compared for performance difference with proposed OFDM receiver. Simulation results for joint MAP channel estimation are compared with Cramer-Rao Lower Bound (CRLB), and the simulation results for joint MAP data detection are compared with “NO PHN” performance to demonstrate that the proposed joint MAP estimation and detection algorithm achieve near-optimum performance even under multipath channel fading.