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A 19‐GHz low‐phase‐noise PLL‐frequency synthesizer is presented in this letter that is intended to be used in a K‐band FMCW radar which requires strict phase noise for detecting a small unmanned aerial vehicle. The 17.9 to 19.5‐GHz PLL includes a Darlington cross‐coupled capacitive‐degeneration VCO which presents higher maximum attainable oscillation frequency (ƒtrans) and larger negative transconductance (gm), thus resulting in low phase noise. Manufactured using the SiGe BiCMOS process, the K‐band synthesizer demonstrates −114 dBc/Hz at 1 MHz offset and −138 dBc/Hz at 10 MHz offset from 19.456 GHz locking carrier frequency. [ABSTRACT FROM AUTHOR]

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.

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.

Abstract The ever‐expanding horizon of radar applications demands solutions with high‐end radar functionalities and technologies and is often limited by the available radar equipment, cost and time. A practical method to tackle the situation is to rely on the modelling and simulation of radar systems based on the user requirements. The comprehensive system‐level modelling of a pulsed Doppler radar in MATLAB/Simulink consisting of all the fundamental blocks in the transmit chain, the environment, the receive chain, and the data processing chain is presented in this article. The first half of the article discusses the high‐fidelity simulation of each building block in the radar model. In the second half of the article, the range‐Doppler plot generated from the high‐fidelity radar model is compared and validated using the range‐Doppler plot from a real radar trial. The radar phase noise plays a crucial role in the detection of slowly moving, low radar cross‐section targets in the presence of strong clutter. The article also briefly discusses the effects of radar oscillator phase noise in the range‐Doppler plot. The validated, fully flexible radar model has the advantage of supporting the addition of further building blocks and optimising the parameters based on user requirements.

In this paper, a very low spur 5.9-GHz integer-N frequency synthesizer designed for a Cellular Vehicle-to-Everything (C-V2X) receiver is presented. The PLL is referenced to a 10-MHz crystal oscillator and the design is implemented in a 65-nm CMOS process. The output of the synthesizer has differential quadrature topology and provides the local oscillator signal to a downconverter mixer of C-V2X receiver. Post-layout simulations show that the reference spurs are better than −88 dBc through loop sampling technique which was implemented in a 11.8-GHz VCO design for the first time to the best of our knowledge. The best spur level without the loop sampling technique applied is limited to −55 dBc. Using the loop sampling technique provides a spur reduction of 33 dB which is a significant improvement at this frequency. Based on post-layout simulations, the design has a phase noise of −97/−99/−114 dBc for 10 kHz/100 kHz/1 MHz frequency offsets, respectively, which presents competitive numbers with the designs in the literature. The design has 1.2-V nominal supply voltage for the analog and digital blocks. The total power dissipation of the synthesizer core is 6 mW from a 1.2-V supply while the output buffers driving a 100-fF load consumes 18 mW. [ABSTRACT FROM AUTHOR]

This paper develops a calculus around a new β‐Pochhammer symbol of two variables, (a,b)m,n based on the Beta weighting ta−11−tb−1. The approach is a natural rising factorial formulation that offers a new way to express hypergeometric functions of two variables. The results are implemented to solve the problem of finding the phase error probability of a vector perturbed by Gaussian noise with an arbitrary phase threshold in closed form for the first time, in terms of the incomplete confluent hypergeometric function 1ℱ1. This has been an unresolved problem in angle modulation dating back to the 1950s. Closed‐form solutions are developed around the lower and upper incomplete Humbert second Φ2 confluent hypergeometric function of two variables using the new incomplete β‐Pochhammer calculus. [ABSTRACT FROM AUTHOR]

This paper presents an injection locked digitally controlled ring oscillator (IL-DCRO). To reduce jitter variations, minimize oscillator spurious signals, and eliminate periodical phase error, a double edge-injection (window injection) scheme with synchronized edge directions is proposed. A combinational edge generator is utilized to substitute the sequential edge generators for injection timing requirements relaxation. By biasing devices in deep triode, digitally controlled delay cells currents are adopted for frequency tuning. This helps reducing the devices flicker (1/f) noise and minimize the DCRO overall phase noise. At 1 MHz offset of frequency, the proposed oscillator has a measured phase noise of −125.95 dBc/Hz and −115.6 dBc/Hz at oscillation frequencies of 913.4 MHz and 432.6 MHz, respectively. Fabricated in 350 nm CMOS process, with a maximum power consumption of 3.3 mW, and oscillating at 913.4 MHz, this DCRO achieves a tuned oscillator figure of merit (FoM) of −197.35 dBc/Hz. The core area of this edge-injection-based DRCO is only 0.08 mm2. [ABSTRACT FROM AUTHOR]

One credible method for performance evaluation of network timing service was proposed, based on one kind of disciplined time standard with GNSS time transfer, NIMDO. The performance of the NTP timing service were characterized over multiple baselines on both the Internet and the Intranet, and the network delay and the timing offset were analyzed in detail. The results show that on the Internet the averaged timing offsets via the NTP servers are roughly hundreds of μs to several ms level, and on the Intranet the averaged timing offsets via the NTP servers are at about 20 μs level. NTP timing service was mainly affected by white phase noise, and flicker phase noise at the different sites. The maximum change of the timing offset was one-half of the maximum change of RT Delay. The uncertainties have been separately evaluated as less than 30 ms on the Internet and less than 60 μs on the Intranet for NTP timing service. [ABSTRACT FROM AUTHOR]

In this work, we investigate the optical frequency transmission with a magnitude of 100 mW through a 20 m polarization-maintaining fiber, using the phase noise compensation method. In order to minimize potential noise caused by stray light reflections in the fiber, we incorporate two acoustic-optic modulators to spectrally separate the heterodyne signal, effectively suppressing these sources of noise. Our experimental results demonstrate that the modified Allan deviations of fractional frequency stability for 1 s and 10,000 s are approximately 2.5 · 10−17 and 1 · 10−20, respectively. This research contributes to the advancement of high-power optical frequency transmission via optical fiber. [ABSTRACT FROM AUTHOR]

When the robot interacts with the environment or people, if the stiffness of the environment or people suddenly increases, the robot is prone to instability. Traditional solutions, such as the stability observer based on frequency, are easily affected by high-frequency signal noise or filter phase error, resulting in misdiagnosis. In addition, the adaptive algorithm keeps the contact force stable in the environment-robot interaction by identifying the environmental stiffness. Still, the change in the environmental stiffness is too significant, which may lead to the failure of the adaptive algorithm. Therefore, this paper proposes an improved observer stabilization method, using the ratio of the standard deviation of force to the maximum allowable force to eliminate the influence of high-frequency noise and reduce misdiagnosis. In addition, the designed stability observer can monitor the interaction between the robot and the environment in real-time and ensure the stable operation of the adaptive algorithm by updating the initial environment stiffness. Finally, some comparative experiments are carried out. The results show that the proposed method has good accuracy and robustness in human-robot and environment-robot interaction. [ABSTRACT FROM AUTHOR]

Quantum teleportation is a technique for allowing one party to transfer an unknown state to the other party some distance away. Different types of teleportation, including bidirectional teleportation have been proposed so far. The bidirectional protocol, plays a key role to improve the security and the efficiency of the quantum cryptographic schemas. Another branch of quantum communication is called quantum remote state preparation. Quantum remote state preparation is similar to the teleportation in terms of transferring a quantum state without physically sending it on the quantum channel. However, the difference is that in the latter, the state is known for the sender. In this research, a new bidirectional quantum remote state preparation protocol is proposed, where each party transfers a two-qubit state to each other simultaneously. The efficiency of this protocol is better than the previous ones. In addition, the effects of noise on the performance of the protocol are examined extensively. We estimate and analyze the fidelity of the protocol in a noisy environment with amplitude and phase damping noises. [ABSTRACT FROM AUTHOR]

We examine the effects of imperfect phase estimation of a reference signal on the bit error rate and mutual information over a communication channel influenced by fading and thermal noise. The Two-Wave Diffuse-Power (TWDP) model is utilized for statistical characterization of propagation environment where there are two dominant line-of-sight components together with diffuse ones. We derive novel analytical expression of the Fourier series for probability density function arising from the composite received signal phase. Further, the expression for the bit error rate is presented and numerically evaluated. We develop efficient analytical, numerical and simulation methods for estimating the value of the error floor and identifying the range of acceptable signal-to-noise ratio (SNR) values in cases when the floor is present during the detection of multilevel phase-shift keying (PSK) signals. In addition, we use Monte Carlo simulations in order to evaluate the mutual information for modulation orders two, four and eight, and identify its dependence on receiver hardware imperfections under the given channel conditions. Our results expose direct correspondence between bit error rate and mutual information value on one side, and the parameters of TWDP channel, SNR and phase noise standard deviation on the other side. The results illustrate that the error floor values are strongly influenced by the phase noise when signals propagate over a TWDP channel. In addition, the phase noise considerably affects the mutual information. [ABSTRACT FROM AUTHOR]

Proofs of sharp phase transition and noise sensitivity in percolation have been significantly simplified by the use of randomized algorithms, via the OSSS inequality (proved by O'Donnell et al. and the Schramm–Steif inequality for the Fourier‐Walsh coefficients of functions defined on the Boolean hypercube. In this article, we prove intrinsic versions of the OSSS and Schramm–Steif inequalities for functionals of a general Poisson process, and apply these new estimates to deduce sufficient conditions—expressed in terms of randomized stopping sets—yielding sharp phase transitions, quantitative noise sensitivity, exceptional times and bounds on critical windows for monotonic Boolean Poisson functions. Our analysis is based on a new general definition of "stopping set", not requiring any topological property for the underlying measurable space, as well as on the new concept of a "continuous‐time decision tree", for which we establish several fundamental properties. We apply our findings to the k$$ k $$‐percolation of the Poisson Boolean model and to the Poisson‐based confetti percolation with bounded random grains. In these two models, we reduce the proof of sharp phase transitions for percolation, and of noise sensitivity for crossing events, to the construction of suitable randomized stopping sets and the computation of one‐arm probabilities at criticality. This enables us to settle an open problem suggested by Ahlberg et al. (a special case of which was conjectured earlier by Ahlberg et al. on noise sensitivity of crossing events for the planar Poisson Boolean model with random balls whose radius distribution has finite (2+α)$$ \left(2+\alpha \right) $$‐moments and also show the same for planar confetti percolation model with bounded random balls. We also prove that critical probability is 1/2$$ 1/2 $$ for the planar confetti percolation model with bounded, π/2$$ \pi /2 $$‐rotation invariant and reflection invariant random grains. Such a result was conjectured by Benjamini and Schramm in the case of fixed balls and proved by Müller, Hirsch and Ghosh and Roy in the case of balls, boxes and random boxes, respectively; our results contain all previous findings as special cases. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The frequency synthesizer plays a crucial role in atomic clock technology. In this study, we demonstrate a direct microwave frequency synthesizer for a cesium atomic clock, employing frequency multiplication and a dual-phase-locked loop mode. A mathematical model of the frequency synthesis chain is established to estimate its performance. The phase-settling time and system stability are analyzed and studied in detail, and the obtained results are verified by experiments. An optimized realization of the frequency synthesizer shows that the phase-settling time can be adjusted within the range of 644.5 µs to 1.5 ms. Additionally, we measure the absolute phase noise values to be −63.7 dBc/Hz, −75.7 dBc/Hz, −107.1 dBc/Hz, and −122.5 dBc/Hz at 1 Hz, 10 Hz, 1 kHz, and 10 kHz offset frequencies, respectively. [ABSTRACT FROM AUTHOR]

This paper deals with the optimal design of different VLSI circuits, namely, the CMOS voltage reference circuit and the CMOS ring oscillator (RO). The optimization technique used here is the multiobjective differential evolution algorithm (MDEA). All the circuits are designed for 90 nm technology. The main objective of the CMOS voltage reference circuit is to minimize the voltage variation at the output. The targeted value of the reference voltage is 550 mV. A CMOS ring oscillator (RO) is designed depending on the performance parameters such as power consumption and phase noise. The optimal transistor sizing of each circuit is obtained from MDEA. Each circuit is implemented in SPICE by taking the optimal dimensions of the transistors, and the performance parameters are achieved. The designed voltage reference circuit achieves a reference voltage of 550 mV with 600 nW power dissipation. The reference voltage variation of 8.18% is observed due to temperature variation from −40°C to + 125°C. The MDEA-based optimal design of RO oscillates at 2.001 GHz frequency, has a phase noise of −87 dBc/Hz at 1 MHz offset frequency, and consumes 71 μW power. This work mainly aims to optimize the MOS transistors' sizes using MDEA for better circuit performance parameters. SPICE simulation has been carried out by using the optimal values of MOS transistor sizes to exhibit the performance parameters of the circuit. Simulation results establish that design specifications are closely met. SPICE results show that MDEA is a better technique for the optimal design of the above-mentioned VLSI circuits. [ABSTRACT FROM AUTHOR]

This paper proposes an improved two-stage and four-stage CMOS ring-Voltage Controlled Oscillator (VCO) design with large frequency at output, improved phase noise, and reduced consumption of power. A PMOS varactor is used in conventional circuit to obtain high tuning-range and very low consumption of power. Cadence Virtuoso 90 nm technology was used to simulate this differential ring-VCO with the proposed dual input differential delay cell. This two-stage and four-stage design gives wider range of tuning from 1.254 to 6.694 GHz (81.26%) and 1.821 to 5.259 GHz (65.37%), respectively, with the change in V c from 0.1 to 1 V. The power-consumption of two-stage ring VCO and four-stage ring VCO varies from 48.02 to 89.33 μ W and 66.81 to 157.02 μ W respectively. The proposed two-stage and four-stage VCO exhibits −114.46 and −111.06 dBc/Hz at 1 MHz offset from 6.694 and 5.259 GHz carrier frequency, respectively. The proposed two-stage and four-stage differential ring-VCO results in wider tuning range and very low consumption of power and an improved figure of merit and phase-noise. [ABSTRACT FROM AUTHOR]

Voltage controlled oscillator (VCO) offers the radio frequency (RF) system designer a freedom to select the required frequency. Today's wireless communication system imposes a very stringent requirement in terms of phase noise generated in VCO. This study presents an inductive source degeneration technique to improve the phase noise performance of the inductance-capacitance (LC)-VCO. Double cross-coupled topology has been chosen for the proposed VCO. The post layout simulations with the parasitic resistance, inductance, capacitance (RLC) extracted view is carried out with united microelectronics corporations (UMC) 0.18 µm process by spectre simulator of cadence tools. The proposed VCO provides a phase noise of -124.3 dBc/Hz @ 1 MHz. The tuning range obtained is 19.87% with a centre frequency of 2.46 GHz which makes it suitable for industrial, scientific, and medical (ISM) band applications. It consumes a power of 2.10 mW. Also, a good figure of merit of -189 is achieved. The total layout area occupied is 477×545 µm2. [ABSTRACT FROM AUTHOR]

Reconfigurable architectures are more prominent in modern-day multi-band radio systems. This work has been conceptualized for a flexible 8-bit digitally controlled oscillator (DCO) design to suit reconfigurable RF all-digital phase-locked loop applications. To efficiently utilize the area, power consumption and attend to several operating frequencies, an optimal design of LC-tank based DCO topology with both L and C components contributing to the coarse and fine-tuning of the DCO's frequency of oscillation has been proposed. The design has been carried out in the Cadence Spectre RF tool with UMC180 nm technology. The proposed 8-bit DCO exhibits wide bandwidth, generating 240 oscillating frequencies in the LTE frequency band and occupies less area of 70 × 18 µm. The frequency of oscillation varies from 491.5 MHz to 3.392 GHz designed for an 8-bit digital control word with a tuning range percentage of 149%. The maximum phase noise obtained is −103.57 dBc/Hz @ 10 MHz offset causing a figure of merit (FOM) of −144.167 dBc/Hz. The total power consumed by the DCO ranges from 1.05 to 9.5 mW approximately. [ABSTRACT FROM AUTHOR]

Coupled microwave oscillators could be potentially considered a good replacement for the feed network of frequency‐diverse arrays. However, previous studies showed that the stability region for a mutually weak‐coupled oscillator array in the Mode Lock State (MLS) is too small to be practical. Besides, by increasing the coupling strength or reducing the initial natural frequency of the oscillators, the current analytical methods lose their accuracy. The final steady‐state and dynamic of a non‐linear Van‐der‐Pol medium‐coupled oscillator array in the MLS is investigated. By using the Kuramoto Model results in analysing the biological cells, an alternative approach is suggested and investigated in the entrainment region for the mode‐locked microwave oscillator array. This approach is accurate even for medium‐coupled oscillator arrays, where the locking range to the beat frequency ratio is greater than 0.1. The stability of the oscillator in this region is investigated by imposing some perturbations in the form of phase noise on the initial signals. Also, the optimum initial condition to design large arrays is investigated using the analysis results. In the described initial conditions for small beat frequencies, the simulation results show that the stability region is much greater than the large beat frequency region. This capability initiates a new practical approach for implementing Frequency Diverse Arrays. [ABSTRACT FROM AUTHOR]

Narrow-linewidth lasers have a high spectral purity, long coherent length, and low phase noise, so they have important applications in atomic clocks, precision measurement, and quantum computing. We inject a transmitted laser from a narrow-linewidth (∼15 kHz) flat-concave Fabry–Perot (F-P) cavity made from ultra-low expansion (ULE) optical glass into an 852 nm distributed Bragg reflector-type laser diode (DBR-LD), of which the comprehensive linewidth is 1.67 MHz for the free running case. With an increase in the self-injection power, the laser linewidth gradually narrows, and the injection locking current range gradually increases. The narrowest linewidth measured by the delayed frequency-shifted self-heterodyne (DFSSH) method is about 365 Hz, which is about 1 / 4500 of the linewidth for the free running case. Moreover, to characterize the laser phase noise, we use a detuned F-P cavity to measure the conversion signal from the laser phase noise to the intensity noise for both the free running case and the self-injection lock case. The laser phase noise for the self-injection lock case is significantly suppressed in the analysis frequency range of 0.1–10 MHz compared to the free running case. In particular, the phase noise is suppressed by more than 30 dB at an analysis frequency of 100 kHz. [ABSTRACT FROM AUTHOR]

We demonstrate the use of a low power near-infrared laser illuminating the front facet of a quantum cascade laser (QCL) as an optical actuator for the coherent control of a mid-infrared frequency comb. We show that with appropriate current control of the QCL comb and intensity modulation of the near-infrared laser, a tight phase lock of a comb line to a distributed feedback laser is possible with 2 MHz of locking bandwidth and 200 mrad of residual phase noise. A characterization of the whole scheme is provided, showing the limits of the electrical actuation, which we bypassed using the optical actuation. Both comb degrees of freedom can be locked by performing electrical injection locking of the repetition rate in parallel. However, we show that the QCL acts as a fast near-infrared light detector such that injection locking can also be achieved through modulation of the near-infrared light. These results on the coherent control of a QCL frequency comb are particularly interesting for coherent averaging in dual-comb spectroscopy and for mid-infrared frequency comb applications requiring high spectral purity. [ABSTRACT FROM AUTHOR]

We demonstrate a sub-GHz resolution, fully programmable Fourier-domain pulse shaper capable of generating arbitrary optical pulse patterns for superconducting circuit platforms. This high resolution allows line-by-line pulse shaping of a 1 GHz-spaced comb, and the pulse shaper can accommodate an optical bandwidth as large as 1 THz, which represents the highest resolution programmable line-by-line pulse shaping to our knowledge. Linear optical sampling with a dual-comb system confirms independent control of 1 GHz-spaced optical lines, and the low phase noise of the pulse shaper is characterized. We apply the pulse shaper as an optical drive for an array of Josephson junctions operating at a temperature of 4 K, where cryogenic photodetection of pulse doublets with user-defined separation characterizes the Josephson junction response. Furthermore, we demonstrate a pulse-density modulation pattern of 4 ps duration optical pulses that can serve as the high bandwidth drive of a quantum-based Josephson arbitrary waveform synthesizer. By leveraging the exquisite control, large bandwidth, and low noise of photonics, this represents an important advance toward the realization of high power and high spectral purity AC voltage standards at gigahertz frequencies without requiring 100 GHz bandwidth driving electronics. [ABSTRACT FROM AUTHOR]

The objective of the proposed work is to demonstrate the use of a hybrid approach for the design of a voltage-controlled oscillator (VCO) which can lead to higher performance. The performance is improved in terms of the tuning range, frequency of oscillation, voltage swing, and power consumption. The proposed hybrid VCO is designed using an active load common source amplifier and current starved inverter that are cascaded alternatively to achieve low power consumption. The proposed VCO achieves a measured phase noise of -74 dBc/Hz and a figure of merit (FOM) of -152.6 dBc/Hz at a 1 MHz offset when running at 5.1 GHz frequency. The hybrid current starved-current starved VCO (CS-CS VCO) consumes a power of 289 µW using a 1.8 V supply and attains a wide tuning range of 96.98%. Hybrid VCO is designed using 0.09 µm complementary metal-oxide-semiconductor (CMOS) technology. To justify the robustness, reliability, and scalability of the circuit different corner analysis is performed through 500 runs of Monte-Carlo simulation. [ABSTRACT FROM AUTHOR]

Abstract Due to their perfect periodic autocorrelation property, Zadoff–Chu sequences are often used as stimulus signals in the measurement of radio channel responses. In this letter, the cross‐correlation of a linear shift‐invariant system's response to a Zadoff–Chu sequence is derived for the case that a multiplicative perturbation such as phase noise is present at its output. The perturbation signal is shown to incur a spurious discrete Fourier transform, thus degrading the correlation's peak to sidelobe ratio. The implications for the performance limits of channel measurement systems are discussed.

In this paper, we present the high-speed phase frequency detector where the phase characteristics are enhanced. This PFD has a simple structure where the dead zone is annihilated and blind zone is highly reduced. This PFD generates UP and DN signal only when it gets the distinct phase difference. With the reduction of the reset time, the proposed PFD function is in the order of 1.5 M H z − 4 G H z operating frequency. The design shows the improvement by completely eliminating the dead zone. However, the blind zone is minimised to 74.6 p s in the phase characteristics which improves the output phase noise as −132.9 d B c / H z at 1 M H z offset frequency. The power consumption is minimised upto 417.3 μ W @ 4 G H z operating frequency. The design is simulated in standard 0.18 \mum CMOS technology node with 1.8 V power supply. Furthermore, the achieved frequency band is applicable for high-speed and low-power PLL application such as Zigbee, Wifi, Bluetooth and 4 G communication. [ABSTRACT FROM AUTHOR]

Determining the loop noise bandwidth and the coherent integration time is essential and important for the design of a reliable digital phase-locked loop (DPLL) in global navigation satellite system (GNSS) receivers. In general, designers set such parameters approximately by utilizing the well-known fact that the DPLL is stable if the normalized bandwidth, which is the product of the integration time and the noise bandwidth, is much less than one. However, actual limit points are not fixed at exactly one, and they vary with the loop filter order and implementation method. Furthermore, a lower limit on the normalized bandwidth may exist. This paper presents theoretical upper and lower limits for the normalized bandwidth of DPLL in GNSS receivers. The upper limit was obtained by examining the stability of DPLL with a special emphasis on the digital integration methods. The stability was investigated in terms of z-plane root loci with and without the consideration of the computational delay, which is a delay induced by the calculation of the discriminator and the loop filter. The lower limit was analyzed using the DPLL measurement error composed of the thermal noise, oscillator phase noise, and dynamic stress error. By utilizing the carrier-to-noise density ratio threshold which indicates the crossing point between the measurement error and the corresponding threshold, the lower limit of the normalized bandwidth is obtained. [ABSTRACT FROM AUTHOR]

The generation and manipulation of ultracold atomic ensembles in the quantum regime require the application of dynamically controllable microwave fields with ultra-low noise performance. Here, we present a low-phase-noise microwave source with two independently controllable output paths. Both paths generate frequencies in the range of 6.835 GHz ± 25 MHz for hyperfine transitions in 87Rb. The presented microwave source combines two commercially available frequency synthesizers: an ultra-low-noise oscillator at 7 GHz and a direct digital synthesizer for radio frequencies. We demonstrate a low integrated phase noise of 480 µrad in the range of 10 Hz to 100 kHz and fast updates of frequency, amplitude, and phase in sub-µs time scales. The highly dynamic control enables the generation of shaped pulse forms and the deployment of composite pulses to suppress the influence of various noise sources. [ABSTRACT FROM AUTHOR]

Quasi-monolithic interferometers play a crucial role in high-precision measurement experiments, including gravitational wave detection, inertial sensing, vibrometry, and seismology. Achieving high stability and accuracy in such interferometers requires a method for bonding the optical components to a baseplate. While optical contact bonding and silicate bonding are common methods, UV adhesives offer advantages such as controlled curing and low geometrical requirements for optical components and baseplates. This paper presents a detailed construction method for a quasi-monolithic compact interferometer based on UV-adhesive bonding. We built two types of interferometers using this method: a 100 × 100 × 20 mm3 Mach–Zender homodyne interferometer with unequal arm lengths of about 100 mm for laser frequency noise monitoring and a heterodyne interferometer as a displacement sensing head, sizing 20 × 30 × 20 mm3. Our Mach–Zender interferometer achieved a phase noise level of 2 μ r a d H z at 1 Hz and an equivalent laser frequency noise monitoring sensitivity of about 1 k H z / H z at 1 Hz. The compact heterodyne interferometer sensing head showed a sensitivity level of 1 p m / H z in translation and 0.2 n r a d / H z in two tilts above 0.4 Hz. Our tests demonstrate that quasi-monolithic compact interferometers based on UV-adhesive bonding can achieve high sensitivity levels at the pico-meter and nano-radian scales. [ABSTRACT FROM AUTHOR]

This paper presents a wide‐band charge‐pump phase‐locked loop (CPPLL) with reference spur reduction techniques. To broaden the frequency range without deteriorating phase noise, a 6‐bit capacitor array‐based VCO and an automatic frequency calibrator (AFC) are used. A compact loop filter technique saves the capacitor area and maintains the bandwidth. Also, a novel charge pump with dynamic current matching circuit is proposed to reduce the reference spur of the PLL. The current mismatch is less than 0.22 μA (0.16%) over the voltage range from 0.75 to 1.55 V. Fabricated in 0.13 μm CMOS technology, the proposed PLL achieves a locking range of 7.6–12.3 GHz (47.2%), with a 25 MHz frequency interval. The PLL consumes 23.3 mA from a 2.5 V supply voltage and occupies a core area of 0.92 mm × 0.72 mm. The reference spur of the proposed PLL is measured to be −81.1 dBc, and in‐band phase noise reaches −110.8 dBc/Hz at 1 MHz offset frequency from the 9.5 GHz carrier frequency. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a comprehensive analysis of oscillation frequency, oscillation amplitude, and phase noise is conducted for an LC cross‐coupled oscillator with unequal inductors, active and passive transconductance amplification structure, and very low phase noise. In this study, for the first time, a complete analysis of the phase noise of this oscillator is presented using a novel method that does not require complex simulations to calculate the Impact Sensitivity Function (ISF) and phase noise, and as a result, a closed‐form equation is extracted for the phase noise. The calculated results are compared with the corresponding simulations to evaluate the validity of the extracted equations. Using the closed‐form phase noise equation as well as the oscillation frequency, designers can comprehend the design trade‐offs and design an oscillator for specific phase noise and oscillation frequency. The proposed method of calculating the ISF is also applicable and valid for other second‐order oscillators. In the following, the structure of the proposed oscillator is designed and simulated using the standard 0.18‐μm CMOS technology with a 1.8‐ V power supply and 575.2‐MHz oscillation frequency to have the optimal coupling coefficient in terms of the phase noise and oscillation amplitude. The simulation results as well as the analyses performed based on the phase noise and oscillation amplitude parameters show that the structure proposed in this study provides a better performance with a much lower phase noise comparing with the structure of a conventional cross‐coupled oscillator as well as the proposed cross‐coupled oscillator with equal inductors. [ABSTRACT FROM AUTHOR]

Femtosecond frequency combs are among the most precise measurement tools in existence. They have applications ranging from high‐precision spectroscopy and metrology to time‐domain quantum physics. Maximizing the passive stability of these instruments is essential to achieve their full potential in fundamental science and high‐tech industry. However, the noise mechanisms across the entire operating space of these devices have not been fully characterized. Here the noise properties of fiber‐based frequency combs are studied as a function of intracavity dispersion, pump power, and repetition rate. Distinct minima are discovered in this parameter space where the free‐running linewidth of the carrier‐envelope offset (CEO) frequency fCEO drops below 1 kHz. The individual comb lines are analyzed spread over a wide spectral range producing a complete understanding of the particular contributions to the phase noise and their interplay. Exploiting these findings, combs featuring sharp teeth at specific frequency positions and over the entire spectrum from fCEO to 300 THz are demonstrated. The ultrabroadband stability offered by these compact systems provides a new level of quality for front‐end measurement tasks in both time and frequency domains. [ABSTRACT FROM AUTHOR]

This paper presents a novel low-power four-stage voltage controlled ring oscillator (VCRO) designed in the TSMC 180 nm CMOS technology. Each stage in the proposed VCRO consists of a differential delay cell. Output frequency tuning is controlled by the I-MOS varactor connected at the output of each delay stage. Different performance parameters, including tuning range, power consumption, phase noise and figure of merit, have been obtained in the TSMC 180 nm CMOS technology. Results show that the output oscillation frequency of VCRO is tunable from 0.545 to 1.195 GHz by varying the drain/source voltage (Vids) from 0.6 to 1.8 V with a supply voltage (Vdd) of 1.8 V. Furthermore, it provides a wide tuning range from 0.152 to 1.903 GHz with the variation in Vdd from 1 to 3 V with different I-MOS widths of 0.5, 1, 2 and 4 µm. Furthermore, effects of change in Vids from 0.8 to 1.8 V with Vdd variations from 1 to 3 V have been evaluated with I-MOS varactor width (W) of 2 µm. Frequency range from 0.170 to 1.451 GHz has been achieved for this tuning method. The proposed VCRO exhibits the phase noise of −100.45 dBc/Hz @1 MHz and −96.01 dBc/Hz @0.6 MHz from the centre frequency with power consumption 0.003 to 3.165 mW with a change in Vdd from 1.8 to 3.0 V. The figure of merit (FoM) of the proposed VCRO is 161.77dBc/Hz. [ABSTRACT FROM AUTHOR]

Data-centric inverse problems are a process of inferring physical attributes from indirect measurements. Full-waveform inversion (FWI) is a non-linear inverse problem that attempts to obtain a quantitative physical model by comparing the wave equation solution with observed data, optimizing an objective function. However, the FWI is strenuously dependent on a robust objective function, especially for dealing with cycle-skipping issues and non-Gaussian noises in the dataset. In this work, we present an objective function based on the Kaniadakis κ -Gaussian distribution and the optimal transport (OT) theory to mitigate non-Gaussian noise effects and phase ambiguity concerns that cause cycle skipping. We construct the κ -objective function using the probabilistic maximum likelihood procedure and include it within a well-posed version of the original OT formulation, known as the Kantorovich–Rubinstein metric. We represent the data in the graph space to satisfy the probability axioms required by the Kantorovich–Rubinstein framework. We call our proposal the κ -Graph-Space Optimal Transport FWI (κ -GSOT-FWI). The results suggest that the κ -GSOT-FWI is an effective procedure to circumvent the effects of non-Gaussian noise and cycle-skipping problems. They also show that the Kaniadakis κ -statistics significantly improve the FWI objective function convergence, resulting in higher-resolution models than classical techniques, especially when κ = 0.6 . [ABSTRACT FROM AUTHOR]

Radio telescopes are among the applications with the highest demands on a local oscillator (LO), which is used to receive and process the signals coming from the sky. Therefore the modules providing the required LO signal have traditionally been big and complicated. To overcome this disadvantage, we implement our own integrated frequency synthesizer inside a small LO module in this article. With this synthesizer we are able to achieve a jitter of only 50 fs integrated from 10 Hz to 2.5 GHz offset at a carrier frequency of 75 GHz. This is in part achieved by a very low in-band phase noise of −111.8 dBc at 10 kHz offset. The stabilizable frequency range is 62–88 GHz. Thus achieving promising results to fulfill this very demanding task with integrated frequency synthesizers in the future. [ABSTRACT FROM AUTHOR]

A thorough investigation of major contributors to out-of-band emission (OOBE) in transmitters (TXs) utilizing digital modulation schemes is provided. Specifically, the paper delves into the detrimental effects of phase noise of the local oscillator (LO), typically realized using a phase-locked loop (PLL), on the OOBE phenomenon. Furthermore, the effects of the circuit nonlinearity in a TX, widely recognized as a primary contributor to spectral regrowth and elevated levels of OOBE, are investigated. Additionally, the impact of filtering and bandwidth (BW) limitation on OOBE is taken into account. Comprehensive simulations verify the accuracy of the analytical study. The results provided throughout this paper can be used to determine the linearity and phase noise requirements of different blocks, such as PLL and power amplifier (PA) within a TX chain to design a system complying with a specific mask emission dictated by a particular standard.

Beyond fifth generation (B5G) / sixth generation (6G) wireless systems require full utilization of all spectrums. However, hardware devices operating in the high-frequency bands bring a series of non-ideal behaviors, including nonlinear distortion caused by high-power amplifiers and phase noise generated by radio-frequency oscillators, which will lead to performance degradation of traditional signal modulation technology. To this end, this paper proposes a 5G new radio-compatible constellation design method using projection over quadrature amplitude modulation (QAM). First, to address the nonlinear distortion caused by power amplifiers, the pseudo-amplitude-phase-shift keying (APSK) constellation with a low peak-to-average power ratio is proposed. The signal points are selected from QAM by minimum Euclidean distance with APSK. Second, for a phase noise channel, the pseudo-spiral constellation is designed with the projection of Spiral constellation points onto QAM by the proposed minimum radial-angular weighted distance. Simulation results show that the proposed pseudo-APSK modulation outperforms traditional QAM at medium and high code rates considering nonlinear distortion produced by a power amplifier. Besides, the proposed pseudo-spiral modulation exhibits significant performance gain and improved robustness compared to QAM under phase noise-affected channels, particularly in medium-high signal-to-noise ratio conditions.

An 8-GHz VCO with class-F23 operation was realized in a 40 nm CMOS technology without ultra-thick metals. The class-F23 operation was enabled in a transformer-based LC tank to allow multiple impedance peaks in the common mode (CM) and the differential mode (DM) excitation. With the additional resonance at $2^{nd}$ and $3^{rd}$ harmonic frequency, the circuit noise to phase-noise conversion and 1/f noise up-conversion are reduced significantly. In a 40 nm CMOS technology without ultra-thick metal, a patterned shielding structure was proposed to improve the inductor quality factor. A combined varactor and capacitor array is proposed to provide accurate matching for a desired resonance frequency ratio, reducing AM-FM conversion and it achieves a broad tuning range. With the proposed transformer-based LC bank and class-F23 operation, the oscillator achieves a phase noise of −150.8 dBc/Hz at 10 MHz offset from a 1.85 GHz carrier after an on-chip /4 divider, and the measured 1/f3 flicker noise corner is around 400 kHz. The oscillator core covers a 7.5–9.4 GHz frequency range for a 25% tuning range.

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).

This paper presents a wideband approach for L5 and S-band integer-N phase-locked loop (PLL) targeting Indian Regional Navigation Satellite System (IRNSS) applications. A reference spur reduction technique using a Gm−C filter is proposed. The reference spur is improved by 7 dB when compared with one without any Gm−C filter. The wideband integer-N PLL is designed and fabricated in UMC 65-nm CMOS process. The Gm−C filter block consumes 200 μA current. The wideband voltage-controlled oscillator (VCO) oscillates from 1.6 GHz to 3.2 GHz having a tuning range (TR) of 40%, achieving a best and worst phase noise of ≈−122 dBc/Hz and ≈−116 dBc/Hz at a 1 MHz offset, respectively.

In the field of inter-satellite laser communication, achieving high-quality communication and compensating for the Doppler frequency shift caused by relative motion necessitate lasers with narrow linewidths, low phase noise, and the ability to achieve mode-hop-free tuning within a specific range. To this end, this paper investigates a novel external cavity diode laser (ECDL) with a frequency-selective F-P etalon structure, leveraging the external cavity F-P etalon structure in conjunction with an auxiliary filter to achieve single longitudinal mode selection. The laser undergoes linewidth testing using a delayed self-heterodyne beating method, followed by the testing of its phase noise and frequency noise characteristics using a noise analyzer, yielding beat spectra and noise power spectral density profiles. Furthermore, the paper introduces an innovative bidirectional temperature-scanning laser method to achieve optimal laser-operating point selection and mode-hop-free tuning. The experimental results showcase that the single longitudinal mode spectral side-mode suppression ratio (SMSR) is around 70 dB, and the output power exceeds 10 mW. Enhancing the precision of the F-P etalon leads to a more pronounced suppression of low-frequency phase noise, reducing the Lorentzian linewidth from the initial 10 kHz level to a remarkable 5 kHz level. The bidirectional temperature-scanning laser method not only allows for the selection of the optimal operating point but also enables mode-hop-free tuning within 160 pm.