Phase-modulated Signals Research Articles

A new displacement demodulation algorithm for the phase-modulated self-mixing interferometer based on FPGA

Abstract This paper introduces a design of the phase demodulation system based on FPGA for the phase-modulated self-mixing interferometer. By the processing that the modulation SIN signal and the doubling frequency modulation COS signal are respectively multiplied by the phase-modulated self-mixing signal(PSMI) and then low-pass filtered and shaped in the electrical domain, two orthogonal square wave signals sensitive to the object’s movement direction are obtained for displacement reconstruction. The FPGA signal processing system controls the generation of a highly stable and accurate sinusoidal signal source for the modulation of the electro-optic crystal(EOM). At the same time, the two orthogonal square wave signals obtained after the demodulation processing are subdivided for the high-precision measurement of a uniformly moving object’s displacement. The high-frequency amplifier circuit amplifying the self-mixing interference signal, multiplier & frequency doubler circuits based on MLT04 and low-pass filter circuits are designed. FPGA-based counting programs, DAC circuits and programs used for generating sine waves are also designed. In the experiment, comparison tests for displacement measurement are performed using the PI company’s two-dimensional precision electronically-controlled translation stage, and high-precision displacement measurement can be achieved. The demodulation system does not rely on a PC and a high-precision acquisition card, and can realize real-time measurement of displacement, greatly improving the practicability of the system.

Calculating complex envelope of an received phase modulated signal from results of spectral decomposition of entrance sample correlation matrixes with changing carrier frequency

Calculating complex envelope of an received phase modulated signal from results of spectral decomposition of entrance sample correlation matrixes with changing carrier frequency

ОЦЕНКА ПОМЕХОУСТОЙЧИВОСТИ ЧАСТОТНО-МОДУЛИРОВАННЫХ СИГНАЛОВ С НЕПРЕРЫВНОЙ ФАЗОЙ И ПОЛНЫМ ОТКЛИКОМ НА ОСНОВЕ ИМИТАЦИОННОГО МОДЕЛИРОВАНИЯ

The problem of spectral load of communication channels is now becoming urgent, which determines the efforts of the world’s leading tech communication companies to search for perspective signals. These signals must ensure compliance with international standards governing the use of frequency bands and the permissible level of out-of-band emissions and the required noise immunity of information transmission. The article deals with the noise immunity of continuous phase modulation signals research. A preliminary estimation is carried out by calculating the Euclidean distances between signals. The estimates of the noise immunity were obtained experimentally. The results of simulation are presented for fixed value of the signal to noise ratio for signals. Modulation indices and phase pulse were taken into account. The results of the study make it possible to emphasize the modulation indices for CPM FR signals, having more noise immunity then the known BPSK and MSK signals. Increasing the noise immunity becomes possible due to intersymbol phase communication. These signals are received according to the Viterbi algorithm. The results of the study show the values of the modulation indices to be of practical interest.

A Calibration Scheme With Combination of the Optical Shaft Encoder and Laser Triangulation Sensor for Low-Frequency Angular Acceleration Rotary Table

A low-frequency angular acceleration rotary table (LFAART) is capable of sinusoidal motion around a fixed position and essential to verify dynamic characteristics of a gyroscope device. The table’s performance at different swinging frequencies and amplitudes needs to be calibrated to realize traceability. However, there has been little research on the LFAART calibration. Besides, the existing measurement methods of sinusoidal angular motion parameters are not adequate for the needs of the LFAART calibration in terms of measurement range, precision, and feasibility. This article presents a calibration scheme combining an optical shaft encoder and a laser triangulation sensor. When the rotation amplitude covers sufficient slots of the scale grating, the optical shaft encoder is applied, while the laser triangulation sensor is used for a tiny amplitude motion. An algorithm is proposed to accurately calculate the angular acceleration amplitude and frequency of the rotation utilizing sinusoidal phase-modulated signals of the optical shaft encoder output. Singular zero-crossings of the series are discarded, and intervals of reversing moments are recognized according to the signal derivative’s sign at remaining zero-crossings. Then intervals are divided into subintervals to obtain accurate reversing moments. Finally, angular displacements between two adjacent reversing moments are estimated based on the fringe counting method, and the amplitude and frequency are calculated. The measurement uncertainty analysis and experiment demonstrate that the calibration scheme, including the algorithm, possesses high accuracy and resolution, wide range, and good operability, which perfectly solves the rotation’s angular acceleration amplitude and frequency.

JAMMINGIMMUNITYRESEARCH OF A RADAR OPERATING WITH BARKER CODED PHASE MODULATED SIGNAL

The matched filter is one of the most important elements in the pulse compression technique. Pulse compressed signal enhances the interference immunity of a radar operating with such a signal. A model of the matched filter for a Barker coded phase modulated signal was synthesized using the Simulink tool of the Matlab software. Interference signals were feed to the input of the matched filter and output signals were measured. The matched filters degree of suppression of these interference signals was assessed. Conclusions were made about the jamming immunity of radars operating with Barker coded phase modulated signal.

Wigner matrix formalism for phase-modulated signals.

Laser beams can carry multi-scale properties in space and time that ultimately impact their quality. The study of their evolution along complex optical sequences is of crucial interest, especially in high-intensity laser chains. For such analysis, results obtained with standard numerical methods strongly depend on the sampling. In this paper, we develop an analytic model for a sinusoidal phase modulation inside a sequence of first-order optics elements based on the Wigner matrix formalism. A Bessel decomposition of the Wigner function gives pseudo-Wigner functions that obey the general ABCD matrix law transformation without approximations and sampling considerations. Applied to a Gaussian beam, explicit expressions are obtained for the projections of the Wigner function in the sub-spaces and give a powerful tool for analyzing the laser beam properties. The formalism is established in the spatial and temporal domains and can be used to evaluate the impact of the phase noise on the beam properties and is not limited to small modulation depths. For the sake of illustration, the model is applied to the Talbot effect with the analysis of the propagation in the spatial and phase-space domains. A comparison with full numerical calculations evidences the high accuracy of the analytic model that retrieves all the features of the diffracted beam.

Laser displacement measurement using intensity modulation with a phase-modulated radio-frequency signal

We demonstrate a laser-based displacement measurement using an intensity modulator as a simple and wide-band intensity correlator. The proposed method applies intensity modulation not only to the output probe beam but also to the reflected beam from a target, where the fundamental frequency of modulation signal is the same for both, but the phase of modulation signal for the reflected beam is also modulated. The displacement is measured using harmonic signals from a photodetector. The principle is verified for 40 mm and 16 m ranges of displacement measurement, where the relative measurement uncertainty of is achieved.

Empirical Approach to the Estimating the Immunity of Phase Modulation Signals with Continuous Phase

The high spectral efficiency of signals with continuous phase modulation (CPM) has determined their popularity and active use in various radio engineering projects. The uniqueness of the properties of CPM signals is associated with the preservation of the continuity of their phase when changing information messages for the duration of a symbol. At the same time, until recently, of the entire wide class of signals with continuous phase modulation, the most widespread were various variations, the so-called Minimum Shift Keying (MSK) signals. However, these are far from the only representatives of the class of CPM signals with the property of high spectral compactness. This article examines no less interesting signals of this class, formed by means of Dual Phase Modulation (DPM). In particular, analytical expressions of their synthesis are presented, their belonging to the class of CPM signals is substantiated. In addition, the article investigates the temporal properties of the phase function recommended by ITU-R SM.328-11 for the synthesis of signals with continuous phase modulation, presents the time and frequency fragments of MSK signals in comparison with signals with Binary Phase Shift Keying (BPSK). The stages of the analytical derivation of the model of noise immunity of PCM signals in terms of the probability of a bit error based on an empirical approach are presented. The generality of the obtained model with the known expression for MSK signals is shown by studying the difference function of the approximation error (error of the order of 10-3), which made it possible to obtain a more compact representation of the developed model in relation to DPM signals. It has been proven that DPM signals have higher noise immunity properties in relation to MSK signals (about 0.5 dB at an error level of 10-5), using the results of studying the difference functions determined by the difference between the signal symbols corresponding to the information values "1" and "0". The directions of further research are determined.

Acousto-Optic Devices Based on Multibeam Diffraction

The multibeam acousto-optical Bragg diffraction of laser radiation is considered. This is splitting of an initial beam into several independently controlled beams (channels) without substantial light-power losses. Practically significant relationships that determine the conditions for implementing the multibeam diffraction and its main parameters have been obtained. It is shown that the necessary condition is the form of control radio signal that is close to a frequency (phase) modulated signal. Experimental studies were conducted on a polarization-insensitive acousto-optic deflector based on a paratellurite crystal. Practical applications of the multibeam diffraction are shown: laser image deposition, multichannel transmission (switching) of optical information, and the formation of the laser-beam profile.

Аналіз ефективності застосування двохетапного алгоритму оцінки несучої частоти фазомодульованого сигналу супутникової системи зв’язку при передачі даних в безперервному режимі

В роботі узагальнено процедуру та сформовано двохетапний алгоритм оцінки несучої частоти фазомодульованого сигналу супутникової системи зв’язку при передачі даних в безперервному режимі з врахуванням умови невизначеності всіх параметрів сигналу. Досягнення мінімального інтервалу спостереження в поданому алгоритмі оцінки несучої частоти забезпечується використанням функції швидкого перетворення Фур’є. З метою аналізу ефективності вказаного алгоритму проведено моделювання процесу оцінки несучої частоти фазомодульованого сигналу супутникової системи зв’язку при передачі даних в безперервному режимі та отримані функціональні залежності максимуму частоти в спектрі сигналу та мінімальна дисперсія оцінки несучої частоти. Аналіз оцінки проведено на основі порівняння співвідношення отриманої мінімальної дисперсії оцінки несучої частоти і теоретично можливого кордону мінімальної дисперсії.

Tone injection‐based cancellation technique for nonlinear distortion reduction of modulated signals in BAW resonators

AbstractA technique for the reduction of third‐order intermodulation distortion (IMD3) occurring in bulk acoustic wave (BAW) filters and multiplexers is presented. The method consists of using the intrinsic second‐order intermodulation distortion generated by BAW filters and multiplexers themselves by injecting an externally controlled amplitude and phase modulated signal at low frequency to compensate for the IMD3. The proposed technique has been experimentally verified by performing IMD3 measurements in a single BAW resonator subject to several modulated signals under a nonlinear scenario.

A Novel Demodulation Method Based on Spectral Clustering for Phase-Modulated Signals Interrupted by the Plasma Sheath Channel

The phenomenon of radio blackout due to a plasma sheath during reentry has attracted much attention over the last several decades. However, radio blackout has long puzzled aerospace researchers and has not yet been completely resolved. Owing to the effects of the time-varying plasma sheath channel environment, the constellation of received signals exhibits multiple manifolds, making the traditional algorithms based on Euclidean distance unable to perform demodulation. In the current study, we proposed a novel demodulation method based on spectral clustering for phase-modulated signals interrupted by the plasma sheath channel. Experimental results revealed that as long as the receiving radio waves were above the floor of receiver’s dynamic range, the proposed algorithm effectively classified received signals after time-varying plasma. The parasitic modulation interference caused by time-varying plasma was restrained effectively through the novel algorithm. In contrast to the traditional communication method, the proposed method can be applied to telemetry, track and command, as well as communication between reentry vehicles and near-space hypersonic vehicles in future.

On the Transient Behavior of Single-Loop Optoelectronic Oscillators Under RF Injection-Locking

A study on the transient behavior of a single-loop optoelectronic oscillator (OEO) under a single sinusoidal radio frequency (RF) signal injection is presented. Considering only the phase perturbation imposed by the external RF signal, the phase-dynamic equation is solved to analyze the frequency settling behavior of the loop. A closed form expression for the required time of an OEO under RF injection-locking, reaching the steady state condition, is derived in terms of the initial phase difference, beat frequency and injection signal strength. The phase modulated signal, which is responsible for the perturbation of the free running oscillation, is expanded in a Fourier series and the expression for the output RF spectrum of the injection pulled OEO is derived. The injection-pulling dynamics approach is used to describe the phase noise of the OEO and also, the influence of the phase settling time constant on the phase noise of the injection-locked OEO is studied. The experimental results corroborating the theoretical findings are given.

On-chip programmable microwave photonic filter with an integrated optical carrier processor

We demonstrate a programmable microwave photonic bandpass filter with a rectangular frequency response and a reconfigurable spectral resolution. We achieved these features through dual-sidebands processing of a phase modulated signal using a network of four optical ring resonators in a low-loss silicon nitride (Si3N4) circuit. Furthermore, we integrate a pair of optical ring resonators in the same circuit to precisely control the amplitude and phase of the optical carrier to enhance the noise performance of the filter. We achieved filtering with a tunable bandwidth from 2 to 7 GHz with optical carrier suppression up to 6 dB, a maximum RF gain of -10 dB, and a minimum noise figure of 27 dB. These experiments are expected to provide a feasible design to approach fully integrated microwave photonic filters with improved link gain and reduced noise figure.

Multi-scale orientation estimation using higher order Riesz transforms

In this paper, we unify the Riesz transform with the Teager–Kaiser energy operator (TKEO) and monogenic multi-resolution analysis in comparison to conventional gradient and Riesz transform-based approaches. We show that benefits of our approach maintain the following aspects of different known estimators: the stability of mixed (higher) order of derivatives, like given in TKEO, the all-pass filter characteristics featuring the Riesz transform and the scale-based analysis. Furthermore, we demonstrate the ability of the considered technique for extracting structural defects at different scales, estimating orientation or being used for 2D demodulation of amplitude- and phase modulated signals, like interferometric fringe patterns. Additionally, the abilities of orientation estimation of 3D data is demonstrated. From the viewpoint of mathematical analysis, we will emphasize the connection to monogenic higher dimensional signals, Clifford frames, and monogenic multi-resolution signal analysis. Furthermore, we will discuss higher order Riesz transform.

Low Complexity Method for Recovering Continuous Phase Modulation Signals with Low Signal-to-noise Ratios

A low computational complexity scheme based on the modified Wigner–Ville distribution (MWVD) is developed for estimating the instantaneous frequency of continuous phase modulation (CPM) signals under low signal-to-noise ratio (SNR) scenario. To simplify the computation of the MWVD, a low order Chebyshev polynomial is chosen as the kernel function for suppressing the cross-terms. The implementation of this instantaneous frequency (IF) estimator is done through the Viterbi algorithm. The simulation results show that our scheme outperforms other estimating methods under low SNR scenario.

A Bidirectional FSO Communication Employing Phase Modulation Scheme and Remotely Injection-Locked DFB LD

A bidirectional free-space optical (FSO) communication through a 600-m free-space transmission is built, employing a phase modulation (PM) scheme and a remotely injection-locked distributed feedback laser diode (DFB LD) for presentation. With optimum injection locking, a DFB LD is excellent for duplex transceiver operations. An injection-locked DFB LD not only operates as a PM-to-intensity modulation converter with an optical detector, but also functions as an upstream optical carrier. To be the first one of employing a remotely injection-locked DFB LD to detect a phase-modulated 25-Gb/s/25-GHz four-level pulse amplitude modulation (PAM4) passband signal, the DFB LD with remote injection locking is successfully intensity-modulated with an upstream 25-Gb/s non-return-to-zero (NRZ) signal. Good bit error rate performance and clear PAM4/NRZ eye diagrams show that this FSO communication can use a remotely injection-locked DFB LD to detect the downstream phase-modulated PAM4 signal and concurrently deliver an upstream intensity-modulated NRZ signal. This bidirectional 25-Gb/s/25-GHz (downstream)/25-Gb/s (upstream) FSO communication is prominent due to its enhancement in two-way high-speed optical wireless communications.

Chaotic Optical Communication Over 1000 km Transmission by Coherent Detection

Chaotic optical communication was originally proposed to provide high-level physical layer encryption. For high-speed and long-distance transmission, chaotic signal is very sensitive to channel impairments such as dispersion and Kerr fiber nonlinearity. In the traditional chaotic optical communications, these impairments must be compensated in optical domain before chaos synchronization. However completely compensating the high-order dispersion and fiber nonlinearity in the optical domain has great challenges, therefore limiting the transmission distance of high-speed chaotic optical communications less than 150 km. Here we propose a method aiming to break the limit. Thanks to coherent detection, channel impairments can be compensated in the digital domain using various algorithms. Digital back propagation algorithm is used for jointly compensating linear and nonlinear impairments of the chaotic signals, constant modulus algorithm is used for channel equalization and extended Kalman filter is adopted for carrier phase recovery. After digital processing, the recovered chaos signal is converted back to the optical domain for chaos synchronization. By this means, we demonstrate a 10 Gb/s phase-modulation signal encrypted by phase chaos transmission over record-breaking 1000 km single-mode fiber with bit-rate error less than 1.0 × 10−3 by simulation, and support the results with extensive numerical analysis.

Passband-Switchable and Frequency-Tunable Dual-Passband Microwave Photonic Filter

A passband-switchable and frequency-tunable dual passband microwave photonic filter (MPF) implemented using a broadband optical source (BOS) in a delay-line configuration is proposed and experimentally demonstrated. In the proposed MPF, the BOS is sliced by a Mach-Zehnder interferometer (MZI), in which a phase modulator (PM) is incorporated in the upper arm. The phase-modulated light signal combined with an unmodulated light at the output of the MZI is sent through a dispersive delay line and detected at a photodetector (PD). The entire operation is equivalent to a microwave bandpass filter with its central frequency determined by the time delay difference between the two arms of the MZI. To implement a dual passband MPF, a second lower arm with a different arm length corresponding to a different time delay is added. The independent switchability of the passband is realized by controlling the polarization state of the light wave in each of the lower arms to be parallel or orthogonal with that of the upper arm. The independent frequency tunability is achieved by tuning the time delay of each of the lower arms. The proposed MPF is experimentally evaluated. A dual-passband MPF with independent passband switchability and independent frequency tunability is demonstrated. The results show that each of the two passbands can be switched on and off with an extinction ratio of about 20 dB. The passband frequency can also be continuously tuned with a tunable range from 1 to 18 GHz.

Rydberg Atoms for Radio-Frequency Communications and Sensing: Atomic Receivers for Pulsed RF Field and Phase Detection

In this article we describe the basic principles of Rydberg atom-based RF sensing and present the development of atomic pulsed RF detection and RF phase sensing establishing capabilities pertinent to applications in communications and sensing. To date advances in Rydberg atom-based RF field sensors have been rooted in a method in which the fundamental physical quantity being detected and measured is the electric field amplitude, $E$, of the incident RF electromagnetic wave. The first part of this paper is focused on using atom-based $E$-field measurement for RF field-sensing and communications applications. With established phase-sensitive technologies, such as synthetic aperture radar (SAR) as well as emerging trends in phased-array antennas in 5G, a method is desired that allows robust, optical retrieval of the RF phase using an enhanced atom-based field sensor. In the second part of this paper we describe our fundamentally new atomic RF sensor and measurement method for the phase of the RF electromagnetic wave that affords all the performance advantages exhibited by the atomic sensor. The presented phase-sensitive RF field detection capability opens atomic RF sensor technology to a wide array of application areas including phase-modulated signal communication systems, radar, and field amplitude and phase mapping for near-field/far-field antenna characterizations.