Frequency Synchronization

The aim of the present paper is to increase the reliability of a Kalman filter-based DS-SS receiver by considering in the state space models the multipath coefficients and associated delays. The objective being to operate at very low SNRs in shallow water (to achieve furtive transmissions) and with the need of a limited computational cost, the implementation relies on the Unscented Kalman Filter, which is known to be more robust than the popular Extended Kalman Filter. The proposed receiver schemes are discussed and compared using experimental data.

1Student, Dept. of Electronics and Communication Engineering, Madhav Institute of Technology and Science, Gwalior,India 2Asssociate Professor, Dept. of Electronics and Communication Engineering, Madhav Institute of Technology and Science, Gwalior, India ---------------------------------------------------------------------***--------------------------------------------------------------------Abstract The proposed paper utilized the concept of Coherent detection. A field received by advances in Digital Signal Processing (DSP), has renewed interest in optical communication systems with spectrally efficient modulation formats. Phase Noise and Gaussian Noise has been analyzed in terms of Average Bit Error Rate (BER) and Optical Signal to Noise Ratio (OSNR). OSNR component is used in order to introduce noise in the dual polarization Quadrature Amplitude Modulation (DP 16-QAM) optical coherent receiver system. The Noise is analyzed under the influence of different filters. Finally the best...

The OFDM system carries the message data on orthogonal subcarriers for parallel transmission, combating the distortion caused by the frequency selective channel or equivalently, the intersymbol-interference in the multi-path fading channel. However, the advantage of the OFDM can be useful only when the orthogonality is maintained, thus In an OFDM system, the transmitter modulates the message bit sequence into PSK/QAM symbols, performs IFFT on the symbols to convert them into time domain signals, and sends them out through a (wireless) channel The received signal is usually distorted by the channel characteristics. In order to recover the transmitted bits, the channel effect must be estimated and compensated in the receiver. First we will discuss synchronization techniques to manage the STO and CFO potential problems in OFDM systems, and the use of DFT technique for estimating the mobile radio channel response. Finally, we simulate the synchronization technique STO, and LS-linear, LS...

In a recent paper the filter bank multicarrier spread spectrum (FB-MC-SS) waveform was proposed as an new method for wideband spread spectrum communications in the HF band. FB-MC-SS is well suited for this application because of its robustness against narrow and partial band interference and because it has good performance over a wide range of delay and Doppler spreads. In this paper we present a study of bit error rate (BER) for this system. In this study channel estimation error and correlation between subcarriers are taken into account. Tailoring the analysis from a different application we give equations for BER that closely match the simulated performance in most situations.

Accurate estimation and correction of channel distortions and carrier frequency offset (CFO) are of a great importance in any multicarrier communication system. Hence, in this paper, we propose data-aided CFO and channel estimation techniques for both multiuser uplink and downlink of the generalized frequency division multiple access (GFDMA). Our proposed solutions jointly estimate the CFO and channel responses based on the maximum-likelihood criterion. To simplify the implementation of the proposed estimation algorithms, we suggest a preamble composed of two similar Zadoff-Chu training sequences in a generalized frequency division multiplexing block. It is worth mentioning that our proposed technique can estimate both integer and fractional CFO values without any limitation on the acquisition range of CFO. In the uplink phase, each user aligns its carrier frequency with the base station using the estimated CFO in the downlink. However, the CFO estimates may get outdated for the uplink transmission. Thus, residual CFOs may still remain in the received signal at the base station. While being trivial in the downlink, CFO correction is a challenging task in the uplink. Thus, we also propose a joint CFO correction and channel equalization technique for the uplink of GFDMA systems. Finally, we evaluate our proposed estimation and correction algorithms in terms of estimation mean square error and bit error rate performance through simulations.

The stability of synchronized states ͑frequency locked states͒ in networks of phase oscillators is investigated for several network topologies. It is shown that for some topologies there is more than one stable synchronized state according to the sign of coupling strength between oscillators. It is also shown that in some cases the synchronized state corresponds to zero order parameter.

The aim of the present paper is to increase the reliability of a Kalman filter-based DS-SS receiver by considering in the state space models the multipath coefficients and associated delays. The objective being to operate at very low SNRs in shallow water (to achieve furtive transmissions) and with the need of a limited computationnal cost, the implementation relies on the Unscented Kalman Filter, which is known to be more robust than the popular Extended Kalman Filter. The proposed receiver schemes are discussed and compared using experimental datas.

This paper proposes four-parallel pipelined fast Fourier transform (FFT) architecture for the discrete Fourier transform (DFT) computation of quadrature-phase-shiftkeying Orthogonal Frequency Division Multiplexing (QPSK-OFDM) signals. The first stage of the architecture is optimized with the multiplexer blocks that contain output values of QPSK as inputs. Furthermore, the proposed architecture employs a complex constant multipliers (CCMs) using adders and shifters that can reduce the total hardware of the design. The proposed 64-point pipeline architecture is modeled and implemented using UMC 65 nm CMOS technology with a supply voltage of 1.2 V. The results demonstrate that the proposed FFT architecture significantly reduces the hardware cost and power consumption in comparison to the recent FFT architecture.

We analytically establish and numerically show that anomalous frequency synchronization occurs in a pair of asymmetrically coupled chaotic space extended oscillators. The transition to anomalous behaviors is crucially dependent on asymmetries in the coupling configuration, while the presence of phase defects has the effect of enhancing the anomaly in frequency synchronization with respect to the case of merely time chaotic oscillators.

We study the dynamics of a triangular single-plaquette Josephson-junction array in the development of the fractional Shapiro steps. We show that synchronization on fractional steps can happen due to an intricate interplay of the three junctions as the plaquette is made dynamically unsymmetric, either by applying an external magnetic field or by changing the configuration of external currents. We propose a mechanism for synchronization when the asymmetry is only due to the frustration induced by the magnetic field.

L2EP-Campus de Lille THÈSE présentée par : Taoufik QORIA soutenue le : 5 Novembre 2020 pour obtenir le grade de : Docteur d'HESAM Université préparéeà :École Nationale Supérieure d'Arts et Métiers Spécialité : Génie Electrique Grid-forming control to achieve a 100% power electronics interfaced power transmission systems "Nouvelles lois de contrôle pour former des réseaux de transport avec 100% d'électronique de puissance"

With Denmark dedicated to maintaining its leading position in the integration of massive shares of wind energy, the construction of new offshore energy islands has been recently approved by the Danish government. These new islands will be zero-inertia systems, meaning that no synchronous generation will be installed in the island and that power imbalances will be shared only among converters. To this end, this paper proposes a methodology to calculate and update the frequency droops gains of the offshore converters in compliance with the N-1 security criterion in case of converter outage. The frequency droop gains are calculated solving an optimization problem which takes into consideration the power limitations of the converters as well as the stability of the system. As a consequence, the proposed controller ensures safe operation of offshore systems in the event of any power imbalance and allows for greater loadability at prefault state, as confirmed by the simulation results.

We demonstrate 20-times greater tolerance to temperature variation using hollow core fibres compared to SMF-28 in a fast optical switching system. With frequency and once-only phase synchronisation, we obtained error-free transmission of short packets with <625ps clock recovery time in 25.6 Gb/s real-time systems.

On the basis of Monte Carlo simulations, the present work systematically investigates how conductivity exponents depend on the ratio of stick-stick junction resistance to stick resistance for two-dimensional stick percolation. Simulation results suggest that the critical conductivity exponent extracted from size-dependent conductivities of systems exactly at the percolation threshold is independent of the resistance ratio and has a constant value of 1.280Ϯ 0.014. In contrast, the apparent conductivity exponent extracted from densitydependent conductivities of systems well above the percolation threshold monotonically varies with the resistance ratio, following an error function, and lies in the vicinity of the critical exponent.

Timing and carrier synchronization is a fundamental requirement for any wireless communication system to work properly. Timing synchronization is the process by which a receiver node determines the correct instants of time at which to sample the incoming signal. Carrier synchronization is the process by which a receiver adapts the frequency and phase of its local carrier oscillator with those of the received signal. In this paper, we survey the literature over the last 5 years (2010-2014) and present a comprehensive literature review and classification of the recent research progress in achieving timing and carrier synchronization in single-input single-output (SISO), multiple-input multiple-output (MIMO), cooperative relaying, and multiuser/multicell interference networks. Considering both single-carrier and multi-carrier communication systems, we survey and categorize the timing and carrier synchronization techniques proposed for the different communication systems focusing on the system model assumptions for synchronization, the synchronization challenges, and the state-of-the-art synchronization solutions and their limitations. Finally, we envision some future research directions.

We report rare and recurrent large spiking events in a heterogeneous network of superconducting Josephson junctions (JJ) connected through a resistive load and driven by a radio-frequency (rf) current in addition to a constant bias. The intermittent large spiking events show characteristic features of extreme events (EE) since they are larger than a statistically defined significant height. Under the influence of repulsive interactions and an impact of heterogeneity of damping parameters, the network splits into three subgroups of junctions, one in incoherent rotational, another in coherent librational motion and a third subgroup originating EE. We are able to scan the whole population of junctions with their distinctive individual dynamical features either in EE mode or non-EE mode in parameter space. EE migrates spatially from one to another subgroup of junctions depending upon the repulsive strength and the damping parameter. For a weak repulsive coupling, all the junctions originate frequent large spiking events, in rotational motion when the average inter-spike-interval (ISI) is small, but it increases exponentially with repulsive interaction; it largely deviates from its exponential growth at a break point where EE triggers in a subgroup of junctions. The probability density of inter-event-intervals (IEI) in the subgroup exhibits a Poisson distribution. EE originates via bubbling instability of in-phase synchronization.

We summarize our recent research works on enabling coherent optical transmission systems for metro and access networks with low-complexity digital signal processing techniques, focusing on reduction of laser linewidth requirement with efficient carrier phase recovery.

Analytical results are presented which characterize the behavior of a dc-biased, two-dimensional circular array of overdamped Josephson junctions subject to increasing levels of disorder. It is shown that high levels of disorder can abruptly destroy the synchronous functioning of the array. We identify the transition boundary between synchronized and desynchronized behavior, along with the mechanism responsible for the loss of frequency locking. Comparisons with recent results for arrays with rectangular lattice geometries are described.

We demonstrate a complementary polarization-diversity coherent receiver (C-PDCR) to accommodate arbitrarily varying SOP of remotely delivered LO. The polarization tracking speed can reach 1 Mrad/s without performance degradation and exceed 2 Mrad/s with a 1-dB OSNR penalty for a 1.08-Tb/s dual-polarization (DP) PCS-256QAM signal.

In this work, we develop the conventional hardware architecture of the orthogonal time frequency space modulation (OTFS) based wireless transmitter to achieve highly reliable communication between high-speed moving devices. In this work, we are using parallel and depth pipelined hardware architecture of fast Fourier transforms/inverse fast Fourier transforms (FFTs/IFFTs) to accelerate the execution of the OTFS on field-programmable gate array (FPGA) with high accuracy and maximum throughput. Additionally, we propose an optimized OTFS transmitter architecture with modified Booth multiplier and memory that i) requires low hardware resources and, ii) provides high throughput. We observe from the synthesis results that the maximum throughput of conventional OTFS architecture achieves 186.95 Tbps with 132,233 lookup tables (LUTs) at 100 MHz clock frequency and 26,586 flip-flops. We however observe that the proposed OTFS hardware achieves a better throughput of 196.67 Tbps with 75,026 LUTs at 139.64 MHz maximum operating frequency on 7vx485tffg1157-1 FPGA device.

A new method for analyzing the time frequency dynamics of brain's background electrical activ ity is described. It is used to detect at least three main features of Parkinson's disease (PD) in its early stages: (1) hemispheric asymmetry in the time frequency characteristics (EEG) in the central recording areas of the motor cortex, (2) the emergence in these recording areas of EEG rhythms in the frequency range of 4-6 Hz and its relation to electromyograms (EMG) and the mechanical tremor of contralateral limbs in the case of tremor dominant PD, and (3) the disruption of the dominant rhythm corresponding to views generally held on the disorganization of different systems in PD.

We report rare and recurrent large spiking events in a heterogeneous network of superconducting Josephson junctions (JJ) connected through a resistive load and driven by a radio-frequency (rf) current in addition to a constant bias. The intermittent large spiking events show characteristic features of extreme events (EE) since they are larger than a statistically defined significant height. Under the influence of repulsive interactions and an impact of heterogeneity of damping parameters, the network splits into three subgroups of junctions, one in incoherent rotational, another in coherent librational motion and a third subgroup originating EE. We are able to scan the whole population of junctions with their distinctive individual dynamical features either in EE mode or non-EE mode in parameter space. EE migrates spatially from one to another subgroup of junctions depending upon the repulsive strength and the damping parameter. For a weak repulsive coupling, all the junctions originate frequent large spiking events, in rotational motion when the average inter-spike-interval (ISI) is small, but it increases exponentially with repulsive interaction; it largely deviates from its exponential growth at a break point where EE triggers in a subgroup of junctions. The probability density of inter-event-intervals (IEI) in the subgroup exhibits a Poisson distribution. EE originates via bubbling instability of in-phase synchronization.

The application of physical-layer network coding (PNC) in optical communications is explored. We propose and demonstrate a practical optical PNC prototype for multicast protection in optical flow, burst, and packet switching networks. Different from conventional theoretical PNC studies, our proposed optical PNC system does not require bit synchronization and can be easily implemented.

Circular harmonic expansion-based carrier frequency offset estimation is investigated for optical MQAM communication systems. The proposed method, combined with a gradient-descent algorithm, shows better performance compared to already proposed VVMFOE and 4 th power methods.

In this paper, we model and analyze the end-to-end energy consumption of 100-Gbps coherent long-haul transmission systems. In particular, we investigate the impact of forward error correction (FEC) on the end-to-end energy consumption. We compare the energy efficiency of commonly used modulation formats in 100-Gbps transmission, namely dual polarizationquadrature phase-shift-keying (DP-QPSK) and dual polarization-16-quadrature amplitude modulation (DP-16-QAM), for different transmission distance and input bit error rate. Our energy model includes consumption of transmitter, booster, link amplifier as well as receiver. Compared with previous digital signal processing models, we provide a very detailed model that not only includes all the significant functional blocks (such as timing and carrier recovery, chromatic and polarization mode dispersion compensation, and FEC), but also takes into account impact of the number of samples processed every clock cycle and of operations other than multiplications. We have found that receiver energy consumption dominates in transmission systems that use electronic dispersion compensation over long transmission distances. Our results show that for short transmission distances where hard-decision decoding is adequate for both modulation formats, DP-16-QAM is more energy efficient than DP-QPSK. However, as the transmission distance increases, the energy saving due to the low symbol rate of DP-16-QAM is offset by the energy consumption of soft-decision decoding. In this case, the two modulation formats have approximately similar energy consumption. Index Terms-Digital signal processing (DSP), erbium-doped fiber amplifiers, low density parity check (LDPC) codes, optical modulation. I. INTRODUCTION C OHERENT detection, along with polarization-multiplexed modulation formats, is an enabling technology for the deployment of high speed, spectrally-efficient long-distance transmission systems. Coherent polarizationmultiplexed quadrature phase-shift-keying, also called dual-Manuscript

This paper addresses robust design of the active-power and dc-link control loops of powersynchronization control. Robustness is obtained by analytic gain selections which give large enough stability margins. The proposed design allows robust stability irrespective of the grid strength and of the operating point, the latter with one exception. The proposed design is compared to design based on the principle virtual synchronous machine. Experiments show that the time-domain results correlate well with the frequency-domain results.

A regular array of oscillators with random coupling exhibits a transition from synchronized motion to desynchronized but ordered waves as a global coupling parameter is increased, due to the spread of localized instability of eigenvectors of the Laplacian matrix. We find that shortcuts, which make a regular network small-world, can destroy ordered desynchronization wave patterns. Wave patterns in a small-world network are usually destroyed gradually as the degree of regularity in the network deteriorates. No ordered wave patterns are observed in scale-free and random networks. The formation of ordered wave patterns in a coupled oscillator network can be explained by considering the time evolution of phase in each oscillator. We derive a general type of the Kardar-Parisi-Zhang equation for phase evolution in a prototype oscillator network. The equation demonstrates well the ordered desynchronized wave patterns found in the network with and without shortcuts. Our results provide a qualitative justification for the requirement of certain degree of regularity in the network for ordered wave patterns to arise.

The aim of the present paper is to increase the reliability of a Kalman filter-based DS-SS receiver by considering in the state space models the multipath coefficients and associated delays. The objective being to operate at very low SNRs in shallow water (to achieve furtive transmissions) and with the need of a limited computationnal cost, the implementation relies on the Unscented Kalman Filter, which is known to be more robust than the popular Extended Kalman Filter. The proposed receiver schemes are discussed and compared using experimental datas.

We analytically establish and numerically show that anomalous frequency synchronization occurs in a pair of asymmetrically coupled chaotic space extended oscillators. The transition to anomalous behaviors is crucially dependent on asymmetries in the coupling configuration, while the presence of phase defects has the effect of enhancing the anomaly in frequency synchronization with respect to the case of merely time chaotic oscillators.

Since the original proposal of 1996 by Floría et al. ͓Europhys. Lett. 36, 539 ͑1996͔͒ of intrinsic localization in Josephson ladders, many efforts have been devoted to the theoretical, numerical, and experimental study of such dynamical states in Josephson arrays. Such efforts have already produced around 20 papers on the subject. In this article we will try to review the basic aspects of the physics of discrete breathers in Josephson arrays.

We study the localization properties of disordered one-dimensional tight-binding lattices driven by ac fields. The localization length of the electrons increases when the frequency of the driving field is smaller than the bandwidth. We show that there is an optimal value of the amplitude of the driving field for which the localization length of the system is maximal. This maximum localization length increases with the inverse of the driving frequency.

We demonstrate a digital optical communication system based on minimum shift keying (MSK) signal transmission with coherent detection. 5-Gb/s MSK signal can transmit over a 160-km standard single mode fiber (SSMF) without phase compensation. At the receiver, we use data-aided channel estimation and frequency domain equalization (FDE) techniques in the digital signal processing (DSP) algorithm, then analyze its performance characteristics compared with quadrature phase shift keying (QPSK) format. The simulation results show that the MSK format will be a potential candidate for next-generation access network.

We report on oscillations of a Josephson-junction system revealing a close analogy with fundamental effects known in laser physics. The experiments are performed on series arrays of junctions whose IV curves show evidence of a mode in which all the junctions oscillate in synchronism on resonances appearing, in zero external magnetic field, at multiples of the first cavity mode. Evidence is provided that the mode is generated by collective oscillations which develop spontaneously because the frequencies of the modes are equal within a 1% uncertainty. Numerical simulations are employed to elucidate the reasons leading to the synchronous collective excitation and to explain why it is characterized by a low emission of electromagnetic radiation.

We analytically establish and numerically show that anomalous frequency synchronization occurs in a pair of asymmetrically coupled chaotic space extended oscillators. The transition to anomalous behaviors is crucially dependent on asymmetries in the coupling configuration, while the presence of phase defects has the effect of enhancing the anomaly in frequency synchronization with respect to the case of merely time chaotic oscillators.

We propose the design of frequency domain block least-mean-square and recursiveleast-square equalizers for adaptive zero-guard-interval CO-OFDM systems. Improvements in the channel estimation accuracy and channel tracking speed are experimentally and numerically demonstrated.

We study the time evolution of perturbations in spatially extended chaotic systems in the presence of quenched disorder. We find that initially random perturbations tend to exponentially localize in space around static pinning centers that are selected by the particular configuration of disorder. The spatiotemporal behavior of typical perturbations ␦u͑x , t͒ is analyzed in terms of the Hopf-Cole transform h͑x , t͒ϵln͉␦u͑x , t͉͒. Our analysis shows that the associated surface h͑x , t͒ self-organizes into a faceted structure with scale-invariant correlations. Scaling analysis of critical roughening exponents reveals that there are three different universality classes for error propagation in disordered chaotic systems that correspond to different symmetries of the underlying disorder. Our conclusions are based on numerical simulations of disordered lattices of coupled chaotic elements and equations for diffusion in random potentials. We propose a phenomenological stochastic field theory that gives some insights on the path for a generalization of these results for a broad class of disordered extended systems exhibiting space-time chaos.

Optical time-domain reflectometer (OTDR) has long been and is still considered the main test tool for characterizing fiber optic links, i.e. identify and localize refractive and reflective events such as breaks, splices and connectors, and measure their insertion/return loss. Specifically, sufficient dynamic range and thus alike signal-to-noise-ratio (SNR) enable clear far-end visibility even of long fiber links. Moreover, under such conditions, the highest achievable optical bit-error-rate (BER) floor is to the large extent determined by major reflective events such as the specific trace distortion caused by connectors and splices, each with significant return loss. Realizing this has provided the opportunity window to extend the standard OTDR capabilities list by the appropriate trace postprocessing to predict the BER floor. Accordingly, considering the SNR high, and thereby the inter-symbol interference dominant error generating mechanism, we applied the time-dispersion channel model that determines the BER floor by the rms delay spread of the (fiber) channel power-delay profile. We verified the BER floor prediction in the exemplar practical test situation, by measuring the actual BER on the same fiber link, and found the obtained values well matching the OTDR-based predicted ones. Furthermore, when no dominant reflective events are identified on the OTDR trace, it implies very small time dispersion allowing the OFDM symbol cyclic prefix to always prevent inter-symbol interference. This retains the CFO to solely determine the residual BER floor and vice versa, enabling indirect estimation of CFOinduced phase distortion by simple BER testing. With this regard, we abstracted CFO with the AWGN being justified by the Central Limiting Theorem to enable efficient and quite accurate short-term BER (and so CFO phase error) predictions.

The rich dynamical behavior stemming from unidirectional coupling in a single array of overdamped nonlinear elements has, recently, been extensively studied. By adjusting control parameters, one obtains regimes of oscillations with a frequency that scales in a characteristic way with the control parameter. With an external time-sinusoidal driving signal, a richness of synchronized ͑to the drive frequency or its subharmonics depending on the control parameter͒ dynamical behavior ensues. Including M ജ 2 arrays with a suitably chosen cross coupling has also been shown to lead to multifrequency patterns in the emergent dynamics. Here, we consider this arrangement and demonstrate that, under the appropriate conditions, the oscillation frequency of each successive array decreases by a rational factor with increasing M. This frequency down-conversion, obtainable without a heterodyning signal, affords the promise of very efficient signal processing in a variety of applications wherein, currently, the frequency down-conversion stage typically involves multistep processes with complicated and ͑often͒ noisy circuitry.

We show that the topology and dynamics of a network of unsynchronized Kuramoto oscillators can be simultaneously controlled by means of a forcing mechanism which yields a phase locking of the oscillators to that of an external pacemaker in connection with the reshaping of the network's degree distribution. The entrainment mechanism is based on the addition, at regular time intervals, of unidirectional links from oscillators that follow the dynamics of a pacemaker to oscillators in the pristine graph whose phases hold a prescribed phase relationship. Such a dynamically based rule in the attachment process leads to the emergence of a power-law shape in the final degree distribution of the graph whenever the network is entrained to the dynamics of the pacemaker. We show that the arousal of a scale-free distribution in connection with the success of the entrainment process is a robust feature, characterizing different networks' initial configurations and parameters.

I study various cooperation phenomena on dierent network topologies. To these belong synchronization of Kuramoto oscillators, entrained by pacemakers; evolutionary algorithms on spin systems, reinterpreted as an approach to social balance or as the solution of optimization problems in computer science; and the in uence of enforced synchronization in the updating procedure of algorithms. In the case of synchronization of oscillators, my results allow the prediction of whether a pacemaker is able to entrain a given set of oscillators, depending on their number, their coupling strength and their connections. Furthermore, I use spin dynamics to establish a mapping between an approach of social balance and the solution of a special optimization problem, called the XOR-SAT problem in the context of computer science (XOR refers to the logical operator and SAT stands for satisability). In the language of spin dynamics, the equivalence of both problems becomes evident. Along with these coope...

There is a huge rapid growth in the deployment of data centers, mainly driven from the increasing demand of internet services as video streaming, e-commerce, Internet Of Things (IOT), social media, and cloud computing. This led data centers to experience an expeditious increase in the amount of network traffic that they have to sustain due to requirement of scaling with the processing speed of Complementary metal–oxide–semiconductor (CMOS) technology. On the other side, as more and more data centers and processing cores are on demand, as the power consumption is becoming a challenging issue. Unless novel power efficient methodologies are innovated, the information technology industry will be more liable to a future power crunch. As such, low complex novel transmission formats featuring both power efficiency and low cost are considered the major characteristics enabling large-scale, high performance data transmission environment for short-haul optical interconnects and metropolitan r...

In this paper we consider complete synchronization in small-world networks of identical Rössler oscillators. By applying a simple but effective dynamical optimization coupling scheme, we realize complete synchronization in networks with undelayed or delayed couplings, as well as ensuring that all oscillators have uniform intensities during the transition to synchronization. Further, we obtain the coupling matrix with much better synchronizability in a certain range of the probability p for adding long-range connections. Direct numerical simulations fully verify the efficiency of our mechanism.

We studied the motion of a variable mass oscillator. The mass used is a container full of sand that loses sand at a constant rate and hangs from a spring. The spring was suspended from a force sensor connected to a data acquisition system that let us study the evolution of the system. In the underdamped regime we identified three distinct types of behavior for the system, depending on the relation between the energy loss due to the exit of mass and the energy loss through friction. The experimental results are well described by both the numerical solution to the equations of motion and our model, which makes it simple to predict the different types of behavior and to assess the relevant physical parameters involved in the dynamics of this system.

In this letter, we propose the extension of a previously presented analytical model for the estimation of the signalto-noise ratio (SNR) at the output of an adaptive equalizer in coherent optical transmission systems when transmission is modeled as a generic 2x2 matrix transfer functions, to be applied to polarization multiplexed communications based on advanced modulation formats (PM-QAM). We present the model and then we extensively test its accuracy on an possible application environment. Our findings show a remarkable agreement, with maximum SNR discrepancies of about 0.5 dB between timedomain simulations and analytical results.