Nonlinear Cancellation Research Articles

Methods for crosstalk measurement and reduction in dense WDM systems

We propose a scheme for the monitoring and reduction of crosstalk arising from the limited stop-band rejection of optical bandpass filters in dense WDM systems. The optical carrier at each wavelength is modulated with a subcarrier tone unique to that wavelength. The level of crosstalk from a given channel can be determined by measuring the power of the corresponding tone. Crosstalk from other channels can be cancelled in a linear fashion by weighting and summing the photocurrents of the desired channel and several adjacent interfering channels. Alternatively, in nonlinear crosstalk cancellation, decisions are made on the interfering signals, and these decision are weighted and summed with the photocurrent of the desired channel. For example, assuming an optical filter having a Gaussian passband, the channel density can be increased from 20 to 30%, depending on the number of adjacent channels detected. The signal-to-interference ratio can be increased by 10-20 dB and the system can achieve a BER<10/sup -9/ under conditions where, without interference cancellation, the signal-to-interference ratio would be less then 10 dB.

Nonlinear clutter cancellation and detection using a memory-based predictor

In this paper, a nonlinear prediction (NLP) method is proposed as an alternative to the conventional linear prediction (LP) method for clutter cancellation. Because of the nonlinearity and non-Gaussianity of a clutter process, a nonlinear predictor is therefore needed to suppress clutter optimally. A memory-based predictor which uses a table look-up strategy to perform NLP is used in this work. The advantages of the memory-based approach are fast learning, algorithmic simplicity, robustness and suitability for parallel implementation. The memory-based predictor is then used as an adaptive detector for small surface target detection embedded in clutter. The effectiveness of the new method is demonstrated using real sea clutter data, and the results show improvement when compared with the conventional LP techniques.

Single-capacitor MOSFET-C integrator using OTRA

A highly linear MOS operational transresistance amplifier (OTRA) integrator with reduced number of capacitors and MOSFET transistors is proposed. Only one capacitor is required for an integrator to achieve cancellation of MOSFET nonlinearities. The proposed integrator is insensitive to the effects of parasitic capacitances and can be interconnected without adding any buffers. Experimental results are given to verify the theoretical analysis.

Compensating the compensator: a demonstration of nonlinearity cancellation in a WDM system

Spectral inversion was used in a three-channel WDM system to reduce an infinite four-photon-mixing penalty to 1.5 dB. This reduction was made possible by compensation of phase-conjugator-induced distortions of the signal.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An output feedback globally stable controller for induction motors

We present a globally stable nonlinear dynamic output feedback controller for torque tracking and flux regulation of induction motors. The control law is globally defined, requires only measurement of stator variables and rotor speed, and does not rely on cancellation of the systems nonlinearities. Our work extends the result of the paper by Ortega et al.(1993), where the torque tracking problem was solved for a model and the variables are expressed in a frame rotating at an arbitrary angular frequency (dq model). First, we obviate the need to transfer the dq control signals of the paper by Ortega et al., to the physical input variables in the stator frame, hence providing a directly implementable control law. Second, besides the torque tracking objective, we include the practically important rotor flux regulation task. Third, by choosing a more suitable representation of the motor model, we simplify the controller structure and provide a better understanding of its derivation and behavior. >

Recurrent radial basis function networks for adaptive noise cancellation

Radial basis function neural network architectures are introduced for the nonlinear adaptive noise cancellation problem. Both FIR and IIR filter designs are considered, and it is shown that by exploiting the duality with system identification, the nonlinear IIR filter can be configured as a recurrent radial basis function network. Details of network training that is based on a combined k-means clustering and Givens routine, the inclusion of linear dynamic network links, and metrics for performance monitoring are also discussed. Examples are included to demonstrate the degree of noise suppression that can be achieved based on the new design.

Adaptive non-linear equalisation of digital communications channels

Non-linear distortion introduced by communications channels increases the probability of error. In this paper, an adaptive non-linear canceller is presented which attempts to remove non-linear interference from the output of a feedforward or decision feedback equaliser, improving the error rate. It may be implemented using a memory look-up table architecture, making it suitable for high speed real time operation.

Volterra series based nonlinear simulation of HBTsusing analytically extracted models

An accurate HBT large signal model has been developed using an analytical equivalent circuit element extraction technique. Nonlinear characteristics are analysed by means of a Volterra series and agree with experiment. Nonlinear current cancellation effects can be analysed. Their presence also enhances convergence and the applicability of Volterra series to large-signal modelling.

Elimination of adjacent channel interference Via nonlinear filters

In recent years, eliminating adjacent channel interference (ACI) for effective utilization of frequency resources has been considered important in digital radio communications. As an effective method for eliminating interference, adaptive equalizers have been utilized and limitations associated with their linear form processing have also been clarified. In this study, as equalizers showing better interfering wave-eliminating characteristics of adaptive linear equalizers (ALEs), an adaptive nonlinear equalizer (ANLE) containing the conventional nonlinear ALE and a nonlinear canceller, which eliminates ACI by nonlinear processing, in its body are proposed and their efficiencies are verified by computer simulations. First, the optimal number of taps of the proposed ANLE was determined by computer simulations and the characteristics obtained with an optimal number of taps have been compared with those of the conventional method. The results showed that the proposed ANLE can effectively eliminate the interfering wave component whose spectrum has become overlapped with a desired wave and thus gives better interfering wave-eliminating characteristics than the ALE and the nonlinear canceller.

Nonlinear echo cancelling using look-up tables and Volterra systems

Two classical approaches to nonlinear echo cancellation are to use look-up tables combined with FIR filters and Volterra systems; their practical interest is higher when adapted with LMS-type algorithms, because results are easily implementable and offer good tracking capabilities. A complete analysis of look-up-table-based schemes is presented, and a new one is introduced which offers near optimal characteristics but without requiring variable steps: in practice a piecewise-constant adaptation algorithm is enough. The theoretical equivalence of these schemes with those based on Volterra kernels is established; a comparison of operational characteristic is then made. The important option of applying growing Volterra structures is proposed for the first time, and its possibilities are verified (as well as the previous analysis) by means of simulation examples. The paper ends with suggestions to be explored to obtain more efficient nonlinear echo cancellers.

The identification of nonlinear discrete-time fading-memory systems using neural network models

A fading-memory system is a system that tends to forget its input asymptotically over time. It has been shown that discrete-time fading-memory systems can be uniformly approximated arbitrarily closely over a set of bounded input sequences simply by uniformly approximating sufficiently closely either the external or internal representation of the system. In other words, the problem of uniformly approximating a fading-memory system reduces to the problem of uniformly approximating continuous real-valued functions on compact sets. The perceptron is a parametric model that realizes a set of continuous real-valued functions that is uniformly dense in the set of all continuous real-valued functions. Using the perceptron to uniformly approximate the external and internal representations of a discrete-time fading-memory system results, respectively, in simple finite-memory and infinite-memory parametric system models. Algorithms for estimating the model parameters that yield a best approximation to a given fading-memory system are discussed. An application to nonlinear noise cancellation in telephone systems is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The theory of the early nonlinear stage of m=1 reconnection in tokamaks*

The theory of the early nonlinear stage of reconnection, when the plasma central core displacement ξ0 is still small with respect to the q=1 radius r1 but exceeds the characteristic width of the singular layer, is considered. The two-dimensional magnetic geometry of m=1 reconnection is determined by solving Waelbroeck’s equations [Phys. Fluids B 1, 2372 (1989)]. Fast nonlinear exponential growth of the mode in contemporary high-temperature experiments is explained on the basis of the nonlinear two-fluid magnetohydrodynamic theory. It is shown that the stabilization of the reconnecting m=1 mode by ω*-effects is in qualitative agreement with experimental observations. A nonlinear cancellation of the ω*-stabilization is proposed as explanation of the triggering of the sawtooth crash.

Reducing the effects of transmission impairments in digital fiber optic systems

The major impairments in lightwave systems and the signal-processing techniques that can be used to reduce these impairments are discussed. Guidelines for the use of these techniques are presented. These guidelines are used to determine the techniques with the most potential for providing improved performance in long-haul systems, local-area networks, and local loop systems. Although many of the techniques have been previously considered for these applications, few have been implemented in commercial products. Some of the most promising techniques include dispersion-compensating fibers, polarization control, nonlinear cancellation (NLC), and coding for reducing the effect of distortion in long-haul single-frequency-laser direct-detection systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Structure and second harmonic generation of Langmuir-Blodgett films of two chiral amphiphilic azo dyes

The properties and structure of Langmuir-Blodgett films of two new amphiphilic nonlinear optical dyes containing stereogenic (chiral) centers were studied. The dye molecule 4-[[4'-[(3R)-palmitoylpyrrolidin-1-yl]phenyl]azo]-3-nitrobenzoic acid (KZ16) forms homogeneous structures in the plane of the substrate when the monolayers are transferred into multilayers. Multilayers of 4-[[4'-[(3R,4R)-dipalmitoylpyrrolidin-1-yl]phenyl]azo]-3-nitrobenzoic acid (KDEZ16) which contains two alkyl chains on the pyrrolidine ring showed flow-induced orientation in the plane of the film. The tilt angles of the molecules in the multilayer were determined by polarized FT-IR measurements combined with X-ray diffraction. Tilt angles of approximately 55-degrees to the surface normal for the chromophore unit and approximately 35-degrees for the alkyl chain of KZ16 were revealed. KDEZ16 molecules showed a tilt angle of approximately 35-degrees for both the chromophore unit and the alkyl chain with the surface normal in the multilayer. The second harmonic generation (SHG) properties of mono- and multilayers of KZ16 with different architectures on glass were studied. When a nonpolar alignment (Y-type bilayer) was measured, a complete cancellation of the second-order nonlinearity was observed. The stereogenic center did not contribute to a noncentrosymmetric structure at a measurable scale. Alternating layers of the KZ16 dye and arachidic acid behave almost ideal, giving a SHG depending quadratically on the number of bilayers.

Torque regulation of induction motors

A controller design methodology to solve an output tracking problem for a class of systems described by its Euler-Lagrange equations with less control actions than degrees of freedom was recently presented by Ortega and Espinosa. The procedure is based on the idea of “shaping” the total energy of the closed-loop system with the nice feature that it achieves the tracking objective without the need of cancelling dynamics but by associating a natural reference (“steady state”) behaviour for all state variables. In this paper we use the procedure to solve the problem of torque regulation of a nonlinear induction motor model which includes both electrical and mechanical dynamics. We derive a nonlinear state observer plus state feedback control that insures exponential stability provided the desired torque does not exceed a given value. The latter condition can be removed if the motor full state is measurable. An adaptive version of the scheme that does not require exact knowledge of the rotor resistance or load torque is also shown to be asymptotically convergent. Three key features of the proposed scheme are: first, it attains the field orientation objective of the highly successful “vector control” strategies. Second, using the energy balance equation of the induction motor, identifies the nonlinear terms that represent “workless forces” to avoid (intrinsically nonrobust) exact cancellation of model nonlinearities. Third, the control law calculation is extremely simple and globally defined, thus the strategy is applicable for all motor operation regimes including start-up. Some simulation results illustrate the controller performance.

Dynamic aperture of electron storage rings with noninterleaved sextupoles.

A detailed study of a dynamic aperture is given for electron storage rings with noninterleaved sextupole magnets. As a result of a cancellation of major transverse nonlinearities of sextupoles by -I transformers, other tiny terms such as fringe fields of quadrupoles and kinematical terms of drift spaces come to limit the transverse dynamic aperture. Results for transverse aperture in simulations can be explained by a simple one-dimensional model including these terms. In the longitudinal direction, a modulation of linear betatron motion by synchrotron oscillation is investigated as the source of the aperture limit.

A new family of biquads with applications to MOSFET-C filters

A new family of RC-active biquadratic building blocks are proposed in this communication. These biquads are especially designed for MOSFET-C applications, since they achieve a complete MOS nonlinearity cancellation. The proposed circuits can realize all the generic transfer functions such as lowpass, highpass, bandpass, band-rejection, and allpass. They also enjoy low passband sensitivities with respect to passive elements. The gain-bandwidth product-sensitivity is investigated too. An example of a high Q-bandpass filter is given with its Monte-Carlo simulation to verify its sensitivity performance.

Performance of combined trellis coded modulation and nonlinear cancellation

The performance of nonlinear cancellation schemes is limited by the accuracy of tentative decisions. This correspondence analyzes the performance of combined trellis coded modulation and nonlinear cancellation. A scheme is proposed to make use of the redundancy of the code. It is shown that performance close to optimum can be achieved with this scheme. >

Signal transmission characteristics of diversity reception with least‐squares combining—relationship between desired signal combining and interference canceling

AbstractThis paper considers the diversity reception system where the combining coefficients are controlled by the least‐squares method. The CNR characteristics in the presence of the interference wave are derived, and the signal transmission characteristics are analyzed.First, the optimal coefficients are determined by the MMSE criterion. The expression for the optimal CNR is derived in two ways, i.e., from the macroscopic and the microscopic viewpoints. It is shown that the two results agree and the variables are related through the Pythagorean theorem. Then CNR is represented by the projection matrix which is specified by the correlation matrix for the noise and the interference wave. The signal combining/interference canceling characteristics are examined.Next, the eigenvector expansion for the correlation matrix is applied and the representation for CNR under fading condition is derived, using the statistical properties of the eigenvalue, the probability density function and the probability distribution function for CNR are derived in two ways. Then the expression for the average BER is derived for CBPSK and DBPSK. The extension of the idea to the nonlinear interference canceler and the application to the cellular mobile communication also are discussed.

Performance monitoring in non-linear adaptive noise cancellation

Correlation-based model validity tests are introduced to monitor the operation of non-linear adaptive noise cancellation filters and to detect whether the filters are operating correctly or incorrectly. The tests are derived for a NARMAX (Non-linear Autor-Regressive Moving Average model with eXogenous inputs) filter design based on a Sub-Optimal Least Squares (SOLS) estimation algorithm. Simulation studies are included to illustrate the performance of the new tests.