Nonlinear Cancellation Research Articles

Adaptive Combination of Volterra Kernels and Its Application to Nonlinear Acoustic Echo Cancellation

The combination of filters concept is a simple and flexible method to circumvent various compromises hampering the operation of adaptive linear filters. Recently, applications which require the identification of not only linear, but also nonlinear systems are widely studied. In this paper, we propose a combination of adaptive Volterra filters as the most versatile nonlinear models with memory. Moreover, we develop a novel approach that shows a similar behavior but significantly reduces the computational load by combining Volterra kernels rather than complete Volterra filters. Following an outline of the basic principles, the second part of the paper focuses on the application to nonlinear acoustic echo cancellation scenarios. As the ratio of the linear to nonlinear echo signal power is, in general, a priori unknown and time-variant, the performance of nonlinear echo cancellers may be inferior to a linear echo canceller if the nonlinear distortion is very low. Therefore, a modified version of the combination of kernels is developed obtaining a robust behavior regardless of the level of nonlinear distortion. Experiments with noise and speech signals demonstrate the desired behavior and the robustness of both the combination of Volterra filters and the combination of kernels approaches in different application scenarios.

Optimized optical phase conjugation configuration for fiber nonlinearity compensation in CO-OFDM systems

The optimized optical phase conjugation (OPC) configuration is proposed for the 40-Gb/s CO-OFDM system. The proposed configuration for nonlinear cancellation is systematically depicted in transmission links with lumped amplification. Numerical simulations are performed to demonstrate effectiveness. Simulation results show that mid-span spectral inversion (MSSI) can partially compensate for nonlinear distortions. Moreover, its optimized configuration can further improve system performances and increase nonlinear compensation effectiveness. Compared with MSSI, the maximal Q factor, nonlinear threshold, and transmission distance of optimized OPC configuration increase by over 1.6 dB, 2 dB, and 2 times, respectively.

A correlation test-based validity monitoring procedure for online detecting the quality of nonlinear adaptive noise cancellation

In the present study, a new correlation test-based nonlinear adaptive noise cancellation (ANC) validity monitoring procedure is proposed by following the insight and formulations which were developed by the authors for validating identified nonlinear dynamic models. The new method is based on the concept that if an ANC is valid, the recovered signal should be uncorrelated to the noise source. Then, a new correlation test between recovered signal and noise source is periodically computed to online check the validity of noise cancellers when ANCs are in operation. Simulation demonstrations on validity monitoring for recursive least squares-based ANC are conducted to illustrate the effectiveness and efficiency of the new procedure.

Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case

Extending previous results of Oh–Zumbrun and Johnson–Zumbrun, we show that spectral stability implies linearized and nonlinear stability of spatially periodic traveling wave solutions of viscous systems of conservation laws for systems of generic type, removing a restrictive assumption that wave speed be constant to first order along the manifold of nearby periodic solutions. Key to our analysis is a nonlinear cancellation estimate observed by Johnson and Zumbrun, along with a detailed understanding of the Whitham averaged system. The latter motivates a careful analysis of the Bloch perturbation expansion near zero frequency and suggests factoring out an appropriate translational modulation of the underlying wave, allowing us to derive the sharpened low-frequency estimates needed to close the nonlinear iteration arguments.

Fast and Robust Adaptation of DFT-Domain Volterra Filters in Diagonal Coordinates Using Iterated Coefficient Updates

This paper presents a novel data-reusing technique for implementing adaptive discrete Fourier transform (DFT) domain Volterra filters in diagonal coordinates having arbitrary nonlinear order. In general, a major drawback of such nonlinear filters is the large number of parameters. Thus, a weak excitation of higher-order kernels results in a slow convergence for system identification tasks. In order to exploit the available innovation of the signals more effectively, each data frame is processed for a specified number of iterations in an overlap-save scheme, thereby enhancing the convergence performance. Due to inherent recursions of the repeated filtering and updating steps, this concept also lends itself to a fast algorithm, requiring only a moderate increase in algorithmic complexity over a baseline implementation. A detailed comparison of the required number of multiplications is given for several different algorithm versions. Despite the relatively simple concept, the outlined iteration algorithm exhibits significant gains in both adaptation speed and steady-state convergence. This is demonstrated by various experiments for both stationary noise and speech input considering an application of nonlinear acoustic echo cancellation. Finally, investigations on the tracking behavior for time-variant nonlinearities and robustness against misdetection of double-talk situations confirm the promising benefits and good trade-off of the proposed iterated coefficient updates Volterra filters approach.

SINR-maximizing spreading code allocation for non-linear serial interference cancellation

This paper considers the issue of spreading code allocation and receiver optimization in a CDMA-based multiuser data network. Assuming that non-linear serial interference cancellation is performed at the receiver, the problem of noncooperative SINR maximization with respect to each user's spreading code and uplink receiver is first considered. It is shown that iterative SINR maximization converges in a finite number of steps, and that the equilibrium resulting from noncooperative behavior is also Pareto-optimal. Next, the problem of optimal multiuser detection for a system using the above optimal spreading codes is also considered, and it is shown that, for such a system, maximum likelihood detection entails a computational complexity that is exponential in the ratio between the number of users and the system processing gain, thus providing huge savings with respect to the general case wherein the optimal receiver has a complexity exponential in the number of users. While initially considering a simple frequencyflat synchronous CDMA system, the obtained results are then extended to more general scenarios, such as asynchronous CDMA systems, multipath CDMA channels, and multiuser multiantenna systems. Finally, the issue of non-cooperative power minimization and choice of the spreading code subject to a QoS constraints is also considered, and comparisons with the corresponding cooperative solution are also discussed. Numerical results corroborate the validity of the theoretical analysis, and show that the use of non-linear interference cancellation coupled with waveform adaptation brings remarkable performance gains with respect to linear multiuser receivers.

DTD-free nonlinear acoustic echo cancellation based on independent component analysis

An adaptive acoustic echo cancellation method based on independent component analysis, which can remove nonlinear echo components, is presented. Since this method takes into account the independence between a far-end signal and the echo-cancelled output to cancel acoustic echoes which are independent of near-end signals, it can continue to update AEC parameters even in double-talk situations, thereby improving the cancellation performance. Experiments show that the proposed method provides better performance than the conventional least-mean-square methods for both linear and nonlinear AEC systems without requiring separate double-talk detection (DTD).

A Common-Gate Amplifier With Transconductance Nonlinearity Cancellation and Its High-Frequency Analysis Using the Volterra Series

A common-gate (CG) amplifier employing a transconductance nonlinearity cancellation technique is designed for transmitter circuitry. The major contributor to the third-order nonlinearity in the CG amplifier is the second derivative of the transconductor ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">''</sup> ), which is the same case with a common-source (CS) amplifier. The multiple gated transistor (MGTR) technique, which was developed in the CS amplifier for transconductor nonlinearity cancellation, is applied to a CG amplifier. However, in the CG amplifier, the input driving impedance of a CG amplifier comprises a voltage-current feedback loop. Thus, a second-order interaction with feedback components generates a third-order distortion that limits input-referred third-order intercept point (IIP3) enhancement. This feedback influence on IIP3 can be relaxed by eliminating harmonic feedback components. Based on high-frequency analysis on a CG amplifier using the Volterra series, an RF current source is proposed to replace the conventional current source in the CG amplifier to eliminate harmonic feedback components at 2omega and Deltaomega. By adapting the CG MGTR technique combined with the RF current source, a 2.4-GHz driver amplifier for Wibro/Wimax applications was implemented using a 0.18-mum 1P 6M CMOS process. Measurement results show a 9-dB output third-order intercept point improvement at an output power of -3 dBm.

Integrated Design for Configuration/Vibration Control of Hexapod Platform

The Hexapod configuration and vibration control integrated design is treated as an optimal problem of choosing minimum control energy index among a family of Hexapod with optimal Jacobian condition number. Based on the theory of optimal Jacobian condition number, a programming problem is given, which takes control parameter of nonlinear feedback adaptive disturbance canceller(ADC) method, radius of Hexapod base plate and half separation angle between adjacent actuator attachment points on the up plate as design variables, control convergence condition, workspace, and space between attachment points as constrained conditions, and weighted sum of six actuators’ average energy consumption and its variance component as objective function. As the optimal model and its sensitivities contain implicit functions of design variables, the primal problem is approached by 2-rank elliptical response surface method with D-optimal test design. The original programming problem is settled by solving sequence of approximate problems. The example result gives out rules and key points of controller and configuration design of Hexapod, and demonstrates validity and feasibility of the proposed method. Compared with original developed Hexapod, the optimized Hexapod has the minimum condition number, and the advantages in control energy consumption and distribution.

Simple robust technique using time delay estimation for the control and synchronization of Lorenz systems

This work presents two simple and robust techniques based on time delay estimation for the respective control and synchronization of chaos systems. First, one of these techniques is applied to the control of a chaotic Lorenz system with both matched and mismatched uncertainties. The nonlinearities in the Lorenz system is cancelled by time delay estimation and desired error dynamics is inserted. Second, the other technique is applied to the synchronization of the Lü system and the Lorenz system with uncertainties. The synchronization input consists of three elements that have transparent and clear meanings. Since time delay estimation enables a very effective and efficient cancellation of disturbances and nonlinearities, the techniques turn out to be simple and robust. Numerical simulation results show fast, accurate and robust performance of the proposed techniques, thereby demonstrating their effectiveness for the control and synchronization of Lorenz systems.

A Nonlinear Acoustic Echo Canceller Using Sigmoid Transform in Conjunction With RLS Algorithm

Nonlinearity of amplifiers and/or loudspeakers gives rise to nonlinear echo in acoustic systems, which seriously degrades the performance of speech and audio communications. Many nonlinear acoustic echo cancellation (AEC) methods have been proposed. In this paper, a simple yet efficient nonlinear echo cancellation scheme is presented by using an adaptable sigmoid function in conjunction with a conventional transversal adaptive filter. The new scheme uses the least mean square (LMS) algorithm to update the parameters of sigmoid function and the recursive least square (RLS) algorithm to determine the coefficient vector of the transversal filter. The proposed AEC is proved to be convergent under some mild assumptions. Computer simulations show that the proposed scheme gives a superior echo cancellation performance over the well known Volterra filter approach when the echo path suffers from the saturation-type nonlinear distortion. More importantly, the new AEC has a much lower computational complexity than the Volterra-filter-based method.

그룹화 CMA 알고리즘을 이용한 RF 중계기의 적응 간섭 제거 시스템(Adaptive Interference Cancellation System)에 관한 연구

본 논문에서는 RF(Radio Frequency) 중계기에서 그룹화 CMA(Constant Modulus Algorithm)와 LMS(Least Mean Square) 알고리즘을 이용하여 적응 필터를 적용시킨 새로운 혼합 간섭 제거기를 제안한다. 송신 안테나에서 수신안테나로 궤환되는 신호는 수신 시스템의 성능을 저하시킨다. 제안한 간섭 제거기는 그룹화 CMA 알고리즘 간섭 제거 기법을 적용시키기 때문에 기존 구조보다 나은 채널 적응 성능과 낮은 MSE(Mean Square Error)을 가진다. 이 구조는 기존 비선형 간섭 제거기에 비해 같은 MSE(Mean Square Error)에 대한 반복수와 하드웨어 복잡도를 줄여준다. 즉, 제안한 알고리즘은 LMS 알고리즘에 비해 평균 자승 에러가 적응 상수에 따라 2.5 dB 또는 4 dB 정도 낮은 값을 보였다. 또한, VSS(Variable Step Size)-LMS 알고리즘에 비해 수렴 속도가 빠르고, 비슷한 평균 자승 에러를 가진다. In this paper, we proposed a new hybrid interference canceller using the adaptive filter with Grouped CMA(Constant Modulus Algorithm)-LMS(Least Mean Square) algorithm in the RF(Radio Frequency) repeater. The feedback signal generated from transmitter antenna to receiver antenna reduces the performance of the receiver system. The proposed interference canceller has better channel adaptive performance and a lower MSE(Mean Square Error) than conventional structure because it uses the cancellation method of Grouped CMA algorithm. This structure reduces the number of iterations fur the same MSE performance and hardware complexity compared to conventional nonlinear interference canceller. Namely, MSE values of the proposed algorithm were lower than those of LMS algorithm by 2.5 dB and 4 dB according to step sizes. And the proposed algorithm showed fast speed of convergence and similar MSE performance compared to VSS(Variable Step Size)-LMS algorithm.

Decision feedback data detection in frequency domain for single carrier cyclic prefix assisted CDMA systems: A sequential quadratic programming approach

This paper proposes a frequency domain decision feedback data receiver for the uplink transmission of broadband single carrier cyclic prefix-assisted CDMA systems. The optimum data detection problem based on the maximal-likelihood criteria for this system is addressed as a combinatorial optimization problem. A sequential quadratic programming approach is proposed to solve this problem. The parallel gradient projection method and projected successive over relaxation algorithm are proposed to solve the sequential quadratic programming problem, which corresponds to low-complexity nonlinear parallel and successive interference cancellation schemes in frequency domain. The convergence properties and the complexities of these methods are analyzed and compared with conventional methods. The simulation results show that, with a few iterations, the proposed scheme gives near single user performance even for fully loaded systems.

Performance Tradeoff in Multiuser Equalization for CDMA over Flat Channels

We study the bit-error rate (BER) for different code lengths and number of users in CDMA system with linear minimum mean squared error (MMSE) and non-linear equalizations. We first show that for a fix channel and a fix number of users, BER of each symbol after linear equalization degrades with a decrease in the code length. Then, we prove that for a fix code length, the BER averaged over random channels improves with a decrease in the number of users. Furthermore, in the non-linear serial-interference cancellation (SIC) scheme, we prove analytically that the BER improves with each step of symbol cancellation for any channel not just at high signal-to-interference noise ratio (SINR) but at all range of SINR. Simulation results are presented to substantiate our theoretical findings.

The nonlinearity cancellation phenomenon in micromechanical resonators

In this paper, we present comprehensive analysis of the nonlinearities in a micromechanical clamped-clamped beam resonator. A nonlinear model which incorporates both mechanical and electrostatic nonlinear effects is established for the resonator and verified by experimental results. Both the nonlinear model and experimental results show that the first-order cancellation between the mechanical and electrostatic nonlinear spring constants occurs at about 45 V dc polarization voltage for a 193 kHz resonator in vacuum pressure of 37.5 µTorr. Our study also reveals that the nonlinearity cancellation is helpful in optimizing the overall resonator performance. On top of improving the frequency stability of the resonator by reducing its amplitude-frequency coefficient to almost zero, the nonlinearity cancellation also boosts the critical vibration amplitude of the resonator (0.57 µm for the beam resonator with 2 µm nominal gap spacing), leading to better power handling capabilities. The results from the clamped-clamped beam resonator studied in this work can be easily generalized and applied to other types of resonators.

Nonlinearity in micromechanical free–free beam resonators: modeling and experimental verification

In this paper, we present a systematic characterization and modeling technique for the micromechanical free–free beam resonator to analyze its nonlinear vibration behavior. Different from the conventional FEM-based approach whose simulation accuracy is usually limited around 60–70%, the proposed modeling method is able to accurately identify both the mechanical and electrostatic nonlinear parameters from just a few preliminary experimental observations. The nonlinear equation of motion is then numerically solved, demonstrating both the spring hardening and softening effects in the system. The simulated nonlinear behavior of the resonator under different driving conditions is validated by comparing them with the experimental data. In addition, based on the verified nonlinear model, design guidelines such as the nonlinearity cancellation are also highlighted. Although this work focuses on the free–free beam resonators, the proposed modeling approach can be applied to any other electrostatically driven microresonator to reveal different intrinsic nonlinear properties of the device.

Compensation for Nonlinearity in a Hammerstein System Using the Coherence Function With Application to Nonlinear Acoustic Echo Cancellation

This correspondence addresses compensation for nonlinearity in Hammerstein nonlinear systems. Specifically, we propose two predistortion methods that are based on coherence function criteria. The proposed methods carry out linearization without knowing the linear block in the Hammerstein system. This is particularly desirable for nonlinear acoustic echo cancellation applications, where dealing with the linear block can be computational cumbersome due to the long room acoustic impulse response.

Digital Domain Measurement and Cancellation of Residue Amplifier Nonlinearity in Pipelined ADCs

Digital correction and calibration techniques have been extensively used to cancel linear circuit imperfections in pipelined analog-to-digital converters (ADCs). The self-calibration technique proposed in this paper provides a means of measuring and canceling nonlinear errors of interstage amplifiers in the digital domain. The calibration of nonlinearity coefficients is based on pseudorandom signal modulation and evaluation of digital code histograms. The scheme does not introduce additional precision hardware or test signals and operates in the background without interrupting normal converter operation. The simulation results of a 12-bit ADC show that the calibration is capable of improving the effective number of bits from 7 to 11.8 while achieving parameter adaptation time constants on the order of 100 ms at a sampling rate of 100 MS/s.

Receiver Cancellation Technique for Nonlinear Power Amplifier Distortion in SDMA–OFDM Systems

Space-division multiple access (SDMA) and orthogonal frequency-division multiplexing (OFDM) can be combined to design a robust communications system with increased spectral efficiency and system capacity. This combination is one of the most promising candidates for future wireless local area network implementations. However, one drawback of OFDM systems is the high peak-to-average power ratio, which imposes strong requirements on the linearity of power amplifiers (PAs). Such linearity requirements translate into high back-off that results in low power efficiency. In order to improve power efficiency, a PA nonlinearity cancellation (PANC) technique is introduced in this paper. This technique reduces the nonlinear distortion effects on the received signal. The performance of the new technique is evaluated with simulations, which show significant power efficiency improvements. To obtain meaningful results for comparison purposes, we derive a theoretical upper bound on the bit error rate performance of an SDMA-OFDM system subject to PA nonlinearities. In addition, a novel channel estimation technique that combines frequency- and time-domain channel estimation with PANC is also presented. Simulation results show the robustness of the cancellation method also when channel estimation is included.

Echo canceler algorithm for adaptive Volterra filters in double talk states

AbstractIn an acoustic echo canceler, it is necessary to consider the nonlinearity of an echo path in order to attenuate an echo signal conventionally, and various methods using adaptive Volterra filters have been proposed. Many of those methods have not resulted in a decisive solution about the double talk states in a nonlinear acoustic echo canceler. In this paper, we propose an echo canceler algorithm for adaptive Volterra filters using the idea of the OECLMS (Orthogonal Expanded Correlation Least Mean Squares) algorithm in consideration of the double talk problem. The convergence speed of the proposed method is improved by using Gram‐Schmidt orthogonalization for the input signal. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 161(2): 42– 51, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20369