Memoryless Nonlinearity Research Articles

Unknown Input Reconstruction Observer for Hammerstein-Wiener Systems in the Errors-in-Variables Framework

In this paper an approach for reconstructing an unknown input in the case when input and output signals are both subject to measurement uncertainties, i.e. errors-in-variables framework, is presented. The algorithm is applicable to Hammerstein-Wiener systems, i.e. systems composed from a dynamic linear system followed and preceded by a memoryless nonlinearity. It is based on a parity equations concept and forms an extension of the idea developed previously by the authors for linear systems. The only requirement is that the function used to describe the component static output nonlinearity must be strictly monotonic. The order of the parity space can be treated as a tuning parameter allowing for a trade-off between the smoothness of the reconstructed unknown input and a phase lag to be obtained. An analytical solution of the overall problem is obtained by using a Lagrange multiplier method.

Frequency Identification of Wiener Systems with Backlash Operators using Separable Least Squares Estimators

This paper deals with the identification of Wiener models that involve backlash operators bordered by possibly noninvertible parametric lines. The latter are also allowed to cross each other making possible to account for general-shape static nonlinearities. The linear dynamic subsystem is not-necessarily parametric but is BIBO stable. A frequency identification method is developed that provides estimates of the nonlinear operator parameters as well as estimates of the linear subsystem frequency gain. The method involves standard and separable least squares estimators that all are shown to be consistent. Backlash operators and memoryless nonlinearities are handled within a unified framework.

Generalised Hammerstein–Wiener system estimation and a benchmark application

This paper examines the use of a so-called “generalised Hammerstein–Wiener” model structure that is formed as the concatenation of an arbitrary number of Hammerstein systems. The latter are taken here to be memoryless non-linearities followed by linear time invariant dynamics. Hammerstein, Wiener, Hammerstein–Wiener and Wiener–Hammerstein models are all special cases of this structure. The parameter estimation of this model is investigated using a standard prediction error criterion coupled with a robust gradient based search algorithm. This approach is profiled using a Wiener–Hammerstein Benchmark example, which illustrates it to be effective and, via Monte-Carlo simulation, relatively robust against capture in local minima.

Steady-State Performance Analysis and Step-Size Selection for LMS-Adaptive Wideband Feedforward Power Amplifier Linearizer

Balancing between power amplifier (PA) linearity and power efficiency is one of the biggest implementation challenges in radio communication transmitters. Among various linearization methods, the feedforward linearization technique is a fairly established principle offering a good tradeoff between linearity and power-efficiency even under wideband operation. Moreover, adaptive techniques for such linearizer have been proposed in literature to track parameter changes in the main PA and other circuitry. Among those, least mean squares (LMS) method for adapting signal cancellation loop (SCL) and error cancellation loop (ECL) coefficients is an attractive low-complexity alternative. In this paper, we carry out extensive closed-form performance analysis of the achievable intermodulation distortion (IMD) reduction of the overall LMS-adaptive feedforward linearizer, as a function of the used step-sizes and essential waveform statistics. Such analysis is currently missing from the state-of-the-art literature. Both memoryless nonlinearities and Wiener-Hammerstein type PA memory models are studied for which IMD suppression expressions are derived. Comprehensive computer simulations are also provided to illustrate the accuracy of the analysis when practical OFDM waveforms are used. Design examples are given as well where the analysis results are used to choose proper linearizer step-sizes to meet given transmitter spectral mask specifications.

Maximizing the Stability Region in the Parameter Space for a Nonlinear Control System

This paper shows some results on maximizing the stability region in the parameter space for a nonlinear control system consisting of an LTI system with uncertain parameters and of a memoryless nonlinearity in the feedback. This problem is solved in the framework of dissipativity theory using LMIs. The usefulness of the procedure is demonstrated for a fuzzy control system.

Recent Advances on Signal Processing Solutions for Distortion Mitigation Due to Power Amplifier and Non-Ideality of Transmitter System

Recent research in communication is inclined towards modulation and assesses techniques that are more spectrally efficient to support more users per base station to reduce overall network costs and make the services affordable to subscribers. However, these signals are highly envelope varying that invokes distortion in transmitted signal due to transmitter nonlinearity and other linear impairments. Therefore, to extract optimum benefits in terms of cost and performance, transmitter linearization solutions are constantly evolving. This patent review highlights developments in this arena from past decade to current and futuristic trends, focusing on the evolution from bulky analogue to reconfigurable digital predistortion and from memoryless nonlinearity based distortion mitigation to recent trends to compensate for memory and other transmitter line-up imperfections. Keywords: Predistortion, power amplifier linearization, memory effects, IQ imbalance in modulators, power amplifier behavioral models, neural networks, Wiener-Hammerstein, adaptive filters, power amplifier, modulators, wireless communication systems, FEEDFORWARD TECHNIQUE, transmitted signal, linearization techniques, error amplifier

Observations Concerning the Generation of Spurious Tones in Digital Delta-Sigma Modulators Followed by a Memoryless Nonlinearity

In mixed-signal systems, nonlinear distortion due to nonideal analog circuitry can act on quantized digital sequences, giving rise to spurious tones. In this brief, generation of spurious tones in digital delta-sigma modulators, followed by memoryless nonlinearity, is investigated. Inherent modulator periodicity that persists even with the use of least-significant-bit dither is identified.

Performance evaluation of a narrowband power line communication for smart grid with noise reduction technique

Performance of the narrowband power line communication (PLC) is significantly degraded by the impulsive noise with very large amplitudes and short durations. In practical applications, the simple memoryless nonlinearity techniques (Clipping, Blanking, and Clipping/Blanking) are often used in order to mitigate the effect of the impulsive noise. In this paper, we propose an optimal Clipping/Blanking technique for impulsive noise reduction in narrowband (9-490 kHz) PLC system. This optimal technique is based on the minimum bit error rate (BER) search. To this end, we have derived the transfer function of a typical low voltage (LV) PLC network using the common bottom-up approach and scattering matrix method. Our simulation results, in terms of BER versus signal to noise ratio (SNR), show that the proposed technique slightly improves the BER performance of the narrowband PLC system for smart grid applications and two-way communication between smart meters and utilities <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> .

Effects of hysteresis and eddy currents in magnetostrictive harvesting devices

The paper tackles the analysis of the magnetostrictive energy harvesting phenomena by formulating a model where the hysteretic static characteristic of the material and eddy currents induced by Villari effect are taken into account. The study aims to analyze the main loss mechanisms involved in this kind of devices, highlighting the impact of the hysteretic material behavior with respect to the linear and non-linear memoryless approaches.

Digitally Equalized CMOS Transmitter Front-End With Integrated Power Amplifier

An energy-efficient, 3.5-GHz, direct-conversion RF transmitter with integrated 23-dBm, Class-B power amplifier (PA) is fabricated in a 0.13- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu{\hbox {m}}$</tex></formula> CMOS process for the reliable transmission of 20-MHz bandwidth OFDM signals. Assisted by an integrated feedback path, a two-dimensional, digital look-up table (2-D LUT) adapted by complex gradient-descent algorithms compensates for the I/Q mismatch and memoryless nonlinearities of the whole transmit path, including the severe amplitude and phase distortions of the on-chip PA. Fifth-order Butterworth transmit filters with 34-MHz cutoff frequency sufficiently attenuate the aliases of the 80-MS/s digital-to-analog converters (DACs), while retaining high in-band fidelity without corrupting the predistorted signal. When a 20-MHz, 64-QAM OFDM signal with 9.6-dB peak-to-average power ratio (PAPR) was transmitted, the measured average drain efficiency (DE) of the PA was 12.5% at 9.6-dB back-off and 17.5% at 7-dB back-off, and the corresponding error-vector magnitude (EVM) was measured to be <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$-$</tex> </formula> 29.6 dB and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$-$</tex> </formula> 26.3 dB with equalization, respectively. A peak DE of 55% and a 25-dBm saturated output power were also measured for the same PA in a stand-alone package.

Identification of Hammerstein Systems with Quantized Observations

This work is concerned with identification of Hammerstein systems whose outputs are measured by quantized sensors. The system consists of a memoryless nonlinearity that is polynomial and possibly noninvertible, followed by a linear subsystem. The parameters of linear and nonlinear parts are unknown but have known orders. Input design, identification algorithms, and their essential properties are presented under the assumptions that the distribution function of the noise is known and the quantization thresholds are known. The concept of strongly scaled full rank signals is introduced to capture the essential conditions under which the Hammerstein system can be identified with set-valued observations. Under strongly scaled full rank conditions, a strongly convergent algorithm is constructed. Asymptotic consistency and efficiency of the algorithm are investigated.

An Improved Doherty Amplifier Using Cascaded Digital Predistortion and Digital Gate Voltage Enhancement

This paper describes algorithms used to improve linearity, efficiency, and peak power of a Doherty amplifier whose auxiliary transistor gate voltage is adjusted digitally as a function of the signal envelope. Two predistortion stages are used to compensate for high-order memoryless nonlinearities and low-order memory effects. The digital gate voltage waveform is a sigmoid function of the predistorted signal's envelope with two voltage limits corresponding to class C and AB bias levels. The instantaneous gate voltage is controlled by two adjustable parameters: a breakpoint and a slope. The parameters are adjusted to reduce the variance of the AM-AM curve of the power amplifier. The enhancement of the gate voltage at higher signal envelope levels increases the peak power and enhances improves the efficiency of the Doherty amplifier structure. The cascaded digital predistortion ensures sufficient linearity to keep the ACPR2 below - 55 dBc.

Optimum and suboptimum memoryless nonlinearities for the detection of ultrashort light pulses in Gaussian noise

Detection of ultrashort light pulses with conventional bandlimited photodetectors can lead to substantial performance degradation in digital lightwave communication systems. All-optical nonlinear processing of the received field prior to the optical to electrical conversion can greatly overcome this problem. In this letter, through a decision-theoretic framework and using a basic invariance property of the photodetector, we obtain the optimal zero-memory nonlinear element and evaluate its performance. Possible suboptimum nonlinearities are also investigated and their performance is examined. The results in this letter strongly justify the intuitive use of power-law devices, such as those implemented via two photon absorption (TPA) or second harmonic generation (SHG), in the detection of ultrashort light pulses and show how by using them almost optimal performance can be achieved.

Tensor Analysis-Based Model Structure Determination and Parameter Estimation for Block-Oriented Nonlinear Systems

A block-oriented nonlinear system is composed of a concatenation of blocks representing either memoryless nonlinearities or linear dynamic subsystems. Wiener, Hammerstein, and Wiener-Hammerstein (WH) models are the most commonly used ones for modeling such block-oriented nonlinear systems. In this paper, we develop a tensor analysis-based approach for determining both the structure and the parameters of the most appropriate model among the three above listed models. The structure is deduced from the rank of a tensor obtained by convolving a random finite impulse response (FIR) linear filter with a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> th-order Volterra kernel ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> > 2), associated with the block-oriented nonlinear system to be identified. The parameters of the linear subsystems are obtained from the PARAllel FACtor analysis (PARAFAC) decomposition of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> th-order Volterra kernel associated with the original nonlinear system and/or an extended WH system, whereas those of the nonlinear subsystem are estimated using the least squares method. The performance of the proposed identification scheme is illustrated by means of some simulation results.

A Wideband Analog Predistortion Power Amplifier With Multi-Branch Nonlinear Path for Memory-Effect Compensation

A wideband, multi-branch analog predistorter (MBAPD) is reported to compensate for memory effects as well as memoryless nonlinearity of the power amplifier (PA) for repeater systems with wideband modulated signals. For verification, the MBAPD with three-branch nonlinear path is implemented with a 30 W class-AB PA and tested using a two-carrier wideband code division multiple access (WCDMA) signal with 15 MHz tone spacing at 2.14 GHz. From the measured results at an average output power of 33 dBm, the proposed MBAPD shows the adjacent channel leakage ratios (ACLRs) at plusmn15 MHz offset of -60.4 dBc and -60.2 dBc, which are an improvement of over 25 dB and 12 dB, compared to the PAs without APD and with conventional APD, respectively.

Input Nonlinearity Recovering in a Class of Systems

A system in which a nonlinear memoryless part is followed by a nonlinear dynamic one is identified under nonparametric a priori information. The input nonlinearity is recovered with the kernel regression estimate.

Adaptive Predistortion With Direct Learning Based on Piecewise Linear Approximation of Amplifier Nonlinearity

We propose an efficient Wiener model for a power amplifier (PA) and develop a direct learning predistorter (PD) based on the model. The Wiener model is formed by a linear filter and a memoryless nonlinearity in which AM/AM and AM/PM characteristics are approximated as piecewise linear and piecewise constant functions, respectively. A two-step identification scheme, wherein the linear portion is estimated first and the nonlinear portion is then identified, is developed. The PD is modeled by a polynomial and its coefficients are directly updated using a recursive least squares (RLS) algorithm. To avoid implementing the inverse of the PA's linear portion, the cost function for the RLS algorithm is defined as the sum of differences between the output of the PA's linear portion and the inverse of the PA's nonlinear portion. The proposed direct learning scheme, which is referred to as the piecewise RLS (PWRLS) algorithm, is simpler to implement, yet exhibits comparable performance, as compared with existing direct learning schemes.

A Fast Digital Predistortion Algorithm for Radio-Frequency Power Amplifier Linearization With Loop Delay Compensation

An adaptive, digital, baseband predistortion (PD) algorithm that compensates for the memoryless nonlinearities of radio-frequency (RF) power amplifiers (PAs) for wireless systems using non-constant-envelop modulation schemes is presented. Compared with the conventional, complex-gain predistorters based on lookup tables (LUTs), the proposed direct-learning, multilevel lookup table (ML-LUT) approach assisted by a hardware-efficient loop delay compensation scheme achieves a significant reduction in convergence time and an improvement in linearization accuracy in the presence of an unknown loopback delay. The experimental results in an FPGA prototyping platform show that the fast adaptation speed enables the predistorter to track time-varying PA nonlinearities as fast as in the tens of kilohertz range, constituting a potential solution for highly efficient PAs in mobile handsets.

Blind identification of multiuser nonlinear channels using tensor decomposition and precoding

This paper presents two blind identification methods for nonlinear memoryless channels in multiuser communication systems. These methods are based on the parallel factor (PARAFAC) decomposition of a tensor composed of channel output covariances. Such a decomposition is possible owing to a new precoding scheme developed for phase-shift keying (PSK) signals modeled as Markov chains. Some conditions on the transition probability matrices (TPM) of the Markov chains are established to introduce temporal correlation and satisfy statistical correlation constraints inducing the PARAFAC decomposition of the considered tensor. The proposed blind channel estimation algorithms are evaluated by means of computer simulations.

Estimation of Generalised Hammerstein-Wiener Systems

This paper examines the use of a so-called “generalised Hammerstein–Wiener” model structure that is formed as the concatenation of an arbitrary number of Hammerstein systems. The latter are taken here to be memoryless non-linearities followed by linear time invariant dynamics. Hammerstein, Wiener, Hammerstein–Wiener and Wiener–Hammerstein models are all special cases of this structure. The parameter estimation of this model is investigated by using a standard prediction error criterion coupled with a robust gradient based search algorithm. This approach is profiled using the Wiener–Hammerstein system benchmark data, which illustrates it to be effective and, via Monte–Carlo simulation, relatively robust against capture in local minima.