Memoryless Nonlinear Devices Research Articles

On the optimum multicarrier performance with memoryless nonlinearities

One of the major problems associated with multicarrier signals is their high envelope fluctuations that lead to implementation difficulties. Therefore, multicarrier signals are usually submitted to nonlinear operations such as clipping to simplify the power amplification, DAC (Digital-to-Analog Conversion) and other digital signal processing operations. However, these nonlinear operations lead to nonlinear noise that usually is associated with performance degradation. Recently, it was shown that the nonlinear distortion associated to bandpass memoryless nonlinear devices not only does not necessarily means performance degradation, but can even lead to performance gains. In this paper we study the impact of non-bandpass memoryless nonlinearities on the performance of multicarrier signals. We consider both nonlinear devices operating on the real-valued multicarrier signals as well as Cartesian nonlinear devices (also denoted as I-Q nonlinearities) operating separately on the real and imaginary parts of the complex envelope of multicarrier signals. We present a theoretical analysis of the potential performance improvements associated with the optimum detection of multicarrier signals, by deriving accurate theoretical expressions for both the average asymptotic gains in ideal AWGN (Additive White Gaussian Noise) channels and the asymptotic gain distribution for frequency-selective channels with multipath Rayleigh fading.

Asymptotic Hyperstability and Input–Output Energy Positivity of a Single-Input Single-Output System Which Incorporates a Memoryless Non-Linear Device in the Feed-Forward Loop

This paper visualizes the role of hyperstable controllers in the closed-loop asymptotic stability of a single-input single-output system subject to any nonlinear and eventually time-varying controller within the hyperstable class. The feed-forward controlled loop (or controlled plant) contains a strongly strictly positive real transfer function in parallel with a non-linear and memory-free device. The properties of positivity and boundedness of the input–output energy are examined based on the “ad hoc” use of the Rayleigh energy theorem on the truncated relevant signals for finite time intervals. The cases of minimal and non-minimal state-space realizations of the linear part are characterized from a global asymptotic stability (asymptotic hyperstability) point of view. Some related extended results are obtained for the case when the linear part is both positive real and externally positive and for the case of incorporation of other linear components which are stable but not necessarily positive real.

General mechanism for the 1/f noise.

We consider the response of a memoryless nonlinear device that acts instantaneously, converting an input signal ξ(t) into an output η(t) at the same time t. For input Gaussian noise with power-spectrum 1/f^{α}, the nonlinearity can modify the spectral index of the output to give a spectrum that varies as 1/f^{α^{'}} with α^{'}≠α. We show that the value of α^{'} depends on the nonlinear transformation and can be tuned continuously. This provides a general mechanism for the ubiquitous 1/f noise found in nature.

On the Optimum Multicarrier Performance With Memoryless Nonlinearities

It is widely recognized that orthogonal frequency division multiplexing (OFDM) signals are very prone to nonlinear distortion effects, which can lead to significant performance degradation. However, recent results have showed that nonlinear distortion effects do not necessarily mean performance degradation and can actually lead to performance improvements relative to conventional linear OFDM schemes. In this paper, we consider the effects of bandpass memoryless nonlinear devices on OFDM signals and study the optimum asymptotic performance for both nondispersive channels and severely time-dispersive channels. We present analytical methods for obtaining the Euclidean distance between two OFDM signals that are subjected to different nonlinear characteristics. These results are then employed for obtaining the average asymptotic gain relative to conventional linear OFDM schemes in nondispersive channels and the gain distribution for severely time-dispersive channels with Rayleigh-distributed fading on the different multipath components. Our analytical results, which are shown to be very accurate, indicate that the optimum detection of OFDM schemes with strong nonlinear distortion effects allows significant gains when compared with conventional linear OFDM schemes.

Zero-mean proper complex Gaussian random processes through nonlinear channels

The statistical characterisation of the output of a memoryless nonlinear device having, as an input, a zero mean proper complex Gaussian random process is studied. The closed form expression obtained for the high‐order moments involved allowed for neat mathematical expressions for the autocorrelation function and the power spectral density of the signal at the nonlinearity output. Parts of the autocorrelation function and of the power spectral density that correspond to the desired signal and to the intermodulation products of different orders are easily identified.

Analytical evaluation of nonlinear effects in MC-CDMA signals

The MC-CDMA signals (multicarrier coded division multiple access) have strong envelope fluctuations which make them very prone to nonlinear effects. These effects can be both intentional (such as the ones inherent to a nonlinear signal processing for reducing the envelope fluctuations) or not (such as the ones inherent to a nonlinear power amplification). In this paper we present an analytical tool for the performance evaluation of nonlinear effects in MC-CDMA signals which takes advantage of the Gaussian-like behavior of MC-CDMA signals with a large number of subcarriers and employs results on memoryless nonlinear devices with Gaussian inputs so as to characterize statistically the signals at the output of the nonlinear device. This characterization is then used for an analytical computation of the SIR levels (signal-to-interference ratio) and the BER performance (bit error rate). A set of numerical results is presented and discussed, showing the accuracy of the analytical BER performance analysis in the presence of nonlinear effects

Nonlinear Devices Acting as SNR Amplifiers for a Harmonic Signal in Noise

A harmonic signal corrupted by an additive white noise is processed by an arbitrary memoryless nonlinear device. The transformation of the signal-to-noise ratio (SNR) by the nonlinearity is explicitly computed and analyzed for Gaussian and non-Gaussian noise. Simple nonlinearities, easily implementable as electronic circuits, are shown capable of producing an amplification of the SNR. Such an amplification is not obtainable with linear filters, whatever their complexity or high order, but becomes easily accessible with simple nonlinear devices.

Reference Management for Control Systems Under Constraints

A supervision scheme, denoted hereafter to as a Command Governor (CG), is presented for on-line handling the reference signal to be applied to a compensated control system in order to enforce pointwise-in-time input and/or staterelated constraints. A CG is basically a memoryless nonlinear device which, on the base of current plant state and reference signal, produces its action by modifying the reference signal in order to avoid potential constraint violations. An application to a bank-to-turn autopilot design is presented where the CG is used for governing the demanded pitch acceleration in order to avoid violation of physical constraints on the elevator angle.

Nonlinearity compensation in digital radio systems

Digital radio links with bandlimited pulses exhibit a severe performance degradation when the transmitter high power amplifier operates near saturation. To cope with the increase of nonlinear intersymbol interference due to the amplifier nonlinearities, a discrete-time Volterra system can be used to process the transmitted data. We present an efficient technique for implementing adaptive data predistorters with memory based on a discrete-time Volterra system composed of digital linear filters and memoryless nonlinear devices working at the symbol rate. Third- and fifth-order structures are proposed and a system performance evaluation is presented for several realistic situations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Dynamic range and other fundamentals of the complex Bessel function series approximation model for memoryless nonlinear devices

An explanation is given of the application of the complex Bessel function series approximation model of the memoryless amplitude and phase characteristics of nonlinear devices. Confusion had arisen because of the choice of a value of a parameter in the approximating expression. The practice had been to choose this simply as though it was just an arbitrary constant which scales the input, or as an optimizing parameter in the effort to get a best fit of the approximation to the measured data. By examining the derivation of the particular approximation, a determining and important link between this parameter and the desired operating dynamic range of the nonlinear characteristic being approximated is shown. How values for this parameter are calculated in terms of input overdrive relative to device saturation is also shown. In examining the origin of the approximating expressions, an alternative and simpler derivation to that given by J.C. Fuenzalida et al. (1973) is presented that is based on the work of M.J. Eric et al. (1972). >

Modulation-transfer noise effects among FM and digital signals in memoryless nonlinear devices

When two or more frequency-modulated and/or digital carriers of various sizes and modulation formats are transmitted through a common memoryless nonlinear device with AM/AM and AM/PM characteristics such as a traveling-wave tube amplifier, interactions among the carriers will occur. One of the impairments caused by these interactions results in modulation-transfer noise effects. In particular, in satellite communications, depending on the manner multicarrier transponders are used, the modulation-transfer impairment manifests itself under various forms and subjective interference effects. This tutorial-review paper presents an introduction to this type of impairment, methods of analysis and examples, and measurement results. General practical guidelines are suggested for controlling these effects.

On the Spectral Skewness of a Narrow-Band Gaussian Process

This correspondence discusses techniques for estimating the spectral skewness of the baseband spectrum of the complex envelope of a narrow-band Gaussian process from its undistorted and distorted (by memoryless nonlinear devices) in-phase and quadrature components. Some applications of the spectral skewness in communication theory are also mentioned.

Modulation Transfer Noise Effects from TDMA Carriers to FDM/FM Carriers in Memoryless Nonlinear Devices

This paper examines modulation transfer noise effects from TDMA carriers to FDM/FM carriers in a common memoryless nonlinear amplifier. The modulation transfer noise consists of discrete as well as continuous spectral components. Three types of discrete components are identified: those due to pulse filtering only, those due to on-off bursting only, and cross terms due to both mechanisms simultaneously. The continuous spectral component of the modulation transfer noise is due to pulse filtering only. A comparison of the relative intensities of all these noise components is also presented.

Modulation Transfer Noise Effects from a Continuous Digital Carrier to FDM/FM Carriers in Memoryless Nonlinear Devices

An analysis of the modulation transfer noise effects from a continuous (nonbursty) digital carrier to multiple FDM/FM carriers in a common memoryless nonlinear amplifier (e.g., satellite transponder TWTA) is presented. It is shown that the modulation transfer noise, which is caused by the random envelope variations of the digital carrier due to the random data patterns and filtering of the PSK pulses, consists of both discrete and continuous spectral components in the baseband of the FDM/FM carriers. Numerical examples in terms of the noise power ratio as well as a comparison between measured and computed results are given. In general, the discrete or tonal interference component at the symbol rate of the digital carrier is quite significant. Results of this paper should be useful in the planning of FDMA satellite transponders employing the mixed PSK-FM mode of operation.

A Power Series Expansion Approach to Evaluate Modulation Transfer Noise Effects from Digital Carriers to FDM/FM Carriers in Memoryless Nonlinear Devices

This paper presents a power series expansion approach for evaluating modulation transfer noise effects from <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</tex> digital carriers (continuous or bursty) to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</tex> FDM/FM carriers in a common memoryless nonlinear amplifier. The method allows for a complete characterization and assessment of this type of transmission impairment and its effects in satellite communications systems. The baseband modulation transfer noise in the FM carriers caused by the random envelope fluctuations due to filtering of PSK pulses and/or by the on-off bursting of the digital carriers can be calculated. Illustrative numerical results indicate that the mixed PSK-FM mode of operation in satellite transponders should be employed with great care since a number of 4 kHz channels in the basebands of the FM carriers may receive prohibitive interference.

On the Accuracy of the Shimbo Approach to Intermodulation and Crosstalk Calculations

To simplify the mathematics involved and to facilitate derivations of intermodulation and crosstalk formulas, the Shimbo approach uses a double Fourier transformation and represents the characteristics of a memoryless nonlinear device by a Bessel function series. Such an approach seems to be a very brave approximation as the approximated characteristics vary wildly with respect to the number of Bessel function terms <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</tex> and with the amount of actual characteristic data used <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(A_{F})</tex> . However, it is shown here that the approach works well for the case involving two carriers with equal constant amplitudes, provided that one chooses <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</tex> and A <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</inf> properly.

A Stochastic Dynamic Model of Rain Attenuation

A dynamic mathematical model of rain attenuation has been developed and is presented in this paper. This model permits the expression of analytic relationships between parameters commonly used to describe the properties of interest for communication. The dynamic model is based on the lognormal distribution of rain attenuation and utilizes a memoryless nonlinear device to transform attenuation and rain intensity into a one-dimensional Gaussian stationary Markov process. Hence, only one parameter is required to introduce the dynamic properties of rain attenuation into the model. Experimental results and the known properties of rain have been used to derive and to verify the model; comparative results are presented and demonstrate good correspondence. The application of the model to the statistical analysis of the performance of communications systems is illustrated in the paper. The use of a dynamic rain attenuation model is necessary in order to analyze radio communication systems with transmit power control to offset the effects of rain attenuation, and where the finite response time of the control system affects the performance. An advantage of the model is the simplicity with which it allows simulation of communication link performance under the influence of rain attenuation. Such simulations are of great interest for complex models of adaptive networks where several deteriorating effects, including finite response times, are present.

Modulation Transfer from TDMA On-Off Bursting to FM Carriers in Memoryless Nonlinear Devices: Part I--Power Spectra

The modulation transfer noise caused by the bursts of TDMA signals is modeled and analyzed in detail. Expressions of the power spectra of the RF and the baseband modulation transfer noise have been obtained for the most general case of L TDMA and N FM carriers in a zero-memory nonlinear amplifier such as a helix-type TWTA. From these general expressions, the RF power spectrum and the baseband modulation transfer noise onto the FM carriers can be readily computed. It is shown that there are only line spectra and no continuous spectrum in the modulation transfer noise caused by the TDMA on-off bursting. The separation of the spectral lines is equal to the TDMA frame rate. The maximum of the power spectrum of the modulation transfer noise is inversely proportional to the square of the TDMA frame duration and is independent of the separation between TDMA and FM carriers. The modulation transfer noise is in general a complicated function of TDMA burst levels, burst patterns, burst lengths, FM carrier levels, carrier sizes, device nonlinearities, and operating points.

Autocorrelation of output of memoryless nonlinear devices with arbitrary characteristics (Corresp.)

An important class of nonlinear devices is that based on the \nu th-law characteristic. Mathematical methods already employed in the analysis of this class of nonlinearities can be exploited in a rather straightforward manner to obtain ready-made formulas for autocorrelation functions of arbitrary nonlinear characteristics in response to noise plus signal.

Modulation Transfer from TDMA On-Off Bursting to FM Carriers in Memoryless Nonlinear Devices, Part II-Baseband Performance

When TDMA and FM carriers are commonly amplified by a memoryless device with nonlinear amplitude and phase characteristics, modulation transfer noise induced by the on-off bursting of the TDMA signals will be present at the FM carriers. In Part II of this paper, closed form expressions of the power spectra of the modulation transfer noise are derived for many special carrier configurations of interest. Numerical examples are also provided in terms of the signal-to-modulation transfer noise ratio, SNR, in the baseband of the FM carriers. It is shown how SNR varies as a function of TDMA burst levels, burst patterns, burst lengths, FM carrier levels, carrier sizes, and device nonlinearities and operating points. With these detailed analyses and numerical examples, insight can be gained into the mechanism of modulation transfer from TDMA on-off bursting to the FM signals. Results presented in this part of the paper should be useful for transmission systems planning and evaluation, and for TDMA burst scheduling.