Polynomial Model for High-Order and Multi-Carrier Passive Intermodulation Products

Passive intermodulation (PIM) often limits the performance of communication systems, particularly in the presence of multiple carriers. Since the origins of the apparently multiple physical sources of nonlinearity causing PIM in distributed circuits are not fully understood, the behavioural models are frequently employed to describe the process of PIM generation. In this paper, a memoryless nonlinear polynomial model, capable of predicting high-order multi-carrier intermodulation products, is deduced from the third-order two-tone PIM measurements on a microstrip transmission line with distributed nonlinearity. The analytical model of passive distributed nonlinearity is implemented in Keysight Technology’s ADS simulator to evaluate the adjacent band power ratio for three-tone signals. The obtained results suggest that the costly multi-carrier test setups can possibly be replaced by a simulation tool based on the properly retrieved nonlinear polynomial model.

Passive Intermodulation of Analog and Digital Signals on Transmission Lines with Distributed Nonlinearities: Modelling and Characterization

Passive intermodulation (PIM) often limits the performance of communication systems with analog and digitally-modulated signals and especially of systems supporting multiple carriers. Since the origins of the apparently multiple physical sources of nonlinearity causing PIM are not fully understood, the behavioral models are frequently used to describe the process of PIM generation. In this paper a polynomial model of memoryless nonlinearity is deduced from PIM measurements of a microstrip line with distributed nonlinearity with two-tone CW signals. The analytical model of nonlinearity is incorporated in Keysight Technology’s ADS simulator to evaluate the metrics of signal fidelity in the receive band for analog and digitally-modulated signals. PIM-induced distortion and cross-band interference with modulated signals are compared to those with two-tone CW signals. It is shown that conventional metrics can be applied to quantify the effect of distributed nonlinearities on signal fidelity. It is found that the two-tone CW test provides a worst-case estimate of cross-band interference for two-carrier modulated signals whereas with a three-carrier signal PIM interference in the receive band is noticeably overestimated. The simulated constellation diagrams for QPSK signals demonstrate that PIM interference exhibits the distinctive signatures of correlated distortion and this indicates that there are opportunities for mitigating PIM interference and that PIM interference cannot be treated as noise. One of the interesting results is that PIM distortion on a transmission line results in asymmetrical regrowth of output PIM interference for modulated signals.

Model categories for orthogonal calculus

We restate the notion of orthogonal calculus in terms of model categories. This provides a cleaner set of results and makes the role of O(n)-equivariance clearer. Thus we develop model structures for the category of n-polynomial and n-homogeneous functors, along with Quillen pairs relating them. We then classify n-homogeneous functors, via a zig-zag of Quillen equivalences, in terms of spectra with an O(n)-action. This improves upon the classification theorem of Weiss. As an application, we develop a variant of orthogonal calculus by replacing topological spaces with orthogonal spectra.

A multi-output two-stage locally regularized model construction method using the extreme learning machine

This paper investigates the construction of linear-in-the-parameters (LITP) models for multi-output regression problems. Most existing stepwise forward algorithms choose the regressor terms one by one, each time maximizing the model error reduction ratio. The drawback is that such procedures cannot guarantee a sparse model, especially under highly noisy learning conditions. The main objective of this paper is to improve the sparsity and generalization capability of a model for multi-output regression problems, while reducing the computational complexity. This is achieved by proposing a novel multi-output two-stage locally regularized model construction (MTLRMC) method using the extreme learning machine (ELM). In this new algorithm, the nonlinear parameters in each term, such as the width of the Gaussian function and the power of a polynomial term, are firstly determined by the ELM. An initial multi-output LITP model is then generated according to the termination criteria in the first stage. The significance of each selected regressor is checked and the insignificant ones are replaced at the second stage. The proposed method can produce an optimized compact model by using the regularized parameters. Further, to reduce the computational complexity, a proper regression context is used to allow fast implementation of the proposed method. Simulation results confirm the effectiveness of the proposed technique. © 2013 Elsevier B.V.

A Generalized Fuzzy Linguistic Model for Predicting Component Concentrations in an Optical Gas Sensing System

Motivated by environmental protection concerns, monitoring the flue gas of thermal power plant is now often mandatory due to the need to ensure that emission levels stay within safe limits. Optical based gas sensing systems are increasingly employed for this purpose, with regression techniques used to relate gas optical absorption spectra to the concentrations of specific gas components of interest (NOx, SO2 etc.). Accurately predicting gas concentrations from absorption spectra remains a challenging problem due to the presence of nonlinearities in the relationships and the high-dimensional and correlated nature of the spectral data. This article proposes a generalized fuzzy linguistic model (GFLM) to address this challenge. The GFLM is made up of a series of “If-Then” fuzzy rules. The absorption spectra are input variables in the rule antecedent. The rule consequent is a general nonlinear polynomial function of the absorption spectra. Model parameters are estimated using least squares and gradient descent optimization algorithms. The performance of GFLM is compared with other traditional prediction models, such as partial least squares, support vector machines, multilayer perceptron neural networks and radial basis function networks, for two real flue gas spectral datasets: one from a coal-fired power plant and one from a gas-fired power plant. The experimental results show that the generalized fuzzy linguistic model has good predictive ability, and is competitive with alternative approaches, while having the added advantage of providing an interpretable model.

A generalized fuzzy linguistic model for predicting component concentrations in an optical gas sensing system

Motivated by environmental protection concerns, monitoring the flue gas of thermal power plant is now often mandatory due to the need to ensure that emission levels stay within safe limits. Optical based gas sensing systems are increasingly employed for this purpose, with regression techniques used to relate gas optical absorption spectra to the concentrations of specific gas components of interest (NO_x, SO₂ etc.). Accurately predicting gas concentrations from absorption spectra remains a challenging problem due to the presence of nonlinearities in the relationships and the high-dimensional and correlated nature of the spectral data. This article proposes a generalized fuzzy linguistic model (GFLM) to address this challenge. The GFLM is made up of a series of “If-Then” fuzzy rules. The absorption spectra are input variables in the rule antecedent. The rule consequent is a general nonlinear polynomial function of the absorption spectra. Model parameters are estimated using least squares and gradient descent optimization algorithms. The performance of GFLM is compared with other traditional prediction models, such as partial least squares, support vector machines, multilayer perceptron neural networks and radial basis function networks, for two real flue gas spectral datasets: one from a coal-fired power plant and one from a gas-fired power plant. The experimental results show that the generalized fuzzy linguistic model has good predictive ability, and is competitive with alternative approaches, while having the added advantage of providing an interpretable model.