Single-carrier frequency domain equalisation for hammerstein communication systems using complex-valued neural networks

Single-carrier (SC) block transmission with frequency-domain equalisation (FDE) offers a viable transmission technology for combating the adverse effects of long dispersive channels encountered in high-rate broadband wireless communication systems. However, for high bandwidthefficiency and high power-efficiency systems, the channel can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such nonlinear Hammerstein channels, the standard SC-FDE scheme no longer works. This paper advocates a complex-valued (CV) B-spline neural network based nonlinear SC-FDE scheme for Hammerstein channels. Specifically, We model the nonlinear HPA, which represents the CV static nonlinearity of the Hammerstein channel, by a CV B-spline neural network, and we develop two efficient alternating least squares schemes for estimating the parameters of the Hammerstein channel, including both the channel impulse response coefficients and the parameters of the CV B-spline model. We also use another CV B-spline neural network to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can easily be estimated using the standard least squares algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. Equalisation of the SC Hammerstein channel can then be accomplished by the usual one-tap linear equalisation in frequency domain as well as the inverse B-spline neural network model obtained in time domain. Extensive simulation results are included to demonstrate the effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels.

B-spline neural network based single-carrier frequency domain equalisation for Hammerstein channels

A practical single-carrier (SC) block transmission with frequency domain equalisation (FDE) system can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such Hammerstein channels, the standard SC-FDE scheme no longer works. We propose a novel Bspline neural network based nonlinear SC-FDE scheme for Hammerstein channels. In particular, we model the nonlinear HPA, which represents the complex-valued static nonlinearity of the Hammerstein channel, by two real-valued B-spline neural networks, one for modelling the nonlinear amplitude response of the HPA and the other for the nonlinear phase response of the HPA. We then develop an efficient alternating least squares algorithm for estimating the parameters of the Hammerstein channel, including the channel impulse response coefficients and the parameters of the two B-spline models. Moreover, we also use another real-valued B-spline neural network to model the inversion of the HPA’s nonlinear amplitude response, and the parameters of this inverting B-spline model can be estimated using the standard least squares algorithm based on the pseudo training data obtained as a byproduct of the Hammerstein channel identification. Equalisation of the SC Hammerstein channel can then be accomplished by the usual one-tap linear equalisation in frequency domain as well as the inverse Bspline neural network model obtained in time domain. The effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels is demonstrated in a simulation study.

A MATLAB GUI for learning controller design in the frequency domain

A MATLAB GUI is presented which is used to help students learn to design controllers in the frequency domain. It complements the author’s two previous GUIs for plotting and identification of systems in the frequency domain. It also incorporates the concept used in the “electronic calculator that makes students think” to assist learning. Positive student feedback affirms that the GUI has helped their understanding.

Boundary integral methods in high frequency scattering

In this article we review recent progress on the design, analysis and implementation of numerical-asymptotic boundary integral methods for the computation of frequency-domain acoustic scattering in a homogeneous unbounded medium by a bounded obstacle. The main aim of the methods is to allow computation of scattering at arbitrarily high frequency with finite computational resources.

The point source method for inverse scattering in the time domain

Many recent inverse scattering techniques have been designed for single frequency scattered fields in the frequency domain. In practice, however, the data is collected in the time domain. Frequency domain inverse scattering algorithms obviously apply to time-harmonic scattering, or nearly time-harmonic scattering, through application of the Fourier transform. Fourier transform techniques can also be applied to non-time-harmonic scattering from pulses. Our goal here is twofold: first, to establish conditions on the time-dependent waves that provide a correspondence between time domain and frequency domain inverse scattering via Fourier transforms without recourse to the conventional limiting amplitude principle; secondly, we apply the analysis in the first part of this work toward the extension of a particular scattering technique, namely the point source method, to scattering from the requisite pulses. Numerical examples illustrate the method and suggest that reconstructions from admissible pulses deliver superior reconstructions compared to straight averaging of multi-frequency data. Copyright (C) 2006 John Wiley & Sons, Ltd.

A comparison of two time-domain analysis procedures in the determination of VO2 kinetics by pseudorandom binary sequence exercise testing

The purpose of this study was to apply and compare two time-domain analysis procedures in the determination of oxygen uptake (VO2) kinetics in response to a pseudorandom binary sequence (PRBS) exercise test. PRBS exercise tests have typically been analysed in the frequency domain. However, the complex interpretation of frequency responses may have limited the application of this procedure in both sporting and clinical contexts, where a single time measurement would facilitate subject comparison. The relative potential of both a mean response time (MRT) and a peak cross-correlation time (PCCT) was investigated. This study was divided into two parts: a test-retest reliability study (part A), in which 10 healthy male subjects completed two identical PRBS exercise tests, and a comparison of the VO2 kinetics of 12 elite endurance runners (ER) and 12 elite sprinters (SR; part B). In part A, 95% limits of agreement were calculated for comparison between MRT and PCCT. The results of part A showed no significant difference between test and retest as assessed by MRT [mean (SD) 42.2 (4.2) s and 43.8 (6.9) s] or by PCCT [21.8 (3.7) s and 22.7 (4.5) s]. Measurement error (%) was lower for MRT in comparison with PCCT (16% and 25%, respectively). In part B of the study, the VO2 kinetics of ER were significantly faster than those of SR, as assessed by MRT [33.4 (3.4) s and 39.9 (7.1) s, respectively; P<0.01] and PCCT [20.9 (3.8) s and 24.8 (4.5) s; P < 0.05]. It is possible that either analysis procedure could provide a single test measurement Of VO2 kinetics; however, the greater reliability of the MRT data suggests that this method has more potential for development in the assessment Of VO2 kinetics by PRBS exercise testing.

A novel spectral representation of electromyographic signals

Time/frequency and temporal analyses have been widely used in biomedical signal processing. These methods represent important characteristics of a signal in both time and frequency domain. In this way, essential features of the signal can be viewed and analysed in order to understand or model the physiological system. Historically, Fourier spectral analyses have provided a general method for examining the global energy/frequency distributions. However, an assumption inherent to these methods is the stationarity of the signal. As a result, Fourier methods are not generally an appropriate approach in the investigation of signals with transient components. This work presents the application of a new signal processing technique, empirical mode decomposition and the Hilbert spectrum, in the analysis of electromyographic signals. The results show that this method may provide not only an increase in the spectral resolution but also an insight into the underlying process of the muscle contraction.

A time-domain probe method for three-dimensional rough surface reconstructions

The task of this paper is to develop a Time-Domain Probe Method for the reconstruction of impenetrable scatterers. The basic idea of the method is to use pulses in the time domain and the time-dependent response of the scatterer to reconstruct its location and shape. The method is based on the basic causality principle of timedependent scattering. The method is independent of the boundary condition and is applicable for limited aperture scattering data. In particular, we discuss the reconstruction of the shape of a rough surface in three dimensions from time-domain measurements of the scattered field. In practise, measurement data is collected where the incident field is given by a pulse. We formulate the time-domain fieeld reconstruction problem equivalently via frequency-domain integral equations or via a retarded boundary integral equation based on results of Bamberger, Ha-Duong, Lubich. In contrast to pure frequency domain methods here we use a time-domain characterization of the unknown shape for its reconstruction. Our paper will describe the Time-Domain Probe Method and relate it to previous frequency-domain approaches on sampling and probe methods by Colton, Kirsch, Ikehata, Potthast, Luke, Sylvester et al. The approach significantly extends recent work of Chandler-Wilde and Lines (2005) and Luke and Potthast (2006) on the timedomain point source method. We provide a complete convergence analysis for the method for the rough surface scattering case and provide numerical simulations and examples.

Cyclic prefixed OQAM-OFDM and its application to single-carrier FDMA

Single-carrier frequency division multiple access (SC-FDMA) has appeared to be a promising technique for high data rate uplink communications. Aimed at SC-FDMA applications, a cyclic prefixed version of the offset quadrature amplitude modulation based OFDM (OQAM-OFDM) is first proposed in this paper. We show that cyclic prefixed OQAMOFDM CP-OQAM-OFDM) can be realized within the framework of the standard OFDM system, and perfect recovery condition in the ideal channel is derived. We then apply CP-OQAMOFDM to SC-FDMA transmission in frequency selective fading channels. Signal model and joint widely linear minimum mean square error (WLMMSE) equalization using a prior information with low complexity are developed. Compared with the existing DFTS-OFDM based SC-FDMA, the proposed SC-FDMA can significantly reduce envelope fluctuation (EF) of the transmitted signal while maintaining the bandwidth efficiency. The inherent structure of CP-OQAM-OFDM enables low-complexity joint equalization in the frequency domain to combat both the multiple access interference and the intersymbol interference. The joint WLMMSE equalization using a prior information guarantees optimal MMSE performance and supports Turbo receiver for improved bit error rate (BER) performance. Simulation resultsconfirm the effectiveness of the proposed SC-FDMA in termsof EF (including peak-to-average power ratio, instantaneous-toaverage power ratio and cubic metric) and BER performances.

Multivariate analysis of the dielectric response of materials modeled using networks of resistors and capacitors

We discuss the modeling of dielectric responses of electromagnetically excited networks which are composed of a mixture of capacitors and resistors. Such networks can be employed as lumped-parameter circuits to model the response of composite materials containing conductive and insulating grains. The dynamics of the excited network systems are studied using a state space model derived from a randomized incidence matrix. Time and frequency domain responses from synthetic data sets generated from state space models are analyzed for the purpose of estimating the fraction of capacitors in the network. Good results were obtained by using either the time-domain response to a pulse excitation or impedance data at selected frequencies. A chemometric framework based on a Successive Projections Algorithm (SPA) enables the construction of multiple linear regression (MLR) models which can efficiently determine the ratio of conductive to insulating components in composite material samples. The proposed method avoids restrictions commonly associated with Archie’s law, the application of percolation theory or Kohlrausch-Williams-Watts models and is applicable to experimental results generated by either time domain transient spectrometers or continuous-wave instruments. Furthermore, it is quite generic and applicable to tomography, acoustics as well as other spectroscopies such as nuclear magnetic resonance, electron paramagnetic resonance and, therefore, should be of general interest across the dielectrics community.

Dual carrier modulation soft demapper

An Orthogonal Frequency Division Multiplexing (OFDM) communication system with a transmitter and a receiver. The transmitter is arranged to transmit channel estimation sequences on each of a plurality of band groups, or bands, and to transmit data on each of the band groups or bands. The receiver is arranged to receive the channel estimation sequences for each band group or band to calculate channel state information from each of the channel estimation sequences transmitted on that band group or band and to form an average channel state information. The receiver receives the transmitted data, transforms the received data into the frequency domain, equalizes the received data using the channel state information, demaps the equalized data to re-construct the received data as soft bits and modifies the soft bits using the averaged channel state information.

Mapping and controlling molecular processes: The application of control theory and system identification algorithms to ASOPS and other fast pulse spectroscopies

Asynchronous Optical Sampling (ASOPS) [1,2] and frequency comb spectrometry [3] based on dual Ti:saphire resonators operated in a master/slave mode have the potential to improve signal to noise ratio in THz transient and IR sperctrometry. The multimode Brownian oscillator time-domain response function described by state-space models is a mathematically robust framework that can be used to describe the dispersive phenomena governed by Lorentzian, Debye and Drude responses. In addition, the optical properties of an arbitrary medium can be expressed as a linear combination of simple multimode Brownian oscillator functions. The suitability of a range of signal processing schemes adopted from the Systems Identification and Control Theory community for further processing the recorded THz transients in the time or frequency domain will be outlined [4,5]. Since a femtosecond duration pulse is capable of persistent excitation of the medium within which it propagates, such approach is perfectly justifiable. Several de-noising routines based on system identification will be shown. Furthermore, specifically developed apodization structures will be discussed. These are necessary because due to dispersion issues, the time-domain background and sample interferograms are non-symmetrical [6-8]. These procedures can lead to a more precise estimation of the complex insertion loss function. The algorithms are applicable to femtosecond spectroscopies across the EM spectrum. Finally, a methodology for femtosecond pulse shaping using genetic algorithms aiming to map and control molecular relaxation processes will be mentioned.

High signal to noise ratio THz spectroscopy with ASOPS and signal processing schemes for mapping and controlling molecular and bulk relaxation processes

Asynchronous Optical Sampling has the potential to improve signal to noise ratio in THz transient sperctrometry. The design of an inexpensive control scheme for synchronising two femtosecond pulse frequency comb generators at an offset frequency of 20 kHz is discussed. The suitability of a range of signal processing schemes adopted from the Systems Identification and Control Theory community for further processing recorded THz transients in the time and frequency domain are outlined. Finally, possibilities for femtosecond pulse shaping using genetic algorithms are mentioned.

OTHR impulsive interference suppression in strong clutter background

External interferences can severely degrade the performance of an Over-the-horizon radar (OTHR), so suppression of external interferences in strong clutter environment is the prerequisite for the target detection. The traditional suppression solutions usually began with clutter suppression in either time or frequency domain, followed by the interference detection and suppression. Based on this traditional solution, this paper proposes a method characterized by joint clutter suppression and interference detection: by analyzing eigenvalues in a short-time moving window centered at different time position, Clutter is suppressed by discarding the maximum three eigenvalues at every time position and meanwhile detection is achieved by analyzing the remained eigenvalues at different position. Then, restoration is achieved by forward-backward linear prediction using interference-free data surrounding the interference position. In the numeric computation, the eigenvalue decomposition (EVD) is replaced by values decomposition (SVD) based on the equivalence of these two processing. Data processing and experimental results show its efficiency of noise floor falling down about 10-20 dB.

Switching on a two-dimensional time-harmonic scalar wave in the presence of a diffracting edge

This paper concerns the switching on of two-dimensional time-harmonic scalar waves. We first review the switch-on problem for a point source in free space, then proceed to analyse the analogous problem for the diffraction of a plane wave by a half-line (the ‘Sommerfeld problem’), determining in both cases the conditions under which the field is well-approximated by the solution of the corresponding frequency domain problem. In both cases the rate of convergence to the frequency domain solution is found to be dependent on the strength of the singularity on the leading wavefront. In the case of plane wave diffraction at grazing incidence the frequency domain solution is immediately attained along the shadow boundary after the arrival of the leading wavefront. The case of non-grazing incidence is also considered.