State-space model identification of a wireless THz network

We model the large scale fading of wireless THz communications links deployed in a metropolitan area taking into account reception through direct line of sight, ground or wall reflection and diffraction. The movement of the receiver in the three dimensions is modelled by an autonomous dynamic linear system in state-space whereas the geometric relations involved in the attenuation and multi-path propagation of the electric field are described by a static non-linear mapping. A subspace algorithm in conjunction with polynomial regression is used to identify a Wiener model from time-domain measurements of the field intensity.

Classification of lactose and mandelic acid THz spectra using subspace and wavelet-packet algorithms

This work compares classification results of lactose, mandelic acid and dl-mandelic acid, obtained on the basis of their respective THz transients. The performance of three different pre-processing algorithms applied to the time-domain signatures obtained using a THz-transient spectrometer are contrasted by evaluating the classifier performance. A range of amplitudes of zero-mean white Gaussian noise are used to artificially degrade the signal-to-noise ratio of the time-domain signatures to generate the data sets that are presented to the classifier for both learning and validation purposes. This gradual degradation of interferograms by increasing the noise level is equivalent to performing measurements assuming a reduced integration time. Three signal processing algorithms were adopted for the evaluation of the complex insertion loss function of the samples under study; a) standard evaluation by ratioing the sample with the background spectra, b) a subspace identification algorithm and c) a novel wavelet-packet identification procedure. Within class and between class dispersion metrics are adopted for the three data sets. A discrimination metric evaluates how well the three classes can be distinguished within the frequency range 0. 1 - 1.0 THz using the above algorithms.

Subspace system identification framework for the analysis of multimoded propagation of THz-transient signals

We provide a system identification framework for the analysis of THz-transient data. The subspace identification algorithm for both deterministic and stochastic systems is used to model the time-domain responses of structures under broadband excitation. Structures with additional time delays can be modelled within the state-space framework using additional state variables. We compare the numerical stability of the commonly used least-squares ARX models to that of the subspace N4SID algorithm by using examples of fourth-order and eighth-order systems under pulse and chirp excitation conditions. These models correspond to structures having two and four modes simultaneously propagating respectively. We show that chirp excitation combined with the subspace identification algorithm can provide a better identification of the underlying mode dynamics than the ARX model does as the complexity of the system increases. The use of an identified state-space model for mode demixing, upon transformation to a decoupled realization form is illustrated. Applications of state-space models and the N4SID algorithm to THz transient spectroscopy as well as to optical systems are highlighted.

Wiener-System subspace identification for mobile wireless mm-wave networks

We discuss the feasibility of wireless terahertz communications links deployed in a metropolitan area and model the large-scale fading of such channels. The model takes into account reception through direct line of sight, ground and wall reflection, as well as diffraction around a corner. The movement of the receiver is modeled by an autonomous dynamic linear system in state space, whereas the geometric relations involved in the attenuation and multipath propagation of the electric field are described by a static nonlinear mapping. A subspace algorithm in conjunction with polynomial regression is used to identify a single-output Wiener model from time-domain measurements of the field intensity when the receiver motion is simulated using a constant angular speed and an exponentially decaying radius. The identification procedure is validated by using the model to perform q-step ahead predictions. The sensitivity of the algorithm to small-scale fading, detector noise, and atmospheric changes are discussed. The performance of the algorithm is tested in the diffraction zone assuming a range of emitter frequencies (2, 38, 60, 100, 140, and 400 GHz). Extensions of the simulation results to situations where a more complicated trajectory describes the motion of the receiver are also implemented, providing information on the performance of the algorithm under a worst case scenario. Finally, a sensitivity analysis to model parameters for the identified Wiener system is proposed.

Optimization of apodization functions in terahertz transient spectrometry

A quadratic programming optimization procedure for designing asymmetric apodization windows tailored to the shape of time-domain sample waveforms recorded using a terahertz transient spectrometer is proposed. By artificially degrading the waveforms, the performance of the designed window in both the time and the frequency domains is compared with that of conventional rectangular, triangular (Mertz), and Hamming windows. Examples of window optimization assuming Gaussian functions as the building elements of the apodization window are provided. The formulation is sufficiently general to accommodate other basis functions. (C) 2007 Optical Society of America

MIMO Wiener model identification for large scale fading of wireless mobile communications links

The large scale fading of wireless mobile communications links is modelled assuming the mobile receiver motion is described by a dynamic linear system in state-space. The geometric relations involved in the attenuation and multi-path propagation of the electric field are described by a static non-linear mapping. A Wiener system subspace identification algorithm in conjunction with polynomial regression is used to identify a model from time-domain estimates of the field intensity assuming a multitude of emitters and an antenna array at the receiver end.

Comparison of subspace and ARX models of a waveguide's terahertz transient response after optimal wavelet filtering

A quasi-optical deembedding technique for characterizing waveguides is demonstrated using wide-band time-resolved terahertz spectroscopy. A transfer function representation is adopted for the description of the signal in the input and output port of the waveguides. The time-domain responses were discretized and the waveguide transfer function was obtained through a parametric approach in the z-domain after describing the system with an AutoRegressive with eXogenous input (ARX), as well as with a state-space model. Prior to the identification procedure, filtering was performed in the wavelet domain to minimize both signal distortion, as well as the noise propagating in the ARX and subspace models. The optimal filtering procedure used in the wavelet domain for the recorded time-domain signatures is described in detail. The effect of filtering prior to the identification procedures is elucidated with the aid of pole-zero diagrams. Models derived from measurements of terahertz transients in a precision WR-8 waveguide adjustable short are presented.

Measurement of propagation constant in waveguides with wideband coherent terahertz spectroscopy

A quasi-optical technique for characterizing micromachined waveguides is demonstrated with wideband time-resolved terahertz spectroscopy. A transfer-function representation is adopted for the description of the relation between the signals in the input and output port of the waveguides. The time-domain responses were discretized, and the waveguide transfer function was obtained through a parametric approach in the z domain after describing the system with an autoregressive with exogenous input model. The a priori assumption of the number of modes propagating in the structure was inferred from comparisons of the theoretical with the measured characteristic impedance as well as with parsimony arguments. Measurements for a precision WR-8 waveguide-adjustable short as well as for G-band reduced-height micromachined waveguides are presented. (C) 2003 Optical Society of America.

Heterosite effects in novel heteronuclear clusters [OS2Ru(CO)(11)(PPh3)] and Os2Ru(CO)(10)(2-acetylpyridine-N-isopropylimine)]

A new synthetic route towards the mixed-metal cluster [OS2Ru(CO)(12)] is described together with the syntheses of its PPh3 and iPr-AcPy (iPr-AcPy = 2-acetylpyridine-N-isopropylimine) derivatives. The molecular structures of the novel clusters [Os2Ru(CO)(11)(PPh3)] and [Os2Ru(CO)(10)(iPr-AcPy)] were determined on the basis of crystalline solid solutions of the Os2Ru and corresponding Os-3 species. The structures reveal that coordination of the Lewis bases occurs exclusively at the ruthenium site of [Os2Ru(CO)(12)], which is in agreement with density functional theory (DFT) calculations on several structural isomers of these compounds. According to the time-dependent DFT results, the lowest optically accessible excited state of [Os2Ru(CO)(10)(iPr-AcPy)] has a prevailing sigma(Ru-Os-2)pi*(iPr-AcPy) character, with a partial sigma sigma*(Ru-Os-2) contribution. In weakly coordinating 2-chlorobutane, the excited state has a lifetime tau = 10.4 +/- 1.2 ps and produces biradicals considerably faster than observed for [Os-3(CO)10(iPr-AcPy) (tau = 25.3 +/- 0.7ps)]. In coordinating acetonitrile, the excited state of [Os2Ru(CO)(10)(iPr-AcPy)] decays mono-exponentially with a lifetime tau = 2.1 +/- 0.2 ps. In contrast to [Os-3(CO)(10)(iPr-AcPy)] that forms biradicals as the main primary photoproduct even in strongly coordinating solvents, zwitterion formation from the solvated lowest excited state is observed for the heterometallic cluster. This is concluded from time-resolved absorption studies in the microsecond time domain. Due to the lower tendency of the coordinatively unsaturated Ru+(CO)(2)(iPr-AcPy-/0) moiety to bind a Lewis base, the heteronuclear biradical and zwitterionic photoproducts live significantly shorter than their triosmium counterparts. The influence of the weaker Os-2-Ru(iPr-AcPy) bond on the redox reactivity is clearly reflected in very reactive radical anions formed upon electrochemical reduction of [Os2Ru(CO)(10)(iPr-AcPy)]. The dimer [-OS(CO)(4)-Os(CO)(4)-Ru(CO)(2)(iPr-AcPy)](2)(2-) is the only IR-detectable intermediate reduction product. The dinuclear complex [Os-2(CO)(8)](2-) and insoluble [Ru(CO)(2)(iPr-AcPy)](n), are the ultimate reduction products, proving fragmentation of the OS2Ru core.

Relationship between åström control and the kalman linear regulator — Caines revisited

The relationship between minimum variance and minimum expected quadratic loss feedback controllers for linear univariate discrete-time stochastic systems is reviewed by taking the approach used by Caines. It is shown how the two methods can be regarded as providing identical control actions as long as a noise-free measurement state-space model is employed.

Optimal observers for ARMA models

A polynomial-based ARMA model, when posed in a state-space framework can be regarded in many different ways. In this paper two particular state-space forms of the ARMA model are considered, and although both are canonical in structure they differ in respect of the mode in which disturbances are fed into the state and output equations. For both forms a solution is found to the optimal discrete-time observer problem and algebraic connections between the two optimal observers are shown. The purpose of the paper is to highlight the fact that the optimal observer obtained from the first state-space form, commonly known as the innovations form, is not that employed in an optimal controller, in the minimum-output variance sense, whereas the optimal observer obtained from the second form is. Hence the second form is a much more appropriate state-space description to use for controller design, particularly when employed in self-tuning control schemes.

Adaptive deadbeat control of stochastic systems

This paper considers the use of a discrete-time deadbeat control action on systems affected by noise. Variations on the standard controller form are discussed and comparisons are made with controllers in which noise rejection is a higher priority objective. Both load and random disturbances are considered in the system description, although the aim of the deadbeat design remains as a tailoring of reference input variations. Finally, the use of such a deadbeat action within a self-tuning control framework is shown to satisfy, under certain conditions, the self-tuning property, generally though only when an extended form of least-squares estimation is incorporated.

Auto-weighted minimum-variance self-tuning controller

A self-tuning controller which automatically assigns weightings to control and set-point following is introduced. This discrete-time single-input single-output controller is based on a generalized minimum-variance control strategy. The automatic on-line selection of weightings is very convenient, especially when the system parameters are unknown or slowly varying with respect to time, which is generally considered to be the type of systems for which self-tuning control is useful. This feature also enables the controller to overcome difficulties with non-minimum phase systems.

Weighted input predictive controller

A discrete-time algorithm is presented which is based on a predictive control scheme in the form of dynamic matrix control. A set of control inputs are calculated and made available at each time instant, the actual input applied being a weighted summation of the inputs within the set. The algorithm is directly applicable in a self-tuning format and is therefore suitable for slowly time-varying systems in a noisy environment.

Neural networks for linear control: an analysis

This paper considers the use of radial basis function and multi-layer perceptron networks for linear or linearizable, adaptive feedback control schemes in a discrete-time environment. A close look is taken at the model structure selected and the extent of the resulting parameterization. A comparison is made with standard, nonneural network algorithms, e.g. self-tuning control.