This thesis is aimed at analysis of sampled-data feedback systems. Our approach is in the frequency-domain, and stresses the study of sensitivity and complementary sensitivity operators. Frequency-domain methods have proven very successful in the analysis and design of linear time-invariant control systems, for which the importance and utility of sensitivity operators is well-recognized. The extension of these methods to sampled-data systems, however, is not straightforward, since they are inherently time-varying due to the intrinsic sample and hold operations. In this thesis we present a systematic frequency-domain framework to describe sampled-data systems considering full-time information. Using this framework, we develop a theory of design limitations for sampled-data systems. This theory allows us to quantify the essential constraints in design imposed by inherent open-loop characteristics of the analog plant. Our results show that: (i) sampled-data systems inherit the difficulty imposed upon analog feedback design by the plant's non-minimum phase zeros, unstable poles, and time-delays, independently of the type of hold used; (ii) sampled-data systems are subject to additional design limitations imposed by potential non-minimum phase zeros of the hold device; and (iii) sampled-data systems, unlike analog systems, are subject to limits upon the ability of high compensator gain to achieve disturbance rejection. As an application, we quantitatively analyze the sensitivity and robustness characteristics of digital control schemes that rely on the use of generalized sampled-data hold functions, whose frequency-response properties we describe in detail. In addition, we derive closed-form expressions to compute the L2-induced norms of the sampled-data sensitivity and complementary sensitivity operators. These expressions are important both in analysis and design, particularly when uncertainty in the model of the plant is considered. Our methods provide some interesting interpretations in terms of signal spaces, and admit straightforward implementation in a numerically reliable fashion. / PhD Doctorate

The thesis treats model reduction for linear time-varying systems. Time-varying models appear in many fields, including power systems, chemical engineering, aeronautics, and computational science. They can also be used for approximation of time-invariant nonlinear models. Model reduction is a topic that deals with simplification of complex models. This is important since it facilitates analysis and synthesis of controllers. The thesis consists of two parts. The first part provides an introduction to the topics of time-varying systems and model reduction. Here, notation, standard results, examples, and some results from the second part of the thesis are presented. The second part of the thesis consists of four papers. In the first paper, we study the balanced truncation method for linear time-varying state-space models. We derive error bounds for the simplified models. These bounds are generalizations of well-known time-invariant results, derived with other methods. In the second paper, we apply balanced truncation to a high-order model of a diesel exhaust catalyst. Furthermore, we discuss practical issues of balanced truncation and approximative discretization. In the third paper, we look at frequency-domain analysis of linear time-periodic impulse-response models. By decomposing the models into Taylor and Fourier series, we can analyze convergence properties of different truncated representations. In the fourth paper, we use the frequency-domain representation developed in the third paper, the harmonic transfer function, to generalize Bode's sensitivity integral. This result quantifies limitations for feedback control of linear time-periodic systems. / QC 20120206

The problem of information-theoretic optimal resource allocation for the synchronous single-cell CDMA Gaussian multiple access channel is investigated. Several different cases are analyzed including: optimal sequence allocation without power control, optimal sequence allocation with optimal power control and optimal sequence allocation without power control with equal single user capacities. In order to simplify the mathematical description of the multiple access capacity region, a Cholesky decomposition characterization is introduced and utilized to find the optimal sequence allocation for equal single user capacities. The case of randomly chosen spreading sequences in a large system model, i.e. when number of users and processing gain increase without bounds while maintaining their ratio fixed, is also analyzed. Using this model, the performance of a conventional decision feedback receiver in flat fading channels is analyzed. A sequence allocation scheme that uses two sets of orthogonal users that can be decoded with a very simple decision feedback receiver is analyzed. It is shown that the spectral efficiency of this scheme is very close to the maximal possible. Finally, the issue of imperfect channel state information available at the receiver is discussed and the spectral efficiency loss compared to the perfect channel state information case is evaluated for the optimal multiuser receiver. / Graduate

Next generation of wireless communication mostly relies on multiple-input multipleoutput (MIMO) configuration and full-duplex relaying to improve data-rates, spectrale efficiency, spatial-multiplexing, quality-of-service and energy-efficiency etc. However, multiple radio frequency (RF) transceivers in MIMO system and multi-hops in relay networks, accumulate transceiver impairments, rendering an unacceptable system performance. Majority of the technical contributions either assume ideal hardware or inappropriately model hardware impairments which often induce misleading results especially for high data-rate communication systems. We propose statistical mathematical modeling of various hardware impairment (HWI) to characterize their deteriorating effects on the information signal. In addition, we model the aggregate HWI as improper Gaussian signaling (IGS), to fully characterize their asymmetric properties and the self-interfering signal attribute under I/Q imbalance. The proposed model encourages to adopt asymmetric transmission scheme, as opposed to traditional symmetric signaling. First, we present statistical baseband equivalent mathematical models for general MIMO system and two special scenarios of receive and transmit diversity systems under HWI. Then, we express their achievable rate under PGS and IGS transmit schemes. Moreover, we tune the IGS statistical characteristics to maximize the achievable rate. We also present optimal beam-forming/pre-coding and receive combiner vector for multiple-input single-output (MISO) and single-input multiple output (SIMO) systems, which lead to SDNR maximization. Moreover, we propose an adaptive scheme to switch between maximal IGS (MIGS) and PGS transmission based on the described conditions to reduce computational overhead. Subsequently, two case studies are presented. 1) Outage analysis has been carried out for SIMO, under transceiver distortion noise, for two diversity combining schemes 2) The benefits of employing IGS is investigated in full duplex relaying (FDR) suffering from two types of interference, the residual self-interference (RSI) and I/Q distortions. We further optimize the pseudo-variance to compensate the interference impact and improve end-to-end achievable rate. Finally, we validate the analytic expressions through simulation results, to quantify the performance degradation in the absence of ideal transceivers and the gain reaped from adopting IGS scheme compared with PGS scheme.

No description available.

No description available.