Transceiver designs and analysis for LTI, LTV and broadcast channels - new matrix decompositions and majorization theory

Signal processing techniques play important roles in the design of digital communication systems. These include information manipulation, transmitter signal processing, channel estimation, channel equalization and receiver signal processing. By interacting with communication theory and system implementing technologies, signal processing specialists develop efficient schemes for various communication problems by wisely exploiting various mathematical tools such as analysis, probability theory, matrix theory, optimization theory, and many others. In recent years, researchers realized that multiple-input multiple-output (MIMO) channel models are applicable to a wide range of different physical communications channels. Using the elegant matrix-vector notations, many MIMO transceiver (including the precoder and equalizer) design problems can be solved by matrix and optimization theory. Furthermore, the researchers showed that the majorization theory and matrix decompositions, such as singular value decomposition (SVD), geometric mean decomposition (GMD) and generalized triangular decomposition (GTD), provide unified frameworks for solving many of the point-to-point MIMO transceiver design problems.

In this thesis, we consider the transceiver design problems for linear time invariant (LTI) flat MIMO channels, linear time-varying narrowband MIMO channels, flat MIMO broadcast channels, and doubly selective scalar channels. Additionally, the channel estimation problem is also considered. The main contributions of this dissertation are the development of new matrix decompositions, and the uses of the matrix decompositions and majorization theory toward the practical transmit-receive scheme designs for transceiver optimization problems. Elegant solutions are obtained, novel transceiver structures are developed, ingenious algorithms are proposed, and performance analyses are derived.

The first part of the thesis focuses on transceiver design with LTI flat MIMO channels. We propose a novel matrix decomposition which decomposes a complex matrix as a product of several sets of semi-unitary matrices and upper triangular matrices in an iterative manner. The complexity of the new decomposition, generalized geometric mean decomposition (GGMD), is always less than or equal to that of geometric mean decomposition (GMD). The optimal GGMD parameters which yield the minimal complexity are derived. Based on the channel state information (CSI) at both the transmitter (CSIT) and receiver (CSIR), GGMD is used to design a butterfly structured decision feedback equalizer (DFE) MIMO transceiver which achieves the minimum average mean square error (MSE) under the total transmit power constraint. A novel iterative receiving detection algorithm for the specific receiver is also proposed. For the application to cyclic prefix (CP) systems in which the SVD of the equivalent channel matrix can be easily computed, the proposed GGMD transceiver has K/log_2(K) times complexity advantage over the GMD transceiver, where K is the number of data symbols per data block and is a power of 2. The performance analysis shows that the GGMD DFE transceiver can convert a MIMO channel into a set of parallel subchannels with the same bias and signal to interference plus noise ratios (SINRs). Hence, the average bit rate error (BER) is automatically minimized without the need for bit allocation. Moreover, the proposed transceiver can achieve the channel capacity simply by applying independent scalar Gaussian codes of the same rate at subchannels.

In the second part of the thesis, we focus on MIMO transceiver design for slowly time-varying MIMO channels with zero-forcing or MMSE criterion. Even though the GGMD/GMD DFE transceivers work for slowly time-varying MIMO channels by exploiting the instantaneous CSI at both ends, their performance is by no means optimal since the temporal diversity of the time-varying channels is not exploited. Based on the GTD, we develop space-time GTD (ST-GTD) for the decomposition of linear time-varying flat MIMO channels. Under the assumption that CSIT, CSIR and channel prediction are available, by using the proposed ST-GTD, we develop space-time geometric mean decomposition (ST-GMD) DFE transceivers under the zero-forcing or MMSE criterion. Under perfect channel prediction, the new system minimizes both the average MSE at the detector in each space-time (ST) block (which consists of several coherence blocks), and the average per ST-block BER in the moderate high SNR region. Moreover, the ST-GMD DFE transceiver designed under an MMSE criterion maximizes Gaussian mutual information over the equivalent channel seen by each ST-block. In general, the newly proposed transceivers perform better than the GGMD-based systems since the super-imposed temporal precoder is able to exploit the temporal diversity of time-varying channels. For practical applications, a novel ST-GTD based system which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD DFE transceiver is also proposed.

The third part of the thesis considers two quality of service (QoS) transceiver design problems for flat MIMO broadcast channels. The first one is the power minimization problem (min-power) with a total bitrate constraint and per-stream BER constraints. The second problem is the rate maximization problem (max-rate) with a total transmit power constraint and per-stream BER constraints. Exploiting a particular class of joint triangularization (JT), we are able to jointly optimize the bit allocation and the broadcast DFE transceiver for the min-power and max-rate problems. The resulting optimal designs are called the minimum power JT broadcast DFE transceiver (MPJT) and maximum rate JT broadcast DFE transceiver (MRJT), respectively. In addition to the optimal designs, two suboptimal designs based on QR decomposition are proposed. They are realizable for arbitrary number of users.

Finally, we investigate the design of a discrete Fourier transform (DFT) modulated filterbank transceiver (DFT-FBT) with LTV scalar channels. For both cases with known LTV channels and unknown wide sense stationary uncorrelated scattering (WSSUS) statistical channels, we show how to optimize the transmitting and receiving prototypes of a DFT-FBT such that the SINR at the receiver is maximized. Also, a novel pilot-aided subspace channel estimation algorithm is proposed for the orthogonal frequency division multiplexing (OFDM) systems with quasi-stationary multi-path Rayleigh fading channels. Using the concept of a difference co-array, the new technique can construct M^2 co-pilots from M physical pilot tones with alternating pilot placement. Subspace methods, such as MUSIC and ESPRIT, can be used to estimate the multipath delays and the number of identifiable paths is up to O(M^2), theoretically. With the delay information, a MMSE estimator for frequency response is derived. It is shown through simulations that the proposed method outperforms the conventional subspace channel estimator when the number of multipaths is greater than or equal to the number of physical pilots minus one.

Fiber laser processing of amorphous rare earth NeFeB magnetic materials

Since the exchange coupling theory was proposed by Kneller and Hawig in 1991 there has been a significant effort within the magnetic materials community to enhance the performance of rare earth magnets by utilising nano-composite meta-materials. Inclusions of magnetically soft iron smaller than approximately 10 nm in diameter are exchange coupled to a surrounding magnetically hard Nd2Fe14B matrix and provide an enhanced saturisation magnetisation without reducing coercivity. For such a fine nanostructure to be produced, close control over the thermal history of the material is needed. A processing route which provides this is laser annealing from an amorphous alloy precursor. In the current work, relationships between laser parameters, thermal histories of laser processed amorphous stoichiometric NdFeB ribbons and the magnetic properties of the resulting nanocrystalline products have been determined with a view to applying the process to thick film nanocomposite magnet production.

Confidence in beliefs about pain predicts expectancy effects on pain perception and anticipatory processing in right anterior insula.

Psychological factors play a major role in exacerbating chronic pain. Effective self-management of pain is often hindered by inaccurate beliefs about the nature of pain which lead to a high degree of emotional reactivity. Probabilistic models of perception state that greater confidence (certainty) in beliefs increases their influence on perception and behavior. In this study, we treat confidence as a metacognitive process dissociable from the content of belief. We hypothesized that confidence is associated with anticipatory activation of areas of the pain matrix involved with top-down modulation of pain. Healthy volunteers rated their beliefs about the emotional distress that experimental pain would cause, and separately rated their level of confidence in this belief. Confidence predicted the influence of anticipation cues on experienced pain. We measured brain activity during anticipation of pain using high-density EEG and used electromagnetic tomography to determine neural substrates of this effect. Confidence correlated with activity in right anterior insula, posterior midcingulate and inferior parietal cortices during the anticipation of pain. Activity in the right anterior insula predicted a greater influence of anticipation cues on pain perception, whereas activity in right inferior parietal cortex predicted a decreased influence of anticipatory cues. The results support probabilistic models of pain perception and suggest that confidence in beliefs is an important determinant of expectancy effects on pain perception.

Fine structure of the plasmon resonance absorption peak of Ag nanoparticles embedded in partially oxidized Si matrix

Ag/Si nanocomposite films were prepared by the radio-frequency magnetron cosputtering method. The fine structure of the plasmon resonance absorption peak was found in film samples. X-ray photoelectron spectroscopy analysis indicated that the samples were composed of a two-layer structure, which accounted for the structure of the optical absorption spectra. The peak located near 445 nm is the plasmon resonance absorption peak of Ag nanoparticles embedded in a partially oxidized Si matrix. Its intensity decreases with decreasing film thickness and disappears in a very thin sample. The peak located near 380 nm originates from the plasmon resonance absorption of the thoroughly oxidized surface layer of the sample. Its intensity does not change with increasing thickness, but it cannot be observed in the very thick sample. (C) 2001 American Institute of Physics.

Optical image processing using the photoinduced anisotropy of pyrrylfulgide

A synthesized photochromic compound-pyrrylfulgide-is prepared as a thin film doped in a polymethylmethacrylate (PMMA) matrix. Under irradiation by UV light, the film converts from the bleached state into a colored state that has a maximum absorption at 635 nm and is thermally stable at room temperature. When the colored state is irradiated by a linearly polarized 650 nm laser, the film returns to the bleached state; photoinduced anisotropy is produced during this process. Application of optical image processing methods using the photoinduced anisotropy of the pyrrylfulgide/PMMA film is described. Examples in non-Fourier optical image processing, such as contrast reversal and image subtraction and summation, as well as in Fourier optical image processing, such as low-pass filtering and edge enhancement, are presented. (c) 2006 Optical Society of America.

Raman scattering and infrared absorption of silicon nanocrystals in silicon oxide matrix

Structural dependence on annealing of a-SiOx:H was studied by using infrared absorption and Raman scattering. The appearance of Raman peaks in the range of 513-519cm(-1) after 1170 degreesC annealing was interpreted as the formation nanocrystalline silicon with the sizes from 3-10nm. The Raman spectra also show the existence of amorphous-like silicon phase, which is associated with Si-Si bond re-construction at boundaries of silicon nanocrystallites. The presence of the shoulder at 980cm(-1) of Si-O-Si stretching vibration at 1085cm(-1) in infrared spectra imply that except that SiO2 phase, there is silicon sub-oxide phase in the films annealed at 1170 degreesC. This sub-oxide phase is located at the interface between Si crystallites and SiO2, and thus support the shell model for the mixed structures of Si grains and SiO2 matrix.

Spectroscopic Study on Water Diffusion in Poly(ester urethane) Block Copolymer Matrix

The diffusion of water in a phase-separated biodegradable poly(ester urethane) shape-memory polymer with poly(E-caprolactone) (PCL) as the soft segment was investigated using time-resolved FTIR-ATR. On the basis of the band fitting and water ordering in drawn films, the broad water band in the 3800-2800 cm(-1) region was decomposed into four bands located at 3620, 3510, 3400, and 3260 cm(-1), and the first two components at 3620 and 35 10 cm(-1) were assigned to the vibrations of antisymmetric and symmetric stretching of water hydrogen bonded with the C=O group of the soft segment. The other two were associated with water bonded to the urethane hard segments in the forms of N-H:O-H:O=C bridge hydrogen bond and double hydrogen bonds with two C=O groups, respectively. Furthermore, band fitting and two-dimensional correlation analyses revealed that in the diffusion process, water first diffuses into the continuous soft-rich PCL phase and then into the hard-rich urethane domains, forming double hydrogen bonds with two C=O groups prior to the bridge hydrogen bond in the form of N-H:O-H:O=C.

Stress transfer and damage evolution simulations of fiber-reinforced polymer-matrix composites

The stress transfer from broken fibers to unbroken fibers in fiber-reinforced thermosetting polymer-matrix composites and thermoplastic polymer-matrix composites was studied using a detailed finite element model. In order to check the validity of this approach, an epoxy-matrix monolayer composite was used as thermosetting polymer-matrix composite and a polypropylene (PP)-matrix monolayer composite was used as thermoplastic polymer-matrix composite, respectively. It is found that the stress concentrations near the broken fiber element cause damage to the neighboring epoxy matrix prior to the breakage of other fibers, whereas in the case of PP-matrix composites the fibers nearest to the broken fiber break prior to the PP matrix damage, because the PP matrix around the broken fiber element yields. In order to simulate composite damage evolution, a Monte Carlo technique based on a finite element method has been developed in the paper. The finite element code coupled with statistical model of fiber strength specifically written for this problem was used to determine the stress redistribution. Five hundred samples of numerical simulation were carried out to obtain statistical deformation and failure process of composites with fixed fiber volume fraction.

Cure processing modeling and cure cycle simulation of epoxy-terminated poly(phenylene ether ketone) .4. Cure cycle simulation

Epoxy-terminated poly(phenylene ether ketone) (E-PEK) developed in this Institute is a candidate matrix resin for polymer composites as structural materials. Cure cycles for this reaction system were simulated according to the previously established processing model. It is found that for the E-PEK system, the curing process is best completed by a stepwise cure cycle comprising two isothermal processes at different temperatures, T-1 and T-2. The cure cycles over a wide range of processing parameters simulated, based on the established processing model, indicate that the processing window is width-adjustable. Analysis of the mechanical properties of the composite sheets showed that the simulated cure cycles are acceptable and reliable. (C) 1997 John Wiley & Sons, Inc.

Liquid crystalline polymer as a processing agent in blends of poly(ether-ketone)/LCP70

Blends of a liquid crystalline thermotropic copolyester (LCP70) and an amorphous phenolphthalein based poly(ether-ketone)(PEK-C) with two viscosities were prepared by melt blending. The blends' morphology, rheological and mechanical properties were investigated by DSC, SEM, mechanical and rheological tests. It was observed that the optimum composition of the PEK-C/LCP70 blend was 10 wt% LCP for both mechanical and rheological properties. When the LCP content was less than 10%, the LCP phase existed as finely dispersed fibrous domains with a diameter of about 1 mu m in the matrix, and both tensile and flexural properties were improved. In contrast, when the LCP content reached 20% or more, the LCP domains coalesced to ellipsoidal particles with a diameter of about 5 mu m, and the mechanical properties decreased as a result. It is demonstrated that pure PEK-C with a high viscosity which was difficult to process by melt extrusion, could be extruded conveniently when 10% LCP70 was incorporated. It is emphasized that LCP not only can be used as a reinforcing phase but also an effective processing agent for engineering thermoplastics, especially for those with high viscosity and narrow processing window. (C) 1997 Elsevier Science Ltd.

A new inversion procedure for confocal scanning microscopy and other bandlimited signal processing problems

We find a simple analytic expression for the inverse of an infinite matrix related to the problem of data reduction in confocal scanning microscopy and other band-limited signal processing problems. Potential applications of this result to practical problems are outlined. The matrix arises from a sampling expansion approach to the integral equation.

HBrowse: a GRACE tool for browsing R-matrix H-files

An H-file is used to convey information from the inner-region to the outer-region in R-matrix computations. HBrowse is a workstation tool for displaying a graphical abstraction of a local or remote R-matrix H-file. While it is published as a stand-alone tool for post-processing the output from R-matrix inner-region computations it also forms part of the Graphical R-matrix Atomic Collision Environment (GRACE), HBrowse is written in C and OSF/Motif for the UNIX operating system. (C) 2000 Elsevier Science B.V. All rights reserved.