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.

Algorithmic challenges in green data centers

With data centers being the supporting infrastructure for a wide range of IT services, their efficiency has become a big concern to operators, as well as to society, for both economic and environmental reasons. The goal of this thesis is to design energy-efficient algorithms that reduce energy cost while minimizing compromise to service. We focus on the algorithmic challenges at different levels of energy optimization across the data center stack. The algorithmic challenge at the device level is to improve the energy efficiency of a single computational device via techniques such as job scheduling and speed scaling. We analyze the common speed scaling algorithms in both the worst-case model and stochastic model to answer some fundamental issues in the design of speed scaling algorithms. The algorithmic challenge at the local data center level is to dynamically allocate resources (e.g., servers) and to dispatch the workload in a data center. We develop an online algorithm to make a data center more power-proportional by dynamically adapting the number of active servers. The algorithmic challenge at the global data center level is to dispatch the workload across multiple data centers, considering the geographical diversity of electricity price, availability of renewable energy, and network propagation delay. We propose algorithms to jointly optimize routing and provisioning in an online manner. Motivated by the above online decision problems, we move on to study a general class of online problem named "smoothed online convex optimization", which seeks to minimize the sum of a sequence of convex functions when "smooth" solutions are preferred. This model allows us to bridge different research communities and help us get a more fundamental understanding of general online decision problems.

Synthesis and biological activity of anticoagulant heparan sulfate glycopolymers

Heparin has been used as an anticoagulant drug for more than 70 years. The global distribution of contaminated heparin in 2007, which resulted in adverse clinical effects and over 100 deaths, emphasizes the necessity for safer alternatives to animal-sourced heparin. The structural complexity and heterogeneity of animal-sourced heparin not only impedes safe access to these biologically active molecules, but also hinders investigations on the significance of structural constituents at a molecular level. Efficient methods for preparing new synthetic heparins with targeted biological activity are necessary not only to ensure clinical safety, but to optimize derivative design to minimize potential side effects. Low molecular weight heparins have become a reliable alternative to heparin, due to their predictable dosages, long half-lives, and reduced side effects. However, heparin oligosaccharide synthesis is a challenging endeavor due to the necessity for complex protecting group manipulation and stereoselective glycosidic linkage chemistry, which often result in lengthy synthetic routes and low yields. Recently, chemoenzymatic syntheses have produced targeted ultralow molecular weight heparins with high-efficiency, but continue to be restricted by the substrate specificities of enzymes.

To address the need for access to homogeneous, complex glycosaminoglycan structures, we have synthesized novel heparan sulfate glycopolymers with well-defined carbohydrate structures and tunable chain length through ring-opening metathesis polymerization chemistry. These polymers recapitulate the key features of anticoagulant heparan sulfate by displaying the sulfation pattern responsible for heparin’s anticoagulant activity. The use of polymerization chemistry greatly simplifies the synthesis of complex glycosaminoglycan structures, providing a facile method to generate homogeneous macromolecules with tunable biological and chemical properties. Through the use of in vitro chromogenic substrate assays and ex vivo clotting assays, we found that the HS glycopolymers exhibited anticoagulant activity in a sulfation pattern and length-dependent manner. Compared to heparin standards, our short polymers did not display any activity. However, our longer polymers were able to incorporate in vitro and ex vivo characteristics of both low-molecular-weight heparin derivatives and heparin, displaying hybrid anticoagulant properties. These studies emphasize the significance of sulfation pattern specificity in specific carbohydrate-protein interactions, and demonstrate the effectiveness of multivalent molecules in recapitulating the activity of natural polysaccharides.

Structure, chemistry, and energetics of organic and inorganic adsorbates on Ga-rich GaAs and GaP(001) surfaces

The work described in this dissertation includes fundamental investigations into three surface processes, namely inorganic film growth, water-induced oxidation, and organic functionalization/passivation, on the GaP and GaAs(001) surfaces. The techniques used to carry out this work include scanning tunneling microscopy (STM), X-ray photoelectron spectroscopy (XPS), and density functional theory (DFT) calculations. Atomic structure, electronic structure, reaction mechanisms, and energetics related to these surface processes are discussed at atomic or molecular levels.

First, we investigate epitaxial Zn₃P₂ films grown on the Ga-rich GaAs(001)(6×6) surface. The film growth mechanism, electronic properties, and atomic structure of the Zn₃P₂/GaAs(001) system are discussed based on experimental and theoretical observations. We discover that a P-rich amorphous layer covers the crystalline Zn3P2 film during and after growth. We also propose more accurate picture of the GaP interfacial layer between Zn₃P₂ and GaAs, based on the atomic structure, chemical bonding, band diagram, and P-replacement energetics, than was previously anticipated.

Second, DFT calculations are carried out in order to understand water-induced oxidation mechanisms on the Ga-rich GaP(001)(2×4) surface. Structural and energetic information of every step in the gaseous water-induced GaP oxidation reactions are elucidated at the atomic level in great detail. We explore all reasonable ground states involved in most of the possible adsorption and decomposition pathways. We also investigate structures and energies of the transition states in the first hydrogen dissociation of a water molecule on the (2×4) surface.

Finally, adsorption structures and thermal decomposition reactions of 1-propanethiol on the Ga-rich GaP(001)(2×4) surface are investigated using high resolution STM, XPS, and DFT simulations. We elucidate adsorption locations and their associated atomic structures of a single 1-propanethiol molecule on the (2×4) surface as a function of annealing temperature. DFT calculations are carried out to optimize ground state structures and search transition states. XPS is used to investigate variations of the chemical bonding nature and coverage of the adsorbate species.

Development of protein-catalyzed capture (PCC) agents with application to the specific targeting of the E17K Point mutation of Akt1

This thesis describes the expansion and improvement of the iterative in situ click chemistry OBOC peptide library screening technology. Previous work provided a proof-of-concept demonstration that this technique was advantageous for the production of protein-catalyzed capture (PCC) agents that could be used as drop-in replacements for antibodies in a variety of applications. Chapter 2 describes the technology development that was undertaken to optimize this screening process and make it readily available for a wide variety of targets. This optimization is what has allowed for the explosive growth of the PCC agent project over the past few years.

These technology improvements were applied to the discovery of PCC agents specific for single amino acid point mutations in proteins, which have many applications in cancer detection and treatment. Chapter 3 describes the use of a general all-chemical epitope-targeting strategy that can focus PCC agent development directly to a site of interest on a protein surface. This technique utilizes a chemically-synthesized chunk of the protein, called an epitope, substituted with a click handle in combination with the OBOC in situ click chemistry libraries in order to focus ligand development at a site of interest. Specifically, Chapter 3 discusses the use of this technique in developing a PCC agent specific for the E17K mutation of Akt1. Chapter 4 details the expansion of this ligand into a mutation-specific inhibitor, with applications in therapeutics.

Nanophotonic Light Trapping In Thin Solar Cells

Over the last several decades there have been significant advances in the study and understanding of light behavior in nanoscale geometries. Entire fields such as those based on photonic crystals, plasmonics and metamaterials have been developed, accelerating the growth of knowledge related to nanoscale light manipulation. Coupled with recent interest in cheap, reliable renewable energy, a new field has blossomed, that of nanophotonic solar cells.

In this thesis, we examine important properties of thin-film solar cells from a nanophotonics perspective. We identify key differences between nanophotonic devices and traditional, thick solar cells. We propose a new way of understanding and describing limits to light trapping and show that certain nanophotonic solar cell designs can have light trapping limits above the so called ray-optic or ergodic limit. We propose that a necessary requisite to exceed the traditional light trapping limit is that the active region of the solar cell must possess a local density of optical states (LDOS) higher than that of the corresponding, bulk material. Additionally, we show that in addition to having an increased density of states, the absorber must have an appropriate incoupling mechanism to transfer light from free space into the optical modes of the device. We outline a portfolio of new solar cell designs that have potential to exceed the traditional light trapping limit and numerically validate our predictions for select cases.

We emphasize the importance of thinking about light trapping in terms of maximizing the optical modes of the device and efficiently coupling light into them from free space. To further explore these two concepts, we optimize patterns of superlattices of air holes in thin slabs of Si and show that by adding a roughened incoupling layer the total absorbed current can be increased synergistically. We suggest that the addition of a random scattering surface to a periodic patterning can increase incoupling by lifting the constraint of selective mode occupation associated with periodic systems.

Lastly, through experiment and simulation, we investigate a potential high efficiency solar cell architecture that can be improved with the nanophotonic light trapping concepts described in this thesis. Optically thin GaAs solar cells are prepared by the epitaxial liftoff process by removal from their growth substrate and addition of a metallic back reflector. A process of depositing large area nano patterns on the surface of the cells is developed using nano imprint lithography and implemented on the thin GaAs cells.

Information-theoretic Studies and Capacity Bounds: Group Network Codes and Energy Harvesting Communication Systems

Network information theory and channels with memory are two important but difficult frontiers of information theory. In this two-parted dissertation, we study these two areas, each comprising one part. For the first area we study the so-called entropy vectors via finite group theory, and the network codes constructed from finite groups. In particular, we identify the smallest finite group that violates the Ingleton inequality, an inequality respected by all linear network codes, but not satisfied by all entropy vectors. Based on the analysis of this group we generalize it to several families of Ingleton-violating groups, which may be used to design good network codes. Regarding that aspect, we study the network codes constructed with finite groups, and especially show that linear network codes are embedded in the group network codes constructed with these Ingleton-violating families. Furthermore, such codes are strictly more powerful than linear network codes, as they are able to violate the Ingleton inequality while linear network codes cannot. For the second area, we study the impact of memory to the channel capacity through a novel communication system: the energy harvesting channel. Different from traditional communication systems, the transmitter of an energy harvesting channel is powered by an exogenous energy harvesting device and a finite-sized battery. As a consequence, each time the system can only transmit a symbol whose energy consumption is no more than the energy currently available. This new type of power supply introduces an unprecedented input constraint for the channel, which is random, instantaneous, and has memory. Furthermore, naturally, the energy harvesting process is observed causally at the transmitter, but no such information is provided to the receiver. Both of these features pose great challenges for the analysis of the channel capacity. In this work we use techniques from channels with side information, and finite state channels, to obtain lower and upper bounds of the energy harvesting channel. In particular, we study the stationarity and ergodicity conditions of a surrogate channel to compute and optimize the achievable rates for the original channel. In addition, for practical code design of the system we study the pairwise error probabilities of the input sequences.

Superionic Noble Metal Chalcogenide Thermoelectrics

Measurements and modeling of Cu₂Se, Ag₂Se, and Cu₂S show that superionic conductors have great potential as thermoelectric materials. Cu₂Se and Ag₂Se are predicted to reach a zT of 1.2 at room temperature if their carrier concentrations can be reduced, and Cu-vacancy doped Cu₂S reaches a maximum zT of 1.7 at 1000 K. Te-doped Ag₂Se achieves a zT of 1.2 at 520 K, and could reach a zT of 1.7 if its carrier concentration could be reduced. However, superionic conductors tend to have high carrier concentrations due to the presence of metal defects. The carrier concentration has been found to be difficult to reduce by altering the defect concentration, therefore materials that are underdoped relative to the optimum carrier concentration are easier to optimize. The results of Te-doping of Ag₂Se show that reducing the carrier concentration is possible by reducing the maximum Fermi level in the material.

Two new methods for analyzing thermoelectric transport data were developed. The first involves scaling the temperature-dependent transport data according to the temperature dependences expected of a single parabolic band model and using all of the scaled data to perform a single parabolic band analysis, instead of being restricted to using one data point per sample at a fixed temperature. This allows for a more efficient use of the transport data. The second involves scaling only the Seebeck coefficient and electrical conductivity. This allows for an estimate of the quality factor (and therefore the maximum zT in the material) without using Hall effect data, which are not always available due to time and budget constraints and are difficult to obtain in high-resistivity materials. Methods for solving the coherent potential approximation effective medium equations were developed in conjunction with measurements of the resistivity tensor elements of composite materials. This allows the electrical conductivity and mobility of each phase in the composite to be determined from measurements of the bulk. This points out a new method for measuring the pure-phase electrical properties in impure materials, for measuring the electrical properties of unknown phases in composites, and for quantifying the effects of quantum interactions in composites.

A Multiwavelength Study of the Intracluster Medium and the Characterization of the Multiwavelength Sub/millimeter Inductance Camera

The first part of this thesis combines Bolocam observations of the thermal Sunyaev-Zel’dovich (SZ) effect at 140 GHz with X-ray observations from Chandra, strong lensing data from the Hubble Space Telescope (HST), and weak lensing data from HST and Subaru to constrain parametric models for the distribution of dark and baryonic matter in a sample of six massive, dynamically relaxed galaxy clusters. For five of the six clusters, the full multiwavelength dataset is well described by a relatively simple model that assumes spherical symmetry, hydrostatic equilibrium, and entirely thermal pressure support. The multiwavelength analysis yields considerably better constraints on the total mass and concentration compared to analysis of any one dataset individually. The subsample of five galaxy clusters is used to place an upper limit on the fraction of pressure support in the intracluster medium (ICM) due to nonthermal processes, such as turbulent and bulk flow of the gas. We constrain the nonthermal pressure fraction at r500c to be less than 0.11 at 95% confidence, where r500c refers to radius at which the average enclosed density is 500 times the critical density of the Universe. This is in tension with state-of-the-art hydrodynamical simulations, which predict a nonthermal pressure fraction of approximately 0.25 at r500c for the clusters in this sample.

The second part of this thesis focuses on the characterization of the Multiwavelength Sub/millimeter Inductance Camera (MUSIC), a photometric imaging camera that was commissioned at the Caltech Submillimeter Observatory (CSO) in 2012. MUSIC is designed to have a 14 arcminute, diffraction-limited field of view populated with 576 spatial pixels that are simultaneously sensitive to four bands at 150, 220, 290, and 350 GHz. It is well-suited for studies of dusty star forming galaxies, galaxy clusters via the SZ Effect, and galactic star formation. MUSIC employs a number of novel detector technologies: broadband phased-arrays of slot dipole antennas for beam formation, on-chip lumped element filters for band definition, and Microwave Kinetic Inductance Detectors (MKIDs) for transduction of incoming light to electric signal. MKIDs are superconducting micro-resonators coupled to a feedline. Incoming light breaks apart Cooper pairs in the superconductor, causing a change in the quality factor and frequency of the resonator. This is read out as amplitude and phase modulation of a microwave probe signal centered on the resonant frequency. By tuning each resonator to a slightly different frequency and sending out a superposition of probe signals, hundreds of detectors can be read out on a single feedline. This natural capability for large scale, frequency domain multiplexing combined with relatively simple fabrication makes MKIDs a promising low temperature detector for future kilopixel sub/millimeter instruments. There is also considerable interest in using MKIDs for optical through near-infrared spectrophotometry due to their fast microsecond response time and modest energy resolution. In order to optimize the MKID design to obtain suitable performance for any particular application, it is critical to have a well-understood physical model for the detectors and the sources of noise to which they are susceptible. MUSIC has collected many hours of on-sky data with over 1000 MKIDs. This work studies the performance of the detectors in the context of one such physical model. Chapter 2 describes the theoretical model for the responsivity and noise of MKIDs. Chapter 3 outlines the set of measurements used to calibrate this model for the MUSIC detectors. Chapter 4 presents the resulting estimates of the spectral response, optical efficiency, and on-sky loading. The measured detector response to Uranus is compared to the calibrated model prediction in order to determine how well the model describes the propagation of signal through the full instrument. Chapter 5 examines the noise present in the detector timestreams during recent science observations. Noise due to fluctuations in atmospheric emission dominate at long timescales (less than 0.5 Hz). Fluctuations in the amplitude and phase of the microwave probe signal due to the readout electronics contribute significant 1/f and drift-type noise at shorter timescales. The atmospheric noise is removed by creating a template for the fluctuations in atmospheric emission from weighted averages of the detector timestreams. The electronics noise is removed by using probe signals centered off-resonance to construct templates for the amplitude and phase fluctuations. The algorithms that perform the atmospheric and electronic noise removal are described. After removal, we find good agreement between the observed residual noise and our expectation for intrinsic detector noise over a significant fraction of the signal bandwidth.

Late Transition Metals Supported by Aryl Ethers and Phenoxides Bearing Pendant Phosphines: Mechanistic Insights Relevant to Ether C-O Bond Cleavage

Terphenyl diphosphines bearing pendant ethers were prepared to provide mechanistic insight into the mechanism of activation of aryl C–O bonds with Group 9 and Group 10 transition metals. Chapters 2 and 3 of this dissertation describe the reactivity of compounds supported by the model phosphine and extension of this chemistry to heterogenous C–O bond activation.

Chapter 2 describes the synthesis and reactivity of aryl-methyl and aryl-aryl model systems. The metallation of these compounds with Ni, Pd, Pt, Co, Rh, and Ir is described. Intramolecular bond activation pathways are described. In the case of the aryl-methyl ether, aryl C–O bond activation was observed only for Ni, Rh, and Ir.

Chapter 3 outlines the reactivity of heterogenous Rh and Ir catalysts for aryl ether C–O bond cleavage. Using Rh/C and an organometallic Ir precursor, aryl ethers were treated with H2 and heat to afford products of hydrogenolysis and hydrogenation. Conditions were modified to optimize the yield of hydrogenolysis product. Hydrogenation could not be fully suppressed in these systems.

Appendix A describes initial investigations of bisphenoxyiminoquinoline dichromium compounds for selective C2H4 oligomerization to afford α-olefins. The synthesis of monometallic and bimetallic Cr complexes is described. These compounds are compared to literature examples and found to be less active and non-selective for production of α-olefins.

Appendix B describes the coordination chemistry of terphenyl diphosphines, terphenyl bisphosphinophenols, and biphenyl phosphinophenols proligands with molybdenum, cobalt, and nickel. Since their synthesis, terphenyl diphosphine molybdenum compounds have been reported to be good catalysts for the dehydrogenation of ammonia borane. Biphenyl phosphinophenols are demonstrated provide both phosphine and arene donors to transition metals while maintaining a sterically accessible coordination sphere. Such ligands may be promising in the context of the activation of other small molecules.

Appendix C contains relevant NMR spectra for the compounds presented in the preceding sections.