Visible light communication (VLC) is the promise of a high data rate wireless network for both indoor and outdoor uses. It competes with 5G radio frequency (RF) system as well. Even though the breakthrough of Gallium Nitride (GaN) based micro-light-emitting-diodes (micro-LEDs) enhances the -3dB modulation bandwidth dramatically from tens of MHz to hundreds of MHz, the optical power onto a fast photo receiver drops exponentially. It determines the signal to noise ratio (SNR) of VLC. For full implementation of the useful high data-rate VLC link enabled by a GaN-based micro-LED, it needs focusing optics and a tracking system. In this dissertation, we demonstrate a novel active on-chip monitoring system for VLC using a GaN-based micro-LED and none-return-to-zero on-off keying (NRZ-OOK) modulation scheme. By this innovative technique without manual focusing, the field of view (FOV) was enlarged to 120° and data rates up to 600 Mbps at a bit error rate (BER) of 2.1×10⁻⁴ were achieved. This work demonstrates the establishment of a VLC physical link. It shows improved communication quality by orders, making it optimized for real communications.

This dissertation also gives an experimental demonstration of non-line-of-sight (NLOS) visible light communication (VLC) using a single 80 μm gallium nitride (GaN) based micro-light-emitting diode (micro-LED). IEEE 802.11ac modulation scheme with 80 MHz bandwidth, as an entry level of the fifth generation of Wi-Fi, was employed to use the micro-LED bandwidth efficiently. These practical techniques were successfully utilized to achieve a demonstration of line-of-sight (LOS) VLC at a speed of 433 Mbps, and a bit error rate (BER) of 10⁻⁵ with a free space transmit distance 3.6 m. Besides this, we demonstrated directed NLOS VLC links based on mirror reflections with a data rate of 433 Mbps and a BER of 10⁻⁴. For non-directed NLOS VLC using a print paper as the reflective material, 195 Mbps data rate and a BER of 10⁻⁵ was achieved.

Distributed wireless sensor networks (WSNs) have attracted researchers recently due to their advantages such as low power consumption, scalability and robustness to link failures. In sensor networks with no fusion center, consensus is a process where

all the sensors in the network achieve global agreement using only local transmissions. In this dissertation, several consensus and consensus-based algorithms in WSNs are studied.

Firstly, a distributed consensus algorithm for estimating the maximum and minimum value of the initial measurements in a sensor network in the presence of communication noise is proposed. In the proposed algorithm, a soft-max approximation together with a non-linear average consensus algorithm is used. A design parameter controls the trade-off between the soft-max error and convergence speed. An analysis of this trade-off gives guidelines towards how to choose the design parameter for the max estimate. It is also shown that if some prior knowledge of the initial measurements is available, the consensus process can be accelerated.

Secondly, a distributed system size estimation algorithm is proposed. The proposed algorithm is based on distributed average consensus and L2 norm estimation. Different sources of error are explicitly discussed, and the distribution of the final estimate is derived. The CRBs for system size estimator with average and max consensus strategies are also considered, and different consensus based system size estimation approaches are compared.

Then, a consensus-based network center and radius estimation algorithm is described. The center localization problem is formulated as a convex optimization problem with a summation form by using soft-max approximation with exponential functions. Distributed optimization methods such as stochastic gradient descent and diffusion adaptation are used to estimate the center. Then, max consensus is used to compute the radius of the network area.

Finally, two average consensus based distributed estimation algorithms are introduced: distributed degree distribution estimation algorithm and algorithm for tracking the dynamics of the desired parameter. Simulation results for all proposed algorithms are provided.

This dissertation aims to study and understand relevant issues related to the electronic, spin and valley transport in two-dimensional Dirac systems for different given physical settings. In summary, four key findings are achieved.

First, studying persistent currents in confined chaotic Dirac fermion systems with a ring geometry and an applied Aharonov-Bohm flux, unusual whispering-gallery modes with edge-dependent currents and spin polarization are identified. They can survive for highly asymmetric rings that host fully developed classical chaos. By sustaining robust persistent currents, these modes can be utilized to form a robust relativistic quantum two-level system.

Second, the quantized topological edge states in confined massive Dirac fermion systems exhibiting a remarkable reverse Stark effect in response to an applied electric field, and an electrically or optically controllable spin switching behavior are uncovered.

Third, novel wave scattering and transport in Dirac-like pseudospin-1 systems are reported. (a), for small scatterer size, a surprising revival resonant scattering with a peculiar boundary trapping by forming unusual vortices is uncovered. Intriguingly, it can persist in arbitrarily weak scatterer strength regime, which underlies a superscattering behavior beyond the conventional scenario. (b), for larger size, a perfect caustic phenomenon arises as a manifestation of the super-Klein tunneling effect. (c), in the far-field, an unexpected isotropic transport emerges at low energies.

Fourth, a geometric valley Hall effect (gVHE) originated from fractional singular Berry flux is revealed. It is shown that gVHE possesses a nonlinear dependence on the Berry flux with asymmetrical resonance features and can be considerably enhanced by electrically controllable resonant valley skew scattering. With the gVHE, efficient valley filtering can arise and these phenomena are robust against thermal fluctuations and disorder averaging.

In this dissertation, I propose potential techniques to improve the quality-of-service (QoS) of real-time applications in cognitive radio (CR) systems. Unlike best-effort applications, real-time applications, such as audio and video, have a QoS that need to be met. There are two different frameworks that are used to study the QoS in the literature, namely, the average-delay and the hard-deadline frameworks. In the former, the scheduling algorithm has to guarantee that the packet's average delay is below a prespecified threshold while the latter imposes a hard deadline on each packet in the system. In this dissertation, I present joint power allocation and scheduling algorithms for each framework and show their applications in CR systems which are known to have strict power limitations so as to protect the licensed users from interference.

A common aspect of the two frameworks is the packet service time. Thus, the effect of multiple channels on the service time is studied first. The problem is formulated as an optimal stopping rule problem where it is required to decide at which channel the SU should stop sensing and begin transmission. I provide a closed-form expression for this optimal stopping rule and the optimal transmission power of secondary user (SU).

The average-delay framework is then presented in a single CR channel system with a base station (BS) that schedules the SUs to minimize the average delay while protecting the primary users (PUs) from harmful interference. One of the contributions of the proposed algorithm is its suitability for heterogeneous-channels systems where users with statistically low channel quality suffer worse delay performances. The proposed algorithm guarantees the prespecified delay performance to each SU without violating the PU's interference constraint.

Finally, in the hard-deadline framework, I propose three algorithms that maximize the system's throughput while guaranteeing the required percentage of packets to be transmitted by their deadlines. The proposed algorithms work in heterogeneous systems where the BS is serving different types of users having real-time (RT) data and non-real-time (NRT) data. I show that two of the proposed algorithms have the low complexity where the power policies of both the RT and NRT users are in closed-form expressions and a low-complexity scheduler.

The radar performance of detecting a target and estimating its parameters can deteriorate rapidly in the presence of high clutter. This is because radar measurements due to clutter returns can be falsely detected as if originating from the actual target. Various data association methods and multiple hypothesis filtering approaches have been considered to solve this problem. Such methods, however, can be computationally intensive for real time radar processing. This work proposes a new approach that is based on the unsupervised clustering of target and clutter detections before target tracking using particle filtering. In particular, Gaussian mixture modeling is first used to separate detections into two Gaussian distinct mixtures. Using eigenvector analysis, the eccentricity of the covariance matrices of the Gaussian mixtures are computed and compared to threshold values that are obtained a priori. The thresholding allows only target detections to be used for target tracking. Simulations demonstrate the performance of the new algorithm and compare it with using k-means for clustering instead of Gaussian mixture modeling.

Full-duplex communication has attracted significant attention as it promises to increase the spectral efficiency compared to half-duplex. Multi-hop full-duplex networks add new dimensions and capabilities to cooperative networks by facilitating simultaneous transmission and reception and improving data rates.

When a relay in a multi-hop full-duplex system amplifies and forwards its received signals, due to the presence of self-interference, the input-output relationship is determined by recursive equations. This thesis introduces a signal flow graph approach to solve the problem of finding the input-output relationship of a multi-hop amplify-and-forward full-duplex relaying system using Mason's gain formula. Even when all links have flat fading channels, the residual self-interference component due to imperfect self-interference cancellation at the relays results in an end-to-end effective channel that is an all-pole frequency-selective channel. Also, by assuming the relay channels undergo frequency-selective fading, the outage probability analysis is performed and the performance is compared with the case when the relay channels undergo frequency-flat fading. The outage performance of this system is performed assuming that the destination employs an equalizer or a matched filter.

For the case of a two-hop (single relay) full-duplex amplify-and-forward relaying system, the bounds on the outage probability are derived by assuming that the destination employs a matched filter or a minimum mean squared error decision feedback equalizer. For the case of a three-hop (two-relay) system with frequency-flat relay channels, the outage probability analysis is performed by considering the output SNR of different types of equalizers and matched filter at the destination. Also, the closed-form upper bounds on the output SNR are derived when the destination employs a minimum mean squared error decision feedback equalizer which is used in outage probability analysis. It is seen that for sufficiently high target rates, full-duplex relaying with equalizers is always better than half-duplex relaying in terms of achieving lower outage probability, despite the higher RSI. In contrast, since full-duplex relaying with MF is sensitive to RSI, it is outperformed by half-duplex relaying under strong RSI.

Biological and biomedical measurements, when adequately analyzed and processed, can be used to impart quantitative diagnosis during primary health care consultation to improve patient adherence to recommended treatments. For example, analyzing neural recordings from neurostimulators implanted in patients with neurological disorders can be used by a physician to adjust detrimental stimulation parameters to improve treatment. As another example, biosequences, such as sequences from peptide microarrays obtained from a biological sample, can potentially provide pre-symptomatic diagnosis for infectious diseases when processed to associate antibodies to specific pathogens or infectious agents. This work proposes advanced statistical signal processing and machine learning methodologies to assess neurostimulation from neural recordings and to extract diagnostic information from biosequences.

For locating specific cognitive and behavioral information in different regions of the brain, neural recordings are processed using sequential Bayesian filtering methods to detect and estimate both the number of neural sources and their corresponding parameters. Time-frequency based feature selection algorithms are combined with adaptive machine learning approaches to suppress physiological and non-physiological artifacts present in neural recordings. Adaptive processing and unsupervised clustering methods applied to neural recordings are also used to suppress neurostimulation artifacts and classify between various behavior tasks to assess the level of neurostimulation in patients.

For pathogen detection and identification, random peptide sequences and their properties are first uniquely mapped to highly-localized signals and their corresponding parameters in the time-frequency plane. Time-frequency signal processing methods are then applied to estimate antigenic determinants or epitope candidates for detecting and identifying potential pathogens.

In recent years, there has been an increased interest in sharing available bandwidth to avoid spectrum congestion. With an ever-increasing number wireless users, it is critical to develop signal processing based spectrum sharing algorithms to achieve cooperative use of the allocated spectrum among multiple systems in order to reduce interference between systems. This work studies the radar and communications systems coexistence problem using two main approaches. The first approach develops methodologies to increase radar target tracking performance under low signal-to-interference-plus-noise ratio (SINR) conditions due to the coexistence of strong communications interference. The second approach jointly optimizes the performance of both systems by co-designing a common transmit waveform.

When concentrating on improving radar tracking performance, a pulsed radar that is tracking a single target coexisting with high powered communications interference is considered. Although the Cramer-Rao lower bound (CRLB) on the covariance of an unbiased estimator of deterministic parameters provides a bound on the estimation mean squared error (MSE), there exists an SINR threshold at which estimator covariance rapidly deviates from the CRLB. After demonstrating that different radar waveforms experience different estimation SINR thresholds using the Barankin bound (BB), a new radar waveform design method is proposed based on predicting the waveform-dependent BB SINR threshold under low SINR operating conditions.

A novel method of predicting the SINR threshold value for maximum likelihood estimation (MLE) is proposed. A relationship is shown to exist between the formulation of the BB kernel and the probability of selecting sidelobes for the MLE. This relationship is demonstrated as an accurate means of threshold prediction for the radar target parameter estimation of frequency, time-delay and angle-of-arrival.



For the co-design radar and communications system problem, the use of a common transmit waveform for a pulse-Doppler radar and a multiuser communications system is proposed. The signaling scheme for each system is selected from a class of waveforms with nonlinear phase function by optimizing the waveform parameters to minimize interference between the two systems and interference among communications users. Using multi-objective optimization, a trade-off in system performance is demonstrated when selecting waveforms that minimize both system interference and tracking MSE.

Information divergence functions, such as the Kullback-Leibler divergence or the Hellinger distance, play a critical role in statistical signal processing and information theory; however estimating them can be challenge. Most often, parametric assumptions are made about the two distributions to estimate the divergence of interest. In cases where no parametric model fits the data, non-parametric density estimation is used. In statistical signal processing applications, Gaussianity is usually assumed since closed-form expressions for common divergence measures have been derived for this family of distributions. Parametric assumptions are preferred when it is known that the data follows the model, however this is rarely the case in real-word scenarios. Non-parametric density estimators are characterized by a very large number of parameters that have to be tuned with costly cross-validation. In this dissertation we focus on a specific family of non-parametric estimators, called direct estimators, that bypass density estimation completely and directly estimate the quantity of interest from the data. We introduce a new divergence measure, the $D_p$-divergence, that can be estimated directly from samples without parametric assumptions on the distribution. We show that the $D_p$-divergence bounds the binary, cross-domain, and multi-class Bayes error rates and, in certain cases, provides provably tighter bounds than the Hellinger divergence. In addition, we also propose a new methodology that allows the experimenter to construct direct estimators for existing divergence measures or to construct new divergence measures with custom properties that are tailored to the application. To examine the practical efficacy of these new methods, we evaluate them in a statistical learning framework on a series of real-world data science problems involving speech-based monitoring of neuro-motor disorders.