Compressed sensing (CS) is a novel approach to collecting and analyzing data of all types. By exploiting prior knowledge of the compressibility of many naturally-occurring signals, specially designed sensors can dramatically undersample the data of interest and still achieve high performance. However, the generated data are pseudorandomly mixed and must be processed before use. In this work, a model of a single-pixel compressive video camera is used to explore the problems of performing inference based on these undersampled measurements. Three broad types of inference from CS measurements are considered: recovery of video frames, target tracking, and object classification/detection. Potential applications include automated surveillance, autonomous navigation, and medical imaging and diagnosis.



Recovery of CS video frames is far more complex than still images, which are known to be (approximately) sparse in a linear basis such as the discrete cosine transform. By combining sparsity of individual frames with an optical flow-based model of inter-frame dependence, the perceptual quality and peak signal to noise ratio (PSNR) of reconstructed frames is improved. The efficacy of this approach is demonstrated for the cases of \textit{a priori} known image motion and unknown but constant image-wide motion.



Although video sequences can be reconstructed from CS measurements, the process is computationally costly. In autonomous systems, this reconstruction step is unnecessary if higher-level conclusions can be drawn directly from the CS data. A tracking algorithm is described and evaluated which can hold target vehicles at very high levels of compression where reconstruction of video frames fails. The algorithm performs tracking by detection using a particle filter with likelihood given by a maximum average correlation height (MACH) target template model.



Motivated by possible improvements over the MACH filter-based likelihood estimation of the tracking algorithm, the application of deep learning models to detection and classification of compressively sensed images is explored. In tests, a Deep Boltzmann Machine trained on CS measurements outperforms a naive reconstruct-first approach.



Taken together, progress in these three areas of CS inference has the potential to lower system cost and improve performance, opening up new applications of CS video cameras.

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.

For a sensor array, part of its elements may fail to work due to hardware failures. Then the missing data may distort in the beam pattern or decrease the accuracy of direction-of-arrival (DOA) estimation. Therefore, considerable research has been conducted to develop algorithms that can estimate the missing signal information. On the other hand, through those algorithms, array elements can also be selectively turned off while the missed information can be successfully recovered, which will save power consumption and hardware cost.

Conventional approaches focusing on array element failures are mainly based on interpolation or sequential learning algorithm. Both of them rely heavily on some prior knowledge such as the information of the failures or a training dataset without missing data. In addition, since most of the existing approaches are developed for DOA estimation, their recovery target is usually the co-variance matrix but not the signal matrix.

In this thesis, a new signal recovery method based on matrix completion (MC) theory is introduced. It aims to directly refill the absent entries in the signal matrix without any prior knowledge. We proposed a novel overlapping reshaping method to satisfy the applying conditions of MC algorithms. Compared to other existing MC based approaches, our proposed method can provide us higher probability of successful recovery. The thesis describes the principle of the algorithms and analyzes the performance of this method. A few application examples with simulation results are also provided.

Utility scale solar energy is generated by photovoltaic (PV) cell arrays, which are often deployed in remote areas. A PV array monitoring system is considered where smart sensors are attached to the PV modules and transmit data to a monitoring station through wireless links. These smart monitoring devices may be used for fault detection and management of connection topologies. In this thesis, a compact hardware simulator of the smart PV array monitoring system is described. The voltage, current, irradiance, and temperature of each PV module are monitored and the status of each panel along with all data is transmitted to a mobile device. LabVIEW and Arduino board programs have been developed to display and visualize the monitoring data from all sensors. All data is saved on servers and mobile devices and desktops can easily access analytics from anywhere. Various PV array conditions including shading, faults, and loading are simulated and demonstrated.

Additionally, Electrical mismatch between modules in a PV array due to partial shading causes energy losses beyond the shaded module, as unshaded modules are forced to operate away from their maximum power point in order to compensate for the shading. An irradiance estimation algorithm is presented for use in a mismatch mitigation system. Irradiance is estimated using measurements of module voltage, current, and back surface temperature. These estimates may be used to optimize an array’s electrical configuration and reduce the mismatch losses caused by partial shading. Propagation of error in the estimation is examined; it is found that accuracy is sufficient for use in the proposed mismatch mitigation application.

The research on the topology and dynamics of complex networks is one of the most focused area in complex system science. The goals are to structure our understanding of the real-world social, economical, technological, and biological systems in the aspect of networks consisting a large number of interacting units and to develop corresponding detection, prediction, and control strategies. In this highly interdisciplinary field, my research mainly concentrates on universal estimation schemes, physical controllability, as well as mechanisms behind extreme events and cascading failure for complex networked systems.

Revealing the underlying structure and dynamics of complex networked systems from observed data without of any specific prior information is of fundamental importance to science, engineering, and society. We articulate a Markov network based model, the sparse dynamical Boltzmann machine (SDBM), as a universal network structural estimator and dynamics approximator based on techniques including compressive sensing and K-means algorithm. It recovers the network structure of the original system and predicts its short-term or even long-term dynamical behavior for a large variety of representative dynamical processes on model and real-world complex networks.

One of the most challenging problems in complex dynamical systems is to control complex networks.

Upon finding that the energy required to approach a target state with reasonable precision

is often unbearably large, and the energy of controlling a set of networks with similar structural properties follows a fat-tail distribution, we identify fundamental structural ``short boards'' that play a dominant role in the enormous energy and offer a theoretical interpretation for the fat-tail distribution and simple strategies to significantly reduce the energy.

Extreme events and cascading failure, a type of collective behavior in complex networked systems, often have catastrophic consequences. Utilizing transportation and evolutionary game dynamics as prototypical

settings, we investigate the emergence of extreme events in simplex complex networks, mobile ad-hoc networks and multi-layer interdependent networks. A striking resonance-like phenomenon and the emergence of global-scale cascading breakdown are discovered. We derive analytic theories to understand the mechanism of

control at a quantitative level and articulate cost-effective control schemes to significantly suppress extreme events and the cascading process.

In many applications, measured sensor data is meaningful only when the location of sensors is accurately known. Therefore, the localization accuracy is crucial. In this dissertation, both location estimation and location detection problems are considered.

In location estimation problems, sensor nodes at known locations, called anchors, transmit signals to sensor nodes at unknown locations, called nodes, and use these transmissions to estimate the location of the nodes. Specifically, the location estimation in the presence of fading channels using time of arrival (TOA) measurements with narrowband communication signals is considered. Meanwhile, the Cramer-Rao lower bound (CRLB) for localization error under different assumptions is derived. Also, maximum likelihood estimators (MLEs) under these assumptions are derived.

In large WSNs, distributed location estimation algorithms are more efficient than centralized algorithms. A sequential localization scheme, which is one of distributed location estimation algorithms, is considered. Also, different localization methods, such as TOA, received signal strength (RSS), time difference of arrival (TDOA), direction of arrival (DOA), and large aperture array (LAA) are compared under different signal-to-noise ratio (SNR) conditions. Simulation results show that DOA is the preferred scheme at the low SNR regime and the LAA localization algorithm provides better performance for network discovery at high SNRs. Meanwhile, the CRLB for the localization error using the TOA method is also derived.

A distributed location detection scheme, which allows each anchor to make a decision as to whether a node is active or not is proposed. Once an anchor makes a decision, a bit is transmitted to a fusion center (FC). The fusion center combines all the decisions and uses a design parameter $K$ to make the final decision. Three scenarios are considered in this dissertation. Firstly, location detection at a known location is considered. Secondly, detecting a node in a known region is considered. Thirdly, location detection in the presence of fading is considered. The optimal thresholds are derived and the total probability of false alarm and detection under different scenarios are derived.

The power of science lies in its ability to infer and predict the

existence of objects from which no direct information can be obtained

experimentally or observationally. A well known example is to

ascertain the existence of black holes of various masses in different

parts of the universe from indirect evidence, such as X-ray emissions.

In the field of complex networks, the problem of detecting

hidden nodes can be stated, as follows. Consider a network whose

topology is completely unknown but whose nodes consist of two types:

one accessible and another inaccessible from the outside world. The

accessible nodes can be observed or monitored, and it is assumed that time

series are available from each node in this group. The inaccessible

nodes are shielded from the outside and they are essentially

``hidden.'' The question is, based solely on the

available time series from the accessible nodes, can the existence and

locations of the hidden nodes be inferred? A completely data-driven,

compressive-sensing based method is developed to address this issue by utilizing

complex weighted networks of nonlinear oscillators, evolutionary game

and geospatial networks.

Both microbes and multicellular organisms actively regulate their cell

fate determination to cope with changing environments or to ensure

proper development. Here, the synthetic biology approaches are used to

engineer bistable gene networks to demonstrate that stochastic and

permanent cell fate determination can be achieved through initializing

gene regulatory networks (GRNs) at the boundary between dynamic

attractors. This is experimentally realized by linking a synthetic GRN

to a natural output of galactose metabolism regulation in yeast.

Combining mathematical modeling and flow cytometry, the

engineered systems are shown to be bistable and that inherent gene expression

stochasticity does not induce spontaneous state transitioning at

steady state. By interfacing rationally designed synthetic

GRNs with background gene regulation mechanisms, this work

investigates intricate properties of networks that illuminate possible

regulatory mechanisms for cell differentiation and development that

can be initiated from points of instability.

I propose a new communications scheme where signature signals are used to carry digital data by suitably modulating the signal parameters with information bits. One possible application for the proposed scheme is in underwater acoustic (UWA) communications; with this motivation, I demonstrate how it can be applied in UWA communications. In order to do that, I exploit existing parameterized models for mammalian sounds by using them as signature signals. Digital data is transmitted by mapping vectors of information bits to a carefully designed set of parameters with values obtained from the biomimetic signal models. To complete the overall system design, I develop appropriate receivers taking into account the specific UWA channel models. I present some numerical results from the analysis of data recorded during the Kauai Acomms MURI 2011 (KAM11) UWA communications experiment.

It is shown that the proposed communication scheme results in approximate channel models with amplitude-limited inputs and signal-dependent additive noise. Motivated by this observation, I study capacity of amplitude-limited channels under different transmission scenarios. Specifically, I consider fading channels, signal-dependent additive Gaussian noise channels, multiple-input multiple-output (MIMO) systems and parallel Gaussian channels under peak power constraints.

I also consider practical channel coding problems for channels with signal-dependent noise. I consider two specific models; signal-dependent additive Gaussian noise channels and Z-channels which serve as binary-input binary-output approximations to the Gaussian case. I propose a new upper bound on the probability of error, and utilize it for design of codes. I illustrate the tightness of the derived bounds and the performance of the designed codes via examples.

Access Networks provide the backbone to the Internet connecting the end-users to

the core network thus forming the most important segment for connectivity. Access

Networks have multiple physical layer medium ranging from fiber cables, to DSL links

and Wireless nodes, creating practically-used hybrid access networks. We explore the

hybrid access network at the Medium ACcess (MAC) Layer which receives packets

segregated as data and control packets, thus providing the needed decoupling of data

and control plane. We utilize the Software Defined Networking (SDN) principle of

centralized processing with segregated data and control plane to further extend the

usability of our algorithms. This dissertation introduces novel techniques in Dynamic

Bandwidth allocation, control message scheduling policy, flow control techniques and

Grouping techniques to provide improved performance in Hybrid Passive Optical Networks (PON) such as PON-xDSL, FiWi etc. Finally, we study the different types of

software defined algorithms in access networks and describe the various open challenges and research directions.

The recent proposal of two-way relaying has attracted much attention due to its promising features for many practical scenarios. Hereby, two users communicate simultaneously in both directions to exchange their messages with the help of a relay node. This doctoral study investigates various aspects of two-way relaying. Specifically, the issue of asynchronism, lack of channel knowledge, transmission of correlated sources and multi-way relaying techniques involving multiple users are explored.

With the motivation of developing enabling techniques for two-way relay (TWR) channels experiencing excessive synchronization errors, two conceptually-different schemes are proposed to accommodate any relative misalignment between the signals received at any node. By designing a practical transmission/detection mechanism based on orthogonal frequency division multiplexing (OFDM), the proposed schemes perform significantly better than existing competing solutions. In a related direction, differential modulation is implemented for asynchronous TWR systems that lack the channel state information (CSI) knowledge. The challenge in this problem compared to the conventional point-to-point counterpart arises not only from the asynchrony but also from the existence of an interfering signal. Extensive numerical examples, supported by analytical work, are given to demonstrate the advantages of the proposed schemes.

Other important issues considered in this dissertation are related to the extension of the two-way relaying scheme to the multiple-user case, known as the multi-way relaying. First, a distributed source coding solution based on Slepian-Wolf coding is proposed to compress correlated messages close to the information theoretical limits in the context of multi-way relay (MWR) channels. Specifically, the syndrome approach based on low-density parity-check (LDPC) codes is implemented. A number of relaying strategies are considered for this problem offering a tradeoff between performance and complexity. The proposed solutions have shown significant improvements compared to the existing ones in terms of the achievable compression rates. On a different front, a novel approach to channel coding is proposed for the MWR channel based on the implementation of nested codes in a distributed manner. This approach ensures that each node decodes the messages of the other users without requiring complex operations at the relay, and at the same time, providing substantial benefits compared to the traditional routing solution.