With the rapid development of wireless communications, security becomes extremely important. In many applications, each transmitter desires to send independent and confidential message to its intended receiver while ensuring mutual information-theoretic secrecy. In this dissertation, I study strategies for enhanced secrecy in wireless communication systems with limited rate feedback and transmitter cooperation. The two-user Gaussian channel model is considered under different scenarios. The transmitters both require channel state information (CSI), which is quantized at the receiver and fed back through the sum-rate-limited feedback channels. The quantization errors reduce the beamforming gain from the direct transmitter, and cause interference leakage from the cross transmitter. In the first scenario, I introduce the wiretap channel model where one receiver is a known eavesdropper, and a second transmitter is used to send a cooperative jamming signal to degrade the eavesdropper's channel. I consider two cases, one where no information about the eavesdroppers is available, and one where statistical CSI is available. With no information about the eavesdroppers, I show how to choose the allocation of feedback bits to the transmitters in order to maximize the amount of jamming power available to interfere with the eavesdroppers, subject to maintaining the lower bound on the rate at a minimum quality-of-service level. For the case of statistical CSI, I derive an approximate lower bound on the average secrecy rate, and optimize the bound to find a suitable bit allocation and the transmit power allocated to the transmitters. In the second scenario, I consider the interference channel model where the two transmitters are amenable to cooperation for improving the overall secrecy performance of the system. I derive an approximation for the average secrecy rate of each link, and optimize the sum secrecy rate over the transmit power and feedback bits allocated to the transmitters. Interestingly, increasing the transmit power beyond a certain point decreases the secrecy performance. When the transmitters have the same number of antennas, I derive the results in closed form. Simulations validate the theoretical analysis and demonstrate the significant performance gains that result from the use of optimal transmit power control and intelligent feedback bit allocation.

Motivated by the many applications associated with sparse multivariate models, the estimation of the directional interactions between imperfectly measured nodes of a network is studied.

First, the node dynamics and interactions are assumed to follow a linear multivariate autoregressive (MVAR) model. The observations consist of noisy linear combinations of the underlying node activities. Maximum a posteriori (MAP) criterion is adopted for parameter estimation. Due to the intractability of the MAP problem, the Expectation Maximization (EM) algorithm is used to iteratively solve the MAP problem. To impose sparsity on state transition parameters, the EM algorithm is augmented with an $\ell_1$ regularization of the connectivity matrix. Multiple techniques have been used to lower the computational complexity. Importantly, an efficient coordinate descent algorithm utilizing a closed-form solution is designed to solve the $\ell_1$-regularized EM. For noise covariance estimation, the Cholesky factors of the unknown covariance matrices are used directly in the optimization process in order to impose positive definiteness and guarantee the functionality of the $\ell_1$ optimization.

The algorithm is first applied to synthetic data to evaluate the estimation accuracy. Comparison with previous work over an extensive set of configurations shows that our method is superior under moderate to high sparsity.

The algorithm is then evaluated on real data for two different applications: temperature prediction and estimation of effective brain connectivity. Applied to real temperature data obtained from 98 stations across the U.S. mainland, the algorithm is able to identify the predictive interactions between the time series that not only are consistent with previous work, but also reveal predictive power for coastal stations.

The algorithm, however, does not perform well in the estimation of effective brain connectivity from real electroencephalography (EEG) data. We show that this shortcoming is due to the inflexibility of the linear model to capture EEG dynamics. The Neural Mass Model (NMM) is then adopted to realistically model the underlying mechanisms of EEG signals. The estimation algorithm is tailored to the nonlinearity of the NMM model. The modified algorithm is then applied to a simple synthetic system, and it is observed that the results are insensitive to the source of the connection. The root cause of the problem is then analyzed and the challenges facing the future work are discussed.

In this thesis, we discuss the theoretical background and the practical aspects of the design of a simulation toolchain for prototyping and testing new consumer imaging technologies during the design cycle. To enable a fully computer-aided design and test process, mechanisms are provided to model and investigate all the entities involved in the imaging system. In particular, modeling of the scenes, optics, and sensors are included.

In addition, the computational and storage bottlenecks of the simulator are examined and more efficient methods are provided when appropriate. In particular, a method based on Singular Value Decomposition (SVD) is proposed to lower the storage-footprint of the scene model. Furthermore, an efficient algorithm based on Principal Component Analysis (PCA) and Fast Fourier Transform (FFT) is proposed to implement the convolution of the scene with the spatially-varying optical kernels. The quality and complexity of the proposed method are compared with previous work and it is shown that higher quality is achievable with lower complexity.

With the advancement of signal processing and other enabling technologies, new products and services have appeared in large numbers over the past decade, and are changing people's daily lives quickly and profoundly. They could not have occurred without the rapid development in areas like digital communications, information theory, detection and estimation, where resource allocation plays a crucial role.

In this work, we study resource allocation for two classes of problems. The first class is rate allocation in digital systems. The functionality of modern digital systems can be broadly divided into two parts: communications and source coding. For communications, we systematically study the allocation problem from a game theory perspective for the multiuser downlink broadcast channel, and apply the solutions to the special case where spatial block diagonalization is combined with time-sharing to multiplex a subset of the users. For source coding, we consider the achievable sum-rate/distortion tradeoff for the Gaussian central estimation officer problem with a scalar source having arbitrary memory. We formulate the variational problem of minimizing the sum rate subject to a distortion constraint, and the conventional Lagrange method is extended to solve the problem. A sufficient condition is also found that can be used to verify if the necessary solution results in the minimal sum rate.

The second class of problems is target localization. We analyze the performance of a reduced-dimension separable space-time adaptive processing algorithm for radar systems under the large array assumption. The study shows that in the asymptotic sense the simplified scheme performs as well as the fully adaptive algorithm with a significant saving in computational complexity. For target localization in wireless systems, we propose a two-stage approach in order to handle non-line-of-sight transmission based on mild assumptions regarding the propagation environments. For the first stage of positioning, we analyze the cases of scattering and reflection respectively, and propose methods to estimate the position and velocity of the moving target. Once the estimation is done, the results can be used as the initial values of extended Kalman filters in the second stage to track the subsequent movements of the target.