Mathematical optimization techniques for cognitive radar networks

This thesis discusses mathematical optimization techniques for waveform design in cognitive radars. These techniques have been designed with an increasing level of sophistication, starting from a bistatic model (i.e. two transmitters and a single receiver) and ending with a cognitive network (i.e. multiple transmitting and multiple receiving radars). The environment under investigation always features strong signal-dependent clutter and noise. All algorithms are based on an iterative waveform-filter optimization. The waveform optimization is based on convex optimization techniques and the exploitation of initial radar waveforms characterized by desired auto and cross-correlation properties. Finally, robust optimization techniques are introduced to account for the assumptions made by cognitive radars on certain second order statistics such as the covariance matrix of the clutter. More specifically, initial optimization techniques were proposed for the case of bistatic radars. By maximizing the signal to interference and noise ratio (SINR) under certain constraints on the transmitted signals, it was possible to iteratively optimize both the orthogonal transmission waveforms and the receiver filter. Subsequently, the above work was extended to a convex optimization framework for a waveform design technique for bistatic radars where both radars transmit and receive to detect targets. The method exploited prior knowledge of the environment to maximize the accumulated target return signal power while keeping the disturbance power to unity at both radar receivers. The thesis further proposes convex optimization based waveform designs for multiple input multiple output (MIMO) based cognitive radars. All radars within the system are able to both transmit and receive signals for detecting targets. The proposed model investigated two complementary optimization techniques. The first one aims at optimizing the signal to interference and noise ratio (SINR) of a specific radar while keeping the SINR of the remaining radars at desired levels. The second approach optimizes the SINR of all radars using a max-min optimization criterion. To account for possible mismatches between actual parameters and estimated ones, this thesis includes robust optimization techniques. Initially, the multistatic, signal-dependent model was tested against existing worst-case and probabilistic methods. These methods appeared to be over conservative and generic for the considered signal-dependent clutter scenario. Therefore a new approach was derived where uncertainty was assumed directly on the radar cross-section and Doppler parameters of the clutters. Approximations based on Taylor series were invoked to make the optimization problem convex and {subsequently} determine robust waveforms with specific SINR outage constraints. Finally, this thesis introduces robust optimization techniques for through-the-wall radars. These are also cognitive but rely on different optimization techniques than the ones previously discussed. By noticing the similarities between the minimum variance distortionless response (MVDR) problem and the matched-illumination one, this thesis introduces robust optimization techniques that consider uncertainty on environment-related parameters. Various performance analyses demonstrate the effectiveness of all the above algorithms in providing a significant increase in SINR in an environment affected by very strong clutter and noise

Proceedings of the Fall 1995 Advanced Digital Communication Systems

Coordinated Science Laboratory was formerly known as Control Systems Laborator

Timing and Carrier Synchronization in Wireless Communication Systems: A Survey and Classification of Research in the Last 5 Years

Timing and carrier synchronization is a fundamental requirement for any wireless communication system to work properly. Timing synchronization is the process by which a receiver node determines the correct instants of time at which to sample the incoming signal. Carrier synchronization is the process by which a receiver adapts the frequency and phase of its local carrier oscillator with those of the received signal. In this paper, we survey the literature over the last 5 years (2010–2014) and present a comprehensive literature review and classification of the recent research progress in achieving timing and carrier synchronization in single-input single-output (SISO), multiple-input multiple-output (MIMO), cooperative relaying, and multiuser/multicell interference networks. Considering both single-carrier and multi-carrier communication systems, we survey and categorize the timing and carrier synchronization techniques proposed for the different communication systems focusing on the system model assumptions for synchronization, the synchronization challenges, and the state-of-the-art synchronization solutions and their limitations. Finally, we envision some future research directions

Learning from High-Dimensional Multivariate Signals.

Modern measurement systems monitor a growing number of variables at low cost. In the problem of characterizing the observed measurements, budget limitations usually constrain the number n of samples that one can acquire, leading to situations where the number p of variables is much larger than n. In this situation, classical statistical methods, founded on the assumption that n is large and p is fixed, fail both in theory and in practice. A successful approach to overcome this problem is to assume a parsimonious generative model characterized by a number k of parameters, where k is much smaller than p. In this dissertation we develop algorithms to fit low-dimensional generative models and extract relevant information from high-dimensional, multivariate signals. First, we define extensions of the well-known Scalar Shrinkage-Thresholding Operator, that we name Multidimensional and Generalized Shrinkage-Thresholding Operators, and show that these extensions arise in numerous algorithms for structured-sparse linear and non-linear regression. Using convex optimization techniques, we show that these operators, defined as the solutions to a class of convex, non-differentiable, optimization problems have an equivalent convex, low-dimensional reformulation. Our equivalence results shed light on the behavior of a general class of penalties that includes classical sparsity-inducing penalties such as the LASSO and the Group LASSO. In addition, our reformulation leads in some cases to new efficient algorithms for a variety of high-dimensional penalized estimation problems. Second, we introduce two new classes of low-dimensional factor models that account for temporal shifts commonly occurring in multivariate signals. Our first contribution, called Order Preserving Factor Analysis, can be seen as an extension of the non-negative, sparse matrix factorization model to allow for order-preserving temporal translations in the data. We develop an efficient descent algorithm to fit this model using techniques from convex and non-convex optimization. Our second contribution extends Principal Component Analysis to the analysis of observations suffering from circular shifts, and we call it Misaligned Principal Component Analysis. We quantify the effect of the misalignments in the spectrum of the sample covariance matrix in the high-dimensional regime and develop simple algorithms to jointly estimate the principal components and the misalignment parameters.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91544/1/atibaup_1.pd