Short-Range Millimeter-Wave Sensing and Imaging: Theory, Experiments and Super-Resolution Algorithms

Recent advancements in silicon technology offer the possibility of realizing low-cost and highly integrated radar sensor and imaging systems in mm-wave (between 30 and 300 GHz) and beyond. Such active short-range mm-wave systems have a wide range of applications including medical imaging, security scanning, autonomous vehicle navigation, and human gesture recognition. Moving to higher frequencies provides us with the spectral and spatial degrees of freedom that we need for high resolution imaging and sensing application. Increased bandwidth availability enhances range resolution by increasing the degrees of freedom in the time-frequency domain. Cross-range resolution is enhanced by the increase in the number of spatial degrees of freedom for a constrained form factor. The focus of this thesis is to explore system design and algorithmic development to utilize the available degrees of freedom in mm-wave frequencies in order to realize imaging and sensing capabilities under cost, complexity and form factor constraints. We first consider the fundamental problem of estimating frequencies and gains in a noisy mixture of sinusoids. This problem is ubiquitous in radar sensing applications, including target range and velocity estimation using standard radar waveforms (e.g., chirp or stepped frequency continuous wave), and direction of arrival estimation using an array of antenna elements. We have developed a fast and robust iterative algorithm for super-resolving the frequencies and gains, and have demonstrated near-optimal performance in terms of frequency estimation accuracy by benchmarking against the Cramer Rao Bound in various scenarios.Next, we explore cross-range radar imaging using an array of antenna elements under severe cost, complexity and form factor constraints. We show that we must account for such constraints in a manner that is quite different from that of conventional radar, and introduce new models and algorithms validated by experimental results. In order to relax the synchronization requirements across multiple transceiver elements we have considered the monostatic architecture in which only the co-located elements are synchronized. We investigate the impact of sparse spatial sampling by reducing the number of array antenna elements, and show that ``sparse monostatic'' architecture leads to grating lobe artifact, which introduces ambiguity in the detection/estimation of point targets in the scene. At short ranges, however, targets are ``low-pass'' and contain extended features (consisting of a continuum of points), and are not well-modeled by a small number of point scatterers. We introduce the concept of ``spatial aggregation,'' which provides the flexibility of constructing a dictionary in which each atom corresponds to a collection of point scatterers, and demonstrate its effectiveness in suppressing the grating lobes and preserving the information in the scene.Finally, we take a more fundamental and systematic approach based on singular decomposition of the imaging system, to understand the information capacity and the limits of performance for various geometries. In general, a scene can be described by an infinite number of independent parameters. However, the number of independent parameters that can be measured through an imaging system (also known as the degrees of freedom of the system) is typically finite, and is constrained by the geometry and wavelength. We introduce a measure to predict the number of spatial degrees of freedom of 1D imaging systems for both monostatic and multistatic array architectures. Our analysis reveals that there is no fundamental benefit in multistatic architecture compared to monostatic in terms of achievable degrees of freedom. The real benefit of multistatic architecture from a practical point of view, is in being able to design sparse transmit and receive antenna arrays that are capable of achieving the available degrees of freedom. Moreover, our analytical framework opens up new avenues to investigate image formation techniques that aim to reconstruct the reflectivity function of the scene by solving an inverse scattering problem, and provides crucial insights on the achievable resolution

Capacity-Achieving Distributions of Gaussian Multiple Access Channel with Peak Constraints

Characterizing probability distribution function for the input of a communication channel that achieves the maximum possible data rate is one of the most fundamental problems in the field of information theory. In his ground-breaking paper, Shannon showed that the capacity of a point-to-point additive white Gaussian noise channel under an average power constraint at the input, is achieved by Gaussian distribution. Although imposing a limitation on the peak of the channel input is also very important in modelling the communication system more accurately, it has gained much less attention in the past few decades. A rather unexpected result of Smith indicated that the capacity achieving distribution for an AWGN channel under peak constraint at the input is unique and discrete, possessing a finite number of mass points. In this thesis, we study multiple access channel under peak constraints at the inputs of the channel. By extending Smith's argument to our multi-terminal problem we show that any point on the boundary of the capacity region of the channel is only achieved by discrete distributions with a finite number of mass points. Although we do not claim uniqueness of the capacity-achieving distributions, however, we show that only discrete distributions with a finite number of mass points can achieve points on the boundary of the capacity region. First we deal with the problem of maximizing the sum-rate of a two user Gaussian MAC with peak constraints. It is shown that generating the code-books of both users according to discrete distributions with a finite number of mass points achieves the largest sum-rate in the network. After that we generalize our proof to maximize the weighted sum-rate of the channel and show that the same properties hold for the optimum input distributions. This completes the proof that the capacity region of a two-user Gaussian MAC is achieved by discrete input distributions with a finite number of mass points