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
