The vast amount of spectrum available in the millimeter-wave (mmW) bands offer a path for exponential growth in data rates for wireless communications networks. In emerging systems such as fifth-generation (5G) networks, the use of mmW frequencies will potentially enable unprecedented improvements in network capacity, mobility, and spectral efficiency. However, the exploitation of mmW bands requires solutions to many technical challenges. In particular, the technology limitations present in today's implementations require new paradigms in algorithms, signal processing methods, circuit architectures, and integration methods in order for 5G wireless to become a reality. For example, there is a need for advanced channel models that let designers implement the wireless network infrastructure of the future. There is also a need for new algorithms, software, hardware, and electronic circuits for efficient mmW antenna array processing. This project will exploit well-known physics arising from Einstein's Special Theory of Relativity, namely the causality light-cone, to significantly improve the performance of key array signal processing components in mmW wireless basestations. Specifically, the spatio-temporal properties of electromagnetic waves, as described by Special Relativity, are exploited in novel architectures to improve the energy efficiency, reduce the noise, and improve the linearity of array receivers. A system-wide study of spatio-temporal properties of mmW channels is combined with these architectures to design new types of mmW array receivers and optimum beam forming algorithms. The Special Theory of Relativity describes a region in the multidimensional spacetime continuum that is not occupied by propagating waves due to the constant speed of light and the nature of the wave equation. As a result, the region of support (ROS) of all propagating waves, which correspond to wireless propagation channels, are confined inside a ``Light Cone''. The region of spacetime outside this cone (known as ``Elsewhere'') is a void within which wireless communications signals cannot propagate. Although devoid of waves, the Elsewhere is occupied by both electronic noise and nonlinear distortion arising from real-world amplifiers and data converters. The project explores the possibility of spatially over-sampling the mmW antenna arrays and thereafter applying multidimensional extensions of well-known sigma-delta modulation techniques across both discrete space and continuous-time dimensions to achieve noise and distortion shaping, which effectively move the unwanted received components into Elsewhere. Although sigma-delta algorithms have been employed in analog-to-digital converters (ADCs), it is here proposed that multidimensional extensions of these algorithms are not limited to just ADCs; rather, it is possible to apply these algorithms to low-noise amplifiers, ADCs and other circuit components used in arrays, which in turn leads to the creation of new concepts in multi-dimensional circuit theory for array processing. The technique is expected to lead to improved amplifier noise figure and linearity and exponentially improved ADC figure-of-merit for array digitization at a linear cost in the number of antennas and receivers. The resulting mmW array processors have applications in wireless communications, phased-array radar, and radio telescope antenna apertures. The project is a multi-institutional collaboration between four universities in Ohio and New York, and has multiple education and community outreach activities, which will be implemented via the annual Brooklyn 5G Summit. The project includes mentoring for female engineers and students, development of new educational material, and engagement of underrepresented groups in wireless communications topics. Outreach will be achieved through community activities, workshops, the Brooklyn 5G Summit including events for women in 5G, and scientific outreach and academic events organized within IEEE conferences. The mmW circuits research and education program combines theory with hands-on system prototyping. Industry engagement, which is critically important for emerging wireless technologies, is planned throughout the project, and facilitated via the annual Brooklyn 5G Summit. Open source models, designs and prototype chips will be offered to the public and wireless industry.