The Brigham Young University (BYU) Radio Astronomy Systems group, in collaboration with the National Radio Astronomy Observatory (NRAO), the Center for Astrophysics at West Virginia University (WVU), and the Green Bank Observatory (GBO) have developed, and commissioned, a broadband real-time digital back end processing system for a 38-element phased array feed (PAF) with 150 MHz of instantaneous bandwidth. This system is capable of producing coarse and fine channel correlations, and implements a real-time beamformer that forms 7 simultaneous dual-polarized beams. This thesis outlines the hardware and software development for the digital back end and presents on-telescope commissioning results. This system has been measured to provide an unprecedented low Tsys/η noise level of 28 K and can perform maps of galactic hydrogen observations in a fraction of the time of a conventional single horn feed. The National Radio Astronomy Observatory (NRAO) has recently announced the concept and development of the next generation Very Large Array (ngVLA), a large interferometric array consisting of 300 radio telescopes and longest baseline (distance between a pair of antennas) of 300 km. Large interferometric arrays have been shown to attenuate radio frequency interference (RFI) because it is decorrelated as it propagates across long baselines. This is not always sufficient, especially with dense core array geometries and with the ever-increasing amount of strong RFI sources. Conventional RFI projection-based mitigation techniques have performed poorly on large interferometers because of covariance matrix estimation error due to decorrelation when identifying interference subspace parameters. This thesis presents an algorithm that overcomes the challenge of decorrelation by applying subspace projection via subarray processing (SP-SAP). Each subarray is designed to have a set of elements with high mutual correlation in the interferer for better estimation of subspace parameters. In simulation, compared to the former approach of applying subspace projection on the full array, SP-SAP improves mitigation of the RFI on the order of 9 dB. A signal of interest is shown then to be observable through the RFI in a full synthetic image.