Phased array feeds (PAFs) are a promising new technology for astronomical radio telescopes. While PAFs have been used in other fields, the demanding sensitivity and calibration requirements in astronomy present unique new challenges. This dissertation presents some of the first astronomical PAF results demonstrating the lowest noise temperature and highest sensitivity at the time (66 Kelvin and 3.3 m^2/K, respectively), obtained using a narrowband (425 kHz bandwidth) prototype array of 19 linear co-polarized L-band dipoles mounted at the focus of the Green Bank 20 Meter Telescope at the National Radio Astronomy Observatory (NRAO) in Green Bank, West Virginia. Results include spectral line detection of hydroxyl (OH) sources W49N and W3OH, and some of the first radio camera images made using a PAF, including an image of the Cygnus X region. A novel array Y-factor technique for measuring the isotropic noise response of the array is shown along with experimental measurements for this PAF. Statistically optimal beamformers (Maximum SNR and MVDR) are used throughout the work. Radio-frequency interference (RFI) mitigation is demonstrated experimentally using spatial cancelation with the PAF. Improved RFI mitigation is achieved in the challenging cases of low interference-to-noise ratio (INR) and moving interference by combining subspace projection (SP) beamforming with a polynomial model to track a rank 1 subspace. Limiting factors in SP are investigated including sample estimation error, subspace smearing, noise bias, and spectral scooping; each of these factors is overcome with the polynomial model and prewhitening. Numerical optimization leads to the polynomial subspace projection (PSP) method, and least-squares fitting to the series of dominant eigenvectors over a series of short term integrations (STIs) leads to the eigenvector polynomial subspace projection (EPSP) method. Expressions for the gradient, Hessian, and Jacobian are given for use in numerical optimization. Results are given for simulated and experimental data, demonstrating deeper beampattern nulls by 6 to 30dB. To increase the system bandwidth toward the hundreds of MHz bandwidth required by astronomers for a fully science-ready instrument, an FPGA digital backend is introduced using a 64-input analog-to-digital converter running at 50 Msamp/sec and the ROACH processing board developed at the University of California, Berkeley. International efforts to develop digital back ends for large antenna arrays are considered, and a road map is proposed for development of a hardware correlator/beamformer at BYU using three ROACH boards communicating over 10 gigabit Ethernet.

Among the research topics needing to be addressed to further the development of phased array feeds (PAFs) for radio astronomical use are challenges associated with calibration, beamforming, and imaging for single dish observations. This dissertation addresses these concerns by providing analysis and solutions that provide a clearer understanding of the effort required to implement PAFs for complex scientific research. It is shown that calibration data are relatively stable over a period of five days and may still be adequate after 70 days. A calibration update system is presented with the potential to refresh old calibrators. Direction-dependent variations have a much greater affect on calibration stability than temporal variations. There is an inherent trade-off in beamformer design between achieving high sensitivity and maintaining beam pattern stability. A hybrid beamformer design is introduced which uses a numerical optimizer to balance the trade-off between these two conflicting goals to provide the greatest sensitivity for a desired amount of pattern control. Relative beam variations that occur when electronically steering beams in the field of view must be reduced in order for a PAF to be useful for source detection and imaging. A dual constraint beamformer is presented that has the ability to simultaneously achieve a uniform main beam gain and specified noise response across all beams. This alone does not reduce the beam variations but it eliminates one aspect of the problem. Incorporating spillover noise control through the use of rim calibrators is shown to reduce the variations between beams. Combining the dual constraint and rim constraint beamformers offers a beamforming option that provides both of these benefits.