Optimum filter-and-sum beamforming is useful for array systems that suffer from spatially correlated noise and interference over large bandwidth. The set of finite impulse response (FIR) filter coefficients used to implement the optimum filter-and-sum beamformer are selected to optimize signal-to-noise ratio (SNR) and reduce interference from the certain directions. However, these array systems may also be vulnerable to dispersion caused by physical components such as antennas and cables, especially when the dispersion is unequal between sensors. The unequal responses can be equalized by using FIR filters. Although the problems of optimum-SNR beamforming, interference mitigation, and per-sensor dispersion have previously been individually investigated, their combined effects and strategies for mitigating their combined effects do not seem to have been considered.

In this dissertation, combination strategies for optimum filter-and-sum beamforming and sensor dispersion correction are investigated. Our objective is to simultaneously implement optimum filter-and-sum beamforming and per-sensor dispersion correction using a single FIR filter per sensor. A contribution is to reduce overall filter length, possibly also resulting in a significant reduction in implementation complexity, power consumption, and cost.

Expressions for optimum filter-and-sum beamforming weights and per-sensor dedispersion filter coefficients are derived. One solution is found via minimax optimization. To assess feasibility, the cost is analyzed in terms of filter length. These designs are considered in the context of LWA1, the first ``station'' of the Long Wavelength Array (LWA) radio telescope, consisting of 512 bowtie-type antennas and operating at frequencies between 10 MHz and 88 MHz. However, this work is applicable to a variety of systems which suffer from non-white spatial noise and directional interference and are vulnerable to sensor dispersion; e.g., sonar arrays, HF/VHF-band riometers, radar arrays, and other radio telescopes.