This thesis presents methods for modeling the pattern of large axisymmetric paraboloidal focus-fed reflector antenna systems. The intended application of these methods is to improve the performance of time-domain interference canceling (TDC) in radio astronomy. The first method yields a closed-form expression for the antenna pattern with parameters accounting for the focal ratio and feed pattern. In subsequent adaptive methods, parameters of this model are calculated using measurements of interference signals. The corrected pattern model improves the prediction of the change in the true pattern for future times. The methods are compared by (1) comparing the error in the pattern model with respect to the true pattern and (2) comparing the pattern value update period required to achieve a specified level of residual interference when used in TDC. The efficacy of the pattern modeling methods is demonstrated by showing that the error in the pattern model decreases and the pattern value needs to be updated at a much slower rate for effective TDC. / Master of Science / Radio astronomy is the study of astronomical objects at radio frequencies. Radio telescopes, employing large reflector antennas, are often used to detect and measure extremely weak signals received from distant astronomical bodies. A growing problem for radio astronomy is that human-made communication satellites, orbiting around the earth, interfere with the radio signals. A satellite traversing the antenna pattern interferes with the signal of interest and contaminates it. Presently, this interference is managed by scheduling (avoidance) or by deleting the afflicted data. However, satellite interference is expected to become worse in the future with the increase in the number of satellites in orbit. Therefore, it will become increasingly difficult to avoid the interference by scheduling observations, and there may be too much afflicted data to delete. Hence, more sophisticated techniques may soon be required. One possible method for interference mitigation is Time Domain Canceling (TDC), which is the method addressed in this thesis. This method involves generating an estimate of the interference signal from the interfering satellite. This estimated interference signal is then subtracted from the measured signal contaminated with the interference signal. Ideally, this process should completely remove the interference while preserving the signal of interest and the noise (important in radio astronomy). To improve the accuracy of estimation of the interference signal, we require precise knowledge of the antenna pattern because the interference signal is seen through the antenna pattern. However, the pattern for large reflector antennas employed in radio telescopes is not precisely known and is often difficult to measure or analyze. In this work, we address this problem of lack of pattern knowledge by developing methods for modeling the pattern of large axisymmetric paraboloidal focus-fed reflector antenna systems. We have shown that the pattern model can be significantly improved using measurements of the interference signal in real time. We have also demonstrated that the performance of TDC improves with the incorporation of the developed pattern models.