A common problem encountered in phased array signal processing is how to remove sources of interference from a desired signal. Two existing methods to accomplish this are the Linearly Constrained Minimum Variance (LCMV) beamformer and the Side-Lobe Canceller (SLC). LCMV provides better performance than SLC, but comes with much higher computational costs. The Steered Auxiliary Beam Canceller (SABC) presented in this thesis is a new algorithm developed to improve the performance of SLC without the computational costs of LCMV. SABC performs better than SLC because it uses high-gain auxiliary channels for cancellation. This new technique is now possible because digital arrays allow for direction finding algorithms such as Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) to estimate the directions of the interference sources. With this added knowledge, high gain beams similar to the main beam may be used as auxiliaries instead of low-gain antenna elements. Another contribution is a method introduced to calculate the computational complexity of LCMV, SLC, and SABC much more accurately than existing methods which only provide order-of-magnitude estimates. The final contribution is a derivation of the signal loss experienced by SLC and SABC and simulations that verify the performance of LCMV, SLC, and SABC. / Master of Science