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Three adaptive beamforming algorithms are proposed that have a prescribed quiescent beam pattern and utilize the remaining degrees of freedom to reduce interference. The algorithms do not require explicit knowledge of the direction of arrival for the signal of interest. However, a correlated reference is required. These algorithms have well-behaved transient response and fast convergence making them suitable for time-varying channels. The algorithms have improved SINR over the generalized side-lobe canceller (GSC) when multiple interferers impinge upon the main beam of the quiescent pattern.