In this dissertation two categories of adaptive beamforming algorithms have been studied. In first category the adaptive beamforming has been applied for null steering whereas in second category it has been applied for direction of arrival mismatch problem to avoid performance degradation of the beamformers. New algorithms have been contributed in both categories. In case of first category a specific structure has been proposed which provides independent steering of all the available nulls present in the radiation pattern of an array antenna. The idea is based on decoupling of the complex weights employed with each antenna element to provide adaptively by controlling their values. This results in a proposed specific structure. The proposed structure is further improved by incorporating sidelobe suppression capability. Second Order Cone Programming has been used to get the appropriate set of weights to be utilized in the proposed structure. Similarly, the method for improving beam symmetry around the desired signal direction is also incorporated. These additional features are included over the cost of number of steerable nulls. A tailored Genetic Algorithm is proposed to compute the weight vector required to incorporate the proposed structure for beam symmetry. The second part of dissertation is meant for the second category of adaptive beamformers applied for direction of arrival mismatch problem. Performance of these beamformers degrades severely whenever there is a mismatch between the presumed and actual direction of desired signal impinging on an antenna array. A Robust Generalized Sidelobe Canceller has been proposed in this domain as remedial measure to restore the performance. The major advantage of proposed algorithm is that it provides improved results without broadening the main beam. This feature is an added advantage in comparison with the previously existing techniques. For this purpose the blocking matrix present in GSC has been modified without disturbing the quiescent weight vector. This results in robustness against signal look direction error without broadening the main beam. The simulation results confirm the improved performance of the beamformer. Another approach in this domain is based on diagonal loading of signal and data covariance matrices, involved in subsequent computations. The amount of this diagonal loading level is very critical which must not exceed a specific level to ensure the positive definite behavior of signal covariance matrix. This is a standard requirement for the convergence of existing general rank algorithms. Currently, there exists no reliable criterion for deciding the amount of diagonal loading level. In this context a new algorithm has been contributed to decide the amount of diagonal loading. Proposed algorithm is iterative in nature and uses the beam symmetry around the presumed signal direction to decide the level.