An algorithm has been developed to control the antenna array beam pattern for multiple beam antenna (MBA) or phased array systems. The algorithm is motivated by military satellite communications applications where the uplink received antenna is desired to provide beamforming capability for selective earth coverage and jamming protection. The problem can be formulated as to determine the control weight to meet the user gain and jammer null requirements in their known directions subject to the norm constraint of the weight defined by the power conservation law. The algorithm makes use of an orthogonal decomposition of the weight vector into the constraint weight vector and the zero-output weight vector. If the constraint weight vector satisfies the norm bound constraint, the zero-output vector can further be optimized to minimize the deviation of the resulting weight from the quiescent weight. If the constraint weight vector does not satisfy the norm bound constraint, a recursive procedure has been developed which provides flexibility in the determination of the constraint vectors, the constraint order and the constraint phase optimization. This algorithm provides a practical means to achieve the constraints subject to the norm bound condition.
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