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This report examines the influence of surplus antenna elements in an adaptive array. It is demonstrated that the judicious placement of a few extra antenna elements provides significant performance improvement. In particular, the speed of convergence is improved, and the quality of the antenna beam pattern is enhanced. Convergence rates and beam patterns are closely related to the eigenvalues of the antenna/signal system. A closed form expression is derived for the eigenvalues of a general antenna array with two jammers. From this, expressions for the convergence rate and the optimum beam pattern are found. Computer simulations are used to verify the theoretical developments concerning convergence rates and final beam patterns for a variety of element configurations. (Author)

Most adaptive filters are designed to achieve minimization of estimation error. Other design goals could include satisfaction of constraints as well as minimization of mean square error. The paper proposes a particular set of performance criteria, involving 'soft constraints'. A 'soft-constraint LMS algorithm' is derived from a performance function which is the sum of mean square error and weighted squared constraint violation errors. The soft constraint algorithm is applied to adaptive antenna arrays as an example, which includes a demonstration of the effects of varying the softness of the constraints. Also, convergence properties of the algorithm are presented. A relation between the output power of a signal from a converged soft constraint LMS adaptive filter and the signal's input power is derived, which demonstrates some unexpected behavior. (Author), Prepared in cooperation with Stanford Univ., CA under contract N00019-78-C-0276.