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A system consisting of an antenna array and an adaptive processor can perform filtering in both the space and the frequency domains, thus reducing the sensitivity of the signal-receiving system to interfering directional noise sources. Variable weights of a signal processor can be automatically adjusted by a simple adaptive technique based on the least-mean-squares (LMS) algorithm. During the adaptive process an injected pilot signal simulates a received signal from a desired "look" direction. This allows the array to be "trained" so that its directivity pattern has a main lobe in the previously specified look direction. At the same time, the array processing system can reject any incident noises, whose directions of propagation are different from the desired look direction, by forming appropriate nulls in the antenna directivity pattern. The array adapts itself to form a main lobe, with its direction and bandwidth determined by the pilot signal, and to reject signals or noises occurring outside the main lobe as well as possible in the minimum mean-square error sense. Several examples illustrate the convergence of the LMS adaptation procedure toward the corresponding Wiener optimum solutions. Rates of adaptation and misadjustments of the solutions are predicted theoretically and checked experimentally. Substantial reductions in noise reception are demonstrated in computer-simulated experiments. The techniques described are applicable to signal-receiving arrays for use over a wide range of frequencies.