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This paper introduces a new mutual coupling compensation method based on the minimum norm solution to an underdetermined system of equations. The crucial advantage over previous techniques is that the formulation is valid independent of the type of antenna element and provides good results in situations where signal strengths vary considerably. In using the matrix pencil algorithm to estimate the directions of arrival, the examples show that the proposed method results in significantly lower bias than the traditional open circuit method. The analysis of mutual coupling is also applied in the context of a code division multiple access communication system.