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The design of direction finding (DF) systems intended to operate over large frequency ranges involves various compromises. Typical implementations involve the use of multiple antenna arrays, each of which is scaled to cover a portion of the frequency range of interest. To minimize the size of the resulting multiband antenna assembly, two or more arrays can be combined in a coplanar antenna configuration. However, this introduces the issue of mutual coupling between the elements of the different arrays. A comprehensive study of the effects of mutual coupling on the estimation error for this type of antenna array configuration for two commonly used DF techniques is provided. Several important results clarify key design issues and trade-offs. It is shown that proper design choices are required to avoid uncorrectable ambiguities and the resulting large estimation errors.