This article proposes a novel formula to design two-element arrays with antenna mode switch techniques for direction-of-arrival estimation. This formula can mathematically predict and physically explain how the back-lobe and element spacing of an antenna array influence the errors and failure rates of direction-of-arrival estimation. In addition, a practical antenna design for implementing the proposed antenna mode switch technique is also given. Practical implementation of the antenna design covers frequencies of 2,300 to 2,690 MHz, which is commonly used in modern wireless communication systems.
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