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© 2013 IEEE. Previously, the alternating convex optimization (ACO) was used to reduce the number of elements in the single-pattern linear array. This work extends the ACO method to synthesize the unequally spaced sparse linear arrays with reconfigurable multiple patterns. In this extended ACO, the minimum interspacing constraint can be easily incorporated in the sparse array synthesis by performing a set of constrained alternating convex optimizations. Three examples for synthesizing sparse linear array with different multiple-pattern requirements are conducted to validate the effectiveness, robustness, and advantages of the proposed method. The synthesis results show that the proposed method can effectively reduce the number of elements in the reconfigurable multiple-pattern linear arrays with good control of the sidelobe levels and minimum interspacing. The comparisons with other methods are also given in the examples.