In problems with large number of antenna elements and small number of receive channels, sequential antenna selection allows to obtain high spatial accuracy and resolution, similar to the full array configuration. By using this configuration in passive or active array processing, the system cost can be significantly reduced. In conventional single-input multiple-output (SIMO) radar systems, direction-of-arrival (DOA) estimation and Doppler estimation are decoupled. However, sequential antenna selection introduces coupling between DOA and Doppler. In this paper, the ambiguity function of switched antenna radar system is formulated and its properties are investigated. A number of switching schemes are studied and analyzed. It is shown that judicious design of the antenna switching scheme can greatly reduce the sidelobes in the DOA-Doppler ambiguity function.