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We address diversity schemes for synchronization signal transmission in MIMO systems. We provide both analytical and numerical evaluation of different diversity schemes in different scenarios in terms of signal-to-noise ratio, spatial correlation and maximum Doppler frequency. We first derive an expression for probability of detection in presence of transmit, receive and time diversity. We establish statistical properties of optimum spatial diversity transmission schemes and analytically characterize also the performance of more practical diversity schemes. Analytical results are verified with simulations. Finally we provide extensive results on both optimum schemes as well as the more practical open-loop schemes in different diversity scenarios. The results of the paper can be used to facilitate practical design and implementation of synchronization in multi-antenna wireless systems.