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OFDM transmitter diversity systems that do not required a cyclic prefix have recently been proposed as means to improve bandwidth efficiency. For these systems, knowledge of the channel parameters is required at the receivers for interference cancellation, diversity combining, and decoding. In this paper, we propose a low complexity pilot-symbol-assisted channel estimator for OFDM transmitter diversity systems without a cyclic prefix. The pilot symbols are constructed to be periodic within an OFDM symbol interval in order to avoid ISI and ICI and to be non-overlapping in frequency to allow for the simultaneous sounding of the multiple diversity channels. The time-varying channel responses are then tracked by interpolating a set of estimates obtained through periodically transmitted pilot symbols. The effectiveness and limitations of the proposed estimator are verified by computer simulations.