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Orthogonal frequency division multiplexing (OFDM) is an appealing modulation and multiplexing technique for frequency-selective wireless channels. OFDM is sensitive to carrier frequency offset (CFO), arising due to oscillator mismatch, drift, or mobility-induced Doppler. This is because CFO destroys subcarrier orthogonality. Pilot symbols, repetition coding, or (possibly hopped) null subcarriers; have been proposed and exploited for CFO estimation, but all sacrifice data rate. In this paper, we show that employing two or more antennas at the receiver affords not only a direct receive-diversity benefit, but also important side-benefits as well: in fact CFO can be blindly estimated and the transmitted symbols can be directly recovered, under very relaxed blind identifiability conditions. This follows by recognizing that the resulting baseband model is suitable for parallel factor (PARAFAC) analysis. The results are general enough to cover both single input multiple output (SIMO) and multiple input multiple output (MIMO) OFDM systems with multiple users or multiple transmit antennas. Computer simulation results show that the proposed PARAFAC receiver can achieve performance that is only a few dB away from the non-blind minimum mean-squared error (MMSE) receiver and works well for a wide range of carrier frequency offsets.