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In this paper, we consider the design of statistical multiple-input-multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) beamformers for millimeter wave (mmWave) channels. The transmitter designs the subcarrier beamformers based on the statistics of the channel, without instantaneous channel information. To overcome the radio frequency (RF) limitation in mmWave application, the subcarrier beamformers are implemented in a hybrid structure, which imposes constraints on the design of subcarrier beamformers. We analyze the unconstrained statistical subcarrier beamformers using spectral analysis of the subcarrier channels. The analysis shows that, for each subcarrier channel, the optimal statistical beamformer is approximately a linear combination of optimal statistical beamformers for some appropriately defined narrowband single-cluster subchannels. The result suggests a design of the subcarrier beamformers that can be readily implemented in a hybrid structure. Furthermore, a hybrid design for the receiver is proposed based on the concept of vector quantization. Simulations are given to show that the use of a hybrid beamforming structure incurs a minor degradation in transmission rate. With three RF chains, the performance is close to that of all digital statistical beamforming.