Orthogonal frequency division multiplexing (OFDM) has been widely adopted for high data rate wireless transmissions. By deploying multiple receiving antennas, single-input multiple-output- (SIMO-) OFDM can further enhance the performance with spatial diversity. However, due to the large dynamic range of OFDM signals and the nonlinear nature of analog components, it is pragmatic to model the transmitter with a peak-power constraint. A natural question to ask is whether SIMO-OFDM transmissions can still enjoy the antenna diversity in this case. In this paper, the effect of the peak-power limit on the error performance of uncoded SIMO-OFDM systems is studied. In the case that the receiver has no information about the transmitter nonlinearity, we show that full antenna diversity can still be collected by carefully designing the transmitters, while the receiver performs a maximum ratio combining (MRC) method which is implemented the same as that in the average power constrained case. On the other hand, when the receiver has perfect knowledge of the peak-power-limited transmitter nonlinearity, zero-forcing (ZF) equalizer is able to collect full antenna diversity. In addition, an iterative method on joint MRC and clipping mitigation is proposed to achieve high performance with low complexity.