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To achieve diversity with a single antenna, a fractional sampling (FS) scheme in OFDM has been proposed. FS achieves path diversity with a higher sampling rate and multiple demodulation branches. In the previous literatures for FS, the sampling interval is fixed even though the initial phase selection of the sampling has been investigated. The fixed sampling interval limits the diversity gain through FS. Thus, in this study, a non-uniform sampling point selection scheme according to the frequency response of a channel is proposed. Numerical results through computer simulation show that the proposed scheme improves the BER performance by about 2 dB when the number of the demodulation branches is 2. While the proposed scheme further improves bit error rate (BER) performance it requires a larger rate and more computational complexity for the selection of the sampling points. Therefore the complexity reduction for the sampling point selection is also investigated. The complexity reduction scheme eliminates the specific sets of the sampling points and reduces the computational complexity of the sampling point selection for the proposed scheme by a factor of 2. Computer simulation also shows that the low complexity version of the proposed scheme even achieves the equivalent BER compared to the original proposed scheme.