In this paper, we provide a numerical bit error rate (BER) estimation approach for direct-detected orthogonal frequency division multiplexing (OFDM) signals in the presence of optical preamplified receivers. The individual BER of each subcarrier is first computed by considering their electrical signal-to-noise ratio (SNR), and then the ensemble BER is derived simply by taking the average of all the subcarriers' BERs. The calculated BER is verified by the conventional error-counting approach with high precision and is still accurate with higher quadratic-amplitude modulation (QAM) formats, even under the influences of the optical filtering and polarization mode dispersion (PMD) effects. Based on our simulation approach, the required extra power budget for 16- and 64-QAM relative to 4-QAM format are found to be ~3.8 and 8.2 dB, respectively, at a BER of 10-9. Furthermore, we use this approach to compare the receiving sensitivities and PMD tolerances for the previous proposed gapped and interleaved radio-frequency (RF)-tone-assisted OFDM systems. The results show that the gapped OFDM has a better sensitivity while the interleaved OFDM has a more PMD-tolerable capability.