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Polarization-mode dispersion (PMD) can cause frequency-selective fading in direct-detection optical orthogonal frequency division multiplexing (DDO-OFDM) systems. In this paper, we examine the effects of this fading. We begin with an analysis of the frequency-selective fading caused by first-order PMD. We then estimate the impact of PMD in single-receiver DDO-OFDM using all-order simulations to generate outage probabilities as a function of signal-to-noise ratio (SNR) penalty. The performances of three single-receiver DDO-OFDM formats are compared and a new format that minimizes the frequency difference between the carrier and sideband is found to be more tolerant to PMD. We then introduce a DDO-OFM system that includes polarization diversity and carrier boost in the receiver. The effects of various configurations are simulated and the results suggest that a data rate of 42.7 Gb/s can be achieved within an optical bandwidth of 40 GHz, and with negligible PMD penalties.