Different from the use of IQ modulator or a dual-drive Mach-Zehnder modulator, we investigate an optical vestigial sideband orthogonal frequency division multiplexing (OVSB-OFDM) transmission system using a low-cost directly modulated laser. Precoding techniques and Kramers-Kronig (KK) algorithm are employed to enhance the bit error rate (BER) performance. The KK receiver is applied to eliminate the signal-signal beat interference caused by the square-law detection of the photodetector. Discrete Fourier transform (DFT) and orthogonal circulant matrix transform (OCT) precoding techniques can effectively average the signal-to-noise ratio over the data-carrying subcarriers and improve the BER performance. Through numerical simulation, we discuss the relationship between the order and center frequency of the optical filter and the carrier signal power ratio (CSPR). Furthermore, we study the influence of the KK algorithm and precoding techniques on receiver sensitivity under different transmission distances. The results show that both KK algorithm and precoding technologies can improve receiver sensitivity and extend the transmission distance. The performance of DFT precoding is better than that of OCT precoding. When there is no KK algorithm, the transmission distance of OCT precoding or no precoding is only 20 km at the BER of 3.8e-3; while DFT precoding can extend the transmission distance up to 60 km. With the help of the KK algorithm, OCT precoding and DFT precoding can further extend the transmission distance by up to 40 and 60 km, respectively, compared to the DFT precoding and without the KK algorithm case. The DFT precoding with the KK algorithm can improve the receiver sensitivity of more than 7 dB in terms of received optical power, compared to the no precoding and without the KK algorithm case.