In this paper, we present self-interference (SI) cancellation techniques in the digital domain for in-band full-duplex systems employing orthogonal frequency division multiple access (OFDMA) in the downlink (DL) and single-carrier frequency division multiple access (SC-FDMA) in the uplink (UL), as in the long-term evolution (LTE) system. The proposed techniques use UL subcarrier nulling to accurately estimate SI channels without any UL interference. In addition, by exploiting the structures of the transmitter imperfection and the known or estimated parameters associated with the imperfection, the techniques can further improve the accuracy of SI channel estimation. We also analytically derive the lower bound of the mean square error (MSE) performance and the upper bound of the signal-to-interference-plus-noise ratio (SINR) performance for the techniques, and show that the performance of the techniques are close to the bounds. Furthermore, by utilizing the SI channel estimates and the nonlinear signal components of the SI caused by the imperfection to effectively eliminate the SI, the proposed techniques can achieve SINR performance very close to the one in perfect SI cancellation. Finally, because the SI channel estimation of the proposed techniques is performed in the time domain, the techniques do not require symbol time alignment between SI and UL symbols.