In Chap. 2 a reduced-complexity partial transmit sequences (PTS) approach is proposed for the reduction of peak-to-average power ratio (PAPR) in OFDM systems. In a PTS scheme, we need several IFFTs (inverse fast Fourier transforms) to compute the partial transmit sequences. There are two main contributions in the paper. Firstly, we propose to partition the input symbols into disjoint subblocks in an interleaving manner. In this way, we can significantly reduce the complexity by sharing the arithmetic in the IFFT computations. Secondly, we show that in the new partition scheme, the number of rotation factors can be reduced by one without affecting the PAPR reduction ability. As a result, the search time for the optimal rotation factor can be reduced by 75\%. Simulation results show that the PAPR of the proposed method is only slightly worse than the original PTS scheme but it has a much lower complexity. In Chap. 3 a time-domain method for joint estimation of in-phase and quadrature-phase (IQ) imbalance, direct current (DC) offset and channel response for orthogonal frequency division multiplexing (OFDM) system is proposed. Using the fact that in an OFDM system the block size is usually much larger than the cyclic prefix length, we show that without knowing the channel impulse response, we are able to accurately estimate the IQ mismatch and DC offset, from which the channel response can be obtained. Only one OFDM block is needed for training. Simulation results demonstrate that the performance of the proposed method is very close to the ideal case when IQ mismatch, DC offset and channel response are perfectly known at the receiver. In Chap. 4 a time-domain method for joint estimation of sampling frequency offset (SFO) and channel response for OFDM systems is proposed. A SFO compensation method using signal processing technique is also described. AS using the same idea in Chap. 3, we are able to accurate estimate the SFO and the channel impulse response. Only one training block is need and there is no need to design it. Simulation results shows that the performance is good and close to ideal case in high SNR.