"Full-duplex (FD) wireless communications can potentially double the spectral efficiency by transmitting and receiving simultaneously over the same frequency at a cost of a large power difference between the high-power self-interference (SI), and the low-power intended signal received from the remote transmitter. SI can be reduced gradually by a combination of radio-frequency (RF) and baseband SI-cancellation stages. Each stage requires the estimation of various distortions that the SI endures, such as SI-channel and transceiver nonlinearities. This thesis deals with the development of SI-cancellation techniques that are well adapted to FD operations.We address SI-cancellation for FD operations in the presence of imperfect RF components. In particular, we develop a new scheme to jointly estimate the IQ mixer imbalance, power amplifier (PA) nonlinearities, up-/down-conversion phase-noise and SI-channel. First, we study and develop a baseband model that captures the most significant transceiver RF imperfections, for both separate- and common-oscillator structures used in the up- and down-conversions. A basis expansion model (BEM) is then derived to approximate the time-varying phase-noise, and to transform the problem of estimating the time-varying phase-noise into the estimation of a set of static coefficients. Using the method of maximum likelihood (ML) criterion, the likelihood function is derived in the presence of the unknown intended signal, which leads to the joint estimation of the intended channel, the SI-channel, the nonlinear impairments and the phase-noise. When the intended signal is unknown, an iterative procedure is developed to find the ML estimate of the different parameters based on its own known transmitted data, the known pilot symbols, and the statistic of the unknown intended signal received from the intended transmitter. We consider the two pilot-insertion structures used in LTE for the frequency-multiplexed pilots and the time-multiplexed pilots. Compared to training-based techniques, the full use of the received signal significantly reduces the required number of pilot symbols. Simulation results indicate that the proposed algorithms can offer a superior SI-cancellation performance, with the resulting signal-to-SI-and-noise ratio (SINR) being very close to the signal-to-noise ratio (SNR).Moreover, we study the power of SI after each cancellation stage, taking into account the transceiver impairments. One SI-cancellation scheme, which combines antenna cancellation, RF cancellation and digital cancellation, provides results from real world experiments that show the feasibility of an FD design. In general, it is difficult to assess the exact level of the SI reduction that is obtainable due to the interactions among factors such as transceiver impairments, wireless propagation channel and estimation error. We hereby identify the main factors that affect the cancellation performance. This allows for a better understanding of the obtained performance, and leads to the development of new methods that improves the cancellation capability of FD systems. We address the impact of each transceiver impairment in FD systems, and specify the limiting factors of the RF and baseband SI-cancellation stages for a given architecture. In addition, we demonstrate that reducing the SI before the LNA/ADC, via the RF SI-cancellation stage is necessary to avoid high quantization noise from the ADC. The analysis further reveals that the transmitter nonlinearities need to be modeled and canceled in the baseband SI-cancellation stage. Finally, in light of our simulation results, we discuss the trade-off between the amount of SI-cancellation and the number of cancellation stages, and propose the potential case scenarios for operations with one digital cancellation." --