This dissertation addresses some challenging problems emerging from practical implementations of high-speed physical-layer communication schemes. The challenges are caused by the underlying physical-layer analog/RF (radio frequency) processing, which inevitably introduces distortions into the baseband demodulation stage. Such distortions arise, for example, in Orthogonal Frequency Division Multiplexing (OFDM) modulation, which has been adopted by several wireless standards. OFDM systems are known to be sensitive to the IQ imbalance and phase noise distortions introduced in the signal down-conversion process. These distortions seriously limit the applicable constellation size and reduce the attainable transmission data rate. Traditionally, the problem has been alleviated by increasing the transmission power of the carrier signal. In this dissertation, an alternative approach is pursued by exploiting signal processing techniques in the digital domain. Chapter 2 develops a two-stage scheme to compensate for phase noise distortion in wireless OFDM systems. In the first stage, block-type pilot symbols are transmitted and the channel coefficients are jointly estimated with the phase noise. In the second stage, comb-type OFDM symbols are transmitted such that the receiver can jointly estimate the data symbols and the phase noise. The joint effects of IQ imbalance and phase noise on OFDM systems are analyzed in Chapter 3, where compensation schemes are proposed and their performance is studied. In Chapter 4, the nonlinear effects caused by the front-end analog processing are investigated in the context of wideband software-defined radio systems. In the presence of strong blocker (interference) signals, such nonlinearities introduce severe cross modulation over the desired signal. The proposed digital solution scans the wide spectrum and locates the desired signal and blocker signals. After down-converting these signals separately to the baseband, they are jointly processed to mitigate the cross-modulation interferences. It is shown that the proposed schemes can effectively mitigate these impairments, consequently, simplifying the RF and analog circuitry design in terms of implementation cost and power consumption. The proposed approach demonstrates how mixed-signal, i.e., joint analog and digital, processing techniques play a critical role in emerging radio technologies.