Broadband wireless communication systems require high transmission rates, where the bandwidth of the transmitted signal is larger than the channel coherence bandwidth. This gives rise to time dispersion of the transmitted symbols or frequency-selectivity with different frequency components exhibiting different gains. The time dispersion of the transmitted symbols induces intersymbol interference (ISI) due to multipath propagation, with multipath delays exceeding the transmitted symbol period. On the other hand, recent wireless communication standards such as WiMAX and Long Term Evolution (LTE) not only require high rates, but they also need to support high mobile speeds. High-mobility terminals and scatterers induce Doppler shifts which give rise to a fast fading channel, where the channel coherence time is smaller than the symbol period, and the channel changes rapidly within the symbol duration. The Doppler spreads induce frequency dispersion or time selectivity. LTE is a major step in next generation wireless networks. The LTE physical layer relies on a multiple-access scheme based on orthogonal frequency-division multiplexing (OFDM) with a cyclic prefix (CP) in the downlink, and on single-carrier frequency-division multiple access (SC-FDMA) with a CP in the uplink. OFDM is one of the most important transmission schemes for wireless communications, and it has been used in many standards such as DVB-T/H, DAB, and IEEE 802.11. OFDM can eliminate ISI introduced in a static frequency-selective channel by turning it into a set of parallel frequency-flat channels, and therefore it enables simple one-tap equalization for each subcarrier. An SC system, which can also be viewed as a discrete Fourier transform (DFT) precoded OFDM system, has a smaller peak-to-average-power ratio than conventional OFDM, with complexity and performance comparable to OFDM, but with the complexity shifted from the transmitter to the receiver. Hence, it leads to more power-efficient terminals suitable for uplink transmission. However, both OFDM system and SC system using frequency-domain equalization suffer from time-varying channels, where the orthogonality among the subcarriers is destroyed due to the Doppler shifts. The resulting intercarrier interference (ICI) severely degrades the performance of the one-tap equalizer. The ICI caused by Doppler spreading also makes the channel estimation problem more challenging, which is important for a coherent communication system, with the equalizer at the receiver relying on accurate channel state information. Therefore, advanced techniques are needed to accurately model time- and frequency-selective (i.e., doubly-selective) channels and to counteract the related performance degradation. In the last decade, multi-antenna systems have attracted a lot of research interest for future wireless systems. Using multiple transmit and/or receive antennas can significantly enhance communication system performances such as channel capacity and reliability. Space-time block coding (STBC) has been introduced to achieve the spatial diversity offered by multiple transmit and/or receive antennas. However, as STBC is typically designed for flat-fading channels, the time- and frequency-selectivity will seriously degrade the system performance. Thus, it is crucial to design efficient STBC schemes to counteract its effects. The first part of the thesis focuses on the receiver design for block transmission over doubly-selective channels, specifically, iterative channel estimation and low-complexity turbo equalization for OFDM and SC systems. The second part of the thesis focuses on STBC design for multi-antenna systems in doubly-selective channels. The proposed STBC is designed for a multiple-input single-output (MISO) system with 2 transmit antennas and 1 receive antenna, i.e., a $2 \times 1$ system, but it is straightforward to extend the ideas to a general multiple-input multiple-output (MIMO) system.