To satisfy the growing demands of the mobile and personal broadband communications, recently, many innovative technologies have been devised and extensively used for wireless transmission and reception. In the wireless communication systems, even though the performance would be degraded due to channel characteristics, such as multipath fading and background noise, those impacts can be eliminated dramatically through the utilization of diversity and combining. However, some different kinds of interfering sources, including the significant structure interference due to their operation as multiple access in the cellular communication systems, referred to as the multiple access interference (MAI), and inevitable jammers appeared in the overlapped frequency band for common utility, are still existing and now become the main difficulties to collapse the reception performance and system capacity. To suppress the interferences, some advanced signal processing methods, e.g., smart antenna (SA), multiuser detection, interference cancellation, adaptive optimization, and frequency/ frame synchronization, have been suggested to not only alleviate the effects fundamentally but also enhance the signal quality. Orthogonal frequency division multiplexing (OFDM) is a significant multicarrier (MC) technology, and has been widely employed in some commercial communications, such as digital broadcasting and wireless local area network (WLAN). It is considered to be the one of the most promising techniques to combat multipath fading and MAI for the downlinks transmission of the broadband systems. Moreover, spatial processing exploits the diversity provided by SA or intelligent antenna arrays, in which the adaptive beamformer is utilized, and it is an alternative approach to increase the efficiency of wireless system capacity and performance without allocating additional frequency spectrum. It allows the system to make full use of spatial diversity due to multiple antennas. In this dissertation, the wireless communications based on the OFDM technique and the applications of SA are considered. Also, an adaptive linearly constrained (LC) approach via inverse QR-decomposition (IQRD) recursive least-squares (RLS) algorithm is emphasized. The proposed LC-IQRD-RLS algorithm has the merits, such as numerical stability, fast convergence rate, and implementation efficiency, over the conventional adaptive algorithms. Furthermore, by incorporating with derivative constraint, the narrowband array could improve the robustness against to the wideband and coherent jammers. Here, the iterative quadratic maximum likelihood (IQML) algorithm with norm constraint set is utilized to estimate the jammer subspace. Computer simulations verify that the use of narrowband beamformer with an appropriate algorithm, e.g., LC-IQRD-RLS or IQML, could achieve the desired performance for jammer suppression. Next, their applications to the MC-CDMA system with frequency combining process will be fully addressed. In fact, the frequency diversity is achieved through the optimization approach, based on constrained minimum output energy (CMOE) criterion. Unfortunately, it is very sensitive to the signal mismatch due to channel estimation error. To deal with the mismatch problem, the invariant-property provided by constant modulus (CM) criterion along with the LC-IQRD-RLS algorithm is developed. Simulation results show that the frequency combiner with the robust LCCM IQRD-RLS algorithm could be used to recover the transmitted signal without channel mismatch or distortion, and mitigate the MAI efficiently even in the significant near-far effect environment. To further enhance the detection performance and increase system capacity, the space-time MC-CDMA receiver is proposed by combining the advantages of SA and multicarrier transmission technique. This direct fully space-time MC-CDMA receiver can be implemented via a mathematical operator, i.e., kronecker product. For further investigation, a theoretical analysis could be evaluated under certain assumptions to obtain a closed-form expression of bit error rate (BER). This will help us look more inside the impacts due to the numbers of subcarriers and array sensors. In the last chapter, the familiar problem of carrier frequency offset (CFO) is investigated following the standard of IEEE 802.11 a/g OFDM-based WLAN. The overall frequency synchronization scheme consists of three parts, viz., the coarse and fine automatic frequency control (AFC) circuits, and phase locked loop (PLL). With the proposed frequency synchronization scheme, it reserves 2dB power consumption compared with the current specification even some timing issues presented.