Master of Science / Department of Electrical and Computer Engineering / Balasubramaniam Natarajan / In recent years, orthogonal frequency division multiplexing (OFDM) scheme has received significant research interest due to its capability of supporting high data rates in hostile environments. As compared to conventional single-carrier modulation schemes, OFDM benefits from low complexity equalization filters and high spectral efficiency. A multiple access implementation of OFDM, i.e., orthogonal frequency division multiple access (OFDMA) has been considered as the multiple access (MA) scheme in 3GPP LTE, or LTE advanced downlink. In cellular OFDMA, frequency hopping (FH) is widely used to exploit frequency diversity gain and improve system throughput; and pilot patterns that have low-cross correlation are employed to improve the quality of channel estimation. However, there are numerous unsolved problems that need to be addressed in frequency hopped and pilot assisted OFDMA systems. Surveying the prior works in the literature, we find that limited research efforts have focused on coping with the inherent disadvantages regarding OFDM in cellular OFDMA systems. In this thesis, we employ the so-called residue number system (RNS) arithmetic concentrating on (a) FH pattern design for minimizing/averaging intra/inter-cell interference, (b) pilot pattern design for improving the quality of channel estimation, and (c) pilot pattern design for facilitating time-frequency synchronization and device identification in multi-cell OFDMA. Regarding (a), RNS-based FH patterns not only preserve orthogonality within the same cell, but also have the minimum number of symbol collisions among adjacent cells. Additionally, the RNS-based method exhibits consistent system performance and more frequency diversity gains as compared to previous efforts. With respect to (b), RNS-based pilot pattern design generates more unique pilot patterns than conventional methods. This results in low probability of pilot-to-pilot collisions, which in turn, significantly improves the quality of channel estimation from the system level perspective. For (c), as a special case of linear congruence sequences, RNS-based pilot patterns have good auto-correlation properties, which are extremely helpful in time-frequency synchronization and device identification.