In this thesis, efficient lattice reduction (LR) algorithms are developed using matrix structures. As a well-known LR algorithm, LLL algorithm developed by Lenstra, Lenstra, and $Lov\acute{a}sz$ is considered. First, by understanding the LLL algorithm, a class of matrices for which the LLL algorithm requires much less computational complexities is identified. Furthermore, by reformulating the conventional minimum mean-square-error decision feedback equalizer (MMSE-DFE) algorithm using matrix operations, it is shown that the matrix appearing in MMSE-DFE is a special case of our identified class and, accordingly, a new MMSE-DFE adopting the LLL algorithm for a multi-path channel is proposed. Second, by decoupling a given matrix into multiple submatrices having smaller dimension through linear preprocessing based on the correlations among the columns of the given matrix, the computational complexity of LLL algorithm is reduced. As its application, LR aided successive interference cancellation (SIC) combined with linear preprocessing is developed for clustered mobile stations (MSs). LR aided SIC has been extensively studied due to its near-maximum-likelihood (ML) performance. However, the LLL algorithm and the computation of nulling vectors in SIC inherently incurs considerable computational complexity overhead. To reduce their computational complexities, the entire system is decoupled into multiple lower dimensional subsystems using linear preprocessing based on the spatial correlation among MSs. The LR aided SIC is then utilized parallel in each subsystem. Furthermore, to maximize the system performance, MS grouping algorithms are also proposed. Here, the computational complexity and diversity gain of the proposed LR aided SIC with preprocessing are analyzed. Third, a modified lattice reduction algorithm robust to perturbation errors is proposed. The parameters used in the LLL algorithm are statistically analyzed when the perturbation errors are independent and i...