In this paper, we propose a new vector perturbation scheme which reduces the complexity associated with finding perturbation vectors by searching for the real and imaginary components individually. To minimize a performance loss induced from decoupling joint search, we apply diagonal precoding at the transmitter whose phase angles are iteratively optimized according to the criterion of maximizing the chordal distance between subspaces spanned by the real and imaginary components. Since our main objective is to reduce the system cost, we also propose a simple non-iterative method of finding phase angles with slight performance loss. Simulation results show that the proposed decoupled vector perturbation reduces the average number of search candidate by 56% in comparison to the original vector perturbation in 4-by-4 system. It is also noted that the simple choice of phase angles provides the performance almost identical to that of the iteratively optimized angles. Moreover, we develope a receive antenna combining method for the vector perturbation systems with multiple-antenna receivers. The proposed algorithm designs receive combiners based on the criterion of optimizing the performance metric via a block-coordinate ascent approach.