In this thesis we first proposed a limited feedback system which sends back only the bit allocation (BA) information. The system will be termed a BA system. we show that the proposed BA system can achieve full di- versity order. we will also derive the optimal bit allocation for minimum bit error rate when the transmission rate is given. Secondly, we develop low-complexity selection criteria for conventional one-step precoder system which feedbacks only the precoder information. A two-step system is pro- posed to reduce the number of searches. In simulations, the usefulness of the proposed systems will be demonstrated.