Multiple antennas employed at the transmitter and receiver can significantly increase a MIMO system capacity, especially when channel knowledge is available at the transmitter. Channel state information may be provided to the transmitter by the receiver in a codebook based precoding feedback. In a proposed approach is proposed in which the receiver conducts a search of precoder elements of a codebook to provide the transmitter with rank information and precoder control index that enhances capacity. Unlike the conventional exhaustive search, the proposed approach reduces complexity by reducing the search space of precoder elements for consideration. Performance loss is minimized by reducing the search space of higher rank precoder elements. For some ranks, the complexity is reduced without any performance sacrifice by grouping the precoder elements of the rank into groups of equivalent capacities and including at most one precoder element from each group into the search space.