A method performed by a receiver to provide channel state information as feedback to a transmitter in a multi-antenna wireless communication system, the method comprising: estimating a channel between the transmitter and the receiver; determining a precoder subset comprising one or more precoder elements, each precoder element being a precoder element of a codebook, and the precoder subset including less than all precoder elements of the codebook; for each precoder element in the precoder subset, determining a capacity corresponding to that precoder element based on the channel estimation; determining the CSI associated with the precoder element whose corresponding capacity is maximum among the capacities corresponding to the precoder elements of the precoder subset; and providing the CSI to the transmitter as the feedback, the CSI comprising a rank information and a precoding control index, wherein the codebook is defined for a plurality of ranks, wherein for each rank, the codebook comprises a plurality of precoder elements corresponding to that rank, wherein at least one rank is an equivalence capacity rank, the precoder elements of each equivalence capacity rank being grouped into one or more capacity groups (A, B, C, D, E) in which each precoder element is a member of one capacity group, at least one capacity group includes multiple precoder elements, and within each capacity group, individual capacities of the precoder elements of that capacity group are equal, and wherein the step of determining the precoder subset comprises, for at least one equivalence capacity rank, including at most one precoder element from each capacity group of that equivalence capacity rank into the precoder subset. estimating a channel between the transmitter and the receiver; determining a precoder subset comprising one or more precoder elements, each precoder element being a precoder element of a codebook, and the precoder subset including less than all precoder elements of the codebook; for each precoder element in the precoder subset, determining a capacity corresponding to that precoder element based on the channel estimation; determining the CSI associated with the precoder element whose corresponding capacity is maximum among the capacities corresponding to the precoder elements of the precoder subset; and providing the CSI to the transmitter as the feedback, the CSI comprising a rank information and a precoding control index, wherein the codebook is defined for a plurality of ranks, wherein for each rank, the codebook comprises a plurality of precoder elements corresponding to that rank, wherein at least one rank is an equivalence capacity rank, the precoder elements of each equivalence capacity rank being grouped into one or more capacity groups (A, B, C, D, E) in which each precoder element is a member of one capacity group, at least one capacity group includes multiple precoder elements, and within each capacity group, individual capacities of the precoder elements of that capacity group are equal, and each precoder element is a member of one capacity group, at least one capacity group includes multiple precoder elements, and within each capacity group, individual capacities of the precoder elements of that capacity group are equal, and wherein the step of determining the precoder subset comprises, for at least one equivalence capacity rank, including at most one precoder element from each capacity group of that equivalence capacity rank into the precoder subset.