A transmitter is for use with multiple transmit antennas and includes a precoder unit configured to precode data for a transmission using a precoding matrix selected from a codebook, wherein the codebook corresponds to the following three transmission properties for an uplink transmission: 1) all precoding elements from the precoding matrix have a same magnitude, 2) each precoding element from the precoding matrix is taken from a set of finite values and 3) there is only one non-zero element in any row of the precoding matrix. The transmitter also includes a transmit unit configured to transmit the precoded data.