A method of identifying a precoding matrix corresponding to a wireless network channel comprises the steps of identifying a capacity metric that includes an identity matrix, approximating the capacity metric using an approximation metric that ignores the identity matrix, using the approximation metric to search over all matrices in a matrix codebook in order to identify a particular precoding matrix that increases a capacity of the wireless network channel, and transmitting across the wireless network channel a matrix index that corresponds to the particular precoding matrix. Additional techniques for identifying precoding matrices are also described herein, as is a method of approximating a capacity of a wireless network channel in a wireless network.