are used to achieve link-level MIMO channel capacity. In addition, random unitary precoding can achieve the open-loop MIMO channel capacity with no signaling overhead in the uplink. The SVD precoding, on the other hand, has been shown to achieve the MIMO channel capacity when channel state information is signaled to the transmitter. In a precoded SU-MIMO system with N transmit antennas and Nr receive antennas, the input-output relationship can be described as y = HWs + n where S = [S1, S2,..., SM] is an M X 1 vector of normalized complex-valued modulated symbols, y = [y1, y2,..., ynr] the N X 1 vectors of received signal and noise, respectively, H is the N X N complex-valued channel matrix, and W is the N X M linear precoding matrix. The superscript "t" denotes the transpose operator. In the receiver, a hard decoded symbol vector S is obtained by decoding the received vector y by a vector decoder, assuming perfect knowledge of the channel and the precoding matrices. We assume 10.4 Multi-antenna transmission schemes the entries of H are independent and distributed according to Z(0,1) and the entries of noise vector n are independent and distributed according to Z(0,No). The input vector S is assumed to be normalized, thus E[ssH] = I where I is an identity matrix. Let's further assume that precoding matrix W is unitary, thus WWH = I. The receiver selects a precoding matrix W,i = 1,2, Ncodebook from a finite set of quantized precoding matrices Q = {W1, W2, WNcodebook} and sends the index of the chosen precoding matrix back to the transmitter over a low-delay feedback channel. There are two questions that need to be answered: (1) the optimal selection criterion for choosing a precoding matrix from S; and (2) the design of codebook O. The matrix W,i = 1,2, ..,Ncodebook can be selected from S by using either of the following optimization criterion [57]: (1) minimizing the trace of the mean squared error (MMSE-trace selection); (2) minimizing the determinant of the mean squared error (MMSE-determinant selection); (3) ma