Method and apparatus for antenna array channel feedback

An apparatus comprising:

• a receiver configured to receive a set of channel state information reference signals;
• a controller coupled to the receiver, the controller configured to determine, based on the received set of channel state information reference signals, a precoding matrix that is a product of a first precoding matrix and a second precoding matrix, where the first precoding matrix has at least a representation in terms a representation matrix, where the representation matrix is based on a matrix selected from a first codebook, and where the second precoding matrix is based on a second codebook;
• and
• a transmitter coupled to the controller, the transmitter configured to transmit a representation of at least one of the first precoding matrix and the second precoding matrix;
• wherein the product is a block-Kronecker product;
• wherein the block-Kronecker product of two matrices is a horizontal concatenation of a sequence of one or more matrix block products where each of the two matrices is composed of a sequence of one or more horizontally concatenated matrix blocks;
• wherein an ith matrix block product of the sequence of horizontally concatenated matrix blocks is equal to a Kronecker matrix product of the ith matrix block of a first matrix of the two matrices and the ith matrix block of a second matrix of the two matrices;
• wherein the block-Kronecker product comprises:
• PV*PH=[PV(:,1)PH(:,1)PV(:,2)PH(:,2) . . . PV(:,r)PH(:,r)],
• where PV is the first precoding matrix, and
• where PH is the second precoding matrix, and
• r is the number of spatial layers.