Precoding codebooks for MIMO communication systems

A method for communication, comprising:

• configuring a communication system that includes a transmitter and a receiver with a first codebook of first matrices for mapping up to N data streams onto N transmit antenna ports of the transmitter, each of at least some of the first matrices in the first codebook derived from respective second and third matrices selected respectively from a second codebook and a third codebook, wherein the second and third codebooks are configured for mapping data onto respective numbers of transmit antenna ports that are less than N;
• mapping the data streams onto the N transmit antenna ports using a scheme based on one of the first matrices;
• and
• transmitting the mapped data streams over the N transmit antenna ports from the transmitter to the receiver,
• wherein the first matrices map R1 data streams onto the N antenna ports, R1≦N, wherein configuring the communication system comprises defining a set of the matrices for mapping r data streams onto the N transmit antenna ports, r<R1, each matrix in the set comprising a subset of columns of a given matrix selected from the first matrices, and wherein defining the set comprises including a candidate matrix in the set responsively to verifying that the candidate matrix cannot be expressed as a weighted permutation of the columns of another matrix in the set.