Low complexity precoding matrix selection

An apparatus that determines indices for matrix codewords in a matrix codeword codebook, the matrix codewords adapted for communicating information between a transmitter and a receiver, the apparatus comprising:

• an electronically accessible storage that is to store an eigenmode representation for a communications channel, wherein the representation of the eigenmode is based upon a received signal precoded by a first matrix codeword;
• control logic coupled to the temporary storage and that is to perform a test on multiple vector codewords to identify a first vector codeword among the multiple vector codewords, wherein the test includes determining a relationship between the first vector codeword and the eigenmode representation, the first vector codeword is associated with a first vector codeword index that identifies the first vector codeword;
• and
• wherein the control logic generates a matrix codeword index associated with a second matrix codeword in the matrix codeword codebook, wherein the matrix codeword index is based upon the first vector codeword index, and the order of the first vector codeword is different from the order of the second matrix codeword.

A method of determining indices for matrix codewords in a matrix codeword codebook, the matrix codewords adapted for communicating information between a transmitter and a receiver, the method comprising:

• determining number of transmit antennas, Nt, being used to transmit to the receiver and the number of data streams, Ns, being transmitted to the receiver;
• identifying a Householder operation and a vector codebook for generating a matrix codeword codebook, CB(Nt, Ns, L), wherein L is a representation of a number of bits in an index for identifying each matrix codeword in the matrix codeword codebook;
• based upon the identified Householder operation and the vector codebook, performing a first test on multiple vector codewords associated with the vector codebook, wherein the result of the first test is a first vector code index that identifies a first vector codeword among the multiple vector codewords;
• and
• based upon the result of the first test generating a matrix codeword index associated with a second matrix codeword in the matrix codeword codebook, wherein the order of the first vector codeword is different from the order of the second matrix codeword.