Patent ID: 8619542

Claim:
A method comprising: calculating a first precoding matrix index I from a codebook using a received signal; calculating a second codebook index J* using the first precoding matrix index I to approximate a covariance matrix; calculating a quantized coefficient Î±* to approximate the covariance matrix wherein the quantized coefficient Î±* is determined using the first precoding matrix index I, wherein J* and Î±* are determined as, J * , Î± * = arg â¢ â¢ min J âˆˆ C 1 â€² , Î± âˆˆ C 0 â¢ ï˜… R tr â¡ ( R ) - [ 1 1 + Î± â¢ V 1 â¢ V 1 H + Î± 1 + Î± â¢ V â¡ ( : , J ) â¢ V H â¡ ( : , J ) ] ï˜† F 2 where Î± is a real scalar and takes any value contained in a scalar codebook C 0 , V 1 is a precoding vector from a rank-1 codebook C 1 , V(:,J) denotes a vector (the J th vector) from C 1 â€², R is the covariance matrix, âˆ¥Aâˆ¥ F 2 is the sum of the magnitudes of all entries of matrix A, and C 1 â€² is a set of vectors and forms a rank-1 codebook, and transmitting a codebook based covariance matrix using the first precoding matrix index I, the second codebook index J* and the quantized coefficient Î±*.