Patent ID: 8346193

Claim:
A method implemented in a transmitter used in a wireless communications system, the method comprising: precoding a symbol with a precoding matrix selected from a codebook comprising a plurality of matrices; and transmitting to a receiver the precoded symbol using at least two transmit antennas, wherein the plurality of matrices have a nested structure and are in accordance with the following expression: A ⁡ ( v i 1 1 , v i 2 2 , v i 3 3 , … ⁢ , ) = [ v i 1 1 , HH ⁡ ( v i 1 1 - ⅇ 1 M ) ⁡ [ 0 v i 2 2 ] , HH ⁡ ( v i 1 1 - ⅇ 1 M ) [ 0 HH ⁡ ( v i 2 2 - ⅇ 1 M - 1 ) ⁡ [ 0 v i 3 3 ] ⁢ ] , ⁢ … ⁢ ] , wherein ⅇ 1 N = [ 1 , 0 , … ⁢ , 0 ] T ∈ C N M is the number of transmit antennas, C N is an N-dimensional complex space, and HH ⁡ ( w ) = { I - 2 ⁢ ww H  w  2 I ⁢ if ⁢ ⁢ w ≠ 0 if ⁢ ⁢ w = 0 ⁢ and ⁢ ⁢ { v i j j ∈ C M - j + 1 } is a vector codebook, and wherein the wireless communications system comprises a multi-rank beamforming (MRBF) system.