1. A method implemented in a multi-rank beamforming wireless communications system, comprising: precoding a signal in accordance with a codebook comprising a plurality of codebook entries per rank; and transmitting the precoded signal, wherein the codebook restricts elements of codebook entries to be within a predetermined finite set of complex numbers, and each entry in the codebook has both equal column norm and equal row norm, wherein the wireless communications system has at least 4 transmission antennas, and wherein the codebook entries are matrices A that satisfy the following expression: A = [ 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 ] ] , … ⁢ ] , where M is the number of transmit antennas, e 1 N =[1,0 ,. .. , 0] T εC N , C N is an N-dimensional complex space, HH ⁡ ( w ) = { I - 2 ⁢ ⁢ ww H   w   2 if w ≠ 0 I if w = 0 , v i l j ∈ C M - j + 1 ⁢ ⁢ ( l = 1 , 2 , 3 , … ⁢ ) denotes a column vector, and i l denotes an index of the column vector.