Patent ID: 8494459

Claim:
A method of operating a precoding system comprising: modulating a data signal to generate modulated symbols; precoding the modulated symbols using a precoder matrix drawn from a plurality of precoder matrices; and transmitting the precoded modulated symbols using eight transmit antennas, wherein the plurality of precoder matrices include: 8×1 vectors having the form [1, e jv , e j2v , e j3v , e jΘ , e jΘ e jv , e jΘ e j2v , e jΘ e j3v ] T /2√{square root over (2)}, where (.) T denotes the transpose operation, j=√{square root over (−1)} and v,Θ are real-valued scalars lying in the interval [0,2π) and drawn from a finite set; 8×2 matrices having the form [ 1 , ⅇ j ⁢ ⁢ v , ⅇ j ⁢ ⁢ 2 ⁢ v , ⅇ j ⁢ ⁢ 3 ⁢ v , ⅇ j ⁢ ⁢ ϑ , ⅇ j ⁢ ⁢ ϑ , ⅇ j ⁢ ⁢ v , ⅇ j ⁢ ⁢ ϑ ⁢ ⅇ j ⁢ ⁢ 2 ⁢ v , ⅇ j ⁢ ⁢ ϑ ⁢ ⅇ j ⁢ ⁢ 3 ⁢ v 1 , ⅇ j ⁢ ⁢ v , ⅇ j ⁢ ⁢ 2 ⁢ v , ⅇ j ⁢ ⁢ 3 ⁢ v , - ⅇ j ⁢ ⁢ ϑ , - ⅇ jϑ ⁢ ⅇ j ⁢ ⁢ v , - ⅇ j ⁢ ⁢ ϑ ⁢ ⅇ j ⁢ ⁢ 2 ⁢ v , - ⅇ j ⁢ ⁢ ϑ ⁢ ⅇ j ⁢ ⁢ 3 ⁢ v ] T / 2 ⁢ 2 and 8×k matrices for 3≦k≦8, whose k columns are mutually orthogonal and have the form [x T ,e jΘ x T ] T where x is a column of a 4×4 matrix E that can be expanded as E=D p (H⊕Q), where ⊕ denotes the Hadamard product of matrices, H is a 4×4 real-valued Hadamard matrix, D p is a 4×4 diagonal matrix of the form D p = [ 1 0 0 0 0 ⅇ j ⁢ ⁢ v 0 0 0 0 ⅇ j ⁢ ⁢ 2 ⁢ v 0 0 0 0 ⅇ j ⁢ ⁢ 3 ⁢ v ] and Q is a real-valued 4×4 matrix of the form Q = [ p r q s q s p r q s p r p r q s ] such that p, q, r, s are real-valued scalars satisfying p 2 +q 2 =r 2 +s 2 =1/2.