Y1,k=[Hu1,k(:,1)Hu2,k(:,1)Hu3,k(:,1)Hu4,k(:,1)]·P4×4
An undo P operation results in calculations of the estimated first stream of each user.
Y1,k·P4×4H=[Hu1,k(:,1)Hu2,k(:,1)Hu3,k(:,1)Hu4,k(:,1)]
The CPE build up at the end of received HE-LTF4 is denoted as θu1, θu2, θu3, and θu4 of users 1, 2, 3, and 4, respectively. A 4×4 CPE matrix is denoted by ?=diag(ejθu1,ejθu2,ejθu3,ejθu4). After receiving HE-LTF8, preamble processor 106 processes signal Y2,k below.
Y2,k=[Hu1,k(:,1)Hu2,k(:,1)Hu3,k(:,1)Hu4,k(:,1)]·?P4×4
An undo P operation using P4×4H and a subsequent zero forcing operation are used to obtain the per-user CPE estimates within ?.
HdY2,k·P4×4H=Hd[Hu1,k(:,1)Hu2,k(:,1)Hu3,k(:,1)Hu4,k(:,1)]·?P4×4·P4×4H=?
where Hd is the pseudo inverse of [Hu1,k(:,1)Hu2,k(:,1)Hu3,k(:,1)Hu4,k(:,1)].