Fast generalized decision feedback equalizer precoder implementation for multi-user multiple-input multiple-output wireless transmission systems

A base station of a multi-user multiple-input multiple-output (MU-MIMO) wireless system having k user terminals (UTs) with Lk antennas each, each user terminal (UT) having associated therewith a feedforward filter represented by F1, F2 . . . ,Fk, the base station including a generalized decision feedback equalizer (GDFE) based precoder comprising:

• a feedforward path;
• a feedback path;
• and
• an interference pre-cancellation block denoted by I−G disposed in the feedback path, I being an identity matrix, G being an interference pre-cancellation matrix;
• wherein the interference pre-cancellation matrix G in the interference pre-cancellation block is determined by
• computing a filter matrix C using the following expression
• C=λ(VΣ1/2)HH†
• for a channel matrix H whose rank is greater than or equal to its number of rows, the channel matrix H representing a channel through which communications occur in the wireless system, where superscript † denotes a Moore-Penrose Generalized Inverse, where V is a unitary matrix, where Σ is a diagonal matrix with non-negative entries, where λ is a scalar variable for a given total transmit power Pt,
• λ=trace(I−[HHDH+I]−1)/Pt,
• where I is an identity matrix, and D is an input covariance matrix for an equivalent Uplink/medium access channel (MAC) in the wireless system which is chosen to be capacity optimal, wherein a feedforward filter matrix F is represented by F=GMHC, where M is a unitary matrix;
• computing the matrix M using QR decomposition (QRD) of C as
• C=MR;
• computing the feedforward filter matrix F as
• F=BlockDiagonal(R)
• where the BlockDiagonal(.) function extracts submatrices F1, F2 . . . , Fk of size {ak×Lk} from block diagonals of the matrix R, and ak is a number of symbols allotted to the kth user terminal (UT) and equals the rank of Fk;
• and
• computing the interference pre-cancellation matrix G as
• G=FR†
• where superscript † denotes a Moore-Penrose Generalized Inverse.

A base station of a multi-user multiple-input multiple-output (MU-MIMO) wireless system having k user terminals (UTs) with Lk antennas each, each user terminal (UT) having associated therewith a feedforward filter represented by F1, F2 . . . , Fk, the base station including a generalized decision feedback equalizer (GDFE) based precoder comprising:

• a feedforward path;
• a feedback path;
• and
• an interference pre-cancellation block denoted by I−G disposed in the feedback path, I being an identity matrix, G being an interference pre-cancellation matrix;
• wherein the interference pre-cancellation matrix G in the interference pre-cancellation block is determined by
• computing a filter matrix C using the following expression
• C=(VΣ1/2)HH†
• for a channel matrix H whose rank is greater than or equal to its number of rows, the channel matrix H representing a channel through which communications occur in the wireless system, where superscript † denotes a Moore-Penrose Generalized Inverse, where V is a unitary matrix, and where Σ is a diagonal matrix with non-negative entries, wherein a feedforward filter matrix F is represented by F=GMHC, where M is a unitary matrix;
• computing the matrix M using QR decomposition (QRD) of C as
• C=MR;
• computing the feedforward filter matrix F as
• F=BlockDiagonal(R)
• where the BlockDiagonal(.) function extracts submatrices F1, F2 . . . , Fk of size {ak×Lk} from block diagonals of the matrix R, and ak is a number of symbols allotted to the kth user terminal (UT) and equals the rank of Fk;
• and
• computing the interference pre-cancellation matrix G as
• G=FR†
• where superscript † denotes a Moore-Penrose Generalized Inverse.