Link layer multicasting systems and methods

1. A beamforming method comprising:

obtaining indications of channel matrices for a plurality of receivers; formulating a beamformer matrix as a linear combination of columns of hermitians of the channel matrices;

determining coefficients of the hermitians in the linear combination to compute the beamformer matrix such that a lowest reception rate among reception rates of each of the receivers is maximized; and

transmitting data signals to the receivers by applying the computed beamformer matrix to data symbols to maximize the lowest reception rate,

wherein the determining coefficients of the hermitians comprises successively orthogonalizing the channel matrices, and

wherein the orthogonalizing comprises determining a given orthogonal channel matrix of a receiver assigned a given index by orthogonailzing the given orthogonal channel matrix to each orthogonal channel matrix of receivers assigned indices that precede or succeed the given index.

2. The method of claim 1 , further comprising selecting a permutation of an assignment of indices to the receivers and performing the successive orthogonalizing for the selected permutation.

3. The method of claim 2 , further comprising selecting a plurality of permutations of an assignment of indices to the receivers and performing the successive orthogonalizing for each of the selected permutations to compute a plurality of corresponding beamforming matrices.

4. The method of claim 3 , further comprising selecting a particular beamforming matrix from the plurality of beamforming matrices that maximizes the lowest reception rate and wherein the transmitting data signals comprises applying the particular beamformer matrix to the data symbols.

5. The method of claim 1 , wherein the determining coefficients further comprises successively calculating each of the coefficients that are non-zero by satisfying a constraint with equality.

6. The method of claim 5 , wherein the determining coefficients further comprises selecting a coefficient at each successive step that minimizes a norm of a corresponding, resulting beamforming matrix.

7. The method of claim 1 , wherein the determining coefficients further comprises accounting for covariances of noise for the receivers.

8. The method of claim 1 , wherein the obtaining comprises receiving a codebook index indicating at least one of a channel direction and channel gain from each of the receivers and wherein the determining comprises assessing a set of matrices that are closer, as determined by a distance metric, to a given codebook matrix denoted by the received codebook index than to codebook matrices denoted by other codebook indices.

9. A non-transitory computer readable storage medium comprising a computer readable program, wherein the computer readable program when executed on a computer causes the computer to:

obtain indications of channel matrices for a plurality of receivers;

formulate a beamformer matrix as a linear combination of columns of hermitians of the channel matrices;

determine coefficients of the hermitians in the linear combination to compute the beamformer matrix such that a lowest reception rate among reception rates of each of the receivers is maximized; and

apply the computed beamformer matrix to data symbols to generate transmit signals that maximize the lowest reception rate,

wherein the determining coefficients of the hermitians comprises successively orthogonalizing the channel matrices, and

wherein the orthogonalizing comprises determining a given orthogonal channel matrix of a receiver assigned a given index by orthogonailzing the given orthogonal channel matrix to each orthogonal channel matrix of receivers assigned indices that precede or succeed the given index.