Steps

Activities

Input

SR channel matrices and noise variance at the relay terminal ( $H_k$ and ${\sigma }_r^{l^2}$ )

1.

Calculation ofthe summation of covariance matrices ${\tilde{S}}_1$ and ${\tilde{S}}_2$ .

2.

Computation of the transform factor $P$ from singular value decomposition of $S$

3.

For $l=1,\cdots ,N_k$ relay receive antennas

4.

For $k=1,\cdots ,K$ number of relays

Using the FKT factor, transform the l^th receive antennas covariance matrix ${\tilde{S}}_1$ from (21)

Transformation of $P$ to ${\tilde{S}}_1$ and selection of the first eigenvector $v^l$ of matrix ${\tilde{S}}_1$

$b_k^l=P{v}^l$ is the relay receive beamforming vector for l^th antennasand k relay receive antennas

5.

Multiplication of $B_k^l$ with $F^j$

6.

End

Output

$F=B_k^l\times F^j$ the relay precoding matrix