From: Joint source and relay precoding for generally correlated MIMO with full and partial CSIT
Initialize \( \mathbf {b}^{(p)} = \frac {p_{1}}{M}\mathbf {I}_{M} \) satisfying (60) | |
Repeat | |
1) | Find v (p) (i.e., the solution to problem (57)) for the fixed b (p) using |
 | \( v_{l}^{(p)} = \left [\sqrt {\left (\frac {\lambda _{1,l}}{2 \gamma \lambda _{\theta,l}}b_{l}^{(p)}\right)^{2} + \frac {\lambda _{1,l}}{\gamma \lambda _{\theta,l}} b_{l}^{(p)} \mu _{v}} - \frac {\lambda _{1,l}}{2 \gamma \lambda _{\theta,l}}b_{l}^{(p)} - \frac {1}{\gamma \lambda _{\theta,l}} \right ]^{+}, \) |
 | where μ v >0 satisfies |
 | \( \sum _{l=1}^{L} {\left [\sqrt {\left (\frac {\lambda _{1,l}}{2 \gamma \lambda _{\theta,l}}b_{l}^{(p)}\right)^{2} + \frac {\lambda _{1,l}}{\gamma \lambda _{\theta,l}} b_{l}^{(p)} \mu _{v}} - \frac {\lambda _{1,l}}{2 \gamma \lambda _{\theta,l}}b_{l}^{(p)} - \frac {1}{\gamma \lambda _{\theta,l}} \right ]^{+}} = p_{2}. \) |
 | Compute \( \mathcal {\dot {I}}_{erg}(\mathbf {b}^{(p)},\mathbf {v}^{(p)})^{(old)}. \) |
2) | Find b (p) (i.e., the solution to problem (59)) with the obtained v (p) using |
 | \( b_{l}^{(p)} = \left [\sqrt {\left (\frac {\gamma \lambda _{\theta,l}}{2 \lambda _{1,l}}v_{l}^{(p)}\right)^{2} + \frac {\gamma \lambda _{\theta,l}} { \lambda _{1,l}} v_{l}^{(p)} \mu _{b}} - \frac {\gamma \lambda _{\theta,l}}{2 \lambda _{1,l}}v_{l}^{(p)} - \frac {1}{\lambda _{1,l}} \right ]^{+}, \) |
 | where μ b >0 meets |
 | \( \sum _{l=1}^{L} {\left [\sqrt {\left (\frac {\gamma \lambda _{\theta,l}}{2 \lambda _{1,l}}v_{l}^{(p)}\right)^{2} + \frac {\gamma \lambda _{\theta,l}} { \lambda _{1,l}} v_{l}^{(p)} \mu _{b}} - \frac {\gamma \lambda _{\theta,l}}{2 \lambda _{1,l}}v_{l}^{(p)} - \frac {1}{\lambda _{1,l}} \right ]^{+}} = p_{1}. \) |
 | Compute \( \mathcal {\dot {I}}_{erg}(\mathbf {b}^{(p)},\mathbf {v}^{(p)})^{(new)}. \) |
Until \( \mathcal {\dot {I}}_{erg}(\mathbf {b}^{(p)},\mathbf {v}^{(p)})^{(new)} - \mathcal {\dot {I}}_{erg}(\mathbf {b}^{(p)},\mathbf {v}^{(p)})^{(old)} \leq \epsilon. \) Here, ε>0 denotes | |
a desired accuracy. |