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Table 1 An algorithm for determining the optimal solution \(\{\mathbf {v}^{\star },{\mathbf {Q}_{J}^{\star }}\}\) which maximizes the worst-case secrecy rate

From: Robust transmit design for secure AF relay networks with imperfect CSI

1. Initialize τ lb =0, \({\tau _{ub}}=P_{s}P_{r}|\mathbf {h}|^{2}/{\sigma _{D}^{2}}\), P s >0, P r >0, P k ≥0, τ=0, τ sz >0 where the step size τ sz is an arbitrarily small positive quantity;
2. while τ [τ lb ,τ ub ]do
3. Calculate \({\bar {g}}(\tau)\) by solving (17) and let \({\bar {f}}(\tau)={\bar {g}}(\tau)\);
4. Let τ=τ+τ sz ;
5. end while
6. Determine τ which maximizes the objective function of (15);
7. Let τ=τ and calculate \({\bar g}(\tau)\) by solving (17);
8. Calculate \(\{ {{\hat {\mathbf {Q}}}_{\mathbf {v}}},{{\hat {\mathbf {Q}}}_{J}} \}\) by solving (10);
8. Do the matrix decomposition \({\hat {\mathbf {Q}}}_{\mathbf {v}}=\hat {\mathbf {v}}{\hat {\mathbf {v}}}^{H}\);
9. The optimal solution \(\mathbf {v}^{\star }=\hat {\mathbf {v}}\), \({\mathbf {Q}_{J}^{\star }}={{\hat {\mathbf {Q}}}_{J}}\).