Table 2 Useful functions for the analysis of the cases described in Section 4
From: DF-based sum-rate optimization for multicarrier multiple access relay channel
(f 1 ( β [k])) −1 | (f 2 ( β [k])) −1 | (f 3 ( β [k])) −1 | (f 4 ( β [k])) −1 | |
|---|---|---|---|---|
Case 1 | \(1+\frac {{\beta _{a}^{2}}[k]|h_{\text {ad}}[k]|^{2}P}{N}\) | \(1+\frac {{\beta _{a}^{2}}[k]|h_{\text {ad}}[k]|^{2}P}{N}\) | \(1+\frac {{\beta _{b}^{2}}[k]|h_{\text {bd}}[k]|^{2}P}{N+{\beta _{a}^{2}}[k]|h_{\text {ad}}[k]|^{2}P}\) | \(1+\frac {{\beta _{b}^{2}}[k]|h_{\text {bd}}[k]|^{2}P}{N+{\beta _{a}^{2}}[k]|h_{\text {ad}}[k]|^{2}P}\) |
Case 2 | \(1+\frac {{\beta _{a}^{2}}[k]|h_{\text {ad}}[k]|^{2}P}{N}\) | \(1+\frac {{\beta _{a}^{2}}[k]|h_{\text {ad}}[k]|^{2}P}{N}\) | \(1+\frac {{\beta _{b}^{2}}[k]|h_{\text {br}}[k]|^{2}P}{N+{\beta _{a}^{2}}[k]|h_{\text {ar}}[k]|^{2}P}\) | \(1+\frac {{\beta _{b}^{2}}[k]|h_{\text {bd}}[k]|^{2}P}{N+{\beta _{a}^{2}}[k]|h_{\text {ad}}[k]|^{2}P}\) |
\(+\frac {\beta _{\text {br}}^{2}[k]|h_{\text {rd}}[k]|^{2}P}{N}\) | ||||
Case 3 | \(1+\frac {{\beta _{a}^{2}}[k]|h_{\text {ar}}[k]|^{2}P}{N}\) | \(1+\frac {{\beta _{a}^{2}}[k]|h_{\text {ad}}[k]|^{2}P}{N}\) | \(1+\frac {{\beta _{b}^{2}}[k]|h_{\text {br}}[k]|^{2}P}{N+{\beta _{a}^{2}}[k]|h_{\text {ar}}[k]|^{2}P}\) | 1+snr b [k] |
\(+ \frac {\beta _{\text {ar}}^{2}[k]|h_{\text {rd}}[k]|^{2}P}{N}\) | ||||
Case 4 | \(1+\frac {{\beta _{a}^{2}}[k]|h_{\text {ar}}[k]|^{2}P}{N+{\beta _{b}^{2}}[k]|h_{\text {br}}[k]|^{2}P}\) | \(1+\frac {{\beta _{a}^{2}}[k]|h_{\text {ad}}[k]|^{2}P}{N}\) | \(1+\frac {{\beta _{b}^{2}}[k]|h_{\text {br}}[k]|^{2}P}{N}\) | 1+snr b [k] |
\(+ \frac {\beta _{\text {ar}}^{2}[k]|h_{\text {rd}}[k]|^{2}P}{N}\) |