we can see that the direct signal that will be received at the destination $N_2$ is $$\label{ML_detection_joint}
y_{N_2}=\sqrt{P}h_1x_A+\sqrt{P}h_8x_B+n_{N_2},$$ while the forwarded signal from the relay is $$\label{ML_detection_joint}
y_{N_3,N_2}=\sqrt{P}h_2h_4gx_A+\sqrt{P}h_7h_4gx_B+h_4gn_{N_3}+n_{N_2}.$$ If node $N_2$ combines the direct and relayed signals with a single ML demodulation step, the estimation will take the form $$\begin{aligned}
\label{ML_detection_joint}
&&    (\tilde{x}_A,\tilde{x}_B)_{N_2} = \arg \min_{x_A \in \mathcal{X_A},x_B
\in \mathcal{X_B}} \Big \{ \| y_{N_2}-\sqrt{P}h_1x_A\nonumber\\ %
        &-&\sqrt{P}h_8x_B\| + \| y_{N_3,N_2}-\sqrt{P}h_2h_4gx_A\nonumber\\
        &-&\sqrt{P}h_4h_7gx_B \| \Big \}.%\end{aligned}$$ At the second receiver, a similar signal recovery formula can be written. The parameters $\sqrt{P} h_4h_7g$, and $\sqrt{P}h_2h_4g$ are obtained by using the training symbols that are inserted in the preambles of RTS, CTS, and CTC packets as we explained in detail earlier in this paper. The performance of the algorithm that we just described and is summarized in , was studied in [@argyriou:twc-ancol] where as we said in the Introduction we also developed a thorough sum-rate analysis for the case of two independent senders.

Complexity and Implementation Issues {#sec:complexity}
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As we pointed out in the Introduction, the proposed system consists of different algorithms of varying complexity. Therefore, we think it is necessary to provide a brief discussion regarding the complexity and implementation issues that might 