Algorithm 1 Simple heuristic algorithm for Lyapunov drift-plus-penalty-based cooperative uplink scheduling

1:Initialize the trade-off parameter V and the maximum iteration number $N_{max}$.  2:Aggregate queue status and channel state information.  3:for $i=1,2,\cdots ,N_{max}$ do  4:      // Lyapunov drift-plus-penalty calculation  5:      Randomly select a subset of stations and associated APs.  6:      Calculate ${\mathrm{P}}_{s_l}^{out}=\mathrm{P}({\gamma }_{s_l,{\widehat{\mathcal{A}}}_{s_l}}<{\gamma }_{th})$ in (8).  7:      Calculate $\mathbb{E}\left\{{\theta }_{s_l}\left(t\right)\right\}=\mathbb{E}\{{\alpha }_{s_l}\left(t\right)-{\mathrm{P}}_{u_l}^{succ}{\beta }_{s_l}\left(t\right)\}, \forall s_l\in \mathcal{S}$ in (7).  8:      Calculate the expected delay $d_{s_l}^{max}$ for $s_l\in \mathcal{S}$ for cooperative scheduling  9:      Store the Lyapunov drift-plus-penalty value by calculating              $U+V{\sum }_{s_l\in \mathcal{S}}{d}_{s_l}^{max}+{\sum }_{s_l\in \mathcal{S}}{B}_{s_l}\left(t\right){\theta }_{s_l}\left(t\right)$. 10:      Store the scheduling decision. 11:end for 12:Select the solution with the minimum Lyapunov drift-plus-penalty value.