# Table 2 Proposed RPA algorithm

Proposed algorithm

1:Initialize maximum iteration number Tmax; Set: iteration t=0, M>0, and L>0; Lagrangian

multipliers $$\lambda (0) > 0,\{\mu _{i}^{k}\}(0) > 0,$$ and $$\{\xi _{i}^{k}\}(0) > 0$$; step sizes α>0,β>0, and θ>0;

upper bound of estimation error in MU-to-FBS link is ωi[0,0.003];

upper bound of estimation error in femtocell link is εi[0,0.1];

upper bound of estimation error in FU-to-MBS link is δi[0,0.003].

2:Set maximum transmit power $$p_{i}^{k,max} >0$$ and initialize power $$p_{i}^{k} >0$$ with different initialization

values among different FUs and MUs.

3:Define interference Ith and minimum rate $$\gamma _{i}^{k,min}$$, randomly generate $$\bar G_{i}^{k}, \bar h_{ij}$$ and $$\bar g_{ij}$$.

4:repeat

5: for t=1 to Tmaxdo

6: for m=1 to Mdo

7: for l=1 to Ldo

8: Calculate transmit power $$p_{i}^{k*}$$ according to (26);

9: Calculate actual SINR received at FU-Rx according to (2) and (26);

10: Calculate Iac according to (1) and (26);

11: Calculate Lagrange multipliers $$\lambda,\mu _{i}^{k},$$ and $$\xi _{i}^{k}$$ from (31) - (33);

12: end for

13: end for

13 t=t+1;

14:end for

15:until t=Tmax or transmit power convergence. 