Algorithm 1. Maximum Weighted Ergodic Energy Efficiency (MWEEE) Algorithm

Input:${P_d}^{max};p_0;{\mathrm{K}}_m,{\mathrm{K}}_{k,m},\mathrm{\forall }m,k;SIN{R}_0$

Output:$P^{*}{{}_{m,k}}^d,P^{*}{{}_k}^c,{{\lambda }^{*}}_{m,k},\mathrm{\forall }m,k;C_{ee}^{*}$

1: Initialize: the number of iteration $i,j=0$, the $U_{ee}(i)=0$, the threshold $ϵ=e^{-5}$, $P_{m,k}^d(0)$ $(\mathrm{\forall }m,k)$, the approximation coefficient $\alpha (j),\beta (j)$, maximum number of iterations $j^{max}$, the learning rate $s1,s2$, the lagrange multiplier ${\mu }_1=0.1,{\mu }_2=0.1$.

2: Obtain ${P_{m,k}}^d$ with the given initialized parameters according to P5.

3: $\mathsf{\Delta }\leftarrow \phi (U_{ee})$

4: $P_{tmp}\leftarrow {P_{m,k}}^d(0)+ϵ$

5: while $\phi (U_{ee})\ge ϵ$ (i-th iteration) do

6:    while $\Vert {P_{m,k}}^d(0)-P_{tmp}\Vert \ge ϵ$ (j-th iteration) do

7:        $P_{tmp}\leftarrow {P_{m,k}}^d(0)$

8:        ${\mu }_1(j+1)={[{\mu }_1(j)-s1*(\mathrm{\sum }{e}^{{{\tilde{P}}_{m,k}}^d}-{P_d}^{max})]}^{+}$

9:        ${\mu }_2(j+1)={[{\mu }_2(j)-s2*(-{{\tilde{P}}_{m,k}}^d-ln(\frac{-SIN{R}_0{N}_0}{{\mathrm{K}}_{m}log(1-p_0)}))]}^{+}$

10.        ${P_{m,k}}^d(0)\leftarrow {P_{m,k}}^d(j)$, obtain $ż{P_{m,k}}^d(j+1)$ with the ${P_{m,k}}^d(0)$ and then obtain $\alpha (j+1),\beta (j+1)$

11:        $j\leftarrow j+1$

12:    end while

13:    ${P_{m,k}}^d(i)\leftarrow {P_{m,k}}^d(j-1)$

14:    Obtain $U_{ee}(i+1)$ according to the formula (4).

15:    Obtain ${P_{m,k}}^d(i+1)$ according to P5.

16:    $\mathsf{\Delta }\leftarrow \Vert \phi (U_{ee})\Vert$

17:    $i\leftarrow i+1$

18: end while

19: Output ${P_{m,k}}^d(i)$ as $P^{*}{{}_{m,k}}^d$.

20: Compute the $P^{*}{{}_k}^c$ with the $P^{*}{{}_{m,k}}^d$, $\mathrm{\forall }m,k$.

21: for $k=1$ to K do

22:    for $m=1$ to M do

23:         Substitute $(P^{*}{{}_k}^c,P^{*}{{}_{m,k}}^d)$ into formula (26) and formula (28) to obtain ${w_{m,k}}^H$ and ${w_{m,k}}^I$ respectively.

24:    end for

25:    Obtain ${{\lambda }^{*}}_{m,k}$ according to formula (22).

26: end for

27: Compute $C_{ee}^{*}$ according to formula (8).

28: Output ${{\lambda }^{*}}_{m,k},C_{ee}^{*}$, $\mathrm{\forall }m,k$.