Table 1 Power allocation procedure

Input:\({\hat {\mathbf {H}}_{k}}\), R_k, ρ_k

Initialization:

1: Obtain B_k for ∀k by (22)

2: Initialize SINR as \({{\hat \gamma }_{k,i}} = \frac {{\tilde {\mathbf {D}}_{k}^{2}}}{{\sigma _{n}^{2}{\text {tr}}\left ({\mathbf {B}_{k}^{H}{\mathbf {B}_{k}}} \right)}}\)

3: Initialize p_k,i by means of water-filling

Repeat N _p times:

4: Update \(\hat \gamma _{k,i}\) by (39)

5: Update p_k,i by means of water-filling

6: Normalize the power by \({p_{k,i}} \leftarrow {p_{k,i}}\sqrt {\frac {{{\text {tr}}\left ({\mathbf {P}_{k}^{2}} \right)}}{{{\text {tr}}\left ({\bar {\mathbf {B}}_{k}^{H}{{\bar {\mathbf {B}}}_{k}}} \right)}}}\)

Output: P _k