Table 1 PCC algorithm

Initialization

Set t=0 and ${\overline{p}}_{\text{var}}\left(0\right)$ equal to a non-negative value.

Step

Operation

Input

Output

1

Solve ICPs at each cell considering the specific users’ utilities as well as the power vector ${\overline{p}}_{\text{var}}\left(t\right)$, via the canonical dual algorithm in Section IV.A, deriving cell’s optimal utility vector, the normalized Lagrangian multiplier and users’ power vector for the specific ${\overline{p}}_{\text{var}}\left(t\right)$. This implies a iterative algorithm.

U _j  ∀ j ∈ S _j ${\overline{p}}_{\text{var}}\left(t\right)$

${\overline{U}}_c^{*}\left({\overline{p}}_c^{*},{\overline{p}}_{\text{var}}\right)$ ${\lambda }_c^{*}\left({\overline{p}}_{\text{var}}\left(t\right)\right)$ ${\overline{p}}_c^{*}\left(t\right)$

∀ c ∈ C

2

Each cell c dynamically updates its maximum transmission power p_c,var(t + 1) in accordance to the gradient algorithm (23). This information is sent to the macro cell using existing 3GPP signaling.

${\lambda }_c^{*}\left({\overline{p}}_{\text{var}}\left(t\right)\right)$a(t)

p_c,var(t + 1)

∀ c ∈ C

3

Set t ← t + 1, disseminate ${\overline{p}}_{\text{var}}\left(t\right)$, a(t) and go to step 1 (until satisfying termination criterion). Upon convergence, optimal CM and power control vector $\left({\overline{p}}_c^{*},{{\overline{p}}^{*}}_{\text{var}}\right)$ have been derived.

$\left({\overline{p}}_c^{*},{{\overline{p}}^{*}}_{\text{var}}\right)$