Table 5 Distributed RA algorithm

1.

Input: \(\mathbf {p}^{(0)}_{k}\), \({{\boldsymbol {\varphi }}}^{(0)}_{k}\forall k \in \mathcal {K}\).

2.

Initialize: j=0, ε _p .

3.

Do

4.

For k=1,⋯,K

5.

Evaluate \({\mathcal {D}}_{\overline {\mathbf {m}}}^{(k,j)}\)

6.

Evaluate \(\mathbf {p}^{(j+1)}_{k}\) and \({{\boldsymbol {\varphi }}}^{(j+1)}_{k}\) applying Algorithm in Table 2 with

Input \({\mathcal {D}}_{\overline {\mathbf {m}}}^{(k,j)}\) and \({\boldsymbol {\gamma }}_{k}(\mathbf {p}_{-k}^{(j)})\) and evaluating the PA vector

according to (22)

7.

End For

8.

Set j←j+1;

9.

Until ||p ^(j)−p ^(j−1)||≤ε _p or j=N _it

10.

Output: \({{\boldsymbol {\varphi }}}_{k}^{*}={{\boldsymbol {\varphi }}}_{k}^{(j)}\), \(\mathbf {p}_{k}^{*}=\mathbf {p}_{k}^{(j)}\), \(\forall k \in {\mathcal {K}}\).