Table 1 The SCA-based algorithm

1: Setting:

Secrecy rate threshold \({\gamma _1}\) and \({\gamma _2}\),and the tolerance error \(\xi\);

2: Initialization:

   The iterative number \(n = 1\), transmitted power \(P_{opt}^{(n)}\),

   approximate values \(\widetilde{x}_i^{(n)}\), \({\widetilde{a}^{(n)}}\), \({\widetilde{u}^{(n)}}\), \({\widetilde{t}^{(n)}}\) and \({\widetilde{q}^{(n)}}\);

3: Repeat:

   Using CVX solver to solve P3 for the given approximate values;

   obtain \(\widetilde{x}_i^{(n + 1)}\), \({\widetilde{a}^{(n + 1)}}\), \({\widetilde{u}^{(n + 1)}}\), \({\widetilde{t}^{(n + 1)}}\) and \({\widetilde{q}^{(n + 1)}}\);

   update the iterative number \(n = n + 1\);

   calculate the total transmitted power \(P_{opt}^{(n + 1)}\);

   if \(\left| {P_{opt}^{(n + 1)} - P_{opt}^{(n)}} \right| \leqslant \xi\)

      break;

   end;

4: Output:

   PS ratio \(\rho\), beamformers \({{\mathbf {W}}_1}\) and \({{\mathbf {W}}_2}\), AN covariance matrix \({{\mathbf {S}}}\).