Algorithm 4 ((Alternating optimization (AO) algorithm of solving P1)

Require: Starting point ${\mathbf{R}}_0$ and ${\mathbf{Q}}_0$, ${ϵ}_4>0$.   1. Set $k=0$, Compute $C_s({\mathbf{R}}_0,{\mathbf{Q}}_0)$.   repeat(AO algorithm)         2. Set $k=k+1$.         3. Optimize global optimal ${\mathbf{R}}_k$ given fixed ${\mathbf{Q}}_{k-1}$ via CVX.         4. Optimize local optimal ${\mathbf{Q}}_k$ given fixed ${\mathbf{R}}_k$ via Algorithm 3.         5. Compute $C_s({\mathbf{R}}_k,{\mathbf{Q}}_k)$.   until$|C_s({\mathbf{R}}_k,{\mathbf{Q}}_k)-C_s({\mathbf{R}}_{k-1},{\mathbf{Q}}_{k-1})|/|C_s({\mathbf{R}}_{k-1},{\mathbf{Q}}_{k-1})|\le {ϵ}_4$.   7. output ${\mathbf{R}}_k$, ${\mathbf{Q}}_k$ as a limit point of P1.