Determination of C_k,1(t) using correlation between the instantaneous amplitudes

Select an optimal solution from the candidates of C_k,1(t) using Eq. (16) in constraint 5. This process is done by selecting C_k,1(t) when the correlation between the instantaneous amplitude (A_k(t) and $A_\ell(t)$) is maximum at any C_k,1(t) within the estimated error region.

$$\hat{C}_{k,1}=\mathop{\arg\max}_{\hat{C}_{k,0}-P_k\leq C_{k,1... ...\vert\hat{A}_k\vert\vert \vert\vert\hat{\hat{A}}_k\vert\vert},$$ (31)

where $<\cdot>$ is an operation of the inner product, $\hat{A}_k(t)$ is the instantaneous amplitude obtained by interpolating C_k(t), and $\hat{\hat{A}}_k(t)$ is the instantaneous amplitude determined as

$$\hat{\hat{A}}_k(t)=\frac{1}{N_{F_0}}\sum_{\ell \in {\bf {L}}}\frac{\hat{A}_{\ell}(t)}{\Vert\hat{A}_{\ell}(t)\Vert},$$ (32)

where, L is the set symbol of $\ell$ that satisfies Eq. (12).