For better clarity we present the specific diagram of $bmPhi$ in Figure 2 The joint sparse spatial polarization and temporal basis matrix $bmPhi in mathbbC^2M_theta M_tau times 2N_theta N_tau $ is m

To provide better clarity, we present a specific diagram of the joint sparse spatial, polarization, and temporal basis matrix $\bm{\Phi}$ in Figure 2. This matrix is of size $\mathbb{C}^{2{M_\theta }{M_\tau } \times 2{N_\theta }{N_\tau }}$ and is composed of $N_\tau$ blocks, such as $b_1$, each of size $2{M_\theta }{M_\tau } \times 2{N_\theta}$. The leftmost figure in Figure 2 illustrates how each block is formed by the Kronecker product of $\bm{A}$ and the $n_\tau$th column of $\bm{C}$.

For example, the $n_\tau$th block $b_1$ (middle figure in Figure 2) consists of two parts that represent the RHCP and LHCP antenna receive signals, respectively. Each part is composed of $N_\theta$ blocks, denoted as $b_2$, of size ${M_\theta }{M_\tau } \times 2$. Each $b_2$ block is formed by the Kronecker product of ${\bm{A}m}\left( {{{\tilde \theta }{{n_\theta }}}} \right)$ and the $n_\tau$th column of $\bm{C}$.

The rightmost figure in Figure 2 further illustrates that the $n_\theta$th block $b_2$ is divided into two parts: the left one with a darker color represents the co-polar component of the RHCP signal, i.e., the Kronecker product of ${\bm{a}{Rc}}\left( {{{\tilde \theta }{{n_\theta }}}} \right)$ and the $n_\tau$th column of $\bm{C}$, while the right one with a lighter color represents the cross-polar component of the LHCP signal, i.e., the Kronecker product of ${\bm{a}{Rx}}\left( {{{\tilde \theta }{{n_\theta }}}} \right)$ and the $n_\tau$th column of $\bm{C}$.