What is the meaning of $l_p$ norm in this model for sparse channel estimation?
The symbol ${||h||}_p$ refers to the p-norm of the vector. It is calculated as

$${||h||}_p=\sqrt[p]{\left|h_1\right|^p+\left|h_2\right|^p+...+\left|h_n\right|^p}$$

When they write ${||h||}^p_p$, it is just that multiplied by itself $p$ times, so that the root disappears. Mathematically:

$${||h||}^p_p=\sum\limits_{i=1}^n \left|h_i\right|^p$$