I see this representation in the paper,but i don't know what does this alphabet mean,neither the paper said.
The sentence about this says:
The energy-carrying information signal is denoted as $\mathbf s_B \in \mathbb C^{N_B} $with covariance matrix $\mathbf W_B = E[\mathbf s_B\mathbf s_B^H ]\in \mathbb C^{N_B \times N_B}$.
Does anyone know that what do $\mathbb C^{N_B \times N_B}$ and $\mathbb C^{N_B} $ mean?
This font - "blackboard bold" - is often used to describe number systems. E.g.:
$\mathbb{N}$ is the natural numbers.
$\mathbb{Z}$ is the integers.
$\mathbb{Q}$ is the rationals.
$\mathbb{R}$ is the reals.
And $\mathbb{C}$, which you specifically ask about, is the complex numbers.
The "exponent notation" $\mathbb{C}^k$ meanwhile refers to tuples: e.g. $\mathbb{C}^3$ is the set of triples of complex numbers.
Finally, there's a bit of an abuse of notation: we sometimes write "$\mathbb{C}^{n\times k}$" to refer to the set, not of $(n\times k)$-ary tuples of complex numbers, but of $n$-by-$k$ matrices whose entries are complex numbers. These aren't really that different - you can think of an $(n\times k)$-ary tuple as being an $n$-by-$k$ matrix which I've cut into separate rows and laid the rows next to each other - but it is a bit off.