Meaning of data stream vector of mutually uncorrelated zero-mean symbols?

Question

In my research work, I came across the following sentence:

$s \in \mathbb{C}^{n}$ is the data stream vector consists of mutually uncorrelated zero-mean symbols, with $\mathbb{E}[s s^*] = I_n$, where $I_n$ is Identity matrix.

My query is if $n = 2$, then how will the vector $s$ look like.

Any help in this regard will be highly appreciated.

Answer 1

It means that $s = \begin{bmatrix} s_1 \\ s_2 \\ \vdots \\ s_n \end{bmatrix}$, and:

1. $\mathbb{E}(s_i) = 0$ (zero mean)
2. $\mathbb{E}(s_i \bar{s_j}) = 0$ for $i \neq j$ (uncorrelated)
3. $\mathbb{E}(s_i \bar{s_i}) = \mathbb{E}(|s_i|^2) = 1$