Let $B(m) \in \{-1,1\}$ be the transmitted symbols, for $m=1,2,\dots,1000$. Based on $B(m) = \pm 1$,
$$\begin{aligned} \psi_{m,0} &= h_m-\alpha f_mg_m \\ \psi_{m,1} &= h_m+\alpha f_mg_m \end{aligned}$$
where $\alpha = 0.5$, $h, f$ and $g$ are complex Gaussian random variables with zero mean and unit variance. Then,
$$ \tilde{s_m(n)} = \underset{s_m(n) \in \mathcal{A}_s}{\operatorname{argmin}} \left| \frac{\psi_{m,0}^H}{\| \psi_{m,0}^H \|^2}-s_m(n) \right|^2 $$
where $s_m(n)$ is quadrature phase shift keying (QPSK) modulated signal, $\mathcal{A}_s$ is modulation alphabet set and $n = 1,2,\dots, 256$. What does $\operatorname{argmin}$ indicate in above expression?
Any help in this regard will be highly appreciated.
For $y = \underset{x} {\operatorname{argmin}} f(x)$, the value of $y$ is the value of $x$ at which the function $f(x)$ attains its minimum. For example,
$$ y = \underset{x} {\operatorname{argmin}} \, (x - 4)^2 = 4, $$
since $x = 4$ is where $(x-4)^2$ attains its minimum value.