I am working on a research paper related to wireless communication, wherein I am facing some doubt while writing expression of SINR (which is a ratio of Signal variance in numerator to Interference variance + Noise variance in denominator).
Let us consider a wireless communication scenario where received signal over random wireless channel is given by
$y=h_1s_1+ h_2s_2+h_1w$ ---(1)
where,
$h_1, h_2$ are wireless channels and are random in nature, so we had modelled as $h_1 \sim \mathcal{C}\mathcal{N}(0,\sigma^2_{h_1}), h_2 \sim \mathcal{C}\mathcal{N}(0,\sigma^2_{h_2})$,
$s_1$ is message signal, $s_2$ is interfering signal and are modelled as $s_1 \sim \mathcal{N}(0,P_1), s_2 \sim \mathcal{N}(0,P_2)$ and $w$ is Gaussian noise modelled as $w\sim \mathcal{N}(0,N_w)$.
My query is that which is the correct way to write the SINR expression eq. (2) or eq. (3)
$\text{SINR} = \frac{|h_1|^2 P_1}{|h_2|^2P_2+\sigma^2_{h_1}N_w}$ ---(2)
$\text{SINR} = \frac{|h_1|^2 P_1}{|h_2|^2P_2+|h_1|^2N_w}$ ---(3)
Please note that in equation (2), I had written $\sigma^2_{h_1}$ in denominator instead of $|h_1|^2$ as $h_1$ is associated with noise. So is it correct to write in this way ?
Any help in this regard will be highly appreciated.
