We have the two channels: $$X_{a,i} = H_{i}s_{i} +N_{a,i} \\ X_{b,i} = H_{i}s_{i} +N_{b,i} $$
for $1 \leq i \leq n$, where $H_i$ denotes the i.i.d. channel coefficient and is a zero-mean complex Gaussian random variable with variance one, i.e., $\mathcal{CN}(0,1)$. Notice that the same $H_i$ is used in the two channels.
$N_{a,i}$ and $N_{b,i} $ represent the noises at node A and node B, respectively, and are independent $\mathcal{CN}(0,\sigma_a^2)$ and $\mathcal{CN}(0,\sigma_b^2)$ random variables.
$s_i$ is the channel input. We consider that a constant $s_i$ here, i.e., $s_i=s$ for all $1 \leq i \leq n$, and the power constraint for the input is $|s|^2 = \textrm{P}$.
The question is how to calculate the mutual information $I(X_a; X_b)$ for the above scenario.
The answer of this question is given as $$I(X_a; X_b) = \log(1+ \gamma_{eq}),$$ where $\gamma_{eq} = \left(\frac{1}{\gamma_a}+ \frac{1}{\gamma_b}+ \frac{1}{\gamma_a \cdot \gamma_b} \right)^{-1}$, $\gamma_a = \frac{\textrm{P}}{\sigma_a^2}$ and $\gamma_b = \frac{\textrm{P}}{\sigma_b^2}$.
Can anyone please tell me how to derive the above mutual information. I really appreaciate it.