I derived the following expression in my analysis
$$ C = \int_{0}^{2\pi} \int_{0}^{r_{max}} \log_{2}\left( 1 + \frac{k \lambda^2}{N(4\pi)^2(h^2+d^2+r^2+2rd\cos(\varphi))}\right)rdrd\varphi. $$
Unfortunately, this seems to be where my abilities end. Could anyone help me in deriving an approximate closed form expression for this expression if obtainable. I had a thought about Chebyshev-Gauss quadrature approximation, but, I don't know how to apply it here.