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The inverse Fourier transform of $H(f) = \operatorname{rect}\left(\frac{f}{2B}\right)$, the transfer function of the ideal lowpass filter of bandwidth $B$ Hz, is, as the OP says, $h(t) = 2B\operatorname{sinc}(2Bt)$. Now, the power transfer function of this ideal lowpass filter (ILPF) of bandwidth $B$ Hz is $|H(f)|^2$ to which we apply low-level math such as ...


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I see this question is open for a long time, I am not sure if I understand it correctly. PDF of the symbols The first probability is a $P_{\mathbf{Y}}: \mathbb{C}^n \to \mathbb{R}$, you are not considering phase noise, the probability of the $n$ symbols are identically distributed, let's say with $P_{\mathbf{Y}_i}: \mathbb{C}^n \to \mathbb{R}$, since the ...


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