Difference between double-sided and single-sided AWGN noise after bandpass filtering?
Both descriptions give the same result. We often use the one-sided noise power spectral density (PSD) because for real-valued processes the negative frequencies are redundant, so defining the PSD for positive frequencies is sufficient. You just have to scale the noise power spectrum such that integrating the one-sided power spectral density (PSD) over the positive frequencies gives the same result as integrating the two-sided PSD over positive and negative frequencies. I.e., for white noise with a constant PSD, defining the one-sided PSD as $N_0$ means that we would need to define the two-sided PSD as $N_0/2$ such that the noise power remains the same: $N_0W=N_0/2\cdot 2W$