Since this question is book-oriented, I will kindly ask you to accompany it with a book that is considered by many researchers the bible of Digital Communication: Proakis - Digital Communications, one from the 4th ed, and another from the 5th ed.
Let $$ x(t) = \text{Re}[x_l(t) e^{j2\pi f_0 t}]$$ be a filtered white Gaussian noise, where $x_l(t) \in \mathbb{C}$ is the complex envelope (also called the lowpass equivalent) of $x(t)$. The Power Spectral Density (PSD) of $x(t)$ is given by
$$S_x(f) = \left\{ \begin{array}{cl} \frac{N_0}{2}, & \vert f \pm f_0 \vert < W/2 \\ 0, & \text{Otherwise} \\ \end{array}\right., \tag{0}$$ where $f_0$ is the carrier frequency and $W$ is the bandwidth of $x(t)$. What is the PSD of the lowpass equivalent of $x(t)$? If you are a Communication Systems Engineer, I am almost sure that you answered it without hesitating: it is $$S_{x_l}(f) = \left\{ \begin{array}{cl} N_0, & \vert f \vert < W/2 \\ 0, & \text{Otherwise} \\ \end{array}\right.,$$ where $x_l(t)$ is the lowpass equivalent of $x(t)$. I suppose you will answer it as I see it everywhere, in any book or any paper. It turns out that it is not necessarily $N_0$.
Until the 4th ed., Proakis had considered a normalization in the autocorrelation function definition
$$R_x(\tau) = \frac{1}{2}E\{x^*(t)x(t+\tau)\}.$$
In the author's own words (on pg 76 of the 4th ed): "The factor of $\frac{1}{2}$ in the definition of the autocorrelation function of a complex-valued stochastic process is an arbitrary but mathematically convenient normalization factor". Indeed, such normalization makes the lowpass equivalent of the autocorrelation function be equal to the autocorrelation function of $x_l(t)$ (I know, that is tortuous, but check both books and you will notice it), which is reasonable.
On the 5th ed (where the book was heavily refactored), Proakis has defined
$$R_x(\tau) = E\{x^*(t)x(t+\tau)\},\tag{1}$$
it changes many mathematical definitions I (and you too, probably) had learned about random signal analysis in communication systems. One of theses is that (see EXAMPLE 2.9–1. of the 5th ed.) $$S_{x_l}(f) = \left\{ \begin{array}{cl} 2N_0, & \vert f \vert < W/2 \\ 0, & \text{Otherwise} \\ \end{array}\right. \tag{2}. $$
I often use different statistical signal processing techniques from related areas (adaptive filters, machine learning, numeric optimization, etc...) in my systems, and they always define the autocorrelation function in the canonical way (equation (1)). Therefore, the mathematical definitions of the 5th ed. is awesome for me. However, the canonical form leads to the equation (2), which I've never seen someone defining $S_{x_l}(f)$ like that, thus making me insecure about how to define it.
The question is: Is it reasonable to define this PSD as $2N_0$?