# Relationship between “received” signal power and “transmitted” energy per bit?

In digital communications textbooks (e.g., Digital Communications by Bernard Sklar), the relationship between the "received" signal power $P_r$ and the "transmitted" energy per bit $E_b$ is given as follows: $P_r=E_b R_b$ where $R_b$ is the bit rate. What confuses me in this equation is that the channel attenuation is not considered in the equation. Shouldn't the equation be as $P_r=\alpha^2E_b R_b$ instead where $\alpha$ is the channel attenuation?

Of course, in many other cases the AWGN model is not appropriate. In the wireless channel, for instance, the channel gain is so fundamental that it gets incorporated into the model. If the channel is narrow-band, then the relationship between power and bit energy is similar to what you propose, with $\alpha$ random and possible time-varying.