As we know, the path loss can be described by the equation as $$ \frac{P_{r}}{P_{t}}=D_{t} D_{r}\left(\frac{\lambda}{4 \pi d}\right)^{2} $$ In the OFDM system, such as Wi-Fi, there are infinite paths exist, assume it is in free space, and only one path exist, for the specific path (LoS path), the channel frequency response(CFR)/channel state information(CSI) describes how is the channel affect the transmitted signal, it calculated by: $$ H = \frac{Y}{X} $$ where Y is the received signal at receiver and X is the transmitted signal at transmitter. the signal power is square of the amplitude of the signal, that is $$ P_{t}=|Y|^2 $$ $$ P_{r}=|X|^2 $$ I have two questions:
- Is the following equation holds? $$ \left|H_{}\right|^{2} = \frac{P_{r}}{P_{t}}=D_{t} D_{r}\left(\frac{\lambda}{4 \pi d}\right)^{2} $$
- According to the first equation, is the following equation holds? $$ \frac{X}{Y}=\sqrt{D_{t} D_{r}\left(\frac{\lambda}{4 \pi d}\right)^{2}} $$
Thanks in advance.