# Path Loss Formula

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If we set the receive antenna gain is G_R, and λ=c/f is the wavelength (in meters), c=3×〖10〗^8 m/s, the effective area A of the transmit antenna is:
A=G_R λ^2/4π (2.2)
Then, the received power as a function of distance d can be calculated as:
P_R (d)=(w∙A)/L=(P_T G_T G_R λ^2)/((4π〖d)〗^2 L) (2.3) where L (L≥1) is the system loss factor.
Commonly, we set G_T=G_R=L=1 in simulations for easier calculation.
From the formula 2.3, it is easy to see that the received signal power falls off inversely proportional to the square of the distance d between the transmit antenna and receive antenna. Also, it is proportional to the square of the signal wavelength λ, which …show more content…

It only considers the wavelength of the carrier frequency and the distance between transmitter and receiver, which is usually used for estimate the channel or system design.
In this model, the receive power at distance d can be expressed as:
P_R (d)=P_T K(d_0/d)^γ (2.7) in term of dB:
P_R (dBm)=P_T (dBm)+K(dB)-10γlog_10 (d/d_0 ) (2.8) where d_0 is the reference distance and it is usually assumed to be 1 m to 10 m for indoor environment and 10 m to 100 m for outdoor environment, γ is the path loss exponent which depends on the surroundings. The value K is sometimes set to be the free space path loss at distance d_0, which can be calculated as:
K(dB)= -20〖log〗_10 ((4πd_0)/λ) (2.9)

2.3.3. Atmosphere gaseous losses
Similar to other microwave wireless communication systems, millimeter wave communications also suffer from a large propagation loss. However, compared with the one using lower carrier frequencies, millimeter wave propagation is facing more challenges. Two most severe attenuations for millimeter wave propagation are atmosphere gaseous losses and precipitation attenuation, which are hardly ever occurring in low frequency wave bands [17].

Figure 2.5. Specific attenuation due to atmospheric gases (Pressure: 1013 hPa, Temperature: 15 ℃, Water Vapor Density: 7.5 g/m^2) [18]

According to the measurements show in Figure 2.5, both water vapour