Simplified Path-Loss Model
Signal propagation is a very complex phenomenon that we cannot obtain a single model to characterize the path loss accurately in different environments.
Calculation of the Path loss in Simplified Path-Loss Model
For general trade-off analysis of various system designs it is better to use a simple model that captures the essence of signal propagation
Thus, the simplified model for path loss as a function of distance is commonly used for system design
The dB attenuation is thus
K is a unitless constant that depends on the antenna characteristics and the average channel attenuation, d0 is a reference distance for the antenna far field, and γ is the pathloss exponent.
When the simplified model is used to approximate empirical measurements, the value of K < 1 is sometimes set to the free-space path gain at distance d0 assuming omnidirectional antennas
and this assumption is supported by empirical data for freespace path loss at a transmission distance of 100 m.
The Value of K can be determined by measurement at d0 oroptimized (alone or together with γ) to minimize the mean-square error (MSE) between the model and the empirical measurements.
The value of γ depends on the propagation environment: for propagation that approximately follows a free-space or two-ray model, γ is set to 2 or 4 (respectively).
The value of γ for more complex environments can be obtained via a minimum mean-square error (MMSE) fit to empirical measurements as you can see in table given below
Questions of this topic
Consider a receiver with noise power -160 dBm within the signal bandwidth of interest. Assume a simplified path loss model with d0 = 1 m, K obtained from the free space path loss formula with omnidirectional antennas and fc = 1 GHz, and γ = 4. For a transmit power of Pt = 10 mW, find the maximum distance between the transmitter and receiver such that the received signal-to-noise power ratio is 20 dB.
Consider the set of empirical measurements of Pr/Pt given in the table below for an indoor system at 900 MHz. Find the path loss exponent γ that minimizes the MSE between the simplified model (2.40) and the empirical dB power measurements, assuming that d0 = 1 m and K is determined from the free space path gain formula at this d0. Find the received power at 150 m for the simplified path loss model with this path loss exponent and a transmit power of 1 mW (0 dBm).