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Pathloss : Large Scale & Small Scale Pathloss and Pathloss Exponent 'n'




In wireless communication, the path loss is proportional to the square of the operating carrier frequency. As a result, the higher the frequency, the greater the path loss. Although path loss is affected by several parameters, including fading, shadowing, angle of arrival (AOA), and angle of departure (AOD). In comparison to lower frequencies, when the frequency is extremely high, it is easily absorbed by atmospheric gases, vapor, and rain. In the case of higher frequencies, however, the penetration loss is also greater. Path loss is proportional to the square of the carrier frequency according to the Friis free space path loss model. Path loss parameters are often divided into two categories: 1. Large Scale Path loss; 2. Small Scale Path loss. Large-scale path losses are basically due to the distance between transmitter and receiver and shadowing. Small-scale path losses are due to multipath fading, angle of arrival, etc.


1. Free Space Pathloss:

This phenomenon occurs when a signal travels across empty space. The formula for free space path loss (FSPL) in decibels is:
FSPL (dB) = 20log10(4ฯ€d/ฮป) ... (1)

Free space path loss, however, is not completely relevant in real-world cellular wireless networks because the environment includes obstacles. In addition, variable environmental conditions result in varied path loss. For various environments, the path-loss exponent (PLE) 'n' changes dramatically as discussed below.

Received signal power in an atmospheric environment can be defined as:

Pr  = Pt + Gt + Gr - [20log10(4ฯ€d/ฮป) + atmospheric pathloss] ……… (2)

                                             Pr = Received Power & Pt = Transmitted Power                                             
                                             ฮป = wavelength of carrier frequency
                                             d = distance between Tx & Rx
                                            Gt & Gr = antenna gains
                                            20log10(4ฯ€d/ฮป) = FSPL component

Try Online Simulator for Free Space Path Loss (FSPL)

2. Close-in Path Loss Model:

The close-in (CI) path loss model is appropriate for current wireless systems operating at sub-6 GHz or higher, including millimeter-wave 5G.

.... (3)

FSPL (d0) denotes free space path loss at a reference distance (typically 1 meter). The letter 'n' stands for path loss exponent. 'd' represents the total distance. The shadowing factor is denoted by ฯ‡ฯƒ.

This allows us to calculate path loss for current bands like UWB with high precision. In 28 GHz transmission, for example, path loss at the first meter is roughly 32 dB. From there, path loss grows based on the environment's path loss exponent value.


3.1. Large Scale Pathloss:

Path loss increases as distance grows because the signal attenuates in the atmosphere. At equal distances, path loss is higher at higher frequencies than at lower frequencies. Similarly, path loss for LOS (Line of Sight) and NLOS (Non-Line of Sight) differs, as NLOS paths typically involve more reflections and longer travel distances. [Read More about LOS and NLOS Paths]


3.2. Small Scale Pathloss:

Factors like fading and angles of arrival (AOA/AOD) contribute to small-scale losses. In built-up areas, signals reflect off walls and foliage, traveling via multiple NLOS paths. This creates Multipath Components (MPCs) at the receiver. Fading occurs due to these MPCs interfering with each other. Common types include slow/fast fading and frequency selective fading. Fast fading occurs when the channel changes rapidly, while frequency selective fading varies across the frequency band.

Also read about
[1] Difference between AWGN and Rayleigh Fading

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