Skip to main content

Pathloss : Large Scale & Small Scale Pathloss and Pathloss Exponent 'n' (with Simulator)




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 Friis formula for free space path loss (FSPL) in decibels is:
FSPL (dB) = 20log10(4蟺d/位) ... (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(4蟺d/位) + atmospheric pathloss] ……… (2)

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

Read More: about Friis Transmission pathloss formula
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 蠂蟽.

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.

4. Path loss exponent 'n':

The path loss exponent 'n' is a significant parameter. In an NLOS scenario, 'n' is typically higher than in a LOS scenario. It is also affected by frequency and antenna heights. It is found that with directional beamforming, the path loss exponent 'n' decreases. For example, the path loss exponent for 28 GHz directional communication is roughly 2.5, whereas for omnidirectional transmission it can reach 5 to 6.

However, we use the close-in path loss model for sub-6 GHz, SHF, and EHF transmissions.




Free Space Path Loss (FSPL) Calculator

Compute FSPL in dB, linear scale, and wavelength with multiple units and optional received power.

Inputs

Results

FSPL(dB): --

FSPL(linear): --

Wavelength 位: -- meters

Received Power Pr: -- dBm

Example Calculation

f = 3500 MHz, d = 1 km

FSPL(dB) = 20 log₁₀(1) + 20 log₁₀(3500) + 32.44
         = 0 + 70.88 + 32.44
         = 103.32 dB

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

Effect of Rayleigh Fading

In wireless communication systems, digital information is transmitted by modulating a high-frequency carrier using techniques such as Amplitude Shift Keying (ASK), Frequency Shift Keying (FSK), or Phase Shift Keying (PSK). During propagation, the transmitted signal reaches the receiver through multiple paths created by reflections, scattering, and diffraction from buildings, vehicles, trees, and other surrounding objects. The received signal is therefore modeled as:

y(t)=h(t)s(t)+w(t)

Here, h(t) denotes the Rayleigh fading channel, which represents the combined effect of multipath propagation, while w(t) represents Additive White Gaussian Noise (AWGN). In environments where no dominant line-of-sight (LOS) path exists, the multiple reflected signal components arrive at the receiver with different amplitudes, phases, and propagation delays. Depending on their relative phases, these components may combine constructively or destructively, producing rapid fluctuations in the received signal envelope known as deep fades.

Rayleigh fading significantly degrades the performance of ASK, FSK, and PSK modulation schemes by reducing the instantaneous received signal power. Consequently, the receiver experiences a lower Signal-to-Noise Ratio (SNR), which increases the Bit Error Rate (BER). Compared with an AWGN channel, Rayleigh fading produces a much slower improvement in BER as SNR increases because random multipath fading remains the dominant source of signal degradation. Among these modulation schemes, coherent PSK generally exhibits better robustness to fading than ASK, although all modulation techniques experience performance loss in severe multipath environments.

Modern wireless systems mitigate the effects of Rayleigh fading through channel equalization, diversity combining, MIMO, OFDM, adaptive modulation, and channel coding. These techniques exploit multipath diversity, compensate for channel distortions, and improve communication reliability in mobile, urban, and indoor wireless environments.

Read More: about Rayleigh Fading Impact of Rayleigh Fading on BPSK



Contact Us

Name

Email *

Message *

Popular Posts

Design of CMOS Flip-Flops (SR, D, JK)

Design of CMOS Flip-Flops (SR, D, JK) A flip-flop or latch is a circuit with two stable states, used to store state information. It is the basic storage element in sequential logic and a fundamental building block in digital electronics systems, including computers and communication devices. Flip-flops and latches act as data storage elements for states, pulse counting, and synchronization of variably-timed input signals to a reference clock. Flip-flops can be transparent/opaque (latches) or clocked (synchronous, edge-triggered). Latches are level-sensitive, while flip-flops are edge-sensitive. In sequential logic, the output depends on current inputs and previous states. Fig.1 shows a sequential circuit combining a combinational block and a memory element. ...

FFT Butterfly Method Explained (with Simulations)

4-Point FFT Using Butterfly Method Given: x[n] = {0, 1, 2, 3} Step 1: Split into Even & Odd Even indices: x e = {x[0], x[2]} = {0, 2} Odd indices: x o = {x[1], x[3]} = {1, 3} Step 2: 2-point DFT For any {a, b}: DFT = {a + b, a - b} Even Part (E): {0+2, 0-2} = {2, -2} Odd Part (O): {1+3, 1-3} = {4, -2} Step 3: Combine Using Butterfly X[k] = E[k] + W 4 k O[k] X[k + 2] = E[k] - W 4 k O[k] Twiddle Factors (N=4): W 4 0 = 1, W 4 1 = -j Final Calculations: X[0] = E[0] + W 4 0 O[0] = 2 + (1)(4) = 6 X[2] = E[0] - W 4 0 O[0] = 2 - (1)(4) = -2 X[1] = E[1] + W 4 1 O[1] = -2 + (-j)(-2) = -2 + 2j X[3] = E[1] - W 4 1 O[1] = -2 - (-j)(-2) = -2 - 2j Final Answer: X[k] = {6, -2 + 2j, -2, -2 - 2j} 8-Point FFT Using Butterfly Method Given: x[n] = {0,1,2,3,4,5,6,7} Step 1: Split into Bit-Reversed Order To perform DIT-FFT, split the 8 points into pairs of two: Group A: {x[0], x[4]} = {0, 4}...

Pulse Amplitude Modulation and Demodulation

馃摌 Overview & Theory of Pulse Amplitude Moduation (PAM) 馃М Pulse Amplitude Demoduation 馃М MATLAB Code for PAM 馃摎 Further Reading 馃搨 Other Topics on Pulse Amplitude Modulation ... 馃М Simulation results for comparison of PAM, PWM, PPM, DM, and PCM 馃М Other Pulse Modulation Techniques (e.g., PWM, PPM, DM, and PCM) 馃М MATLAB Code for Pulse Amplitude Modulation and Demodulation of an Analog Signal (2) 馃М MATLAB Code for Pulse Amplitude Modulation and Demodulation of Digital data  Pulse Amplitude Modulation (PAM) Sampling allow us to represent real world continuous signal, such as audio or video, in a format suitable for digital processing and storage. This sampled discrete-time signal is inherently digital. A digital signal is a discrete-time signal that is further quantized in amplitude. Pulse Amplitude modulation (PAM) is the modulation technique in which amplitude of carrier pulses is...

MATLAB Code for BER performance of QPSK with BPSK, 4-QAM, 16-QAM, 64-QAM, 256-QAM, etc

馃摌 Overview 馃М MATLAB Codes 馃М Online Simulator for Calculating BER of M-ary PSK and QAM 馃М QPSK vs BPSK and QAM: A Comparison of Modulation Schemes in Wireless Communication 馃М Are QPSK and 4-PSK same? 馃摎 Further Reading   QPSK offers double the data rate of BPSK while maintaining a similar bit error rate at low SNR when Gray coding is used. It shares spectral efficiency with 4-QAM and can outperform 4-QAM or 16-QAM in very noisy channels. QPSK is widely used in practical wireless systems, often alongside QAM in adaptive modulation schemes [Read more...] What is the Gray Code? Gray Code: Gray code is a binary numeral system where two successive values differ in only one bit. This property is called the single-bit difference or unit distance code. It is also known as reflected binary code. Let's convert binary 111 to Gray code: Binary bits: B = 1 1 1 Apply the rule: G[0] = B[0] = 1...

MATLAB Code for QPSK Modulation and Demodulation

馃摌 Overview 馃М MATLAB Codes 馃М Theory 馃М BER performance of QPSK with BPSK, 4-QAM, 16-QAM, 64-QAM, 256-QAM, etc 馃摎 Further Reading QPSK Passband Signal Generation Spectral Efficiency in QPSK   Quadrature Phase Shift Keying (QPSK) is a digital modulation scheme that conveys two bits per symbol by changing the phase of the carrier signal. Each pair of bits is mapped to one of four possible phase shifts: 0°, 90°, 180°, or 270° 00  ===> 0 degree phase shift of carrier signal 01  ===> 90 degree 11  ===> 180 degree 10  ===> 270 degree   MATLAB Script clc; clear all; close all; clc; M = 4; data = randi([0 (M-1)], 1000, 1); Phase = 0; modData=pskmod(data,M,Phase); figure(1); scatterplot(modData); channelAWGN = 15; rxData2 = awgn(modData, channelAWGN); figure(2); scatterplot(rxData2); demodData = pskdemod(rxData2,M,Phase);   Result data 1 0 2 2 0 2 1 . . . modData -1.0...

BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...(MATLAB Code + Simulator)

Bit Error Rate (BER) & SNR Guide Analyze communication system performance with our interactive simulators and MATLAB tools. 馃摌 Theory 馃М Simulators 馃捇 MATLAB Code 馃摎 Resources BER Definition SNR Formula BER Calculator MATLAB Comparison 馃搨 Explore M-ary QAM, PSK, and QPSK Topics ▼ 馃М Constellation Simulator: M-ary QAM 馃М Constellation Simulator: M-ary PSK 馃М BER calculation for ASK, FSK, and PSK 馃М Approaches to BER vs SNR Calculation What is Bit Error Rate (BER)? The BER indicates how many corrupted bits are received compared to the total number of bits sent. It is the primary figur...

Frequency Bands : EHF, SHF, UHF, VHF, HF, MF, LF, VLF and Their Uses

Frequency Bands >> EHF, SHF, UHF, VHF, HF, MF, LF... Frequency Bands and Their Uses 1. Extremely High Frequency (EHF) 30 - 300 GHz Uses 5G Networks 5G millimeter wave band 6G and beyond (Experimental) RADAR 2. Super High Frequency (SHF) 3 - 30 GHz Uses Ultra-wideband (UWB) Airborne RADAR Satellite Communication Microwave Link Communication or SATCOM 3. Ultra High Frequency (UHF) 300 - 3000 MHz Uses Satellite Communication Television Surveillance Navigation aids Also, read important wireless communication terms 4....

FM Bandwidth and FM Band Explained

FM radio uses the frequency band from 88 MHz to 108 MHz , which is a 20 MHz-wide spectrum . This is the range of carrier frequencies available to stations. 108 MHz − 88 MHz = 20 MHz However, a single FM station occupies only about 200 kHz . This is the bandwidth of the modulated FM signal. 1. Why One FM Station Needs ~200 kHz FM uses frequency modulation . The bandwidth depends on how far the carrier swings. Carson's Rule gives the approximate FM bandwidth: B = 2 ( 螖f + f m ) ...