Skip to main content
Home Wireless Communication Modulation MATLAB Beamforming Project Ideas MIMO Computer Networks Lab 🚀

Difference between AWGN and Rayleigh Fading



1. Introduction

Rayleigh fading coefficients and AWGN, or additive white gaussian noise [↗], are two distinct factors that affect a wireless communication channel. In mathematics, we can express it in that way. 



Let's explore wireless communication under two common noise scenarios: AWGN (Additive White Gaussian Noise) and Rayleigh fading.

y = hx + n ... (i)

The transmitted signal x is multiplied by the channel coefficient or channel impulse response (h) in the equation above, and the symbol "n" stands for the white Gaussian noise that is added to the signal through any type of channel (here, it is a wireless channel or wireless medium). Due to multi-paths the channel impulse response (h) changes. And multi-paths cause Rayleigh fading.


2. Additive White Gaussian Noise (AWGN)

The mathematical effect involves adding Gaussian-distributed noise to the modulated signal. The received signal y(t) is given by:

y(t) = x(t) + n(t)

Where:
x(t) is the modulated signal.
n(t) is the AWGN.

The effect of AWGN is to add random variations to the amplitude of the signal, which can lead to erroneous detection of the transmitted symbols. The SNR (signal-to-noise ratio) plays a crucial role in determining the quality of demodulation, with higher SNR values leading to better performance.

We measure SNR at the receiver side due to AWGN for a variety of reasons. For additional information about the Gaussian Noise and its PDF, click here. Because the power spectrum density of this type of noise is frequency independent, the term "white Gaussian noise" has been used here.


3. Rayleigh Fading

Mathematically, Rayleigh fading can be represented as a complex Gaussian random variable with zero mean and a certain variance. The received signal y(t) in the presence of Rayleigh fading can be represented as:

y(t) = h . x(t) + n(t)

Where:

h is the complex fading coefficient, representing the channel gain and phase shift.

x(t) is the modulated signal.

n(t) is the noise.

The fading coefficient h introduces random amplitude and phase variations to the signal. Due to the randomness of h, the received signal's amplitude will experience fluctuations, impacting the detection of transmitted symbols. The actual fading distribution might vary depending on the specific channel characteristics.


We will now talk about Rayleigh fading. We'll start by talking about what fading actually is. Any sort of wireless communication uses many paths (LOS or NLOS) [↗] to carry the signal from the transmitter to the receiver. To learn more about multi-paths (MPCs) in wireless communication, click here [↗]. Due to various reflections or diffractions from building walls, vegetation, etc., as they pass through multi-paths, the resulting signal at the receiver may be additive or destructive. Diversity, which is achieved by multi-antenna transmission and reception, is the best method to deal with this scenario. The topic " Diversity" will be covered in a later article.

The Rayleigh fading coefficient, or h in equation (i) above, is a complex coefficient that depends on the signal's attenuation and delay spread.

The Rayleigh distribution describes how the amplitudes of channel coefficients vary over a range. If the amplitude of the channel coefficient, a = |h|, then the distribution of the channel coefficient,

fA(a) = 2ae-a^2,  a>=0

On the other hand, the phases of the fading channel coefficient are distributed over the range of 0 degrees to 2П (or, 2*pi).

 

MATLAB Code to demonstrate the effects of AWGN and Rayleigh fading on wireless communication channels

 

 Output

 

 
Fig 1: Effects of AWGN and Rayleigh Fading in Wireless Communication
 

MATLAB Code to overcome the effect of the Rayleigh Fading with Receiver Diversity Gain

 

Output

 
 
Fig 2: BER vs SNR for Equal Gain Combining (EGC)


Q. Why does Rayleigh fading occur?
A. Due to multi-path

Q. Which kind of fading is Rayleigh fading, exactly?

A. Small-scale fading

Q. What other type of fading is there?

A. Large-scale fading

Q. When deep fade occurs?

You can notice a sudden drop in signal power while performing a signal analysis or spectrum analysis. If the signals that reach the receiver are fully destructive, as we have already discussed, this phenomenon is known as "deep fading." Such a condition may also arise as a result of signal shadowing, etc. [Read More about Fading: Slow & Fast Fading and Large & Small Scale Fading, etc.]


People are good at skipping over material they already know!

View Related Topics to







Admin & Author: Salim

profile

  Website: www.salimwireless.com
  Interests: Signal Processing, Telecommunication, 5G Technology, Present & Future Wireless Technologies, Digital Signal Processing, Computer Networks, Millimeter Wave Band Channel, Web Development
  Seeking an opportunity in the Teaching or Electronics & Telecommunication domains.
  Possess M.Tech in Electronic Communication Systems.


Contact Us

Name

Email *

Message *

Popular Posts

BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...

Modulation Constellation Diagrams BER vs. SNR BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ... 1. What is Bit Error Rate (BER)? The abbreviation BER stands for bit error rate, which indicates how many corrupted bits are received (after the demodulation process) compared to the total number of bits sent in a communication process. It is defined as,  In mathematics, BER = (number of bits received in error / total number of transmitted bits)  On the other hand, SNR refers to the signal-to-noise power ratio. For ease of calculation, we commonly convert it to dB or decibels.   2. What is Signal the signal-to-noise ratio (SNR)? SNR = signal power/noise power (SNR is a ratio of signal power to noise power) SNR (in dB) = 10*log(signal power / noise power) [base 10] For instance, the SNR for a given communication system is 3dB. So, SNR (in ratio) = 10^{SNR (in dB) / 10} = 2 Therefore, in this instance, the signal power i

Comparisons among ASK, PSK, and FSK | And the definitions of each

Modulation ASK, FSK & PSK Constellation MATLAB Simulink MATLAB Code Comparisons among ASK, PSK, and FSK    Comparisons among ASK, PSK, and FSK Comparison among ASK,  FSK, and PSK Performance Comparison: 1. Noise Sensitivity:    - ASK is the most sensitive to noise due to its reliance on amplitude variations.    - PSK is less sensitive to noise compared to ASK.    - FSK is relatively more robust against noise, making it suitable for noisy environments. 2. Bandwidth Efficiency:    - PSK is the most bandwidth-efficient, requiring less bandwidth than FSK for the same data rate.    - FSK requires wider bandwidth compared to PSK.    - ASK's bandwidth efficiency lies between FSK and PSK. Bandwidth Calculator for ASK, FSK, and PSK The baud rate represents the number of symbols transmitted per second Select Modulation Type: ASK FSK PSK Baud Rate (Hz):

MATLAB code for BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ...

Modulation Constellation Diagrams BER vs. SNR MATLAB code for BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ...   MATLAB Script for  BER vs. SNR for M-QAM, M-PSK, QPSk, BPSK %Written by Salim Wireless %Visit www.salimwireless.com for study materials on wireless communication %or, if you want to learn how to code in MATLAB clc; clear; close all; % Parameters num_symbols = 1e5; % Number of symbols snr_db = -20:2:20; % Range of SNR values in dB % PSK orders to be tested psk_orders = [2, 4, 8, 16, 32]; % QAM orders to be tested qam_orders = [4, 16, 64, 256]; % Initialize BER arrays ber_psk_results = zeros(length(psk_orders), length(snr_db)); ber_qam_results = zeros(length(qam_orders), length(snr_db)); % BER calculation for each PSK order and SNR value for i = 1:length(psk_orders) psk_order = psk_orders(i); for j = 1:length(snr_db) % Generate random symbols data_symbols = randi([0, psk_order-1]

FFT Magnitude and Phase Spectrum using MATLAB

MATLAB Code clc; clear; close all; % Parameters fs = 100;           % Sampling frequency t = 0:1/fs:1-1/fs;  % Time vector % Signal definition x = cos(2*pi*15*t - pi/4) - sin(2*pi*40*t); % Compute Fourier Transform y = fft(x); z = fftshift(y); % Frequency vector ly = length(y); f = (-ly/2:ly/2-1)/ly*fs; % Compute phase phase = angle(z); % Plot magnitude of the Fourier Transform figure; subplot(2, 1, 1); stem(f, abs(z), 'b'); xlabel('Frequency (Hz)'); ylabel('|y|'); title('Magnitude of Fourier Transform'); grid on; % Plot phase of the Fourier Transform subplot(2, 1, 2); stem(f, phase, 'b'); xlabel('Frequency (Hz)'); ylabel('Phase (radians)'); title('Phase of Fourier Transform'); grid on;   Output  Copy the MATLAB Code from here % The code is written by SalimWireless.Com clc; clear; close all; % Parameters fs = 100; % Sampling frequency t = 0:1/fs:1-1/fs; % Time vector % Signal definition x = cos(2*pi*15*t -

Channel Impulse Response (CIR)

Channel Impulse Response (CIR) Wireless Signal Processing CIR, Doppler Shift & Gaussian Random Variable  The Channel Impulse Response (CIR) is a concept primarily used in the field of telecommunications and signal processing. It provides information about how a communication channel responds to an impulse signal.   What is the Channel Impulse Response (CIR) ? It describes the behavior of a communication channel in response to an impulse signal. In signal processing,  an impulse signal has zero amplitude at all other times and amplitude  ∞ at time 0 for the signal. Using a Dirac Delta function, we can approximate this.  ...(i) δ( t) now has a very intriguing characteristic. The answer is 1 when the Fourier Transform of  δ( t) is calculated. As a result, all frequencies are responded to equally by  δ (t). This is crucial since we never know which frequencies a system will affect when examining an unidentified one. Since it can test the system for all freq

MATLAB Code for Pulse Amplitude Modulation (PAM) and Demodulation

  Pulse Amplitude Modulation (PAM) & Demodulation MATLAB Script clc; clear all; close all; fm= 10; % frequency of the message signal fc= 100; % frequency of the carrier signal fs=1000*fm; % (=100KHz) sampling frequency (where 1000 is the upsampling factor) t=0:1/fs:1; % sampling rate of (1/fs = 100 kHz) m=1*cos(2*pi*fm*t); % Message signal with period 2*pi*fm (sinusoidal wave signal) c=0.5*square(2*pi*fc*t)+0.5; % square wave with period 2*pi*fc s=m.*c; % modulated signal (multiplication of element by element) subplot(4,1,1); plot(t,m); title('Message signal'); xlabel ('Time'); ylabel('Amplitude'); subplot(4,1,2); plot(t,c); title('Carrier signal'); xlabel('Time'); ylabel('Amplitude'); subplot(4,1,3); plot(t,s); title('Modulated signal'); xlabel('Time'); ylabel('Amplitude'); %demdulated d=s.*c; % At receiver, received signal is multiplied by carrier signal filter=fir1(200,fm/fs,'low'); % low-pass FIR fi