Doppler Delay

 

Doppler Shift Formula

When either the transmitter or the receiver is in motion, or when both are in motion, Doppler Shift is an essential parameter in wireless Communication. We notice variations in reception frequencies in vehicles, trains, or other similar environments. In plain language, the received signal frequency increases as the receiver moves toward the transmitter and drops as the receiver moves in the opposite direction of the transmitter. This phenomenon is called the Doppler shift or Doppler spread.

Doppler Shift Formula:

By equation,                fR = fT (+/-) fD

                                     fR= receiving frequency

                                     fT= transmitted frequency

                                     fD= Doppler frequency

We frequently see an increase or decrease in reception frequencies due to the equation. Now, the Doppler frequency is bounded by several rules, 

Doppler shift of LOS path: ν1 = fc*v/c, 

Doppler shift of reflected path: ν2 = fc*v/c*cos(theta)

where, c = speed of light

v = speed of the vehicle

Doppler spread: ν2 − ν1

Or, Doppler spread, fD = |v/lambda * {cos(theta) - 1}|, 

** '|' indicates mod

where, v = velocity of vehicle

            lambda = wavelength = c/frequency

For example, when MS (in motion) reaches towards BS, cos = cos(0 degrees)=1, and when MS goes away from BS or base station, cos = cos(180 degrees)=-1.

As a result of the preceding equation, the receiving frequency increases if the receiver moves towards the receiver.

fT+fD, here frequency increases as fR = fT + fD

                                                      or, fR = fT + v/lambda * 1

                                                       or, fR =fT + v/lambda

                                                Here, lambda = wavelength of operating frequency

Similarly, when the receiver moves away from BS or the cell tower, the frequency decreases by v/lambda* cos ( 180 degrees) or v/lambda * (-1), as cos180 = -1. So, now the received frequency at the receiver side is,

fR = fT - fD 

Doppler Shift vs Doppler Spread

1. Doppler Shift:

The term "Doppler Shift" refers to a wave's shift in frequency as it relates to an observer moving with respect to the wave source.
The amount that the frequency has changed due to relative motion is represented by a single number.
The Doppler shift, for example, is the difference between the transmitted and received frequencies of a radar signal when it reflects off a moving object.

2. Doppler Spread: 

This is the range of frequency shifts (Doppler shifts) that happen in a multipath environment or when a signal is scattered by several moving objects.
The signal's spectral broadening brought on by these numerous Doppler shifts is indicated by Doppler spread.It affects the channel's coherence time and is a measure of the variance or dispersion of the Doppler shifts. High Doppler spread indicates quick changes in the channel's properties, which may have an impact on the efficiency of a communication system.

To sum up, Doppler spread measures the range of frequency shifts brought on by multipath propagation and the relative motion of multiple scatterers, whereas Doppler shift is a single frequency change resulting from relative motion. 

    

MATLAB Code for Doppler Shift vs Doppler Spread

clc;
clear;
close all;

% Constants
c = 3e8; % Speed of light in m/s (for electromagnetic waves)
f0 = 2.4e9; % Original frequency in Hz (e.g., 2.4 GHz for WiFi)

% Relative velocities (in m/s) for different objects
velocities = [-30, -10, 0, 10, 20]; % Example velocities of objects

% Calculate Doppler Shifts
doppler_shifts = (velocities / c) * f0;

% Calculate Doppler Spread
doppler_spread = max(doppler_shifts) - min(doppler_shifts);

% Display results

fprintf('Relative velocities (in m/s) for different vehicles:\n');
disp(velocities);
fprintf('Doppler Shifts (Hz):\n');
disp(doppler_shifts);
fprintf('Doppler Spread (Hz): %f\n', doppler_spread);

Output 

 Relative velocities (in m/s) for different vehicles:
   -30   -10     0    10    20

Doppler Shifts (Hz):
  -240   -80     0    80   160

Doppler Spread (Hz): 400.000000

 

Copy the MATLAB Code from here

% The code is written by SalimWireless.Com % Clear previous data and plots clc; clear; close all; % Constants c = 3e8; % Speed of light in m/s (for electromagnetic waves) f0 = 2.4e9; % Original frequency in Hz (e.g., 2.4 GHz for WiFi) % Relative velocities (in m/s) for different objects velocities = [-30, -10, 0, 10, 20]; % Example velocities of objects % Calculate Doppler Shifts doppler_shifts = (velocities / c) * f0; % Calculate Doppler Spread doppler_spread = max(doppler_shifts) - min(doppler_shifts); % Display results fprintf('Relative velocities (in m/s) for different vehicles:\n'); disp(velocities); fprintf('Doppler Shifts (Hz):\n'); disp(doppler_shifts); fprintf('Doppler Spread (Hz): %f\n', doppler_spread);

 

 

How Doppler Spread Affects Communication

The Doppler spread causes fading in wireless Communication. Fading occurs when the received power fluctuates or decreases at the receiver side for a short or large amount of time. Fast and slow fading in wireless channels is caused by Doppler spread. All of those topics have already been covered in another article. Please read the full article.

For practical communication systems, if the received symbol or signal is R[t,f], then

R[t, f] = S(τ)*h(τ, f)*exp(2*pi*(t - τ))

where S(τ) is the transmitted signal with some delay τ

h(τ, f) is the Doppler delay channel impulse (DD-CIR) response which characterizes how the signal's amplitude and phase change with respect to time delay τ and frequency f

exp(2*pi*(t - τ)) represents the phase shift due to the Doppler effect

Also, read about

[1] Fading - Slow & Fast and Large & Small Scale Fading