Constellation Diagram of ASK in Detail

A binary bit '1' is assigned a power level of

\sqrt{E_b}

(or energy

E_b

), while a binary bit '0' is assigned zero power (or no energy).

Simulator for Binary ASK Constellation Diagram

SNR (dB): 15

Noisy Modulated Signal (ASK)

Original Modulated Signal (ASK)

Energy per bit (Eb) (Tb = bit duration):

We know that all periodic signals are power signals. Now we’ll find the energy of ASK for the transmission of binary ‘1’.

E_b = ∫₀^Tb(A_c.cos(2П.f_c.t))² dt
= ∫₀^Tb(A_c)².cos²(2П.f_c.t) dt
Using the identity cos²x = (1 + cos(2x))/2:
= ∫₀^Tb((A_c)²/2)(1 + cos(4П.f_c.t)) dt
= ((A_c)²/2) ∫₀^Tb(1) dt + ((A_c)²/2) ∫₀^Tbcos(4П.f_c.t) dt
= ((A_c)²/2) * T_b + 0 (The integral of cos(4П.f_c.t) over a full period is zero, assuming T_b is an integer multiple of 1/(2f_c))
E_b = (A_c²/2).T_b (where T_b is the bit duration)

** where A_c is the amplitude of the carrier signal and f_c is the carrier frequency in Hz.

To save transmitter energy, E_b should be small.

** for transmission of binary ‘0’
E_b = ∫₀^Tb(S₂(t))²dt = 0

** Constellation Diagram
First, we define the orthonormal basis function for this system:
φ₁(t) = √(2/T_b) cos(2Пf_ct) for 0 ≤ t ≤ T_b.
The energy of this basis function is 1.

Now, we can represent our signaling waveforms using this basis function:
For binary '1': S₁(t) = A_c cos(2Пf_ct) = [A_c * √(T_b/2)] * φ₁(t)
The coordinate for S₁(t) in the constellation diagram is g₁₁ = A_c * √(T_b/2).
The energy of S₁(t) is E_b = g₁₁² = (A_c² * T_b)/2.
Therefore, g₁₁ = √(E_b).

For binary '0': S₂(t) = 0. The coordinate for S₂(t) is g₂₁ = 0.

So, in the constellation diagram:
1 => point at √(E_b) along the φ₁ axis
0 => point at 0 (the origin)

High-order Amplitude Shift Keying (ASK) refers to using a large number of amplitude levels to represent digital data. For instance, in binary ASK (BASK), there are two amplitude levels, usually represented as 0 and 1. High-order ASK can have more than two amplitude levels, such as 4, 8, 16, 64, etc.

MATLAB Code For Constellation Diagram of ASK

% The code is written by SalimWireless.Com 
% Clear previous data and plots
clc; 
clear all; 
close all;

% Parameters
Tb = 1;             % Bit duration
fc = 10;            % Carrier frequency
N = 10;             % Number of bits

% Generate carrier signal
t = 0:Tb/100:1;
carrier_signal = sqrt(2/Tb) * sin(2*pi*fc*t);

% Generate message signal
rng(10);            % Set random seed for reproducibility
binary_data = rand(1, N);  % Generate random binary data
t_start = 0; t_end = Tb;

for i = 1:N 
    t = [t_start:0.01:t_end]; 
    
    % Generate message signal
    if binary_data(i) > 0.5 
        binary_data(i) = 1; 
        message_signal = ones(1, length(t)); 
    else 
        binary_data(i) = 0; 
        message_signal = zeros(1, length(t)); 
    end 
    
    % Store message signal
    message(i,:) = message_signal; 
    
    % Modulate message with carrier
    ask_signal(i,:) = carrier_signal .* message_signal; 
    
    % Update time intervals
    t_start = t_start + (Tb + 0.01); 
    t_end = t_end + (Tb + 0.01); 
    
end

% Constellation Diagram 
figure(1);
scatterplot(binary_data);
title('Constellation Diagram of Binary ASK');
xlabel('n --->');
ylabel('b(n)');
grid on;

%%%%%%%%%%%%%% ASK Demodulation %%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ASK Demodulation %%%%%%%%%%%%%%%%%%
t_start = 0; t_end = Tb;
for i = 1:N 
    t = [t_start:Tb/100:t_end]; 
    
    % Correlator
    correlation = sum(carrier_signal .* ask_signal(i,:)); 
    
    % Decision device
    if correlation > 0 
        demodulated_data(i) = 1; 
    else 
        demodulated_data(i) = 0; 
    end 
    
    % Update time intervals
    t_start = t_start + (Tb + 0.01); 
    t_end = t_end + (Tb + 0.01); 
end

% Constellation Diagram after demodulation
figure(2);
scatterplot(demodulated_data);
title('Constellation Diagram of Binary ASK after Demodulation');
xlabel('n --->');
ylabel('b(n)');
grid on;

Output

Effect of Noise on Constellation Diagram of ASK

At SNR = 5 dB

At SNR = 10 dB

At SNR = 15 dB

At SNR = 30 dB

Search This Blog