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

MATLAB Code for Constellation Diagram of QAM configurations such as 4, 8, 16, 32, 64, 128, and 256-QAM


 

One of the best-performing modulation techniques is QAM [↗]. Here, we modulate the symbols by varying the carrier signal's amplitude and phase in response to the variation in the message signal (or voltage variation). So, we may say that QAM is a combination of phase and amplitude modulation. Additionally, it performs better than ASK or PSK [↗]. In fact, any constellation for any type of modulation, signal set (or, symbols) is structured in a way that prevents them from interacting further by being distinct by phase, amplitude, or frequency.


MATLAB Script (for 4-QAM)

% This code is written by SalimWirelss.Com
% This is an example of 4-QAM. Here constellation size is 4
% or total number of symbols/signals is 4
% We need 2 bits once to represent four constellation points
% QAM modulation is the combination of Amplitude modulation plus
% Phase Modulation. We map the decimal value of the input symbols, i.e.,
% 00, 01, 10, 11 to 1 + 1i, -1 + 1i, 1 - 1i, and -1 - 1i, respectively.


clc;clear all;close all;

M = 4; % Number of levels after quantization / size of signal constellation

k = log2(M); % Number of bits per symbol

rng(10) %assaining the value of seed integer

N =10000; % Number of bits to process

InputBits = randi([0 1],1,N); % Generating randon bits

InputSymbol_matrix = reshape(InputBits,length(InputBits)/k,k); % Reshape data into binary k-tuples, k = log2(M)

InputSymbols_decimal = bi2de(InputSymbol_matrix); % Convert binary to decimal

for n= 1:N/k

if InputSymbols_decimal(n)==0

QAM(n)= complex(1,1);

elseif InputSymbols_decimal(n)==1

QAM(n)= complex(-1,1);

elseif InputSymbols_decimal(n)==2

QAM(n)= complex(1,-1);

else

QAM(n)= complex(-1,-1);

end

end



%Transmission of 4QAM data over AWGN channel

snrdB = 10;

Y=awgn(QAM,snrdB); %received signal


%Threshold Detection

for n= 1:N/k

if (real(Y(n))>0 && imag(Y(n))>0)

Z(n)=complex(1,1);

elseif (real(Y(n))>0 && imag(Y(n))<0)

Z(n)=complex(1,-1);


elseif (real(Y(n))<0 && imag(Y(n))>0)

Z(n)=complex(-1,1);

else

Z(n)=complex(-1,-1);

end

end

figure(1)
scatter(real(QAM), imag(QAM))
xlim([-3, 3]);
ylim([-3, 3]);
legend('Transmitted Symbols')

figure(2)
scatter(real(Y), imag(Y))
xlim([-3, 3]);
ylim([-3, 3]);
legend('Received Symbols')
 

Output 

 
 
 
Fig 1: Constellation points of 4-QAM (Transmitted)


 
 
Fig 2: Constellation points of 4-QAM (Received)


Copy the MATLAB Code for 4-QAM


 

Another MATLAB Code (for 16-QAM)

%The code is developed by SalimWireless.Com

clc;
clear;
close all;

% Define parameters
M = 16; % Modulation order for 16-QAM
numSymbols = 10000; % Number of symbols to modulate

% Generate random data
data = randi([0 M-1], numSymbols, 1); % Ensure data is a column vector

% Modulate the data using 16-QAM
modData = qammod_custom(data, M);

snrdB = 15;
Y = awgn(modData,snrdB); %received signal

% Plot the constellation of the modulated signal
figure;
subplot(2,1,1);
scatter(real(modData), imag(modData), 'o');
grid on;
xlabel('In-phase');
ylabel('Quadrature');
title('Constellation Diagram of Modulated Signal (16-QAM)');
axis([-1.5 1.5 -1.5 1.5]); % Set axis limits for better visualization

subplot(2,1,2);
scatter(real(Y), imag(Y), 'o');
grid on;
xlabel('In-phase');
ylabel('Quadrature');
title('Constellation Diagram of Noisy Received Signal before demodulation');
axis([-1.5 1.5 -1.5 1.5]); % Set axis limits for better visualization

% Demodulate the received signal
receivedData = qamdemod_custom(modData, M);

% Ensure receivedData is a column vector for comparison
receivedData = receivedData(:);


% Custom 16-QAM Modulation Function
function modData = qammod_custom(data, M)
% QAMMOD_CUSTOM Modulate data using 16-QAM
% data - Column vector of integers (each element is between 0 and M-1)
% M - Modulation order (should be 16 for 16-QAM)

% Check if M is 16
if M ~= 16
error('This function is designed for 16-QAM modulation.');
end

% Define the 16-QAM constellation
constellation = [-3-3i, -3-1i, -1-3i, -1-1i, ...
-3+3i, -3+1i, -1+3i, -1+1i, ...
+3-3i, +3-1i, +1-3i, +1-1i, ...
+3+3i, +3+1i, +1+3i, +1+1i];

% Normalize constellation
constellation = constellation / sqrt(mean(abs(constellation).^2)); % Scale to unit average power

% Map data to constellation points
modData = constellation(data + 1);
end

% Custom 16-QAM Demodulation Function
function demodData = qamdemod_custom(modData, M)
% QAMDEMOD_CUSTOM Demodulate data using 16-QAM
% modData - Column vector of complex numbers (modulated symbols)
% M - Modulation order (should be 16 for 16-QAM)

% Check if M is 16
if M ~= 16
error('This function is designed for 16-QAM demodulation.');
end

% Define the 16-QAM constellation
constellation = [-3-3i, -3-1i, -1-3i, -1-1i, ...
-3+3i, -3+1i, -1+3i, -1+1i, ...
+3-3i, +3-1i, +1-3i, +1-1i, ...
+3+3i, +3+1i, +1+3i, +1+1i];

% Normalize constellation
constellation = constellation / sqrt(mean(abs(constellation).^2)); % Scale to unit average power

% Ensure modData is a column vector
modData = modData(:);

% Compute the distances from each modData point to all constellation points
numSymbols = length(modData);
numConstellations = length(constellation);
distances = zeros(numSymbols, numConstellations);
for k = 1:numConstellations
distances(:, k) = abs(modData - constellation(k)).^2;
end

% Find the closest constellation point for each modData point
[~, demodData] = min(distances, [], 2);

% Convert to zero-based index
demodData = demodData - 1;
end

Output  


 
 
 
 

Copy the MATLAB Code above from here (for 16-QAM)

 

MATLAB code for M-ary QAM (e.g., 4, 8, 16, 32, 64, 128, 256)

%The code is developed by SalimWireless.com
% M-ary QAM Modulation and Demodulation
clc;
clear;
close all;


% Parameters
M = 32; % Order of QAM (M-QAM)
N = 1000; % Number of symbols
SNR = 10; % Signal-to-Noise Ratio in dB


% Generate random data symbols
dataSymbols = randi([0 M-1], N, 1);


% Modulate using M-QAM
txSignal = qammod(dataSymbols, M);


% Add AWGN noise
rxSignal = awgn(txSignal, SNR, 'measured');


% Demodulate
demodulatedSymbols = qamdemod(rxSignal, M);


% Calculate symbol error rate
symbolErrors = sum(dataSymbols ~= demodulatedSymbols);
SER = symbolErrors / N;


% Display results
disp(['Symbol Error Rate (SER): ', num2str(SER)]);


% Plot constellation diagrams
figure;
subplot(2, 1, 1);
plot(real(txSignal), imag(txSignal), 'o');
grid on;
title('Transmitted Signal Constellation');
xlabel('In-Phase');
ylabel('Quadrature');


subplot(2, 1, 2);
plot(real(rxSignal), imag(rxSignal), 'o');
grid on;
title('Received Signal Constellation');
xlabel('In-Phase');
ylabel('Quadrature');

Output








Copy the MATLAB Code above from here (e.g., for QAM configurations such as 4, 8, 16, 32, 64, 128, and 256-QAM.)


MATLAB Code for BER vs SNR for 4-QAM, 16-QAM, 32-QAM, and so on

 
 
 
(Get MATLAB Code)


Also read about

Next>>

People are good at skipping over material they already know!

View Related Topics to







Admin & Author: Salim

s

  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, ...

📘 Overview of BER and SNR 🧮 Online Simulator for BER calculation of m-ary QAM and m-ary PSK 🧮 Online Simulator for Constellation Diagram of m-ary QAM 🧮 Online Simulator for Constellation Diagram of m-ary PSK 🧮 MATLAB Code for BER calculation of M-ary QAM, M-ary PSK, QPSK, BPSK, ... 🧮 MATLAB Code for BER calculation of ASK, FSK, and PSK 🧮 MATLAB Code for BER calculation of Alamouti Scheme 🧮 Different approaches to calculate BER vs SNR 📚 Further Reading Modulation Constellation Diagrams BER vs. SNR BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ... 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 ...
Read more

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

https://www.salimwireless.com/2024/11/constellation-diagram-in-matlab.html 📘 Overview 🧮 Simulator 🧮 Noise Sensitivity, Bandwidth, Complexity, etc. 🧮 MATLAB Code for BER vs. SNR Analysis of ASK, FSK, and PSK 🧮 MATLAB Code for Constellation Diagrams of ASK, FSK, and PSK 🧮 Simulator for ASK, FSK, and PSK Generation 🧮 Simulator for ASK, FSK, and PSK Constellation 🧮 Some Questions and Answers 📚 Further Reading Modulation ASK, FSK & PSK Constellation MATLAB Simulink MATLAB Code Comparisons among ASK, PSK, and FSK    Comparisons among ASK, PSK, and FSK   Simulator for Calculating Bandwidth of ASK, FSK, and PSK The baud rate represents the number of symbols transmitted per second. Both baud rate and bit rate are same for binary ASK, FSK, and PSK. Select Modulation Type: ASK FSK PSK Baud Rat...
Read more

MATLAB Code for Pulse Amplitude Modulation (PAM) and Demodulation

📘 Overview & Theory 🧮 MATLAB Code 1 🧮 MATLAB Code 2 🧮 MATLAB Code for Pulse Amplitude Modulation and Demodulation of Digital data 🧮 Other Pulse Modulation Techniques (e.g., PWM, PPM, DM, and PCM) 📚 Further Reading   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('Amplitu...
Read more

Constellation Diagrams of ASK, PSK, and FSK

📘 Overview 🧮 Simulator for constellation diagrams of ASK, FSK, and PSK 🧮 Theory 🧮 MATLAB Codes 🧮 Simulator for constellation diagrams of m-ary PSK 🧮 Simulator for constellation diagrams of m-ary QAM 📚 Further Reading BASK (Binary ASK) Modulation: Transmits one of two signals: 0 or -√Eb, where Eb​ is the energy per bit. These signals represent binary 0 and 1.    BFSK (Binary FSK) Modulation: Transmits one of two signals: +√Eb​ ( On the y-axis, the phase shift of 90 degrees with respect to the x-axis, which is also termed phase offset ) or √Eb (on x-axis), where Eb​ is the energy per bit. These signals represent binary 0 and 1.  BPSK (Binary PSK) Modulation: Transmits one of two signals: +√Eb​ or -√Eb (they differ by 180 degree phase shift), where Eb​ is the energy per bit. These signals represent binary 0 and 1.    Simulator for BASK, BPSK, and BFSK Constellation Diagrams ...
Read more

Channel Impulse Response (CIR)

Channel Impulse Response (CIR) 📘 Overview & Theory 📘 How does the channel impulse response affect the signal? 🧮 Online Channel Impulse Response Simulator 🧮 MATLAB Codes 📚 Further Reading 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(...
Read more

UGC NET Electronic Science Previous Year Question Papers

Home / Engineering & Other Exams / UGC NET 2022: Previous Year Question Papers ...   NET | GATE | ESE | UGC-NET (Electronics Science, Subject code: 88 ) UGC Net Electronic Science Questions Paper With Answer Key Download Pdf [December 2024] UGC Net Electronic Science Questions Paper With Answer Key Download Pdf [June 2024] UGC Net Electronic Science Questions Paper With Answer Key Download Pdf [December 2023] UGC Net Electronic Science Questions Paper With Answer Key Download Pdf [June 2023] UGC Net Electronic Science Questions Paper With Answer Key Download Pdf [December 2022]  UGC Net Electronic Science Questions Paper With Answer Key Download Pdf [June 2022]   UGC Net Electronic Science Questions Paper With Answer Key Download Pdf [December 2021] UGC Net Electronic Science Questions With Answer Key Download Pdf [June 2020] UGC Net Electronic Science Questions With Answer Key Download Pdf [December 2019] UGC Net Electronic Science Questions With Answer...
Read more

MATLAB Code for Constellation Diagrams of ASK, FSK, and PSK

  MATLAB Script % The code is developed by SalimWireless.Com clc; clear; close all; % Parameters numSymbols = 1000; % Number of symbols to simulate symbolIndices = randi([0 1], numSymbols, 1); % Random binary symbols (0 or 1) % ASK Modulation (BASK) askAmplitude = [0, 1]; % Amplitudes for binary ASK askSymbols = askAmplitude(symbolIndices + 1); % Modulated BASK symbols % FSK Modulation (Modified BFSK with 90-degree offset) fs = 100; % Sampling frequency symbolDuration = 1; % Symbol duration in seconds t = linspace(0, symbolDuration, fs*symbolDuration); fBase = 1; % Base frequency frequencies = [fBase, fBase]; % Same frequency for both % Generate FSK symbols with 90° phase offset fskSymbols = arrayfun(@(idx) ...     cos(2*pi*frequencies(1)*t) * (1-idx) + ...     1j * cos(2*pi*frequencies(2)*t) * idx, ...     symbolIndices, 'UniformOutput', false); % Extract last points (constellation points) fskConstellation = cellfun(@(x) x(end), fskSymbols); % PSK Mod...
Read more