Skip to main content
Home Wireless Communication Modulation MATLAB Beamforming Project Ideas MIMO Computer Networks Lab 🚀
Electronics Industry Wireless FORUM Work Hub Applications & Games Generate QR for Any Link Sitemap Generator (for Any Website) Play game Electrical & Electronics Calculator Contact Get Newsletter.
☰

MATLAB Code for QAM (Quadrature Amplitude Modulation)

 

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

% 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 QAM


 

Another MATLAB Code

%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

 

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


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

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

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 i...
Read more

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...
Read more

Star to Delta Conversion and Vice Versa | star delta conversion

The transformation of a star to a delta and a delta to a star circuit is a hot topic in electrical science and engineering. Examiners often ask about the conversion of star to delta and delta to star circuit diagram. When solving complex circuits, the conversion procedure can sometimes ease calculations and save time. Without further ado, we'll go over the characteristics of both a star and a delta circuit. As its title suggests, the star circuit looks like a star. Delta circuit, on the other hand, looks like a delta. Now we'll look at the mathematical method for converting delta to star and star to delta. Delta to Star R1 = RaRb / (Ra + Rb + Rc) R2 = RbRc / (Ra + Rb + Rc) R3 = RaRc / (Ra + Rb + Rc) Use star to delta online converter and vice versa Star to Delta Ra = (R1R2 + R2R3 + R3R1) / R2 Rb = (R1R2 + R2R3 + R3R1) / R3 Rc = (R1R2 + R2R3 + R3R1) / R1 Next Page>>
Read more

MIMO, massive MIMO, and Beamforming

  The term 'MIMO' was originally applied to systems with multiple antennas on both the transmitter (Tx) and receiver (Rx) sides. MIMO is a key component of Wi-Fi 4 and 5, 3G, and 4G cellular networks. This method was introduced to increase the capacity of a channel by sending multiple simultaneous data streams through a single channel. All simultaneous data streams in a MIMO system are encoded orthogonally multiplexed, which reduces interference. Massive MIMO is used extensively in 5G to achieve extremely high capacity and to communicate via  beamforming  or directional transmission. 1. Some essential characteristics of a MIMO system 1.1. Spatial Division Multiplexing Access (SDMA) SDMA is a key feature of MIMO, allowing a base station (BS) to communicate with several devices simultaneously (or even using the same frequency) if they are in different locations. There may be no knowledge of channel information at the transmitter. 1.2. Spatial Multiplexing Another essential ...
Read more

MATLAB Code for Rank and Condition Number of a Channel Matrix

To assess the signal strengths of various multipaths between TX and RX and enable communication, the rank and condition numbers of a channel matrix are highly helpful characteristics. Signal multipath propagation is a typical occurrence in wireless communication. Phases shift and the signal weakens during this process. We are discussing signal phases in this context. When numerous multipaths arrive at the receiver, the resulting signal may be additive or destructive because of phase alterations. A channel matrix is referred to as a sparse matrix if it only has a few stronger elements and the majority of the other elements are zero. Finding rank and condition number for sparse matrices is important for numerous reasons. That topic has already been covered in another article [ click here ]. We will just talk about the corresponding MATLAB codes here. MATLAB Code for Rank and Condition Number of a Channel Matrix %Author: Salim Wireless For study materials on wireless %com...
Read more

Difference between AWGN and Rayleigh Fading

Wireless Signal Processing Gaussian and Rayleigh Distribution 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.  Fig: Rayleigh Fading due to multi-paths Let's explore wireless communication under two common noise scenarios: AWGN (Additive White Gaussian Noise) and Rayleigh fading. y = h*x + n ... (i) Symbol '*' represents convolution. 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 fa...
Read more

MATLAB Code for Pulse Width Modulation (PWM) and Demodulation

   Pulse Width Modulation (PWM) MATLAB Script   clc; clear all; close all; fs=5; %frequency of the sawtooth signal fm=5; %frequency of the message signal sampling_frequency = 10e3; a=0.5; % amplitide t=0:(1/sampling_frequency):1; %sampling rate of 10kHz sawtooth=1.01*a.*sawtooth(2*pi*fs*t); %generating a sawtooth wave subplot(4,1,1); plot(t,sawtooth); % plotting the sawtooth wave title('Comparator Wave'); msg=a.*sin(2*pi*fm*t); %generating message wave subplot(4,1,2); plot(t,msg); %plotting the sine message wave title('Message Signal'); for i=1:length(sawtooth) if (msg(i)>=sawtooth(i)) pwm(i)=1; %is message signal amplitude at i th sample is greater than %sawtooth wave amplitude at i th sample else pwm(i)=0; end end subplot(4,1,3); plot(t,pwm,'r'); title('PWM'); axis([0 1 0 1.1]); %to keep the pwm visible during plotting. %% Demodulation % Demodulation: Measure the pulse width to reconstruct the signal demodulated_signal = zeros(size(msg)); for i =...
Read more