Skip to main content

MATLAB Code Constellation Diagrams of M-ary PSK (e.g, 4, 8, 16, 32, 64, 128)



What is the difference between Bit and Symbol in the perspective of transmission?

Symbols use bandwidth more efficiently than bits. For example, in the case of QPSK, one symbol or signal waveform is represented by 2 bits. Hence symbol rate is one-half of the bit rate. As a result, it occupies half bandwidth compared to the BPSK waveform.

We know the primary purpose of modulation [↗] is to multiplex data. Here multiplexing is done so that there is less interference between parallel data streams. Suppose there is a communication channel; we can transmit a single data stream simultaneously. But if we send a symbol instead of a bit, we can send more than 1 bit at a time. In ASK modulation, we assign two amplitude levels to a signal where a higher level is represented by binary '1' and another level as '0'. For BFSK, we apply phase shift in signal (for example, 0 phase shift for consecutive binary '0' bits and 180 phase shift for a binary bit '1'. ASK, FSK, and PSK [↗] - are primary modulation techniques. With the help of those modulation techniques, we derive many other digital modulations capable of carrying more bits thru a channel as a symbol at a time. For example, in QPSK (Quadrature Phase Shift Keying), we can transmit a symbol two bits at a time thru a channel. A total of 4 symbols use 2 bits per symbol and a phase difference of 90 degrees between them. An example of QPSK is shown below. Here you see that the data rate of the channel is getting double when we transmit 2 bits at a time.


1. What is a constellation diagram


A constellation diagram represents a signal modulated by a digital signal, such as quadrature amplitude modulation (QAM) or quadrature phase shift keying (QPSK). [Read More]


QPSK


Assume we need to modulate four signals or symbols with phase differences of Ï€/2 so that the signals can be orthogonal, which will minimize their mutual interference. Then we can modulate those signals in the following way:

s(t)=Acos(2Ï€fct) for 00

= A cos (2Ï€fct + 90) for 01

= A cos (2Ï€fct + 180) for 10

= A cos (2Ï€fct + 270) for 11

Here, the first signal is modulated with a carrier signal. The next signal is modulated with π/2 shifted same carrier signal, the third signal with additional π/2 shifted to the same carrier signal, and so on. The modulated first signal is represented by the symbol '00', the second modulated signal by the symbol '01', and so forth.





In the above figure, we've shown a constellation diagram of 4 QPSK modulations.


Also, read about the Constellation Diagrams of ASK, FSK, and PSK, Constellation Diagrams of M-ary QAM


2. What is the significance of M-ary PSK?


In Mary PSK, given data bits are modulated with any of the M numbers of phase-shifted carrier signals. Let's send M number of data bits modulated with M number of phase-shifted carriers. Theoretically, there will be no interference (theoretically) between them, and we will achieve 8 times the previous data rate (without modulation).

The RF carrier's phase (or frequency) varies instead of only varying the RF signal's phase, frequency, or amplitude. Mary modulation algorithms transfer baseband data into four or more alternative RF carrier signals since the envelope and phase provide two degrees of freedom. We are talking about four carrier signals because here, 2 or more bits form a symbol, and from 2 bits, we can represent 2^(2) or 4 different signals. M-ary modulation is the name given to such modulation schemes. Two or more bits are joined together to create symbols in the M-ary modulation scheme, and one of the available signals S1(t), S2(t),..., Sm(t) is sent during each symbol period Ts. M = 2^n, where n is an integer that defines the number of bits/symbols, the total number of possible signals.

The modulation is called M-ary ASK, M-ary PSK, or M-ary FSK, depending on whether the amplitude, phase, or frequency is altered. M-ary modulation techniques are appealing for application in bandlimited channels because they improve bandwidth efficiency while sacrificing power efficiency. For example, an 8-PSK system utilizes the channel log8 (base 2) = 3 times more efficiently than a 2-PSK (also known as BPSK) system, as the bandwidth of a physical channel is always limited. M-ary signaling, on the other hand, has lower error performance due to the reduced distances between signals in the constellation diagram. The following sections go through a few of the most common M-ary signaling methods.

8-PSK 

 

16-PSK

 

 
 

MATLAB Code for M-ary PSK (e.g, 4, 8, 16, 32, 64, 128)

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

% Parameters
M = 32;  % Order of PSK (M-PSK)
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-PSK
txSignal = pskmod(dataSymbols, M);

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

% Demodulate
demodulatedSymbols = pskdemod(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



3. What can we conclude from the above M-ary PSK


Both QPSK and QAM are used to send signals in the form of symbols and to increase the bit rate. If you send a symbol instead of a single bit at a time, then multiple prior data rates will be achieved. Those mary modulation techniques are used to multiplex data.

If you are using simple ASK, FSK, or 2-PSK, and if the data rate is N

Then, the following modulation techniques increase data rates further.

4-PSK, 4-QAM ==>2N

Because here 2 bits are sent as a symbol once

8-PSK, 8-QAM ==>3N

Because here 3 bits are sent as a symbol once

Read More about OFDM, QAM, QPSK, BPSK, FSK, etc.


constellation diagram of qpsk  # qpsk constellation diagram  # Constellation diagram of ask psk fsk


Further Reading

People are good at skipping over material they already know!

View Related Topics to







Contact Us

Name

Email *

Message *

Popular Posts

BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...(MATLAB Code + Simulator)

Bit Error Rate (BER) & SNR Guide Analyze communication system performance with our interactive simulators and MATLAB tools. 📘 Theory 🧮 Simulators 💻 MATLAB Code 📚 Resources BER Definition SNR Formula BER Calculator MATLAB Comparison 📂 Explore M-ary QAM, PSK, and QPSK Topics ▼ 🧮 Constellation Simulator: M-ary QAM 🧮 Constellation Simulator: M-ary PSK 🧮 BER calculation for ASK, FSK, and PSK 🧮 Approaches to BER vs SNR What is Bit Error Rate (BER)? The BER indicates how many corrupted bits are received compared to the total number of bits sent. It is the primary figure of merit for a...

ASK, FSK, and PSK (with MATLAB + Online Simulator)

📘 ASK Theory 📘 FSK Theory 📘 PSK Theory 📊 Comparison 🧮 MATLAB Codes 🎮 Simulator ASK or OFF ON Keying ASK is a simple (less complex) Digital Modulation Scheme where we vary the modulation signal's amplitude or voltage by the message signal's amplitude or voltage. We select two levels (two different voltage levels) for transmitting modulated message signals. Example: "+5 Volt" (upper level) and "0 Volt" (lower level). To transmit binary bit "1", the transmitter sends "+5 Volts", and for bit "0", it sends no power. The receiver uses filters to detect whether a binary "1" or "0" was transmitted. Fig 1: Output of ASK, FSK, and PSK modulation using MATLAB for a data stream "1 1 0 0 1 0 1 0" ( Get MATLAB Code ) ...

Calculation of SNR from FFT bins in MATLAB

📘 Overview 💻 FFT Bin Method 💻 Kaiser Window 📚 Further Reading SNR Estimation Overview In digital signal processing, estimating the Signal-to-Noise Ratio (SNR) accurately is crucial. Below, we demonstrate how to calculate SNR from periodogram and FFT bins using the Kaiser Window . The beta (β) parameter is the key—it allows you to control the trade-off between main-lobe width and side-lobe levels for precise spectral analysis. 1 Define Sampling rate and Time vector 2 Compute FFT and Periodogram PSD 3 Identify Signal Bin and Frequency resolution 4 Segment Signal Power from Noise floor 5 Logarithmic calculation of SNR in dB Method 1: Estimation from FFT Bins This approach uses a Hamming window to estimate SNR directly from the spectral bins. MATLAB Source Code Copy Code clc...

Online Simulator for ASK, FSK, and PSK

Try our new Digital Signal Processing Simulator!   •   Interactive ASK, FSK, and BPSK tools updated for 2025. Start Now Interactive Modulation Simulators Visualize binary modulation techniques (ASK, FSK, BPSK) in real-time with adjustable carrier and sampling parameters. 📡 ASK Simulator 📶 FSK Simulator 🎚️ BPSK Simulator 📚 More Topics ASK Modulator FSK Modulator BPSK Modulator More Topics Simulator for Binary ASK Modulation Digital Message Bits Carrier Freq (Hz) Sampling Rate (...

Constellation Diagrams of ASK, PSK, and FSK (with MATLAB Code + Simulator)

Constellation Diagrams: ASK, FSK, and PSK Comprehensive guide to signal space representation, including interactive simulators and MATLAB implementations. 📘 Overview 🧮 Simulator ⚖️ Theory 📚 Resources Definitions Constellation Tool Key Points MATLAB Code 📂 Other Topics: M-ary PSK & QAM Diagrams ▼ 🧮 Simulator for M-ary PSK Constellation 🧮 Simulator for M-ary QAM Constellation 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 ...

FIR vs IIR Digital Filters and Recursive vs Non Recursive Filters

Filters >> FIR vs. IIR Digital Filters and Recursive vs. Non-Recursive Filters Key Features The higher the order of a filter, the sharper the stopband transition The sharpness of FIR and IIR filters is very different for the same order A FIR filter has an equal time delay at all frequencies, while the IIR filter's time delay varies with frequency. Usually, the biggest time delay in the IIR filter is at the filter's cutoff frequency. The term 'IR' (impulse response) is in both FIR and IIR. The term 'impulse response' refers to the appearance of the filter in the time domain. 1. What Is the Difference Between an FIR and an IIR Filters? The two major classifications of digital filters used for signal filtration are FIR and IIR....

MATLAB Code for ASK, FSK, and PSK (with Online Simulator)

MATLAB Code for ASK, FSK, and PSK Comprehensive implementation of digital modulation and demodulation techniques with simulation results. 📘 Theory 📡 ASK Code 📶 FSK Code 🎚️ PSK Code 🕹️ Simulator 📚 Further Reading Amplitude Shift Frequency Shift Phase Shift Live Simulator ASK, FSK & PSK HomePage MATLAB Code MATLAB Code for ASK Modulation and Demodulation COPY % The code is written by SalimWireless.Com clc; clear all; close all; % Parameters Tb = 1; fc = 10; N_bits = 10; Fs = 100 * fc; Ts = 1/Fs; samples_per_bit = Fs * Tb; rng(10); binar...

Theoretical BER vs SNR for m-ary PSK and QAM

Relationship Between Bit Error Rate (BER) and Signal-to-Noise Ratio (SNR) The relationship between Bit Error Rate (BER) and Signal-to-Noise Ratio (SNR) is a fundamental concept in digital communication systems. Here’s a detailed explanation: BER (Bit Error Rate): The ratio of the number of bits incorrectly received to the total number of bits transmitted. It measures the quality of the communication link. SNR (Signal-to-Noise Ratio): The ratio of the signal power to the noise power, indicating how much the signal is corrupted by noise. Relationship The BER typically decreases as the SNR increases. This relationship helps evaluate the performance of various modulation schemes. BPSK (Binary Phase Shift Keying) Simple and robust. BER in AWGN channel: BER = 0.5 × erfc(√SNR) Performs well at low SNR. QPSK (Quadrature...