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

Rayleigh vs Rician Fading (with MATLAB + Simulator)

  In Rayleigh fading , the channel coefficients tend to have a Rayleigh distribution, which is characterized by a random phase and magnitude with an exponential distribution. This means the magnitude of the channel coefficient follows an exponential distribution with a mean of 1. In Rician fading , there is a dominant line-of-sight component in addition to the scattered components. The channel coefficients in Rician fading can indeed tend towards 1, especially when the line-of-sight component is strong. When the line-of-sight component dominates, the Rician fading channel behaves more deterministically, and the channel coefficients may tend towards the value of the line-of-sight component, which could be close to 1.   MATLAB Script clc; clear all; close all; % Define parameters numSamples = 1000; % Number of samples K_factor = 5; % K-factor for Rician fading SNR_dB = 20; % Signal-to-noise ratio (in dB) % Generate complex Gaussian random variable for Rayleigh fading channel h_r...

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...

UGC-NET Electronic Science Question Paper With Answer Key and Full Explanation [Dec 2023]

    UGC-NET Electronic Science Question Paper With Answer Key Download Pdf [Dec 2023] Download Question Paper               See Answers   2025 | 2024 | 2023 | 2022 | 2021 | 2020 UGC-NET Electronic Science  2023 Answers with Explanations 51. (A): The stacking fault is the most common area defect found in silicon. These faults typically occur along the 111 plane. In the crystalline structure of silicon, atoms are arranged in a specific pattern known as a diamond lattice. A stacking fault refers to a disruption in the normal order of atomic layers within this lattice, which usually occurs in the 111 plane due to the geometric arrangement of the atoms. This type of defect can affect the electrical and mechanical properties of the material, such as the mobility of charge carriers and mechanical strength. 52. (C): The important figure of merit for the microwave application of a Schot...

Theoretical vs. simulated BER vs. SNR for ASK, FSK, and PSK (MATLAB Code + Simulator)

📘 Overview 🧮 Simulator 💻 Theoretical Code 📊 Simulated Code 📚 Resources Overview BER vs. SNR denotes how many bits in error are received for a given signal-to-noise ratio, typically measured in dB. Common noise types in wireless systems: 🚀 1. Additive White Gaussian Noise (AWGN) 🌊 2. Rayleigh Fading AWGN adds random noise; Rayleigh fading attenuates the signal variably. A good SNR helps reduce these effects. Bit Error Rate (BER) Equations BER formulas for ASK, FSK, and PSK modulation schemes. ASK BER = 0.5 × erfc(0.5 × √SNR) FSK BER = 0.5 × erfc(√(SNR / 2)) PSK BER = 0.5 × erfc(√SNR) erfc / Q-function (Click here) Live BER S...

How to use MATLAB Simulink

Introduction to MATLAB Simulink MATLAB Simulink is a popular add-on of MATLAB. Here, you can use different blocks like modulator, demodulator, AWGN channel, etc. And you can do experiments on your own. Steps to Get Started 1. Go to the 'Simulink' tab at the top navbar of MATLAB. If not found, click on the add-on tab, search 'Simulink,' and then click on it to add. 2. Once you installed the simulation, click the 'new' tap at the top left corner. 3. Then, search the required blocks in the 'Simulink library.' Then, drag it to the editor space. 4. You can double-click on the blocks to see the input parameters. 5. Then, connect the blocks by dragging a line from one block's output terminal to another block's input. 6. If the connection is complete, click the 'run' tab in the middle of the top navbar. 7. After clicking on the run ...

UGC NET Electronic Science Previous Year Question Papers

Home / Engineering & Other Exams / UGC NET 2022 PYQ 📥 Download UGC NET Electronics PDFs Complete collection of previous year question papers, answer keys and explanations for Subject Code 88. Start Downloading UGC-NET (Electronics Science, Subject code: 88) Subject_Code : 88; Department : Electronic Science; 📂 View All Question Papers Q. UGC Net Electronic Science Question Paper [June 2025] A. UGC Net Electronic Science Question Paper With Answer Key Download Pdf [June 2025] with full explanation Q. UGC Net Electronic Science Question Paper [December 2024] A. UGC Net Electronic Science Question Paper With Answer Key Download Pdf [December 2024] Q. UGC Net Electronic Science Question Paper [Aug 2024] A. UGC Net Electronic Scien...

OFDM Waveform with MATLAB Code (with Simulator)

  In OFDM (Orthogonal Frequency Division Multiplexing) , we transmit multiple orthogonal subcarriers simultaneously. Since the subcarriers are orthogonal , they do not interfere with each other, which is one of the main advantages of OFDM. Practically, OFDM converts a wideband signal into multiple narrowband orthogonal subcarriers. For typical wireless communication, if the signal bandwidth (or symbol duration) exceeds the coherence bandwidth of the channel, the signal experiences frequency-selective fading . Fading distorts the signal, making it difficult to recover the original information. By using OFDM, we transmit the same wideband signal across multiple orthogonal narrowband subcarriers, reducing the effect of fading. For example, if we want to transmit a signal of bandwidth 1024 kHz , we can divide it into N = 8 subcarriers . Each subcarrier is then spaced by: Δf = Total Bandwidth N = 1024 8 kHz...

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 on...