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

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

📘 Overview of Energy per Bit (Eb / N0) 🧮 Online Simulator for constellation diagrams of ASK, FSK, and PSK 🧮 Theory behind Constellation Diagrams of ASK, FSK, and PSK 🧮 MATLAB Codes for Constellation Diagrams of ASK, FSK, and PSK 📚 Further Reading 📂 Other Topics on Constellation Diagrams of ASK, PSK, and FSK ... 🧮 Simulator for constellation diagrams of m-ary PSK 🧮 Simulator for constellation diagrams of m-ary QAM 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...
Read more

Fading : Slow & Fast and Large & Small Scale Fading (with MATLAB Code + Simulator)

📘 Overview 📘 LARGE SCALE FADING 📘 SMALL SCALE FADING 📘 SLOW FADING 📘 FAST FADING 🧮 MATLAB Codes 📚 Further Reading LARGE SCALE FADING The term 'Large scale fading' is used to describe variations in received signal power over a long distance, usually just considering shadowing.  Assume that a transmitter (say, a cell tower) and a receiver  (say, your smartphone) are in constant communication. Take into account the fact that you are in a moving vehicle. An obstacle, such as a tall building, comes between your cell tower and your vehicle's line of sight (LOS) path. Then you'll notice a decline in the power of your received signal on the spectrogram. Large-scale fading is the term for this type of phenomenon. SMALL SCALE FADING  Small scale fading is a term that describes rapid fluctuations in the received signal power on a small time scale. This includes multipath propagation effects as well as movement-induced Doppler fr...
Read more

Online Simulator for ASK, FSK, and PSK

Try our new Digital Signal Processing Simulator!   Start Simulator for binary ASK Modulation Message Bits (e.g. 1,0,1,0) Carrier Frequency (Hz) Sampling Frequency (Hz) Run Simulation Simulator for binary FSK Modulation Input Bits (e.g. 1,0,1,0) Freq for '1' (Hz) Freq for '0' (Hz) Sampling Rate (Hz) Visualize FSK Signal Simulator for BPSK Modulation ...
Read more

Theoretical BER vs SNR for binary ASK, FSK, and PSK with MATLAB Code + Simulator

📘 Overview & Theory 🧮 MATLAB Codes 📚 Further Reading Theoretical BER vs SNR for Amplitude Shift Keying (ASK) The theoretical Bit Error Rate (BER) for binary ASK depends on how binary bits are mapped to signal amplitudes. For typical cases: If bits are mapped to 1 and -1, the BER is: BER = Q(√(2 × SNR)) If bits are mapped to 0 and 1, the BER becomes: BER = Q(√(SNR / 2)) Where: Q(x) is the Q-function: Q(x) = 0.5 × erfc(x / √2) SNR : Signal-to-Noise Ratio N₀ : Noise Power Spectral Density Understanding the Q-Function and BER for ASK Bit '0' transmits noise only Bit '1' transmits signal (1 + noise) Receiver decision threshold is 0.5 BER is given by: P b = Q(0.5 / σ) , where σ = √(N₀ / 2) Using SNR = (0.5)² / N₀, we get: BER = Q(√(SNR / 2)) Theoretical BER vs ...
Read more

What is - 3dB Frequency Response? Applications ...

📘 Overview & Theory 📘 Application of -3dB Frequency Response 🧮 MATLAB Codes 🧮 Online Digital Filter Simulator 📚 Further Reading Filters What is -3dB Frequency Response?   Remember, for most passband filters, the magnitude response typically remains close to the peak value within the passband, varying by no more than 3 dB. This is a standard characteristic in filter design. The term '-3dB frequency response' indicates that power has decreased to 50% of its maximum or that signal voltage has reduced to 0.707 of its peak value. Specifically, The -3dB comes from either 10 Log (0.5) {in the case of power} or 20 Log (0.707) {in the case of amplitude} . Viewing the signal in the frequency domain is helpful. In electronic amplifiers, the -3 dB limit is commonly used to define the passband. It shows whether the signal remains approximately flat across the passband. For example, in pulse shapi...
Read more

Pulse Shaping using Raised Cosine Filter (with MATLAB + Simulator)

  MATLAB Code for Raised Cosine Filter Pulse Shaping clc; clear; close all ; %% ===================================================== %% PARAMETERS %% ===================================================== N = 64; % Number of OFDM subcarriers cpLen = 16; % Cyclic prefix length modOrder = 4; % QPSK oversample = 8; % Oversampling factor span = 10; % RRC filter span in symbols rolloff = 0.25; % RRC roll-off factor %% ===================================================== %% Generate Baseband OFDM Symbols %% ===================================================== data = randi([0 modOrder-1], N, 1); % Random bits txSymbols = pskmod(data, modOrder, pi/4); % QPSK modulation % IFFT to get OFDM symbol tx_ofdm = ifft(txSymbols, N); % Add cyclic prefix tx_cp = [tx_ofdm(end-cpLen+1:end); tx_ofdm]; %% ===================================================== %% Oversample the Baseband Signal %% ===============================================...
Read more

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

📘 Overview of BER and SNR 🧮 Online Simulator for BER calculation of m-ary QAM and m-ary PSK 🧮 MATLAB Code for BER calculation of M-ary QAM, M-ary PSK, QPSK, BPSK, ... 📚 Further Reading 📂 View Other Topics on M-ary QAM, M-ary PSK, QPSK ... 🧮 Online Simulator for Constellation Diagram of m-ary QAM 🧮 Online Simulator for Constellation Diagram of m-ary PSK 🧮 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 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. BER = (number of bits received in error) / (total number of tran...
Read more

Theoretical BER vs SNR for BPSK

Theoretical Bit Error Rate (BER) vs Signal-to-Noise Ratio (SNR) for BPSK in AWGN Channel Let’s simplify the explanation for the theoretical Bit Error Rate (BER) versus Signal-to-Noise Ratio (SNR) for Binary Phase Shift Keying (BPSK) in an Additive White Gaussian Noise (AWGN) channel. Key Points Fig. 1: Constellation Diagrams of BASK, BFSK, and BPSK [↗] BPSK Modulation Transmits one of two signals: +√Eb or −√Eb , where Eb is the energy per bit. These signals represent binary 0 and 1 . AWGN Channel The channel adds Gaussian noise with zero mean and variance N₀/2 (where N₀ is the noise power spectral density). Receiver Decision The receiver decides if the received signal is closer to +√Eb (for bit 0) or −√Eb (for bit 1) . Bit Error Rat...
Read more