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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


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