Constellation Space For  M-PSK (M-ary Phase Shift Keying) Modulation Scheme

%  This code shows constellation space for

%  M-PSK (M-ary Phase Keying) modulation scheme.

%  To get more ideas of the used inbuilt function,

%  type 'help the_function' (without inverted comma) in 'Command Window'

%  and press Enter.

%  For example, help pskmod; you will get details.

%  At low SNRs, there is higher probability that a symbol fall into

%  the region of other symbols. This results in higher detection error

%  probability at the receiver. As SNR increases, the symbols are highly

%  likely to fall into their own region, hence reducing the detection error

%  probability or increasing the correct detection probability.

%

clc;

clear all;

close all

M = 4;   % modulation order - should be 2, 4 , 8, 16, and so on

Nsymb = 1e4; % number of symbols

d = randi ([0,M-1],1, Nsymb);  % d stores random symbols

y = pskmod (d, M, 0, "gray");  % symbols 'd' are modulated using M-PSK and stored in y

snr_dB = 0:3:15;  % SNR (signal-to-noise ratio) level (dB)

figure,plot (y, "bo")   ;

grid on;

  axis([-2 2 -2 2]);  % set range of x-axis and y-axis

for ii = 1:length(snr_dB)  % iteration for dirrefernt SNR levels

  snr = 10^(snr_dB(ii)/10) ;  % SNR in linear scale

  z = awgn (y, snr);   % z stores noisy symbols. awgn(y, snr) adds noise in y

  figure,plot (z, "mo", y, "bo")  % plotting z and y (scatter plot)

  title(['Constellation Space for ',num2str(M),'-PSK at SNR = ',...

                                   num2str(snr_dB(ii)),'dB']); % title of the plot

  grid on; % this enalbes grids on the plot

  axis([-3 3 -3 3]);  % set range of x-axis and y-axis

  legend('Symbols under noise (Received)', 'Symbols without noise (Transmitted)')

                % legends. circles in magenta color correspnd to noisy symbols z

                % and circles in blue color correspnd to noiseless symbols y.

  pause(1) % pause for 1 second

end

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