QPSK constellation Diagram - matlab

Question

Below is my MATLAB code for QPSK commnication:
clc;
clear all;
close all;
data=[0 1 0 1 1 1 0 0 1 1]; % information
%Number_of_bit=1024;
%data=randint(Number_of_bit,1);
figure(1)
stem(data, 'linewidth',3), grid on;
title(' Information before Transmiting ');
axis([ 0 11 0 1.5]);
data_NZR=2*data-1; % Data Represented at NZR form for QPSK modulation
s_p_data=reshape(data_NZR,2,length(data)/2); % S/P convertion of data
br=10.^6; %Let us transmission bit rate 1000000
f=br; % minimum carrier frequency
T=1/br; % bit duration
t=T/99:T/99:T; % Time vector for one bit information
% XXXXXXXXXXXXXXXXXXXXXXX QPSK modulation XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
y=[];
y_in=[];
y_qd=[];
for(i=1:length(data)/2)
y1=s_p_data(1,i)*cos(2*pi*f*t); % inphase component
y2=s_p_data(2,i)*sin(2*pi*f*t) ;% Quadrature component
y_in=[y_in y1]; % inphase signal vector
y_qd=[y_qd y2]; %quadrature signal vector
y=[y y1+y2]; % modulated signal vector
end
Tx_sig=y; % transmitting signal after modulation
tt=T/99:T/99:(T*length(data))/2;
figure(2)
subplot(3,1,1);
plot(tt,y_in,'linewidth',3), grid on;
title(' wave form for inphase component in QPSK modulation ');
xlabel('time(sec)');
ylabel(' amplitude(volt0');
subplot(3,1,2);
plot(tt,y_qd,'linewidth',3), grid on;
title(' wave form for Quadrature component in QPSK modulation ');
xlabel('time(sec)');
ylabel(' amplitude(volt0');
subplot(3,1,3);
plot(tt,Tx_sig,'r','linewidth',3), grid on;
title('QPSK modulated signal (sum of inphase and Quadrature phase signal)');
xlabel('time(sec)');
ylabel(' amplitude(volt0');
I am unable to understand which values to use to generate the phase constellation diagram for my code? What way in my code I can generate the correct phase constellation diagram?
============== UPDATE ==============
clc;
clear all;
close all;
data=[0 0 1 1 0 1 1 0 1 1 1 0]; % information
figure(1)
stem(data, 'linewidth',3), grid on;
title(' Information before Transmiting ');
axis([ 0 11 0 1.5]);
data_NZR=2*data-1; % Data Represented at NZR form for QPSK modulation
s_p_data=reshape(data_NZR,2,length(data)/2); % S/P convertion of data
br=10.^6; %Let us transmission bit rate 1000000
f=br; % minimum carrier frequency
T=1/br; % bit duration
t=T/99:T/99:T; % Time vector for one bit information
y=[];
y_in=[];
y_qd=[];
d=zeros(1,length(data)/2);
for i=1:length(data)/2
p=data(2*i);
imp=data(2*i - 1);
y1=s_p_data(1,i)*cos(2*pi*f*t); % inphase component
y2=s_p_data(2,i)*sin(2*pi*f*t) ;% Quadrature component
y_in=[y_in y1]; % inphase signal vector
y_qd=[y_qd y2]; %quadrature signal vector
y=[y y1+y2]; % modulated signal vector
if (imp == 0) && (p == 0)
d(i)=exp(j*pi/4);%45 degrees
end
if (imp == 1)&&(p == 0)
d(i)=exp(j*3*pi/4);%135 degrees
end
if (imp == 1)&&(p == 1)
d(i)=exp(j*5*pi/4);%225 degrees
end
if (imp == 0)&&(p == 1)
d(i)=exp(j*7*pi/4);%315 degrees
end
end
Tx_sig=y; % transmitting signal after modulation
qpsk=d;
tt=T/99:T/99:(T*length(data))/2;
figure(2)
subplot(3,1,1);
plot(tt,y_in,'linewidth',3), grid on;
title(' wave form for inphase component in QPSK modulation ');
xlabel('time(sec)');
ylabel(' amplitude(volt0');
subplot(3,1,2);
plot(tt,y_qd,'linewidth',3), grid on;
title(' wave form for Quadrature component in QPSK modulation ');
xlabel('time(sec)');
ylabel(' amplitude(volt0');
subplot(3,1,3);
plot(tt,Tx_sig,'r','linewidth',3), grid on;
title('QPSK modulated signal (sum of inphase and Quadrature phase signal)');
xlabel('time(sec)');
ylabel(' amplitude(volt0');
figure(3);
plot(d,'o');%plot constellation without noise
axis([-2 2 -2 2]);
grid on;
xlabel('real'); ylabel('imag');
title('QPSK constellation');

Answer 1

The QPSK symbol alphabet has four complex symbols. A set of random QPSK symbols can be created by generating an array of random integer numbers in 1..4 and mapping these numbers to complex symbols:
num_symbols = 1e4;
int_symbols = randi([1, 4], 1, num_symbols);
A = sqrt(2);
qpsk_symbols = zeros(size(int_symbols));
qpsk_symbols(int_symbols == 1) = A + 1i*A;
qpsk_symbols(int_symbols == 2) = A - 1i*A;
qpsk_symbols(int_symbols == 3) = - A + 1i*A;
qpsk_symbols(int_symbols == 4) = - A - 1i*A;
tx_sig = qpsk_symbols;
tx_sig could be the transmitted signal in a communication system. To plot the constellation diagram, use the real part as x-values and the imaginary part as y-values in the plot command. Additionally, use '.' as linestyle, so that every value is just represented by a dot, without line connections:
fh1 = figure;
plot_lims = [-3 3];
plot(real(qpsk_symbols), imag(qpsk_symbols), '.');
xlim(plot_lims);
ylim(plot_lims);
title('QPSK constellation without noise');
xlabel('real part');
ylabel('imaginary part');
This produces
which shows four distinct points. Adding noise makes this more interesting:
snr = 15; %// in dB
rx_sig = awgn(tx_sig, snr, 'measured');
fh2 = figure;
plot(real(rx_sig), imag(rx_sig), '.');
xlim(plot_lims);
ylim(plot_lims);
title(['QPSK constellation at an SNR of ' num2str(snr) ' dB']);
xlabel('real part');
ylabel('imaginary part');
which produces
This could be the received signal in a communications system neglecting inter-symbol interference and other frequency-selective components. (so-called AWGN channel for additive white gaussian noise).