QPSK星座图

Question

以下是我用于QPSK通信的MATLAB代码：

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');

我无法理解使用哪些值来生成代码的相位星座图？在我的代码中，我可以生成正确的相位星座图？

==============更新==============

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

QPSK符号字母表有四个复杂符号。可以通过在1..4中生成随机整数数组并将这些数字映射到复杂符号来创建一组随机QPSK符号：

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可以是通信系统中的传输信号。要绘制星座图，请将实部用作x值，将虚部用作绘图命令中的y值。另外，使用'.'作为linestyle，这样每个值都只用一个点表示，没有行连接：

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');

这会产生

显示了四个不同的点。添加噪音使这更有趣：

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');

产生

这可能是通信系统中的接收信号，忽略了符号间干扰和其他频率选择性分量。 （所谓的AWGN信道用于加性高斯白噪声）。