error in qpsk modulation

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ABDUL 2020-1-12

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/499971-error-in-qpsk-modulation

回答： Omega 2025-4-6

Hi....

i am trying to implement a mimo-ofdm systems in which i have selected qpsk as a modulation technique. at the transmitter i am getting a proper constellation diagram. i have implemented the receiver section in which i am not able to properly get the constellation diagram for the same. please find attached code .

clc;

clear all;

close all;

% All Parameters Initialization to be done here - begin

M=4;% 4,8,16,32,64,128,256,512,1024- 2,3,4,5,6,7,8,9,10 size of constellation

k=log2(M); % number of bits/symbolexit

number_of_data_points=64; % FFT Size or total number of subcarriers=N=64= IFFT size

numPackets=number_of_data_points;

block_size=16; % Block Size, no of rows,data subcarriers

BW=8*10^6; % Bandwidth of the OFDM system

Nsp=52;

%Derived Parameters

deltaf=BW/number_of_data_points;%bandwidth of each subcarriers including used and unused subacarriers

TFFT=1/deltaf; % ofdm_symbol_duration

TGI=TFFT/4; % duration of the cyclic prefix= guard interval duration 25% of the subcarriers to be used as a GI

% possible guard band values 1/4, 1/8, 1/16 and 1/32

Tsignal= TGI+TFFT ; % total ofdm symbol duration

Ncp=number_of_data_points*(TGI/TFFT); % length of the cyclic prefix

cp_len=ceil(0.25*block_size);

fft_points=number_of_data_points;

ifft_points=number_of_data_points;

Nt=2;

Nr=2;

cp_start=block_size-cp_len; % with block_size=4,1x1; block_size=2,1

cp_end=block_size; % with block_size=4,1x1;with block_size=2,1x1,2

actual_cp=zeros(cp_len, block_size);%1x4; with block_size =2, actual_cp= 1x2;

data_subcarriers=cp_start+Nsp;

nsf=8/7;

Fs=ceil(nsf*BW);

EbNo=0:10;

% initialization of SNR

SNRstart=1;

SNRincrement=1;

SNRend=9;

index=0;

EbN0=0:10; % Eb/N0

E12=1;

SNR=10^(EbN0(k)/10); % Eb/N0(dB) to linear value

standar_dev =sqrt((E12/(2*SNR))*(15/11)); % Standard Deviation of Noise

bit_error=0;

%-------------------------------------------------------------------------%

%1. 1st Block of user 1 -Implementation of binary data %

%1st Block -Implementation of bianry data- generation %

%-------------------------------------------------------------------------%

x1U=randi([0 1],1,64);

figure (1) %data input plotbr=BW; %Let us transmission bit rate 1000000

stairs(x1U(1,:), 'linewidth', 3)

xlabel('Data Points')

ylabel('Amplitude')

title('Information before Transmiting');

axis([ 0 63 -1 2 ]);

%-------------------------------------------------------------------------%

c=64;%size(x1,2);

n=64;%size(x1,2);% number of information bits/ message bits/ length of message vector...

wc=4; % enter the number of ones in each columns

wr=(n.*wc)./c; %number of ones in each row

H1=zeros(c,n); %generate the empty matrix and start assigining the 1's c=n; n=k

j=1;

jj=wr;

for i=1:c./wc

H1(i,j:jj) =1;

j=j+wr;

jj=(i.*wr)+wr;

end

for i=1:wc-1

for ii=1:n

colind=(round(rand(1)*(n-1)))+1;

rCol=H1(1:c./wc,colind);

H1((i.*(c./wc))+1:((i.*(c./wc))+1+(c./wc)-1),ii)=rCol;

end

br=BW; %Let us transmission bit rate 1000000

fc=br; % minimum carrier frequency

Tc=1/br; % bit duration

tmod=Tc/99:Tc/99:Tc; % Time vector for one bit information

%-------------------------------------------------------------------------%

%------- encoded data by using LDPC Encoder and Parity Check Matrix-------%

%-------------------------------------------------------------------------%

data_encoded1=x1U*H1;

mod_data1=mod(data_encoded1,2);

figure (2) % data encoded by using LDPC

stairs(mod_data1(1,:), 'linewidth', 3)

% stem(mod_data, 'linewidth',3), grid on;

title(' Information Encoded by LDPC Encoder ');

xlabel('Data Points')

ylabel('Amplitude')

axis([ 0 63 -1 1.5]);

%-------------------------------------------------------------------------%

%---------3. modulation of the data by using psk------------------------- %

%-------------------------------------------------------------------------%

data_NRZ1=2*mod_data1-1; % Data Represented at NZR form for QPSK modulation

s_p_data1=reshape(data_NRZ1,2,length(x1U)/2); % S/P convertion of data

ymod1=[];

ycomplex1=[];

y_in1=[];

y_qd1=[];

% for jmodsp=1:size(s_p_data,1)

for imod = 1:length(x1U)/2

y11 = s_p_data1(1,imod)*cos(2*pi*fc*tmod); % inphase component

y21 = s_p_data1(2,imod)*sin(2*pi*fc*tmod);% Quadrature component

y_in1 = [y_in1 y11]; % inphase signal vector

% y_in1=reshape(y_in,16,[]);

y_qd1 = [y_qd1 y21]; %quadrature signal vector

ymod1 = [ymod1 y11+y21]; % modulated signal vector

ycomplex1 = [ycomplex1 (sign(y11))+(1i*sign(y21))];

end

% end

psk_mod1=ycomplex1;

% psk_mod=ymod;

Tx_sig11=ymod1; % transmitting signal after modulation

Tx_sig1=ycomplex1; % transmitting signal after modulation

Tx_sig_complex1=ycomplex1;

% figure (3)

scatterplot(Tx_sig_complex1)

ttmod=Tc/99:Tc/99:(Tc*length(x1U))/2;

figure (4)

subplot(2,1,1) % plot of inphase compnent

stairs(s_p_data1(1,:),'linewidth',1.5),grid on;

axis([ 0 31 -2 2])

subplot(2,1,2)

plot(ttmod,y_in1,'linewidth',1.5), grid on;

title(' wave form for inphase component in QPSK modulation ');

xlabel('time(sec)');

ylabel(' amplitude');

figure (5)

subplot(2,1,1) % plot of inphase compnent

stairs(s_p_data1(2,:),'linewidth',1.5),grid on;

axis([ 0 31 -2 2])

subplot(2,1,2)

plot(ttmod,y_qd1,'linewidth',1.5), grid on;

title(' wave form for Quadrature component in QPSK modulation ');

xlabel('time(sec)');

ylabel(' amplitude');

figure (6)

subplot(3,1,1);

plot(ttmod,y_in1,'linewidth',1.5), grid on;

title(' Wave form for In-phase component in QPSK modulation ');

xlabel('Time(sec)');

ylabel(' Amplitude');

subplot(3,1,2);

plot(ttmod,y_qd1,'linewidth',1.5), grid on;

title(' Wave form for Quadrature component in QPSK modulation ');

xlabel('Time(sec)');

ylabel(' Amplitude');

subplot(3,1,3);

plot(ttmod,Tx_sig1,'r','linewidth',1.5), grid on;

Warning: Imaginary parts of complex X and/or Y arguments ignored.

title('QPSK modulated signal (sum of inphase and Quadrature phase signal)');

xlabel('Time(sec)');

ylabel(' Amplitude');

% to find out the number of columns after reshaping

num_colums1=ceil((size(Tx_sig_complex1,1)*size(Tx_sig_complex1,2))/block_size);

%-------------------------------------------------------------------------%

% 5.to perform serial to parallel conversion %

%-------------------------------------------------------------------------%

% reshaped_mod_data = reshape(Tx_sig_complex,[block_size,num_colums]);

reshaped_mod_data1 = reshape(Tx_sig11,[block_size, num_colums1]);

% data divided into 4 subcarriers

reshaped_mod_data_11=reshaped_mod_data1(:,1);

reshaped_mod_data_21=reshaped_mod_data1(:,2);

reshaped_mod_data_31=reshaped_mod_data1(:,3);

reshaped_mod_data_41=reshaped_mod_data1(:,4);

%-------------------------------------------------------------------------%

% 6. To Perform IFFT and Cyclic Prefix %

% to create empty matrix to put ifft data %

% 7.operate column wise and do cyclic prefix, column wise cyclic prefix is done

%---------------------------+----------------------------------------------%

% ifft_data_matrix=zeros(size(reshaped_mod_data,1),size(reshaped_mod_data,2));

for ireshape=1:num_colums1

ifft_data_matrix1(:,ireshape)=ifft(reshaped_mod_data1(:,ireshape));

for jcplen= 1:cp_len % compute cyclic prefix data

actual_cp1(jcplen,ireshape) = ifft_data_matrix1(jcplen+cp_start,ireshape).';

end

ifft_data_after_cp1(:,ireshape) = vertcat(actual_cp1(:,ireshape),ifft_data_matrix1(:,ireshape));% perform cyclic prefix

end

%-------------------------------------------------------------------------%

% 8. to perform parallel to serial conversion %

%-------------------------------------------------------------------------%

parallel_serial_tx1 = reshape(ifft_data_after_cp1(:,:),size(ifft_data_after_cp1(:,:),2),size(ifft_data_after_cp1(:,:),1));

[numrows,numcols]=size(parallel_serial_tx1);

x=parallel_serial_tx1;

snr=0:2:20;

error1 = zeros(1, numPackets); BER1 = zeros(1, length(snr));

Taps=1; % Number of Taps

p1=0.5/2.3; % Power of Tap1

gain1=sqrt(p1/2)*[randn(1,numrows) + j*randn(1,numrows)]; % Gain for Tap1

Nc=16;

cp=4;

x11=x(:);

x12=reshape(x11,1,length(x11));

i=1:length(x12);

delay1=1;

for i=delay1+1:length(x12) % Producing one sample delay in Tap2 w.r.t. Tap1

x13(i)=x(i-delay1);

end

x1=reshape(x13,(Nc+cp),ceil(length(x13)/(Nc+cp)));

ch1=repmat(gain1,numcols,1)';

data_channel=x.*ch1; % Passing data through channel

%------------------------Addition of AWGN noise ---------------------------

data_noise1=data_channel(:);

data_noise2=reshape(data_noise1,1,length(data_noise1));

noise = 1/sqrt(2)*[randn(1,length(data_noise2)) + j*randn(1,length(data_noise2))];

snr=0:2:20;

for i = 1:length(snr)

y = data_noise2 + (sqrt(1)*10^(-snr(i)/20))*noise; %Addition of Noise

end

%--------------------------Receiver ---------------------------------------

data_received =y; %fadded data received with awgn noise

% serial_parallel_form_rx = reshape(received_signal,[ifft_rows,ifft_colums]).';%64x2

serial_parallel_form_rx = reshape(data_received,[numrows,numcols]).';%64x2

% To Remove Cyclic Prefix

serial_parallel_form_rx(1:cp_len,:,:)=[];

% To Perform FFT operation

receivd_signal_fft_rx=fft(serial_parallel_form_rx);

% To Perform Parallel to Serial Conversion

parallel_serial_form_rx= reshape(receivd_signal_fft_rx,1,[]);

% To pass through a Demodulator

Rx_data=[];

Rx_sig=parallel_serial_form_rx; % Received signal

Rx_sig_real=(real(Rx_sig));

Rx_sig_imag=(imag(Rx_sig));

for (idemod=1:1:length(x1U)/2)

%%XXXXXX inphase coherent dector XXXXXXX

Z_in=Rx_sig_real((idemod-1)*length(tmod)+1:idemod*length(tmod)).*cos(2*pi*fc*tmod);

% above line indicat multiplication of received & inphase carred signal

Z_in_intg=(trapz(tmod,Z_in))*(2/Tc);% integration using trapizoidal rule

if(Z_in_intg>0) % Decession Maker

Rx_in_data=1;

else

Rx_in_data=0;

end

%%XXXXXX Quadrature coherent dector XXXXXX

Z_qd=Rx_sig_imag(((idemod-1)*length(tmod))+1:idemod*length(tmod)).*sin(2*pi*fc*tmod);

%above line indicat multiplication ofreceived & Quadphase carred signal

Z_qd_intg=(trapz(tmod,Z_qd))*(2/Tc);%integration using trapizoidal rule

if (Z_qd_intg>0)% Decession Maker

Rx_qd_data=1;

else

Rx_qd_data=0;

end

Rx_data=[Rx_data Rx_in_data Rx_qd_data]; % Received Data vector

end

psk_demod_mod=Rx_data;

Hinv=H1.';

[N1decode,N2decode]=size(H1);

iter=3;

for idecode=1:iter

% for jpr=1:Nt

for jd=1:N1decode % for loop along row

cid=find(H1(jd,:));

for kdec=1:length(cid)

E(jd,cid(kdec))=mod(sum(psk_demod_mod(cid))+psk_demod_mod(cid(kdec)),2);

end

% end

% for jpc=1:Nt

for jd=1:N2decode %for loop along columns

rid=find(H1(:,jd));

numberofones=length(find(E(rid,jd)));

numberofzeros=length(rid)-numberofones;

if(numberofones==numberofzeros)

ydd(jd)=psk_demod_mod(jd);

elseif(numberofones>numberofzeros)

ydd(jd)=1;

elseif(numberofones<numberofzeros)

ydd(jd)=0;

end

ydec=ydd;

end

rece_decoder=psk_demod_mod*Hinv;

rece_decoder_mod=mod(rece_decoder,2);

figure (7)

subplot(3,1,1);

stairs(Z_in,'linewidth',1.5), grid on;

title(' Wave form for In-phase component in QPSK modulation ');

xlabel('Time(sec)');

ylabel(' Amplitude');

subplot(3,1,2);

stairs(Z_qd,'linewidth',1.5), grid on;

title(' Wave form for Quadrature component in QPSK modulation ');

xlabel('Time(sec)');

ylabel(' Amplitude');

subplot(3,1,3);

stairs(Rx_data,'r','linewidth',1.5), grid on;

title('QPSK modulated signal (sum of inphase and Quadrature phase signal)');

xlabel('Time(sec)');

ylabel(' Amplitude');

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Answer 1

Omega 2025-4-6

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/499971-error-in-qpsk-modulation#answer_1563231

Hi Abdul,

Since you've mentioned that the constellation diagram looks correct at the transmitter, the issue might be with the receiver.

Here are a few things I suggest you double-check:

Make sure the noise matches the SNR levels you're aiming for. It's easy to get the scaling wrong, which can mess up the received signal.
If you’re simulating a channel, ensure you're compensating for its effects at the receiver. Even a simple AWGN channel can skew results if it's not handled right.
Check that your receiver is properly synchronized. Any mismatch here can throw off the constellation.
Verify that the demodulation matches your QPSK setup. The coherent detection and integration need to be spot-on.
Ensure you’re removing the cyclic prefix correctly and that your FFT implementation is solid. This step is crucial for interpreting the received signal accurately.
Confirm that the scaling of the in-phase and quadrature components matches what you'd expect for QPSK.

I hope this helps!

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