BER OF M-ary PSK and M-ary QAM

Dear All....

I am trying to write a program for the implementation of MIMO-OFDMby using wavelets transfrom . when i plot the BER Curve i am getting a straight line i am not able to get as a standard curve . any help will be appreciated.

Regards

Abdul Azeez

[Walter Roberson]

http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer

[ABDUL]

hi.... find attached below code which i am trying to implement for the ofdm by using the wavelet transforms to plot the BER V/s SNR graph and the Peak to Average Power Ratio (PAPR) for the same . i am trying to plot the BER V/s SNR graph for which i am getting a straight line

Regards

Abdul Azeez

clc
clear all;
close all;

M = 4; % QPSK signal constellatio
N = 64; % number of subcarriers
fft_size = N; % have 128 data poexitint
nbits = 100; 
nDWTsym = ceil(nbits/N) ;% number of symbols for DWT system
nsym = nbits;
snr = 0:8;

% ------------------%
% TRANSMITTER          
% ------------------%
data_source=randsrc(1, fft_size*(nsym-2), 0:M-1); %the data source
sp = reshape(data_source,fft_size,nsym-2).';% s/p
% sp = reshape(qpsk_mod , fft_size, nsym-2);% s/p
[rdwt,cdwt] = size (sp);
tx_dwt= [];
for i=2:nsym-1
    for uu=1:cdwt
        qpsk_mod=pskmod(sp,M);
        DATADWT=qpsk_mod;
        AC = DATADWT(1:rdwt/2,uu);       % approximation coefficients
        DC = DATADWT(rdwt/2+1:rdwt,uu);  % detailed (wavelet) coefficients
        IDWT=idwt(AC,DC,'haar');         % IDWT process
        TXDWT(:,uu)= IDWT;               % transmitted data for DWT
    end
    %%% parallel to serial =======> to the channel
    ps1 = reshape( TXDWT,1,[]);
    ofdm_signal_dwt=TXDWT;
    pilot = zeros(size(TXDWT));
    Signal_Power_dwt = abs(ofdm_signal_dwt.^2);
    Peak_Power = max(Signal_Power_dwt,[],2);
    Mean_Power = mean(Signal_Power_dwt,2);
    PAPR_dwt = 10*log10(Peak_Power./Mean_Power);
    tx_dwt = [tx_dwt ofdm_signal_dwt];
end
figure (1)
[cdf0,PAPR0] = ccdf(PAPR_dwt,0.1);
semilogy(PAPR0,cdf0,'-b')
legend('DWT based MIMO OFDM System')
xlabel('PAPR0 [dB]');
ylabel('CCDF (Pr[PAPR>PAPR0])');
tt_dwt=reshape(TXDWT,1,[]);
tt_dwt =[ pilot tx_dwt pilot];
x_abs_dwt=abs(tt_dwt);
papr_dwt=10*log(max(x_abs_dwt.^2)/mean(x_abs_dwt.^2));
% ------------
% CHANNEL
% ------------
% ---------------
% RECEIVER
% ------------
no_of_error_dwt=[];
ratio_dwt=[];
for ii=1:length(snr)
    rx_dwt= [];
    rx_signal_matrix_dwt = reshape(ps1,rdwt,cdwt).';%98x64, 64x98
    [~, c] = size(rx_signal_matrix_dwt);
for j=1:cdwt
      A1=[];
      received_symbol=[];
      received_symbol_1=[];
      con_dwt=[];
      received_symbol_1=[];
      DWT=[];
      cd=[];
      RXDWT=[];
      channel = 1/sqrt(2)*[randn(1,length(rx_signal_matrix_dwt))+sqrt(-1)*randn(1,length(rx_signal_matrix_dwt))];
    %%% the transmitted signal is corrupted with addtive noise
      A1=channel.*rx_signal_matrix_dwt(j,:);
      received_symbol = awgn(A1, snr(ii));
% equalization:
      received_symbol = conj(channel).* received_symbol;   
% Convert Data back to "parallel" form to perform IDWT
con_dwt=reshape(received_symbol, 1,rdwt);
[DWT,cd]=dwt(con_dwt,'haar');%% DWT
        RXDWT=[DWT cd];% recieved data for DWT
%%% parallel to serial   
RXDWT1 = reshape(RXDWT.',1,[]);% at DWT
qpsk_demod=pskdemod(RXDWT,M);
rx_dwt =[rx_dwt  qpsk_demod];
end
% counting the errors and ratio 
[nDWT,rDWT]=biterr(data_source, rx_dwt);
simBerDWT(ii)=rDWT;%% DWT system
end 
figure (2)
theory_Pb_BPSK = (1/2)*erfc(sqrt(10.^(snr/10)));
semilogy(snr,theory_Pb_BPSK,'bs-','LineWidth',2);
hold on
semilogy(snr,simBerDWT,'mx-','LineWidth',2);
axis([0 8 10^-6 1]); grid on
legend('theory', 'simulation for DWT(Haar)','simulation for FFT');
xlabel('SNR, dB') ; ylabel('Bit Error Rate')
title('BER for qpsk using DWT based ofdm ')

[Walter Roberson]

        qpsk_mod=pskmod(sp,M);

pskmod returns complex values.

        DATADWT=qpsk_mod;
        AC = DATADWT(1:rdwt/2,uu);       % approximation coefficients
        DC = DATADWT(rdwt/2+1:rdwt,uu);  % detailed (wavelet) coefficients

So AC and DC are complex values

        IDWT=idwt(AC,DC,'haar');         % IDWT process

idwt() is restricted to operating on real values.

Your code cannot generate any line; it crashes long before the plotting.

[ABDUL]

is it possible to take ony real values for the qpsk modulated data and implement the wavelet transforms or by taking the absolute values of the psk mod values. is there any method by which i can implement the OFDM technique by using the wavelet transforms ?.

[Walter Roberson]

Of course you can take real() or imag() or abs() of the qpsk modulated data, and do a wavelet transform on that.

The question would be whether you would get anything useful out of doing that.

qpsk uses constellations. With M = 16, you end up with 8 different real() values (4 unique values and their negatives), and cannot tell the difference between the two cases involving A +/- B*1i . And with a constellation, all of the values have the same absolute value: they all have the same magnitude, just with different vector rotations.

You would be safer taking real() and imag() and forming a vector twice as long. Possibly even doing dwt separately on the two parts.

... But I have no idea how this relates to OFDM.

[ABDUL]

when i try to implement the complex data of size 1x64 , by separting the real and imag parts the and computing the idwt of the data i will be getting the data of twice the size i.e., 1x64 for the real values and 1 x 64 for the imag values when i concatenate it i will be getting the data of size 1x 128 after performing the idwt operation how do i change the data to original data of size 1x 64 ?

[Walter Roberson]

ireal = idwt(real(AC), real(DC), 'haar');
icpx  = idwt(imag(AC), imag(AC), 'haar');
IDWT = complex(ireal, icpx);

[ABDUL]

how we go ahead with the implemenation of the dwt as we have 1x98 data samples which are complex ?

[Walter Roberson]

I do not understand where you got the 98 data samples from? You have been talking about 1 x 64.

[ABDUL]

it is 1x 64 only . if it can more generalised to 1xN data samples . it would be better .

[ABDUL]

hi...

if i change the wavelet to other wavelets like db2,db3, sym2, sym3 my data is getting reduced for eg if i have a data of 1x64 , Ac will have 1x32 and Dc will have 1x32 through haar wavelet i will be getting a size of 1x64 but when i use other wavelet like db2 i will be getting the size for 1x30 for Ac and for Dc i will be getting 1x30 the total size of the data will be 1x60 how to retain the same size as 1x64 only when i use the wavelet of db2 and other wavelets