Convolution problem

hello to all

in this code we have an ofdm signal(60 MHZ),with length of 4096x1 (Pxx) and a power line model 0 to 80 Mhz with length of 1x161

the two parameters are shown in frequency domain

we have tried to get the plot after the ofdm signal is transmited threw the power line filter by convolution in time domain , or by multiplexing in frequensy domain

thank alot

the code :

clear all

%%%%%%%%%%%%%%%%%%%%%%   O F D M    S I G N A L  %%%%%%%%%%%%%%%%%%%%%%
nFFTSize =64 ;
% for each symbol bits a1 to a52 are assigned to subcarrier 
% index [-30 to -1 1 to 30] 
subcarrierIndex = [-30:-1 1:30];
nBit = 2500; 
ip1 = rand(1,nBit) >0.5;
ip2=rand(1,nBit) >0.5;
ip=[ip1;ip2] > 0.5; % generating 1's and 0's
nBitPerSymbol = 60;

nSymbol = ceil(nBit/nBitPerSymbol);

j=sqrt(-1)

% QBPSK modulation
% bit00 --> 1
% bit01 --> 1+j
% bit10 -->-1
% bit11 -->-1-j

t1 = ip1==1;
t2 = ip2==1;
ipMod(t1 & t2) = -(1+1i); %11
ipMod(~t1 & t2) = 1+1i;   %01
ipMod(t1 & ~t2) = -1;     %10
ipMod(~t1 & ~t2) = 1;     %00

ipMod = [ipMod zeros(1,nBitPerSymbol*nSymbol-nBit)];
ipMod = reshape(ipMod,nSymbol,nBitPerSymbol);
figure(2)
plot(ipMod)

st = []; % empty vector

for ii = 1:nSymbol

inputiFFT = zeros(1,nFFTSize);

% assigning bits a1 to a52 to subcarriers [-30 to -1, 1 to 30]
inputiFFT(subcarrierIndex+nFFTSize/2+1) = ipMod(ii,:);

%  shift subcarriers at indices [-30 to -1] to fft input indices [38 to 63]
inputiFFT = fftshift(inputiFFT); 

outputiFFT = ifft(inputiFFT,nFFTSize);

% adding cyclic prefix of 16 samples 
outputiFFT_with_CP = [outputiFFT(49:64) outputiFFT];

st = [st outputiFFT_with_CP]; 

end

close all
fsMHz = 60;
[Pxx,W] = pwelch(st,[],[],4096,20);    
figure(3)
plot([-2048:2047]*fsMHz/4096,10*log10(fftshift(Pxx)));
xlabel('frequency, MHz')
ylabel('power spectral density')
title('Transmit spectrum OFDM (based on 802.11a)');

%%%%%%%%%%%%%%%%%%%%%%POWER LINE COMMUNICATION TRANSFER FUNCTION %%%%%%%%%%%%%%%%%%%%%%

w=0:0.5*10^6:80*10^6;                    % [Hz]
l=5   ;                                  % [meter]
zl=50 ;                                  % [ohm/meter]
zs=50 ;                                  % [ohm/meter]
R=1.9884 ;                               % [ohm/meter]
G=0.01686*10^-9   ;                      % [mho/meter]                                          
C=0.13394*10^-9 ;                        % [farad/meter]                                                
L=362.81*10^-9  ;                        % [henrry/meter]                    
zc=sqrt((R+j.*w.*L)./(G+j.*w.*C));       % characteristic impedance [ohm]                                                                           
gama=sqrt((R+j.*w.*L).*(G+j.*w.*C));     % propagation constant     
a=cosh(gama.*l);
b=zc.*sinh(gama.*l);
c=(1./zc).*sinh(gama.*l);
d=cosh(gama.*l);
H= zl./((a.*zl)+b+(c.*zl.*zs)+(d.*zs));  %transfer function [Vl/Vs]
figure(1)
plot(w,20*log10(H))                                                   % clean 
xlabel('frequency  [Hz]');
ylabel('Transfer function magnitude H(f) [dB]');           
figure(5)
subplot(2,1,1)
plot(w,20*log10(H+0.001*[randn(1,length(H)) + j*randn(1,length(H))])) % plus random noise
xlabel('frequency  [Hz]  ');
ylabel('Transfer function + random noise [dB]');
subplot(2,1,2)
plot(w,20*log10(H+0.001*wgn(1,length(H),-10)))                        % plus white gaussian noise
xlabel('frequency  [Hz]  ');
ylabel('Transfer fuction + wgn [dB]');

y=conv(Pxx,H)
figure(4)
plot(20*log10(y))

[Andrew Newell]

And the question is ...?

[yuvi]

i want to know how to do convolution between the ofdm signal and the power line model .

i have tried with conv(Pxx,H)

but it didn't work, maybe because it's in the frequency domain ?

by the way , how do i fix the axis?

[Arturo Moncada-Torres]

What do you want to fix from the axis?

[yuvi]

in this command :

y=conv(Pxx,H)

figure(4)

plot(20*log10(y))

i want to get a plot with "x axis " of frequency

thanks

Answer 1

[Daniel Shub]

Convolution of time domain signals is the same as multiplication of frequency domain signals. You cannot simply multiple Pxx and H since they have different sizes. You could take the ifft of both, conv and then take the fft of the result. Better would be to use W from pwelch instead of w in calculating H (you need to adjust for the sampling rate).

[yuvi]

can i just multiply in frequency instead conv in time ?

and if i can , should i make them the same size with zero padding ?

( y=Pxx.*H )

do you have any ideas how to fix the axis so it will be in frequency domain after multiply?

thanks

[Daniel Shub]

Yes, you can just multiple in frequency, but NO you cannot just zero pad. You need to create H and Pxx with the same spectral spacing. Think about your W and w variables and what they represent.

To get the plot in the frequency domain try plot(W, 20*log10(y)).

On a side note, do you really want 20*log10 with Pxx (an estimate of power).

[yuvi]

THANK'S DANIEL !