MATLAB: Convolution problem

convolutionofdmplcpower linepower line communication

hello to all
in this code we have an ofdm signal(60 MHZ),with length of 4096×1 (Pxx) and a power line model 0 to 80 Mhz with length of 1×161
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))

Best Answer

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).
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