training based channel equalization.m

training based channel equalization

T=1000;   % total number of data
dB=25;  % SNR in dB value

%%%%%%%%% Simulate the Received noisy Signal  %%%%%%%%%%%
N=5; % smoothing length N+1
P=5; % shifting Lh <= P <= N
Lh=5;  % channel length = Lh+1

h=randn(1,Lh+1)+sqrt(-1)*randn(1,Lh+1);   % channel (complex)
h=h/norm(h);                     % normalize

s=round(rand(1,T))*2-1;  % QPSK or 4 QAM symbol sequence
s=s+sqrt(-1)*(round(rand(1,T))*2-1);

% generate received noisy signal
x=filter(h,1,s);
vn=randn(1,T)+sqrt(-1)*randn(1,T);   % AWGN noise (complex)
vn=vn/norm(vn)*10^(-dB/20)*norm(x);  % adjust noise power with SNR dB value
SNR=20*log10(norm(x)/norm(vn))       % Check SNR of the received samples
x=x+vn;                           % received signal

%%%%%%%%%%%%% channel identification
Lp=T-N;   %% remove several first samples to avoid 0 or negative subscript
X=zeros(N+1,Lp);  % sample vectors (each column is a sample vector)
for i=1:Lp
    X(:,i)=x(i+N:-1:i).';
end

hb=zeros(N+1,1);  % estimated channel
for i=1:Lp-10     % need carefully adjust parameter 10 to have positive subscript
    hb=hb+X(:,i+10)*conj(s(i+10+N-P));  % channel estimation (use all data samples)
end
hb=hb(N+1:-1:1)/norm(hb);      % normalized channel estimation

hb1=hb(P-Lh+1:P-Lh+1+Lh).'; hb1=hb1/norm(hb1);  % remove zero head and tail (because N>Lh)
Channel_MSE=norm(hb1-h)  % estimation error MSE
 
if 1
    subplot(222), 
    plot(1:Lh+1,real(h),'bo-',1:Lh+1,real(hb1),'rx-'), grid
    title('Channel #1. o:real, x: estimated')
end