[Blind Channel Estimation] QPSK Simulation of LMS Blind Channel Estimation Based on Matlab

content

1. Software version

2. Core code

3. Operation steps and simulation conclusion

 4. References

5. How to obtain the complete source code

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1. Software version

MATLAB2021a

2. Core code

% CHANNEL EQUALIZATION USING LMS 
clc;
clear all;
close all;
M=3000;    % number of data samples
T=2000;    % number of training symbols
dB=25;     % SNR in dB value

L=20; % length for smoothing(L+1)
ChL=5;  % length of the channel(ChL+1)
EqD=round((L+ChL)/2);  %delay for equalization

Ch=randn(1,ChL+1)+sqrt(-1)*randn(1,ChL+1);   % complex channel
Ch=Ch/norm(Ch);                     % scale the channel with norm

TxS=round(rand(1,M))*2-1;  % QPSK transmitted sequence
TxS=TxS+sqrt(-1)*(round(rand(1,M))*2-1);


x=filter(Ch,1,TxS);  %channel distortion
n=randn(1,M);  %+sqrt(-1)*randn(1,M);   %Additive white gaussian noise
 n=n/norm(n)*10^(-dB/20)*norm(x);  % scale the noise power in accordance with SNR
x=x+n;                           % received noisy signal

K=M-L;   %% Discarding several starting samples for avoiding 0's and negative
X=zeros(L+1,K);  % each vector column is a sample
for i=1:K
    X(:,i)=x(i+L:-1:i).';
end

%adaptive LMS Equalizer
e=zeros(1,T-10);  % initial error
c=zeros(L+1,1);   % initial condition
mu=0.001;        % step size
for i=1:T-10
    e(i)=TxS(i+10+L-EqD)-c'*X(:,i+10);   % instant error
    c=c+mu*conj(e(i))*X(:,i+10);           % update filter or equalizer coefficient
end

sb=c'*X;   % recieved symbol estimation

%SER(decision part)
sb1=sb/norm(c);  % normalize the output
sb1=sign(real(sb1))+sqrt(-1)*sign(imag(sb1));  %symbol detection
start=7;  
sb2=sb1-TxS(start+1:start+length(sb1));  % error detection
SER=length(find(sb2~=0))/length(sb2); %  SER calculation
disp(SER);

% plot of transmitted symbols
    subplot(2,2,1), 
    plot(TxS,'*');   
    grid,title('Input symbols');  xlabel('real part'),ylabel('imaginary part')
    axis([-2 2 -2 2])
    
% plot of received symbols
    subplot(2,2,2),
    plot(x,'o');
    grid, title('Received samples');  xlabel('real part'), ylabel('imaginary part')

% plots of the equalized symbols    
    subplot(2,2,3),
    plot(sb,'o');   
    grid, title('Equalized symbols'), xlabel('real part'), ylabel('imaginary part')

% convergence
    subplot(2,2,4),
    plot(abs(e));   
    grid, title('Convergence'), xlabel('n'), ylabel('error signal')
    %%
    
    %IMPLEMENTATION OF BLIND CHANNEL USING CMA OR GODARD ALGORITHM IMPLEMENTED

clc;
clear all;
close all;
N=3000;    % number of sample data
dB=25;     % Signal to noise ratio(dB)

L=20; % smoothing length L+1
ChL=1;  % length of the channel= ChL+1
EqD=round((L+ChL)/2);  %  channel equalization delay

i=sqrt(-1);
%Ch=randn(1,ChL+1)+sqrt(-1)*randn(1,ChL+1);   % complex channel

%Ch=[0.0545+j*0.05 .2832-.1197*j -.7676+.2788*j -.0641-.0576*j .0566-.2275*j .4063-.0739*j];
Ch=[0.8+i*0.1 .9-i*0.2]; %complex channel
    Ch=Ch/norm(Ch);% normalize
TxS=round(rand(1,N))*2-1;  % QPSK symbols are transmitted symbols
TxS=TxS+sqrt(-1)*(round(rand(1,N))*2-1);
x=filter(Ch,1,TxS); %channel distortion

n=randn(1,N)+sqrt(-1)*randn(1,N);   % additive white gaussian noise (complex)
 n=n/norm(n)*10^(-dB/20)*norm(x);  % scale noise power
x1=x+n;  % received noisy signal

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3. Operation steps and simulation conclusion

 4. References

[1] Chen Guojun, Hu Hanying. A New Method for Adaptive Blind Channel Estimation in OFDM Systems [J]. Signal Processing, 2013, 29(6):5.

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5. How to obtain the complete source code

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