Deconvolution of system output signal using Deconv

I want to recover the message signal by deconv() . the program takes system input(the message) and the impulse response and it convolutes them. However, the ouput signal(result of convolution) is then affected by a noise (sigma*randn(1,length(output_signal))) afterwards.

The target is to recover/restore the original message by using Deconv() function.

The problem is Deconv() returns a single float number i.e a point not the original message .

note : I tested the code the output signl is perfectly plotted however things don't work after that.

I need help!

What I have tried

Y = conv(signals, responses,'same');
% signals is a vector of signals that respresent the message.
% responses is a vector of signals that respresent the impulse response.
% both are user inputs.
sigma = 1;
noise = sigma*randn(1,length(Y));
Y = Y + noise; 
[recovered_message, r] = deconv(Y, signals);
plot(recovered_message);

Answer 1

[Yasir Ahmed]

Please see the code below.

%%%%% QPSK Modulation %%%%%

clear all

close all

symbols=5;

Ns=20;

Eb=sqrt(2);

EbNo=10;

s=([ones(1,Ns)]')*([1+i,-1+i,-1-i,1-i,1+i]);

s=s(:);

s=transpose(s);

plot(s,'bo-');hold on

h=[1.30,0.05,0.34,-0.03,0.40];

r=conv(s,h);

sigma=sqrt(Eb/(2*EbNo));

r=r+sigma*(randn(1,length(r))+i*randn(1,length(r)));

plot(r(1:symbols*Ns),'r*')

[s_est,R]=deconv(r,h);

plot(s_est,'g+');hold off

xlabel('In-phase')

ylabel('Quadrature')

legend('Tx','Rx','Eq')

For complete discussion see the comments section of the following post.

https://www.raymaps.com/index.php/m-qam-bit-error-rate-in-rayleigh-fading/#comment-159469

Answer 2

[Alessio Lodato]

Dear Yasir,

how can i contact you, i have a similar problem.

Thank you,

A

Answer 3

[Andika]

Since R2023b, you can use the deconv function and specify the Method name-value argument as "least-squares".

For example, you can do:

Y = conv(signals,responses,"same");

sigma = 1;

noise = sigma*randn(1,length(Y));

Y = Y + noise;

[recovered_message,r] = deconv(Y,responses,"same",Method="least-squares");

plot(recovered_message);