Pulse shaping on BER

I build a pam-2 modulation, then I make a pulse shaping with half sine (matched filter). Then I send it through the AWGN channel. At the end I do down sampling and demodulation. But i have problem with plotting BER. I don't understand what I'm doing wrong:

clc;
clear;
N=1e4;
N2 = 1e2; 
M = 2;
range = 0:10;
error =  zeros(1,length(range)); %BER

%
% half sine
Rc = 1e3;       % Chip rate
T = 1/Rc;      % inverse of chip rate
Tc = 0.5* T;
Fs = 2e3;      % sampling frequency
dt = 1/Fs;
over = Fs/Rc;   % sampling factor
sps = 10;  

time = 0:dt/sps:2*T;
half_Sine = sin(pi*time/(2*T)).^3; 

%% BER

for i = 1:length(range)
    for n = 1:N2 
        
        % Modulation
        x=randi([0 M-1],N,1);
        h_mod = pammod(x,M);       
        over_data=upsample(h_mod,over); 
        txSig = conv(over_data,half_Sine, 'same'); 
        % AWGN  
        Ps = mean(((txSig)).^2);
        Sigma = sqrt(Ps  * 10^(-range(i)/10) / 2);
        Noise = randn(length(txSig), 1) * Sigma;
        rx_SIG = Noise + txSig; 
        
        % Downsample
        down = rx_SIG(1:over:end);
        
        %  Demodulation 
        hDemod  =  pamdemod(down,M);
        % Errors
        error(i) = error(i)+...
            sum(hDemod~=x) / length(hDemod);
        
    end
    
    BER = error/n;
end
figure(1);
grid on
semilogy(range,BER);
title('BER');

Answer 1

[vidyesh]

Hi Rory,

The issue lies in the below line of code:

txSig = conv(over_data,half_Sine, 'same'); 

Are you trying to simulate the channel or trying to modulate to a higher frequency by using convolution?

In either scenario, you will have to perform deconvolution at the receiever side. But the 'deconv' function is very sensitive to noise, so it may not give the desired results either.

For simulating the channel/modulation, refer the below examples and functions:

1) Rayleigh Channel fading: https://www.mathworks.com/matlabcentral/fileexchange/62779-bpsk-over-rayleigh-fading-channel?s_tid=srchtitle_support_results_3_Rayleigh%2520channel

2) 'comm.Rayleigh' function: https://www.mathworks.com/help/comm/ref/comm.rayleighchannel-system-object.html?searchHighlight=rayleigh&s_tid=srchtitle_support_results_3_rayleigh

3) 'modulate' function: https://www.mathworks.com/help/signal/ref/modulate.html?searchHighlight=modulate&s_tid=srchtitle_support_results_1_modulate

Utilizing the above functions or following the process used in the example will be a better option over using 'conv'