receiver.m

%----------------------------------------------------
%----------------- Demodulator ----------------------
%----------------------------------------------------
phase_rx = 0;                       

Rx_I = Rx .* (sqrt(2)*cos(2*pi*Fc_tx*t+phase_rx));
Rx_Q = Rx .* (-sqrt(2)*sin(2*pi*Fc_tx*t+phase_rx));

%----------------------------------------------------
%----------------- Low Pass FIR Filter --------------
%----------------------------------------------------
%% Low pass FIR filter can be easily implemented with a rectangular
%% function in frequency domain to cut everuthing after the cutoff.
%% Which in the time domain corresponds to a sinc function.
%% Since it's a FIR filter, there is no feedback coefficient, so A = 1
%% Multiplying in frequency corresponds to convolution in temporal
%% So, we reverse the incremental in the for loop using d2
%% And we make sure to not divide by 0 in case we have an odd order
%% And then we got B and we can filter the demodulated signak
%% Fcutoff is normalized, so divided by the Nyquist frequency, Fs/2
%% The order of the FIR can be approximated with the formula
%%                Attenuation of the stopband
%% FIRorder =  ---------------------------------------
%%           22 * (Fstopband - Fpassband) / Fsampling

Att = 20;                   %%in dB
Fpass = Rs/2;               %% Passband frequency
Fstop = 2*Fc_tx - Fpass;    %% Stopband frequency

FIRorder = ceil(Att/ (22 * (Fstop - Fpass) / Fs)); 

Fcutoff = Fpass/(Fs/2);   

A_LPF = 1;
B_LPF = 0;

M = (FIRorder - 1)/2;
for i = 0 : FIRorder-1
  j = i - M;
  
  if (j == 0)
        B_LPF(i+1) = Fcutoff;
  else
        B_LPF(i+1) = sin(pi * Fcutoff * j) / (pi * j);
  endif
end

B_LPF = (1/sum(B_LPF)) * B_LPF; %%gain added to go back to the same range as the mapped symbols

Rx_I_LPF = filter(B_LPF, A_LPF,Rx_I);
Rx_Q_LPF = filter(B_LPF, A_LPF,Rx_Q);


%----------------------------------------------------
%----------------- Matched SRRC filter --------------
%---------------------------------------------------- 
% Using the matched filter of the SRRC to get back the signal

Rx_I_BB = filter(B_SRRC, A_SRRC, Rx_I_LPF); 
Rx_Q_BB = filter(B_SRRC, A_SRRC, Rx_Q_LPF);

%----------------------------------------------------
%----------------- Downsampling ---------------------
%----------------------------------------------------
%% First downsampling is the simplest one, we take the sample
%% at the k * Ns time

%% Second downsampling is a bit more interesting, we use Gardner
%% algorithm to calculate the error. However, there is no interpolator,
%% so the technique only works well with a big samples_per_symbol number (Ns)

%%%%%%%%%%%%%%%%%%%%%%%%%%%% Easy downsampling
sample_timing(1) = 2*Ns*G + 1;

for i = 1 : numberOfSymbols
  
  receivedSymbols_I1(i) = Rx_I_BB(sample_timing(i));
  receivedSymbols_Q1(i) = Rx_Q_BB(sample_timing(i));
  
  if(i <  numberOfSymbols)
    sample_timing(i+1)  = sample_timing(i) + Ns;
  endif
  
end
receivedSymbols1 = complex(receivedSymbols_I1, receivedSymbols_Q1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%% Gardner without interpolator
step = 1;
e = zeros(1, numberOfSymbols);
k(1) = 2 * Ns * G + 1;

for i = 1 : numberOfSymbols
  
  % Downsampling
  receivedSymbols_I2(i) = Rx_I_BB(k(i));
  receivedSymbols_Q2(i) = Rx_Q_BB(k(i));
  
  %% Gardner error
  if (i > 1)
    e(i) = (Rx_I_BB(k(i)) - Rx_I_BB (k(i-1))) * Rx_I_BB(k(i) - Ns/2);
    e(i) = e(i) + (Rx_Q_BB(k(i)) - Rx_Q_BB (k(i-1))) * Rx_Q_BB(k(i) - Ns/2);
  endif
  
  if mean(e) > 0
    delta(i) = -step;
  elseif mean(e) < 0
    delta(i) = step;
  else
    delta(i) = 0;
  endif
  
  %% Change of the sampling time
  if (i < numberOfSymbols)
    k(i+1) = k(i) + Ns + delta(i);
    k_plot(i+1) = mod(k(i+1) +Ns/2, Ns); %%for debugging
  endif
  
endfor
receivedSymbols2 = complex(receivedSymbols_I2, receivedSymbols_Q2);

receivedSymbols = receivedSymbols1;
%----------------------------------------------------
%----------------- QAM Demapper ---------------------
%----------------------------------------------------

% Map symbols to bits
for i = 1:length(receivedSymbols)   
    [diff receivedSymbolsIndex(i)] = min( receivedSymbols(i) - mappingTable) ; 
endfor
receivedSymbolsIndex = receivedSymbolsIndex - 1;

for i = 1:length(receivedSymbols)    
    dataOut(i*2 - 1)  = rem(floor(receivedSymbolsIndex(i)/2), 2);
    dataOut(i*2)      = rem(receivedSymbolsIndex(i), 2);
endfor

%----------------------------------------------------
%----------------- Bit Error Rate -------------------
%----------------------------------------------------

BE = 0;
for i = 1:length(dataIn)    
    if dataIn(i) != dataOut(i)
       BE++;
    endif
endfor

BER = BE/length(dataIn) * 100;

%----------------------------------------------------
%----------------- Figures --------------------------
%----------------------------------------------------
figure(11)
scatter(real(receivedSymbols1), imag(receivedSymbols1) , "filled");
axis([-2 2 -2 2])
title("Received Symbols 1")
##figure(12)
##scatter(real(receivedSymbols2), imag(receivedSymbols2) , "filled");
##axis([-2 2 -2 2])
##title("Received Symbols 2")

##figure(12)
##stem(dataOut,"filled");
##xlabel('Bit Index');
##title('Data Out');
##ylabel('Binary Value');

##figure(13)
##plot(Rx_I_LPF);
##figure(15)
##plot(real(mappedSymbols_upsampled));
##figure(14)
##plot(Rx_Q_LPF);
##figure(16)
##plot(imag(mappedSymbols_upsampled));

##figure(17);
##stem(real(mappedSymbols_upsampled));
##figure(18);
##plot(2*Ns*G +1 :length(Rx_I_BB), Rx_I_BB(2*Ns*G +1 : end));
##hold on
##stem(2*Ns*G +1 :length(Rx_I_BB), Rx_I_BB(2*Ns*G +1 : end));
##hold on
##stem(2*Ns*G +1: Ns :length(Rx_I_BB), Rx_I_BB(2*Ns*G +1 : Ns : end), 'filled');
##
##figure(19);
##plot(Rx_I_BB);
##hold on
##stem(Rx_I_BB);

##figure(21);
##stem(Rx_I_BB);
##hold on
##stem(k, Rx_I_BB(k), 'filled');
##hold on
##stem(sample_timing, Rx_I_BB(sample_timing), 'filled');
##legend("Rx_I_BB", "k", "sample_timing");

%----------------------------------------------------
%----------------- Clear ----------------------------
%----------------------------------------------------

clear Rx Rx_I Rx_Q 
clear Rx_I_LPF Rx_Q_LPF 
%clear Rx_I_BB Rx_Q_BB
clear i j
clear Att Fpass Fstop Fcutoff A_LPF B_LPF FIRorder
clear A_SRRC B_SRRC
clear t
clear receivedSymbolsIndex diff