%%%%%%% MATLAB (R) script to compute TWDP %%%%%%%%%%%%%%%%%%%%%%
%% TP-2 test inputs
%% Units for all optical power values must match.

%% Transmit data file: The transmit data sequence is based on either of the TWDP test patterns defined in
%% Table 68-5. The file format is ASCII with a single column of chronological ones and zeros with no headers
%% or footers.
TxDataFile = 'path\datafilename';

%% Measured waveform. The waveform consists of exactly N samples per bit period T, where N is the
%% oversampling rate. The waveform must be circularly shifted to align with the data sequence. The file
%% format for the measured waveform is ASCII with a single column of chronological numerical samples, in
%% optical power, with no headers or footers.
MeasuredWaveformFile = 'path\waveformfilename';	

%% OMA and steady-state ZERO power must be entered.
MeasuredOMA 		= [OMAvalue];   	% Measured OMA, in optical power
SteadyZeroPower 	= [ZEROvalue]; 		% Measured optical power, steady-state logic ZERO
OverSampleRate 		= 16;           	% Oversampling rate

%% Simulated fiber response, modeled as a set of ideal delta functions with specified amplitudes in optical
%% power and delays in nanoseconds in columns with no headers or footers. The number of test cases is
%% determined by the TWDP requirements in Table 68-3. The vector 'PCoefs' contains the amplitudes, and the
%% vector 'Delays' contains the delays. 
FiberResp = [...
0.000000 0.65 0.88 0.51
0.072727 0.5 0.58 0.89
0.145455 0.91 0.89 0.29
0.218182 0.26 0.1 0.81];
Delays 	    = FiberResp(:, 1);

%% Program constants %%
SymbolPeriod    = 1/(10.3125);  	% Symbol period (ns)
EFilterBW       = 7.5;            	% Front end filter bandwidth (GHz)
EqNf            = 100;          	% Number of feedforward equalizer taps
EqNb            = 50;         		% Number of feedback equalizer taps
EqDel           = ceil(EqNf/2); 	% Equalizer delay
PAlloc          = 6.5;              	% Allocated dispersion penalty (dBo)
Q0              = 7.03;           	% BER = 10^(-12)

%% STEP 1 - Process waveform through simulated fiber channel %%%%%%%%%%%%%%%%%%%
%% Load input waveforms
XmitData	= load(TxDataFile);
yout0 		= load(MeasuredWaveformFile);
PtrnLength 	= length(XmitData);
TotLen 		= PtrnLength*OverSampleRate;
Fgrid 		= [-TotLen/2:TotLen/2-1].'/(PtrnLength*SymbolPeriod);
%% Process through fiber model. Fiber frequency response is normalized to 1 at DC.
for i=1:3
PCoefs 		= FiberResp(:,i+1);
ExpArg 		= -j*2*pi*Fgrid;
Hsys 		= exp(ExpArg * Delays') * PCoefs;
Hx     	      	= fftshift(Hsys/abs(Hsys(find(Fgrid==0))));
yout 		= real(ifft(fft(yout0).*Hx));

%% STEP 2 - Normalize OMA%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
yout 		= (yout - SteadyZeroPower)/MeasuredOMA;

%% STEP 3 - Process signal through front-end antialiasing filter %%%%%%%%%%%%%%%%%%
%% Compute frequency response of front-end Butterworth filter
[b,a] 		= butter(4, 2*pi*EFilterBW,'s');
H_r 		= freqs(b,a,2*pi*Fgrid);
%% Process signal through front-end filter
yout 		= real(ifft(fft(yout) .* fftshift(H_r)));

%% STEP 4 - Sample at rate 2/T %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
yout 		= yout(1:OverSampleRate/2:end);

%% STEP 5 - Compute MMSE-DFE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% The MMSE-DFE filter coefficients computed below minimize mean-squared error at the slicer input.
%% The derivation follows from the fact that the slicer input over one period (which is the same as the
%% period of the input data sequence) can be expressed as Z = (R+N)*W - X*[0 B]', where R and N are
%% Toeplitz matrices constructed from the signal and noise components, respectively, at the sampled out
%% put of the antialiasing filter, W is the feedforward filter, X is a Toeplitz matrix constructed from the
%% input data sequence, and B is the feedback filter. The optimal W and B minimize E[||Z-XIn||^2], where
%% XIn is the input data sequence, and the expectation operator refers to the Gaussian noise component of
%% Z. Compute the noise autocorrelation sequence at the output of the front-end filter and rate-2/T sampler.
%% Constuct a Toeplitz autocorrelation matrix.
N0    	= SymbolPeriod/(2 * Q0^2 * 10^(2*PAlloc/10));
Snn 	= N0/2 * fftshift(abs(H_r).^2) * 1/SymbolPeriod * OverSampleRate;
Rnn 	= real(ifft(Snn));
Corr 	= Rnn(1:OverSampleRate/2:end);
C     	= toeplitz(Corr(1:EqNf));
%% Construct Toeplitz matrix from input data sequence
X     	= toeplitz(XmitData, [XmitData(1); XmitData(end:-1:end-EqNb+1)]);
%% Construct Toeplitz matrix from signal at output of 2/T sampler.
%% This sequence gets wrapped by equalizer delay
R     	= toeplitz(yout, [yout(1); yout(end:-1:end-EqNf+2)]);
R   	= [R(EqDel+1:end,:); R(1:EqDel,:)];
R   	= R(1:2:end, :);
%% Compute least-squares solution for filter coefficients
RINV 	= inv(R'*R+PtrnLength*C);
P     	= X'*(eye(PtrnLength) - R*RINV*R')*X;
P01 	= P(1,2:EqNb+1);
P11 	= P(2:EqNb+1,2:EqNb+1);
B   	= -inv(P11)*P01'; 		% Feedback filter
W     	= RINV*R'*X*[1;B]; 		% Feedforward filter
Z     	= R*W - X*[0;B]; 		% Input to slicer

%% STEP 6 - Compute BER using semi-analytic method %%%%%%%%%%%%%%%%%%%%%%
MseGaussian = W'*C*W;
Ber 	= sum(0.5*erfc((abs(Z-0.5)/sqrt(MseGaussian))/sqrt(2)))/length(Z);

%% STEP 7 - Compute equivalent SNR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% This function computes the inverse of the Gaussian error probability function. The built-in Matlab
%% function erfcinv() is not sensitive enough for the low probability of error case.
Q = inf;
if Ber>10^(-12)         Q = sqrt(2)*erfinv(1-2*Ber);
elseif Ber>10^(-300) 	Q = 2.1143*(-1.0658-log10(Ber)).^0.5024;
end

%% STEP 8 - Compute penalty %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
RefSNR      	= 10 * log10(Q0) + PAlloc;
TrialTWDP(i) 	= RefSNR-10*log10(Q);
end
%TrialTWDP
TWDP        	= max(TrialTWDP)
% End of program