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DB and 400G and minor changes

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This commit is contained in:
Silas Oettinghaus
2024-10-07 08:22:28 +02:00
parent 179a7f9682
commit da3be973e2
20 changed files with 578 additions and 142 deletions
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35
Classes/00_signals/Signal.m
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@@ -192,6 +192,19 @@ classdef Signal
end end
%% Add signals from one signal to another, the first object will sustain
function Difference = minus(X,y)
if isa(y,'Signal')
Difference = X;
Difference.signal = X.signal - y.signal;
elseif isnumeric(y)
Difference = X;
Difference.signal = X.signal - y;
end
end
function Product = times(X,y) function Product = times(X,y)
if isa(y,'Signal') if isa(y,'Signal')
@@ -271,14 +284,22 @@ classdef Signal
N = 2^(nextpow2(length(obj.signal))-8); N = 2^(nextpow2(length(obj.signal))-8);
[p_lin,w] = pwelch(obj.signal,hanning(N),N/2,N,obj.fs,"centered","power","mean"); [p_lin,w] = pwelch(obj.signal,hanning(N),N/2,N,obj.fs,"centered","power","mean");
p_dbm = 10*log10(p_lin)+30; %dB to dBm in case of "power" normalize = 1;
if normalize
p_lin = p_lin./ max(p_lin);
p_dbm = 10*log10(p_lin); %dB to dBm in case of "power"
ylab = "normalized to 0 dB";
else
p_dbm = 10*log10(p_lin)+30; %dB to dBm in case of "power"
ylab = "Power (dBm)";
end
figure(options.fignum); % If figure does not exist, create new figure figure(options.fignum); % If figure does not exist, create new figure
hold on hold on
plot(w.*1e-9,p_dbm,'DisplayName',options.displayname,'LineWidth',1); plot(w.*1e-9,p_dbm,'DisplayName',options.displayname,'LineWidth',1);
xlabel("Frequency in GHz"); xlabel("Frequency in GHz");
%ylabel("Power/frequency (dB/Hz)"); %ylabel("Power/frequency (dB/Hz)");
ylabel("Power (dBm)"); ylabel(ylab);
xlim([-obj.fs/2 obj.fs/2].*1e-9) xlim([-obj.fs/2 obj.fs/2].*1e-9)
edgetick = 2^(nextpow2(obj.fs*1e-9)); edgetick = 2^(nextpow2(obj.fs*1e-9));
% xticks([-edgetick:16:edgetick]); % xticks([-edgetick:16:edgetick]);
@@ -362,7 +383,7 @@ classdef Signal
end end
%% %% Normalize
function obj = normalize(obj,options) function obj = normalize(obj,options)
arguments arguments
@@ -381,7 +402,7 @@ classdef Signal
end end
%% %% Delay
function [obj] = delay(obj,delay,options) function [obj] = delay(obj,delay,options)
arguments arguments
@@ -402,7 +423,7 @@ classdef Signal
end end
%% %% Synchronize with reference
function [obj,D,cuts] = tsynch(obj,options) function [obj,D,cuts] = tsynch(obj,options)
% time sync and cut % time sync and cut
arguments arguments
@@ -446,6 +467,10 @@ classdef Signal
end end
function obj = filter(obj,a,b)
obj.signal = filter(a,b,obj.signal);
end
function er = extinctionratio(obj,fsym,M) function er = extinctionratio(obj,fsym,M)
histpoints = 1024; %% verticale resolution histpoints = 1024; %% verticale resolution
histpoints = floor(histpoints/2)*2+1; %% to have the eye digram centered around one point make the vertical resolution uneven histpoints = floor(histpoints/2)*2+1; %% to have the eye digram centered around one point make the vertical resolution uneven

8
Classes/01_transmit/PAMsource.m
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@@ -10,6 +10,7 @@ classdef PAMsource
randkey randkey
db_precode db_precode
db_encode
mrds_code mrds_code
mrds_blocklength mrds_blocklength
@@ -36,6 +37,7 @@ classdef PAMsource
options.randkey = 0; options.randkey = 0;
options.db_precode = 0; options.db_precode = 0;
options.db_encode = 0;
options.mrds_code = 0; options.mrds_code = 0;
options.mrds_blocklength = 512; options.mrds_blocklength = 512;
@@ -95,11 +97,17 @@ classdef PAMsource
symbols = PAMmapper(obj.M,0).map(bits); symbols = PAMmapper(obj.M,0).map(bits);
symbols.fs = obj.fsym; symbols.fs = obj.fsym;
%%%%%% Duobinary %%%%%%%%%%%
if obj.db_precode if obj.db_precode
symbols = Duobinary().precode(symbols); symbols = Duobinary().precode(symbols);
end
if obj.db_encode
symbols = Duobinary().encode(symbols); symbols = Duobinary().encode(symbols);
end end
% figure(12);hold on;histogram(symbols.signal,'Normalization','probability');
if obj.mrds_code if obj.mrds_code
symbols = MRDS_coding("blocklength",obj.mrds_blocklength).encode(symbols); symbols = MRDS_coding("blocklength",obj.mrds_blocklength).encode(symbols);
end end

17
Classes/04_DSP/Coding/Duobinary.m
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@@ -47,8 +47,12 @@ classdef Duobinary
% Pre coding % Pre coding
bk = zeros(numel(data),1); bk = zeros(numel(data),1);
for k = 1:numel(data)-1 % for k = 1:numel(data)-1
bk(k+1) =mod(data(k)-bk(k),M); % bk(k+1) =mod(data(k)-bk(k),M);
% end
for k = 2:numel(data)
bk(k) =mod(data(k)-bk(k-1),M);
end end
%make bipolar %make bipolar
@@ -107,9 +111,16 @@ classdef Duobinary
assert(isequal((0:M-1)',unique(data)),'Check Duobinary Precoding'); %seems the signal is not unipolar assert(isequal((0:M-1)',unique(data)),'Check Duobinary Precoding'); %seems the signal is not unipolar
% duobinary coding (1+D) % duobinary coding (1+D)
% coeff = [1,1];
%
% data = conv(data,coeff,"same");
coeff = [1,1]; coeff = [1,1];
data = conv(data,coeff,"same"); data = filter(coeff, 1, data);
%data = data ./ rms(data);
% data = ifft(fft(real(data)).*fft(fliplr(coeff'),length(data))) + 1i*ifft(fft(imag(data)).*fft(fliplr(coeff'),length(data)));
%make bipolar %make bipolar
data = (data-round(mean(data),1)); data = (data-round(mean(data),1));

10
Classes/04_DSP/Equalizer/FFE.m
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@@ -51,7 +51,7 @@ classdef FFE < handle
end end
function [X] = process(obj, X, D) function [X,Noi] = process(obj, X, D)
% actual processing of the signal (steps 1. - 3.) % actual processing of the signal (steps 1. - 3.)
% 1 normalize RMS % 1 normalize RMS
@@ -65,10 +65,10 @@ classdef FFE < handle
obj.equalize(X.signal, D.signal,obj.mu_tr,obj.epochs_tr,obj.len_tr,training,showviz); obj.equalize(X.signal, D.signal,obj.mu_tr,obj.epochs_tr,obj.len_tr,training,showviz);
% Decision Directed Mode % Decision Directed Mode
N = X.length; n = X.length;
training = 0; training = 0;
showviz = 0; showviz = 0;
[signal,decision]=obj.equalize(X.signal, D.signal,obj.mu_dd,obj.epochs_dd,N,training,showviz); [signal,decision]=obj.equalize(X.signal, D.signal,obj.mu_dd,obj.epochs_dd,n,training,showviz);
% Output Signal % Output Signal
if obj.decide if obj.decide
@@ -76,10 +76,14 @@ classdef FFE < handle
else else
X.signal = signal; X.signal = signal;
end end
X.fs = D.fs; %change sampling frequency of outgoing signal from fdac e.g. 2 sps to symbol spaced = fsym X.fs = D.fs; %change sampling frequency of outgoing signal from fdac e.g. 2 sps to symbol spaced = fsym
lbdesc = [num2str(obj.order),' tap FFE']; lbdesc = [num2str(obj.order),' tap FFE'];
X = X.logbookentry(lbdesc); % append to logbook X = X.logbookentry(lbdesc); % append to logbook
Noi = X;
Noi = X - D;
end end

68
Classes/04_DSP/Sequence Detection/MLSE.m
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@@ -54,10 +54,12 @@ classdef MLSE
obj.DIR(1:DIR_nonzero(1)-1) = []; obj.DIR(1:DIR_nonzero(1)-1) = [];
end end
if length(obj.DIR) == 1 if isscalar(obj.DIR)
obj.DIR = [0 obj.DIR]; obj.DIR = [0 obj.DIR];
end end
obj.DIR = flip(obj.DIR);
% RMS normalization of input data % RMS normalization of input data
data_in = data_in ./ rms(data_in); data_in = data_in ./ rms(data_in);
@@ -95,10 +97,65 @@ classdef MLSE
% i.e. match the rms values of data_in to noise_free_received % i.e. match the rms values of data_in to noise_free_received
if isreal(data_in) if isreal(data_in)
if obj.M == round(obj.M) if obj.M == round(obj.M)
data_in = data_in * rms(noise_free_received,'all','omitnan'); data_in = data_in * rms(noise_free_received(noise_free_received ~= inf),'all','omitnan');
end end
end end
%
% %% Optimized
% % Preallocate and initialize variables
% data_out = NaN(size(data_in)); % output vector
% sum_path_metrics_res = zeros(length(states), length(data_in));
% path_idx = zeros(length(states), length(data_in));
%
% % Precompute repmat size
% num_states = length(states);
% num_signals = numel(noise_free_received);
%
% % First trellis path (initialize)
% sum_path_metrics = zeros(num_states, num_states);
% path_metrics = (abs(data_in(1) - noise_free_received)).^2; % Use broadcasting instead of repmat
% sum_path_metrics = sum_path_metrics + path_metrics; % Compute initial path metrics
%
% [sum_path_metrics_res(:,1), path_idx(:,1)] = min(sum_path_metrics, [], 2); % Best path for first step
%
% % Preallocate path_metrics and sum_path_metrics to avoid reallocating in each loop
% path_metrics = zeros(num_states, num_signals);
%
% % Loop over remaining trellis paths
% for n = 2:length(data_in)
% % Avoid reallocation of sum_path_metrics, reuse the same matrix and update
% previous_sum_path_metrics = sum_path_metrics_res(:,n-1).'; % Transpose once for broadcasting
% sum_path_metrics = repmat(previous_sum_path_metrics, num_states, 1); % Avoid dynamic resizing
%
% % Calculate path metrics using broadcasting
% path_metrics = (abs(data_in(n) - noise_free_received)).^2; % Avoid repmat
%
% % Update sum path metrics
% sum_path_metrics = sum_path_metrics + path_metrics;
%
% % Find the best path for each state and store results
% [sum_path_metrics_res(:,n), path_idx(:,n)] = min(sum_path_metrics, [], 2);
% end
%
% %% Traceback
% ideal_path = NaN(1, length(data_in)+1); % Preallocate ideal path
% [~, ideal_path(length(data_in)+1)] = min(sum_path_metrics_res(:,length(data_in))); % Start from final state
%
% % Trace back through trellis
% for h = length(data_in):-1:1
% ideal_path(h) = path_idx(ideal_path(h+1),h); % Follow the best path back
% end
%
% % Extract the output indices
% idx_out = ideal_path(2:end);
% OLD
% initilaize the output vector % initilaize the output vector
data_out = NaN(size(data_in)); data_out = NaN(size(data_in));
@@ -132,12 +189,17 @@ classdef MLSE
ideal_path(h) = path_idx(ideal_path(h+1),h); ideal_path(h) = path_idx(ideal_path(h+1),h);
end end
idx_out = ideal_path(1:length(data_in)); idx_out = ideal_path(2:length(data_in)+1);
if obj.duobinary_output if obj.duobinary_output
%use duobinary encoder, output is already scaled inside this %use duobinary encoder, output is already scaled inside this
%one %one
data_out = Duobinary().encode(first_sym(idx_out)); data_out = Duobinary().encode(first_sym(idx_out));
else else
% %
data_out(1:length(data_in)) = first_sym(idx_out); data_out(1:length(data_in)) = first_sym(idx_out);

43
Tests/01_transmit/PAMmapper_test.m
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@@ -1,61 +1,68 @@
classdef PAMmapper_test < matlab.unittest.TestCase classdef PAMmapper_test < matlab.unittest.TestCase
properties properties
Digi_Mod
Tx_bits Tx_bits
Rx_bits PAMmapper
% M = 8; % Modulation order end
fsym = 112e9; % Symbol rate
properties (MethodSetupParameter)
% Define method-level parameters for PRBS and bit pattern
useprbs = struct('false', 0, 'true', 1); % variations: {0, 1}
M = struct('M2', 2, 'M4', 4, 'M6', 6, 'M8', 8); % variations: {2, 4, 6, 8}
O = struct('O10', 10, 'O15', 15, 'O17', 17); % variations: {10, 15, 17}
end end
properties (TestParameter) properties (TestParameter)
M = {4,6,8}; % Define test-level parameters for M and O
end end
methods (TestMethodSetup) methods (TestMethodSetup)
function setupModulation(testCase)
% Setup PRBS and bit pattern for the test case function setupModulation(testCase, useprbs, M, O)
O = 10; % Order of PRBS % Setup PRBS and bit pattern for the test case using parameters
% Setup PRBS parameters
N = 2^(O-1); % Length of PRBS N = 2^(O-1); % Length of PRBS
useprbs = 1; % Flag to use PRBS
randkey = 1; % Random key for random stream randkey = 1; % Random key for random stream
[~, seed] = prbs(O, 1); % Initialize first seed of PRBS [~, seed] = prbs(O, 1); % Initialize first seed of PRBS
bitpattern = []; bitpattern = [];
if useprbs if useprbs
for i = 1:log2(testCase.M) for i = 1:log2(M)
[bitpattern(:, i), seed] = prbs(O, N, seed); [bitpattern(:, i), seed] = prbs(O, N, seed);
end end
else else
s = RandStream('twister', 'Seed', randkey); s = RandStream('twister', 'Seed', randkey);
for i = 1:log2(testCase.M) for i = 1:log2(M)
bitpattern(:, i) = randi(s, [0 1], N, 1); bitpattern(:, i) = randi(s, [0 1], N, 1);
end end
end end
if testCase.M == 6 if M == 6
bitpattern = reshape(bitpattern, [], 1); bitpattern = reshape(bitpattern, [], 1);
bitpattern = bitpattern(1:end-mod(length(bitpattern), 5)); bitpattern = bitpattern(1:end-mod(length(bitpattern), 5));
end end
testCase.Tx_bits = Informationsignal(bitpattern); testCase.Tx_bits = Informationsignal(bitpattern);
testCase.Digi_Mod = PAMmapper(testCase.M, 0); testCase.PAMmapper = PAMmapper(M, 0);
end end
end end
methods (Test) methods (Test, ParameterCombination = 'sequential')
function testBackToBackMapping(testCase) % Test with sequential combination of parameters
function testBackToBackMapping(testCase, M, useprbs, O)
% Test Bits -> Symbols -> Bits (Back-to-Back Mapping) % Test Bits -> Symbols -> Bits (Back-to-Back Mapping)
% Map bits to symbols % Map bits to symbols
Symbols = testCase.Digi_Mod.map(testCase.Tx_bits); Symbols = testCase.PAMmapper.map(testCase.Tx_bits);
% Demap symbols back to bits % Demap symbols back to bits
testCase.Rx_bits = testCase.Digi_Mod.demap(Symbols); Rx_bits = testCase.PAMmapper.demap(Symbols);
% Validate BER is zero % Validate BER is zero
[~, error_num, ber, ~] = calc_ber(testCase.Tx_bits.signal, testCase.Rx_bits.signal, ... [~, error_num, ber, ~] = calc_ber(testCase.Tx_bits.signal, Rx_bits.signal, ...
"skip_front", 0, "skip_end", 0, "returnErrorLocation", 1); "skip_front", 0, "skip_end", 0, "returnErrorLocation", 1);
% Assert that BER is zero % Assert that BER is zero

107
Tests/04_DSP/Coding/Duobinary_test.m
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@@ -1,11 +1,108 @@
classdef Duobinary_test < matlab.unittest.TestCase classdef Duobinary_test < matlab.unittest.TestCase
% Test class for Duobinary
properties
%genereal properties of the test
ber
errors
errorIndice
numbits
numsymbols
end
properties (MethodSetupParameter)
% Define method-level parameters for PRBS and bit pattern
% i.e.: useprbs = {0,1};
useprbs = struct('true', 1,'false', 0); % variations: {0, 1}
M = struct('M2', 2, 'M4', 4, 'M6', 6, 'M8', 8); % variations: {2, 4, 6, 8}
O = struct('O10', 10,'O11', 11,'O12', 12,'O13', 13, 'O15', 15, 'O17', 17); % variations: {10, 15, 17}
end
properties (TestParameter)
% Define test-level parameters for M and O
end
methods (TestMethodSetup, ParameterCombination = 'pairwise')
function setupTest(testCase, useprbs, M, O)
randkey = 1;
datarate = 448e9;
fsym = round(datarate / log2(M)) ;
%%%%% PRBS Generation in correct shape for Modulation Format %%%%%%
N = 2^O; %length of prbs
[~,seed] = prbs(O,1); %initialize first seed of prbs
bitpattern=[];
if useprbs
for i = 1:log2(M)
[bitpattern(:,i),seed] = prbs(O,N,seed);
end
else
s = RandStream('twister','Seed',randkey);
for i = 1:log2(M)
bitpattern(:,i) = randi(s,[0 1], N, 1);
end
end
if M == 6
bitpattern = reshape(bitpattern,[],1);
bitpattern = bitpattern(1:end-mod(length(bitpattern),5));
end
testCase.numbits = length(bitpattern);
Tx_bits = Informationsignal(bitpattern);
Symbols_tx = PAMmapper(M,0).map(Tx_bits);
Symbols_tx.fs = fsym;
testCase.numsymbols = length(Symbols_tx);
Symbols_tx = PAMmapper(M,0).map(Tx_bits);
Symbols_tx.fs = fsym;
Symbols = Duobinary().precode(Symbols_tx);
Symbols = Duobinary().encode(Symbols);
Symbols = Duobinary().decode(Symbols);
Rx_bits = PAMmapper(M,0).demap(Symbols);
[bits,testCase.errors,testCase.ber,testCase.errorIndice] = calc_ber(Tx_bits.signal,Rx_bits.signal,"skip_front",0,"skip_end",0,"returnErrorLocation",1);
end
end
methods (Test) methods (Test)
function testExample(testCase) % Test with sequential combination of parameters
% Example test case for Duobinary
% Add your test code here function checkBerZero(testCase, useprbs, M, O)
testCase.verifyTrue(true); % Assert that BER is zero
testCase.verifyEqual(testCase.ber, 0, ['Numer of Errors is not zero, found ',num2str(testCase.errors), ' errors at position ', num2str(testCase.errorIndice),' out of ', num2str(2^O)]);
end end
function checkBerCloseToZero(testCase, useprbs, M, O)
testCase.verifyLessThan(testCase.errors, 5, ['Found more than 5 errors. Found ',num2str(testCase.errors),' errors.']);
% if ~isempty(testCase.errorIndice)
% testCase.verifyEqual(testCase.errorIndice, 2^O , ['Error is NOT at the End but at: ', num2str(testCase.errorIndice),' of ', num2str(2^O)]);
% testCase.verifyEqual(testCase.errorIndice,1, ['Error is NOT at the Beginning but at: ', num2str(testCase.errorIndice),' of ', num2str(2^O)]);
% end
end
function checkSystemFailure(testCase, useprbs, M, O)
testCase.verifyLessThan(testCase.ber, 0.1, ['BER is higher than 10%. Soemthing is completely wrong! (BER is ',num2str(testCase.ber),')']);
end
end end
end end

50
Tests/Testclass_template.m Normal file
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@@ -0,0 +1,50 @@
classdef Testclass_template < matlab.unittest.TestCase
properties
%genereal properties of the test
end
properties (MethodSetupParameter)
% Define method-level parameters for PRBS and bit pattern
% i.e.: useprbs = {0,1};
useprbs = {0,1};
M = {2,4,6};
end
properties (TestParameter)
% Define test-level parameters for M and O
end
methods (TestMethodSetup)
function setupTest(testCase, useprbs, M)
% Setup everything that is somehow reguired for the test,
% include the MethodSetupParameters here as arguments
end
end
methods (Test)
% Test with sequential combination of parameters
function myTest(testCase, M, useprbs)
% Write the actual test,
% include the MethodSetupParameters here as arguments
% Assert that BER is zero
testCase.verifyEqual(M, M, 'error message');
testCase.verifyEqual(useprbs, useprbs, 'error message');
end
% Test with sequential combination of parameters
function anotherTest(testCase, M)
% Write the actual test,
% include the MethodSetupParameters here as arguments
% Assert that BER is zero
testCase.verifyEqual(M, M, 'error message');
testCase.verifyClass(M,'double');
end
end
end

0
projects/400G_FTN_setups/duobinary_example.m Normal file
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projects/400G_FTN_setups/duobinary_example.mlx
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1
projects/AWG_characterization/output_power.m
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@@ -16,6 +16,7 @@ for i = 1:log2(M)
[bitpattern(:,i),seed] = prbs(O,N,seed); [bitpattern(:,i),seed] = prbs(O,N,seed);
end end
if M == 6 if M == 6
bitpattern = reshape(bitpattern,[],1); bitpattern = reshape(bitpattern,[],1);
bitpattern = bitpattern(1:end-mod(length(bitpattern),5)); bitpattern = bitpattern(1:end-mod(length(bitpattern),5));

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projects/standard_system/400G_simulative_setup.mat
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89
projects/standard_system/imdd_minimal_2.m
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@@ -2,11 +2,17 @@
%% Parameter to simulate and save %% Parameter to simulate and save
params = struct; params = struct;
params.M = [4]; params.M = [8];
params.datarate = [300]; params.datarate = [448];
params.rop = [0]; params.rop = [-12:0];
precomp_mode = 0; %0=do nothing ; 1= measure; 2=precomp active
postfilter = 0; % noise whiten. approach -> Postfilter + MLSE
db_precode = 1;
db_encode = 1;
db_channelapproach = 0;
precomp_mode = 2; %0=do nothing ; 1= measure; 2=precomp active
if ismac if ismac
precomp_path = "/Users/silasoettinghaus/Documents/MATLAB/imdd_simulation/projects/standard_system"; precomp_path = "/Users/silasoettinghaus/Documents/MATLAB/imdd_simulation/projects/standard_system";
@@ -24,7 +30,7 @@ wh = DataStorage(params);
wh.addStorage("ber_ffe"); wh.addStorage("ber_ffe");
%% Init Params %% Init Params
link_length = 0; %meter link_length = 1000; %meter
pn_key = 2; pn_key = 2;
laser_linewidth = 0; laser_linewidth = 0;
@@ -34,7 +40,6 @@ cnt=0;
disp(['Start Simulation of ',num2str(endcnt),' loops...']) disp(['Start Simulation of ',num2str(endcnt),' loops...'])
tic tic
for M = wh.parameter.M.values for M = wh.parameter.M.values
for datarate = wh.parameter.datarate.values for datarate = wh.parameter.datarate.values
@@ -50,32 +55,34 @@ for M = wh.parameter.M.values
%%%%% Symbol Generation %%%%%% %%%%% Symbol Generation %%%%%%
[Digi_sig,Symbols,Bits] = PAMsource("fsym",fsym,"M",M,"order",18,"useprbs",0,... [Digi_sig,Symbols,Bits] = PAMsource("fsym",fsym,"M",M,"order",18,"useprbs",0,...
"fs_out",M8199.fdac,"applyclipping",1,"clipfactor",1.7,... "fs_out",M8199.fdac,"applyclipping",1,"clipfactor",1.5,...
"applypulseform",0,"pulseformer",Pform,"randkey",pn_key,... "applypulseform",0,"pulseformer",Pform,"randkey",pn_key,...
"db_precode",0,... "db_precode",db_precode,"db_encode",db_encode,...
"mrds_code",usemrds,"mrds_blocklength",512).process(); "mrds_code",usemrds,"mrds_blocklength",512).process();
Digi_sig.eye(fsym,M); % Digi_sig.eye(fsym,M);
Digi_sig.spectrum("fignum",11,"displayname",'before precomp'); Digi_sig.spectrum("fignum",123434,"displayname",'Digital Tx Signal');
if precomp_mode == 1 if precomp_mode == 1
freqresp = ChannelFreqResp("Nacq",1024,"Navg",64,"Ncp",63,'f_ref',Digi_sig.fs); freqresp = ChannelFreqResp("Nacq",1024,"Navg",64,"Ncp",63,'f_ref',Digi_sig.fs);
Digi_sig = freqresp.buildOFDM(); Digi_sig = freqresp.buildOFDM();
elseif precomp_mode == 2 elseif precomp_mode == 2
Digi_sig = ChannelFreqResp("Nacq",1024,"Navg",64,"Ncp",63,'f_ref',Digi_sig.fs).precomp(Digi_sig,'maxampdb',3,'loadPath',precomp_path,'fileName',precomp_fn); Digi_sig = ChannelFreqResp("Nacq",1024,"Navg",64,"Ncp",63,'f_ref',Digi_sig.fs).precomp(Digi_sig,'maxampdb',1,'loadPath',precomp_path,'fileName',precomp_fn);
Digi_sig.spectrum("fignum",11,"displayname",'after precomp'); Digi_sig.spectrum("fignum",11,"displayname",'after precomp');
end end
%%%%% AWG %%%%%% %%%%% AWG %%%%%%
El_sig = M8199.process(Digi_sig); El_sig = M8199.process(Digi_sig);
% El_sig.spectrum("displayname",'el','fignum',123434);
% El_sig.signal = awgn(El_sig.signal,-3,'measured',pn_key); % El_sig.signal = awgn(El_sig.signal,-3,'measured',pn_key);
%%%%% Lowpass el. components %%%%%% %%%%% Lowpass el. components %%%%%%
El_sig = Filter('filtdegree',2,"f_cutoff",60e9,"fs",fdac*kover,"filterType",filtertypes.butterworth,"active",true).process(El_sig); El_sig = Filter('filtdegree',2,"f_cutoff",60e9,"fs",fdac*kover,"filterType",filtertypes.butterworth,"active",true).process(El_sig);
%%%%% Electrical Driver Amplifier %%%%%% %%%%% Electrical Driver Amplifier %%%%%%
El_sig = Amplifier("amp_mode","ideal_no_noise","gain_mode","gain","amplification_db",9).process(El_sig); El_sig = Amplifier("amp_mode","ideal_no_noise","gain_mode","gain","amplification_db",3).process(El_sig);
% El_sig = El_sig.setPower(6,"dBm"); % El_sig = El_sig.setPower(6,"dBm");
fprintf('Driver output power: %s dBm\n', num2str(El_sig.power)); fprintf('Driver output power: %s dBm\n', num2str(El_sig.power));
@@ -90,9 +97,8 @@ for M = wh.parameter.M.values
[Opt_sig] = EML("mode",eml_mode.im_cosinus,"power",3,"fsimu",El_sig.fs,"lambda",1290,"bias",vbias,"u_pi",u_pi,"linewidth",laser_linewidth,"randomkey",pn_key).process(El_sig); [Opt_sig] = EML("mode",eml_mode.im_cosinus,"power",3,"fsimu",El_sig.fs,"lambda",1290,"bias",vbias,"u_pi",u_pi,"linewidth",laser_linewidth,"randomkey",pn_key).process(El_sig);
% Opt_sig.eye(fsym,7);
% Opt_sig.eye(fsym,M); %
% %
% figure(10) % figure(10)
% hold on % hold on
% scatter(El_sig.signal(1:100000)+vbias,(abs(Opt_sig.signal(1:100000)).^2)*1e3,0.1,'.','DisplayName','Modulator TF') % scatter(El_sig.signal(1:100000)+vbias,(abs(Opt_sig.signal(1:100000)).^2)*1e3,0.1,'.','DisplayName','Modulator TF')
@@ -104,6 +110,8 @@ for M = wh.parameter.M.values
Optfilter = Filter('filtdegree',6,"f_cutoff",fsym.*0.7,"fs",fdac*kover,"filterType",filtertypes.gaussian,"active",true); Optfilter = Filter('filtdegree',6,"f_cutoff",fsym.*0.7,"fs",fdac*kover,"filterType",filtertypes.gaussian,"active",true);
Opt_sig = Optfilter.process(Opt_sig); Opt_sig = Optfilter.process(Opt_sig);
% Opt_sig.spectrum("fignum",122,"displayname",['Tx SPectrum; PAM ',num2str(M)]);
Opt_sig = Amplifier("amp_mode","ideal_no_noise","gain_mode","output_power","amplification_db",0).process(Opt_sig); Opt_sig = Amplifier("amp_mode","ideal_no_noise","gain_mode","output_power","amplification_db",0).process(Opt_sig);
i_ = wh.parameter.rop.length; i_ = wh.parameter.rop.length;
@@ -143,19 +151,54 @@ for M = wh.parameter.M.values
freqresp.plot(); freqresp.plot();
end end
Scpe_sig.spectrum("displayname",'After Scope','fignum',123434);
%%%%%% Sample to 2x fsym %%%%%% %%%%%% Sample to 2x fsym %%%%%%
Scpe_sig = Scpe_sig.resample("fs_in",fadc,"fs_out",2*fsym); Scpe_sig = Scpe_sig.resample("fs_in",fadc,"fs_out",2*fsym);
%%%%%% Sync Rx signal with reference %%%%%% %%%%%% Sync Rx signal with reference %%%%%%
[Scpe_sig,D,cuts] = Scpe_sig.tsynch("reference",Symbols,"fs_ref",fsym); [Scpe_sig,D,cuts] = Scpe_sig.tsynch("reference",Symbols,"fs_ref",fsym);
%%%%% EQUALIZE %%%%%% %%%%% EQUALIZE %%%%%%
% Eq = FFE("epochs_tr",5,"epochs_dd",5,"len_tr",4096*2,"mu_dd",1e-4,"mu_tr",0,"order",25,"sps",2,"decide",0);
Eq = FFE("epochs_tr",5,"epochs_dd",5,"len_tr",4096*2,"mu_dd",1e-4,"mu_tr",0,"order",25,"sps",2,"decide",1);
%Eq = VNLE("epochs_tr",5,"epochs_dd",5,"len_tr",4096*2,"mu_dd",[0.0004 0.0005 0.0006],"mu_tr",0,"order",[50,7,7],"sps",2,"decide",1); %Eq = VNLE("epochs_tr",5,"epochs_dd",5,"len_tr",4096*2,"mu_dd",[0.0004 0.0005 0.0006],"mu_tr",0,"order",[50,7,7],"sps",2,"decide",1);
[EQ_sig] = Eq.process(Scpe_sig,Symbols);
if db_channelapproach
% ref symbols and transm. sequence are precoded
[EQ_sig, Noi] = Eq.process(Scpe_sig,Duobinary().encode(Symbols));
else
[EQ_sig, Noi] = Eq.process(Scpe_sig,Symbols);
end
if db_encode || db_channelapproach
EQ_sig = MLSE("DIR",[1,1],"duobinary_output",1,"M",M,"trellis_states",PAMmapper(M,0).levels).process(EQ_sig);
EQ_sig = Duobinary().decode(EQ_sig);
end
if postfilter
% Noi.spectrum("displayname",'Noise Spectrum','fignum',1234);
% EQ_sig.spectrum("displayname","Signal Spectrum","fignum",1234);
nc = 2;
burg_coeff = arburg(Noi.signal,nc);
EQ_sig = EQ_sig.filter(burg_coeff,1);
% EQ_sig.spectrum("displayname","Signal Spectrum after Postfilter","fignum",1234);
tic
EQ_sig = MLSE("DIR",burg_coeff,"duobinary_output",0,"M",M,"trellis_states",PAMmapper(M,0).levels).process(EQ_sig);
toc
% EQ_sig.spectrum("displayname","Signal Spectrum after MLSE","fignum",1234);
if 0
[h,w] = freqz(1,burg_coeff,length(Noi),"whole",Noi.fs);
h = h/max(abs(h));
hold on
w_ = (w - Noi.fs/2);
plot(w_.*1e-9,20*log10(fftshift(h)),'DisplayName',['', num2str(nc), ' coefficients for burg alg.']);
end
end
Rx_bits = PAMmapper(M,0).demap(EQ_sig); Rx_bits = PAMmapper(M,0).demap(EQ_sig);
[~,errors_bm,ber_ffe(i),errors] = calc_ber(Rx_bits.signal,Bits.signal,"skip_front",100,"skip_end",150,"returnErrorLocation",1); [~,errors_bm,ber_ffe(i),errors] = calc_ber(Rx_bits.signal,Bits.signal,"skip_front",100,"skip_end",150,"returnErrorLocation",1);
disp(['BER: ',sprintf('%.1E',ber_ffe(i)),' - - ROP: ',num2str(patten(i)),'dBm - - PAM-',num2str(M),' - - ',num2str(fsym*1e-9),' GBd']); disp(['BER: ',sprintf('%.1E',ber_ffe(i)),' - - ROP: ',num2str(patten(i)),'dBm - - PAM-',num2str(M),' - - ',num2str(fsym*1e-9),' GBd']);
@@ -170,19 +213,21 @@ for M = wh.parameter.M.values
end end
toc toc
disp(['Simulated: ',num2str(cnt/endcnt*100),' %']);
% wh.save('C:\Users\Silas\Documents\MATLAB\imdd_simulation\projects\MPI_August\auswertung\') % wh.save('C:\Users\Silas\Documents\MATLAB\imdd_simulation\projects\MPI_August\auswertung\')
end end
end end
disp('Simulation Done!')
cols = linspecer(8); cols = linspecer(8);
%cnt = cnt+1; %cnt = cnt+1;
ber_ffe = wh.getStoValue('ber_ffe',M,datarate,wh.parameter.rop.values); ber_ffe = wh.getStoValue('ber_ffe',M,datarate,wh.parameter.rop.values);
% Create the initial plot % Create the initial plot
figure(44); figure(44);

9
projects/standard_system/sensitivity_analysis.m
View File

@@ -2,6 +2,9 @@ M = wh.parameter.M.values(1);
datarates = wh.parameter.datarate.values; datarates = wh.parameter.datarate.values;
rop = wh.parameter.rop.values; rop = wh.parameter.rop.values;
clear("sens_ffe")
col = flip(cbrewer2("RdYlGn",numel(datarates)));
cnt = 1; cnt = 1;
for dr = datarates for dr = datarates
@@ -10,9 +13,9 @@ for dr = datarates
sens_ffe(cnt) = getIntersection(ber_ffe,rop); sens_ffe(cnt) = getIntersection(ber_ffe,rop);
figure(112) figure(116)
hold on hold on
plot(rop,ber_ffe,"LineWidth",0.5,"LineStyle","-","Marker",".","MarkerSize",15,"DisplayName",['FFE only; ',num2str(dr), ' Gbps']); plot(rop,ber_ffe,"LineWidth",0.5,"LineStyle","-","Marker",".","MarkerSize",15,"DisplayName",['Postfilter + MLSE; ',num2str(dr), ' Gbps'],'Color',col(cnt,:));
yline(3.8e-3,'DisplayName','HD-FEC','LineStyle','--','HandleVisibility','off'); yline(3.8e-3,'DisplayName','HD-FEC','LineStyle','--','HandleVisibility','off');
xlabel('Received Optical Power (dBm)'); xlabel('Received Optical Power (dBm)');
ylabel('Bit Error Rate (BER)'); ylabel('Bit Error Rate (BER)');
@@ -28,7 +31,7 @@ for dr = datarates
end end
figure(223); figure(22);
hold on; % Retain the plot so new points can be added without complete redraw hold on; % Retain the plot so new points can be added without complete redraw
plot(datarates,sens_ffe,"LineWidth",1,"LineStyle","-","Marker",".","MarkerSize",10,"DisplayName",['Linewidth: ',num2str(laser_linewidth.*1e-6),' MHz']); plot(datarates,sens_ffe,"LineWidth",1,"LineStyle","-","Marker",".","MarkerSize",10,"DisplayName",['Linewidth: ',num2str(laser_linewidth.*1e-6),' MHz']);
xlabel('Signal to Interference Ratio (dB)'); xlabel('Signal to Interference Ratio (dB)');

54
test/TestRand_examplecode.m Normal file
View File

@@ -0,0 +1,54 @@
classdef TestRand_examplecode < matlab.unittest.TestCase
properties (ClassSetupParameter)
generator = {'twister','combRecursive','multFibonacci'};
end
properties (MethodSetupParameter)
seed = {0,123,4294967295};
end
properties (TestParameter)
dim1 = struct('small',1,'medium',2,'large',3);
dim2 = struct('small',2,'medium',3,'large',4);
dim3 = struct('small',3,'medium',4,'large',5);
type = {'single','double'};
end
methods (TestClassSetup)
function classSetup(testCase,generator)
orig = rng;
testCase.addTeardown(@rng,orig)
rng(0,generator)
end
end
methods (TestMethodSetup)
function methodSetup(testCase,seed)
orig = rng;
testCase.addTeardown(@rng,orig)
rng(seed)
end
end
methods (Test, ParameterCombination = 'sequential')
function testSize(testCase,dim1,dim2,dim3)
testCase.verifySize(rand(dim1,dim2,dim3),[dim1 dim2 dim3])
end
end
methods (Test, ParameterCombination = 'pairwise')
function testRepeatable(testCase,dim1,dim2,dim3)
state = rng;
firstRun = rand(dim1,dim2,dim3);
rng(state)
secondRun = rand(dim1,dim2,dim3);
testCase.verifyEqual(firstRun,secondRun)
end
end
methods (Test)
function testClass(testCase,dim1,dim2,type)
testCase.verifyClass(rand(dim1,dim2,type),type)
end
end
end

55
test/duobinary_minimal_example.m
View File

@@ -1,11 +1,12 @@
useprbs = 1; useprbs = 1;
M = 8; M = 6;
randkey = 1; randkey = 1;
fsym = 112e9; datarate = 448e9;
fsym = round(datarate / log2(M)) ;
%%%%% PRBS Generation in correct shape for Modulation Format %%%%%% %%%%% PRBS Generation in correct shape for Modulation Format %%%%%%
O = 18; %order of prbs O = 17; %order of prbs
N = 2^(O-1); %length of prbs N = 2^(O); %length of prbs
[~,seed] = prbs(O,1); %initialize first seed of prbs [~,seed] = prbs(O,1); %initialize first seed of prbs
bitpattern=[]; bitpattern=[];
@@ -34,12 +35,6 @@ Symbols = Duobinary().precode(Symbols_tx);
Symbols = Duobinary().encode(Symbols); Symbols = Duobinary().encode(Symbols);
% Symbols.spectrum("displayname","db","fignum",12)
% Symbols = Duobinary().feedbackdetector(Symbols);
% Symbols.eye(fsym,M);
Symbols = Duobinary().decode(Symbols); Symbols = Duobinary().decode(Symbols);
Rx_bits = PAMmapper(M,0).demap(Symbols); Rx_bits = PAMmapper(M,0).demap(Symbols);
@@ -48,15 +43,35 @@ Rx_bits = PAMmapper(M,0).demap(Symbols);
disp(['BER: ',sprintf('%.1E',ber),' - - PAM-',num2str(M)]); disp(['BER: ',sprintf('%.1E',ber),' - - PAM-',num2str(M)]);
% %
figure;hold on
subplot(2,1,1)
title('Bits Compare') figure(3);
stairs(Rx_bits.signal(1:100,1),'LineWidth',2,'DisplayName','Rx Bits') clf
stairs(Tx_bits.signal(1:100,1),'LineStyle',':','LineWidth',2,'DisplayName','Tx Bits'); %sgtitle(['BER: ',num2str(ber),' // Error is at position: ',num2str(error_pos),''])
legend subplot(2,2,1)
subplot(2,1,2)
hold on hold on
title('Symbols Compare') title('First Bits')
stairs(Symbols.signal(1:100,1),'LineStyle',':','LineWidth',2,'DisplayName','Rx Symbols'); stairs(Tx_bits.signal(1:100,1),'LineStyle','-','LineWidth',2,'DisplayName','Tx Bits');
stairs(Symbols_tx.signal(1:100,1),'LineWidth',2,'DisplayName','Tx Symbols') stairs(Rx_bits.signal(1:100,1),'LineWidth',2,'DisplayName','Rx Bits','LineStyle',':')
legend
subplot(2,2,2)
title('Last Bits')
hold on
stairs(Tx_bits.signal(end-50:end,1),'LineStyle','-','LineWidth',2,'DisplayName','Tx Bits');
stairs(Rx_bits.signal(end-50:end,1),'LineWidth',2,'DisplayName','Rx Bits','LineStyle',':')
legend
subplot(2,2,3)
hold on
title('First Symbols Compare')
stairs(Symbols_tx.signal(1:100,1),'LineWidth',2,'DisplayName','Tx Symbols','LineStyle','-')
stairs(Symbols.signal(1:100,1),'LineStyle',':','LineWidth',2,'DisplayName','Rx Symbols');
legend
subplot(2,2,4)
hold on
title('Last Symbols Compare')
stairs(Symbols_tx.signal(end-50:end,1),'LineWidth',2,'DisplayName','Tx Symbols','LineStyle','-')
stairs(Symbols.signal(end-50:end,1),'LineStyle',':','LineWidth',2,'DisplayName','Rx Symbols');
legend legend

5
test/mapping_minimal_example.m
View File

@@ -30,8 +30,6 @@ end
Tx_bits = Informationsignal(bitpattern); Tx_bits = Informationsignal(bitpattern);
%%%%% ACTUAL TEST: Back to Back Mapping: Bits -> Symbols and Symbols -> Bits %%%%%% %%%%% ACTUAL TEST: Back to Back Mapping: Bits -> Symbols and Symbols -> Bits %%%%%%
Digi_Mod = PAMmapper(M,0); Digi_Mod = PAMmapper(M,0);
@@ -41,14 +39,11 @@ Symbols = Digi_Mod.map(Tx_bits);
Rx_bits = PAMmapper(M,0).demap(Symbols); Rx_bits = PAMmapper(M,0).demap(Symbols);
%%%%% VALIDATION: BER is required to be zero %%%%%% %%%%% VALIDATION: BER is required to be zero %%%%%%
[~,error_num,ber,error_pos] = calc_ber(Tx_bits.signal,Rx_bits.signal,"skip_front",0,"skip_end",0,"returnErrorLocation",1); [~,error_num,ber,error_pos] = calc_ber(Tx_bits.signal,Rx_bits.signal,"skip_front",0,"skip_end",0,"returnErrorLocation",1);
%%%%% For User: Show Debug Info and Results %%%%%% %%%%% For User: Show Debug Info and Results %%%%%%
if viewresults if viewresults

47
test/mlse_minimal_example.m
View File

@@ -1,6 +1,6 @@
useprbs = 1; useprbs = 0;
M = 8; M = 4;
randkey = 1; randkey = 2;
fsym = 112e9; fsym = 112e9;
%%%%% PRBS Generation in correct shape for Modulation Format %%%%%% %%%%% PRBS Generation in correct shape for Modulation Format %%%%%%
@@ -31,29 +31,50 @@ Digi_Mod = PAMmapper(M,0);
Symbols_tx = Digi_Mod.map(Tx_bits); Symbols_tx = Digi_Mod.map(Tx_bits);
Symbols_tx.fs = fsym; Symbols_tx.fs = fsym;
Symbols = Duobinary().precode(Symbols_tx); if 0
Symbols = Duobinary().encode(Symbols); Symbols = Duobinary().precode(Symbols_tx);
Symbols = MLSE("DIR",[1,1],"duobinary_output",1,"trellis_states",Digi_Mod.levels,"M",M).process(Symbols); Symbols = Duobinary().encode(Symbols);
Symbols = Duobinary().decode(Symbols); Symbols = MLSE("DIR",[1 1],"duobinary_output",1,"trellis_states",Digi_Mod.levels,"M",M).process(Symbols);
Rx_bits = PAMmapper(M,0).demap(Symbols); Symbols = Duobinary().decode(Symbols);
else
cnt = 1;
Symbols = Symbols_tx;
coeff = [1,0.5,0.2,0.1];
Symbols.signal = filter(coeff, 1, Symbols.signal);
Symbols.spectrum("fignum",129,"displayname",['coeff:',num2str(coeff)]);
Symbols = MLSE("DIR",coeff,"duobinary_output",0,"trellis_states",Digi_Mod.levels,"M",M).process(Symbols);
Rx_bits = PAMmapper(M,0).demap(Symbols);
[~,error_num,ber,error_pos] = calc_ber(Tx_bits.signal,Rx_bits.signal,"skip_front",0,"skip_end",0,"returnErrorLocation",1);
disp(['BER: ',sprintf('%.1E',ber),' - - PAM-',num2str(M)]);
end
[~,error_num,ber,error_pos] = calc_ber(Tx_bits.signal,Rx_bits.signal,"skip_front",0,"skip_end",0,"returnErrorLocation",1);
disp(['BER: ',sprintf('%.1E',ber),' - - PAM-',num2str(M)]);
% %
figure;hold on figure(494)
clf
subplot(2,1,1) subplot(2,1,1)
title('Bits Compare') title('Bits Compare')
hold on
stairs(Rx_bits.signal(1:100,1),'LineWidth',2,'DisplayName','Rx Bits') stairs(Rx_bits.signal(1:100,1),'LineWidth',2,'DisplayName','Rx Bits')
stairs(Tx_bits.signal(1:100,1),'LineStyle',':','LineWidth',2,'DisplayName','Tx Bits'); stairs(Tx_bits.signal(1:100,1),'LineStyle',':','LineWidth',2,'DisplayName','Tx Bits');
legend legend
subplot(2,1,2) subplot(2,1,2)
hold on hold on
title('Symbols Compare') title('Symbols Compare')
stairs(Symbols.signal(1:100,1),'LineStyle',':','LineWidth',2,'DisplayName','Rx Symbols'); stairs(Symbols.signal(1:100,1),'LineStyle','-','LineWidth',2,'DisplayName','Rx Symbols');
stairs(Symbols_tx.signal(1:100,1),'LineWidth',2,'DisplayName','Tx Symbols') stairs(Symbols_tx.signal(1:100,1),'LineWidth',2,'DisplayName','Tx Symbols','LineStyle',':')
legend legend

98
test/test_modulation.m
View File

@@ -1,36 +1,74 @@
classdef test_modulation < matlab.unittest.TestCase
properties
Tx_bits
Digi_Mod
end
properties (MethodSetupParameter)
% Define method-level parameters for PRBS and bit pattern
useprbs = struct('false', 0, 'true', 1); % variations: {0, 1}
M = struct('M2', 2, 'M4', 4, 'M6', 6, 'M8', 8); % variations: {2, 4, 6, 8}
O = struct('O10', 10, 'O15', 15, 'O17', 17); % variations: {10, 15, 17}
end
properties (TestParameter)
% Define test-level parameters for M and O
O = 10; %order of prbs end
N = 2^(O-1); %length of prbs
[~,seed] = prbs(O,1); %initialize first seed of prbs methods (TestMethodSetup)
bitpattern=[];
M=6; function setupModulation(testCase, useprbs, M, O)
% Setup PRBS and bit pattern for the test case using parameters
% Setup PRBS parameters
N = 2^(O-1); % Length of PRBS
randkey = 1; % Random key for random stream
[~, seed] = prbs(O, 1); % Initialize first seed of PRBS
bitpattern = [];
if useprbs
for i = 1:log2(M)
[bitpattern(:, i), seed] = prbs(O, N, seed);
end
else
s = RandStream('twister', 'Seed', randkey);
for i = 1:log2(M)
bitpattern(:, i) = randi(s, [0 1], N, 1);
end
end
if M == 6
bitpattern = reshape(bitpattern, [], 1);
bitpattern = bitpattern(1:end-mod(length(bitpattern), 5));
end
testCase.Tx_bits = Informationsignal(bitpattern);
testCase.Digi_Mod = PAMmapper(M, 0);
end
end
methods (Test, ParameterCombination = 'sequential')
% Test with sequential combination of parameters
function testBackToBackMapping(testCase, M, useprbs, O)
% Test Bits -> Symbols -> Bits (Back-to-Back Mapping)
% Map bits to symbols
Symbols = testCase.Digi_Mod.map(testCase.Tx_bits);
% Demap symbols back to bits
Rx_bits = testCase.Digi_Mod.demap(Symbols);
% Validate BER is zero
[~, error_num, ber, ~] = calc_ber(testCase.Tx_bits.signal, Rx_bits.signal, ...
"skip_front", 0, "skip_end", 0, "returnErrorLocation", 1);
% Assert that BER is zero
testCase.verifyEqual(ber, 0, 'BER should be zero');
testCase.verifyEqual(error_num, 0, 'No errors should occur in the mapping process');
end
end
for i = 1:log2(M)
[bitpattern(:,i),seed] = prbs(O,N,seed);
end end
if M == 6
bitpattern = reshape(bitpattern,[],1);
end
% [bitpattern,seed] = prbs(O,N,seed);
% %
% bitpattern = bitpattern';
% 2 ) Build Inf. signal class
bits = Informationsignal(bitpattern);
% 3) Digi modulation -> PAM-M signal
digimod_out = PAMmapper(M,0).map(bits);
Rx_Bits = PAMmapper(M,0).demap(digimod_out);
[~,errors_bm,BER,errors] = calc_ber(Rx_Bits.signal,bitpattern,"skip_front",0,"skip_end",0,"returnErrorLocation",1);
formatted_ber = sprintf('%.1e', BER);
disp(['BER: ',formatted_ber]);