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New MPI mitigation schemes // Duobinary // Start of FTN schemes

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Silas Oettinghaus
2024-09-06 08:10:04 +02:00
parent bb228ae2bd
commit 03bfd70470
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Classes/04_DSP/Equalizer/EQ_silas_plain.m Normal file
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classdef EQ_silas_plain < handle
%EQ_SILAS FFE and DFE Equalizer Playground
properties
% Important Signals
x_in %Input Sequence to be equalized
x_length
x_norm
d %reference signal
d_norm
d_constellation %constellation points of the reference
y_out %equalizer output signal
% FFE coefficients always named with "e"
Ne
Ce %memory length FFE
Ie1 %Indice Combination of 1nd order FFE
Ie2 %Indice Combination of 2nd order FFE
Ie3 %Indice Combination of 3nd order FFE
e %coefficients for FFE
% DFE coefficients always named with "b"
Nb
Cb %memory length DFE
Ib1 %Indice Combination of 1nd order DFE
Ib2 %Indice Combination of 2nd order DFE
Ib3 %Indice Combination of 3nd order DFE
b %coefficients for DFE
error
e_ffe
e_dfe
e_dc
error_log
mu_dc_train
mu_ffe_train
mu_dfe_train
mu_dc_dd
mu_combined_dd
delay
trainlength
sps
trainloops
ddloops
end
methods
function obj = EQ_silas_plain(options)
%EQ_SILAS Construct an instance of this class
arguments(Input)
options.Ne = [50 5 0] %Number of FFE coefficients (1st, 2nd and 3rd order)
options.Nb = [30 5 3] %Number of DFE coefficients (1st, 2nd and 3rd order)
options.trainloops = 2;
options.trainlength = 4096;
options.ddloops = 2;
options.delay = 0;
options.sps = 2;
options.mu_dc_train = 0.01;
options.mu_ffe_train = 0.005;
options.mu_dfe_train = 0.005;
options.mu_dc_dd = 0.01;
options.mu_combined_dd = [0.0004 0.0005 0.0006 0.0007 ];
end
fn = fieldnames(options);
for n = 1:numel(fn)
obj.(fn{n}) = options.(fn{n});
end
% Generate helpful vectors and initialize the filters with
% correct length:
obj.Ce = obj.calcVNLEMemoryLength(obj.Ne);
[obj.Ie2,obj.Ie3] = obj.calcIndiceVectors(obj.Ne);
obj.e = zeros(sum(obj.Ce),1);
obj.Cb = obj.calcVNLEMemoryLength(obj.Nb);
[obj.Ib2,obj.Ib3] = obj.calcIndiceVectors(obj.Nb);
obj.b = zeros(sum(obj.Cb),1);
end
function [signalclass_out,error_log] = process(obj,signalclass_in, reference_signalclass_in)
assert(signalclass_in.fs / reference_signalclass_in.fs == obj.sps)
% actual processing of the signal (steps 1. - 3.)
% 1 normalize RMS
signalclass_in = signalclass_in.normalize("mode","rms");
% Process the EQ optimization
obj.process_(signalclass_in.signal', reference_signalclass_in.signal');
signalclass_in.signal = obj.y_out';
%change sampling frequency of outgoing signal
signalclass_in.fs = reference_signalclass_in.fs;
% append to logbook
lbdesc = ['EQ von Silas ist gelaufen '];
signalclass_in = signalclass_in.logbookentry(lbdesc);
% write to output
signalclass_out = signalclass_in;
end
function process_(obj,x_in,d_in)
% 1) prepare signals
obj.e_dc = mean(x_in);
% 1.1) Input Signal
obj.x_in = [zeros(1,floor(obj.Ne(1)/2)) x_in zeros(1,obj.Ne(1))];
obj.x_length = length(x_in);
obj.x_norm = obj.calcPowerNormalization(x_in);
% 1.2 Reference Signal // Constellation
obj.d = [zeros(1,obj.Nb(1)-1) d_in zeros(1,obj.Nb(1))];
obj.d_constellation = unique(d_in);
obj.d_norm = obj.calcPowerNormalization(d_in);
% 1.3 Training
obj.trainingMode();
% 1.4 Decision Directed Mode
obj.decisionDirectedMode();
end
%% Adaptive Equalization Modes
function trainingMode(obj)
for tloop = 1:obj.trainloops
m = 1+obj.delay;
cnt = 1;
for n = obj.sps*obj.delay+1:obj.sps:obj.sps*obj.trainlength
m = m+1;
%get Sigal input vectors with correct length for VNLE
x_in_block = obj.x_in(obj.Ne(1)+n+(obj.sps-1):-1:n+obj.sps).';
x_in_vnle_format = obj.calcVNLENonlinVecs(x_in_block,obj.Ie2,obj.Ie3,obj.Ne,obj.x_norm);
%get Reference input vectors with correct length for VNLE
d_block = obj.d(obj.Nb(1)-obj.delay+m-2:-1:m-obj.delay-1).';
d_vnle_format = obj.calcVNLENonlinVecs(d_block,obj.Ib2,obj.Ib3,obj.Nb,obj.d_norm);
% Calculate the Error
obj.e_ffe = obj.e.' * x_in_vnle_format;
obj.e_dfe = obj.b.' * d_vnle_format;
obj.error = obj.e_dc + obj.e_ffe - obj.e_dfe - obj.d(obj.Nb(1)-1+m-obj.delay);
obj.error_log(tloop,cnt) = obj.error;
%update FFE coefficients with LMS
obj.e = obj.e - obj.error*conj(x_in_vnle_format)*obj.mu_ffe_train;
%update DFE coefficients with LMS
obj.b = obj.b + obj.mu_dfe_train*obj.error*d_vnle_format;
%update DC error
obj.e_dc = obj.e_dc - obj.error .* obj.mu_dc_train;
cnt = cnt+1;
end
end
end
function decisionDirectedMode(obj)
%start the dd mode with coefficients from training
coeff = [obj.e;obj.b];
for ddloop = 1:obj.ddloops
m = 0;
if all(obj.mu_combined_dd == obj.mu_combined_dd(1))
mu_mat = obj.mu_combined_dd(1);
else
mu_mat = diag([ones(1,obj.Ce(1))*obj.mu_combined_dd(1)... %1st order ffe
ones(1,obj.Ce(2))*obj.mu_combined_dd(2)... %2nd order ffe
ones(1,obj.Ce(3))*obj.mu_combined_dd(3)... %3rd order ffe
ones(1,sum(obj.Cb))*obj.mu_combined_dd(4)]); %all order dfe
end
y = zeros(1,floor(obj.x_length/obj.sps));
d_feedback = zeros(obj.Cb(1),1);
d_vnle = obj.calcVNLENonlinVecs(d_feedback,obj.Ib2,obj.Ib3,obj.Nb,obj.d_norm);
d_hat = zeros(obj.x_length,1);
for k = 1:obj.sps:obj.x_length
m=m+1;
%get Sigal input vectors with correct length for VNLE
x = obj.x_in(obj.Ne(1)+k-1:-1:k).';
x_vnle = obj.calcVNLENonlinVecs(x,obj.Ie2,obj.Ie3,obj.Ne,obj.x_norm);
%combine FFE with DFE to one vector (cursor between the two sequences)
x_d = [x_vnle;-d_vnle];
%Apply filter
y(m) = obj.e_dc + x_d.'* coeff;
%Decision
[~,symbol_idx] = min(abs(y(m) - obj.d_constellation)); % decision for closest constellation point
d_hat(k) = obj.d_constellation(symbol_idx);
%Error between FFE & DFE filtered signal and Decision
obj.error = y(m) - d_hat(k);
%Update coefficients (both FFE and DFE)
coeff = coeff - (mu_mat * (obj.error * conj(x_d)));
if 1 %mu_mat ~= 0
obj.e_dc = obj.e_dc - obj.mu_dc_dd * obj.error;
end
% Append new decision to decision feedback
if obj.Nb(1) > 0
%shift up one index
d_feedback(2:end) = d_feedback(1:end-1);
%replace 1st index with current estimation
d_feedback(1) = d_hat(k);
%build memorylike VNLE version
d_vnle = obj.calcVNLENonlinVecs(d_feedback,obj.Ib2,obj.Ib3,obj.Nb,obj.d_norm);
end
end
end
obj.y_out = (circshift( y.' ,-(obj.delay))).';
end
%% Functions needed During Adaption
function x_in_vnle_format = calcVNLENonlinVecs(~,x_in_block,I_2,I_3,N_,norm_)
% These are the second and third order input signal products of the VNLE EQ
% ∑ h1 x_in(k-n1) + ∑∑ h2 x_in(k-n1)*x_in(k-n2) + ∑∑∑ h3 x_in(k-n1)*x_in(k-n2)*x_in(k-n3)
l1=length(x_in_block);
l2=length(I_2);
l3=length(I_3);
final_length = l1+l2+l3;
x_in_vnle_format = zeros(final_length,1);
idx = l1;
x_in_vnle_format(1:idx) = x_in_block;
if N_(2) > 0
delta_2 = round((N_(1)-N_(2)) / 2);
input_vec_se = x_in_block(delta_2:end) / norm_(2); %TODO normalization step
% Extract columns from I_2
col1 = input_vec_se(I_2(:,1));
col2 = input_vec_se(I_2(:,2));
x2 = col1 .* col2;
x_in_vnle_format(idx+1:idx+l2) = x2;
end
if N_(3) > 0
delta_3 = round((N_(1)-N_(3))/2);
input_vec_th = x_in_block(delta_3:end) / norm_(3);
% Extract columns from I_3
col1 = input_vec_th(I_3(:,1));
col2 = input_vec_th(I_3(:,2));
col3 = input_vec_th(I_3(:,3));
% Perform matrix multiplication
x3 = col1 .* col2 .* col3;
idx = idx+l2;
x_in_vnle_format(idx+1:idx+l3) = x3;
end
end
%% Functions needed for Preparation
function [C] = calcVNLEMemoryLength(~,N)
%calculates the memory length of VNLE
C = zeros(size(N));
for o = 1:numel(N)
switch o
case 1
C(o) = N(o);
case 2
C(o) = N(o)*(N(o)+1) / 2;
case 3
C(o) = N(o)*(N(o)+1)*(N(o)+2) / 6;
end
end
end
function [indvec2nd, indvec3rd] = calcIndiceVectors(~,N)
% Init vectors of 2nd and 3rd order coefficient indices ->
% yield combination with
for order = 2:numel(N)
n = N(order);
v = 1:n; % Ursprünglicher Vektor
row = 1;
% Schleifen zur Generierung des Indize Vektors
switch order
case 2
indvec2nd = zeros(n*(n+1)/2, order);
for i = 1:n
for j = i:n
indvec2nd(row, :) = [v(i) v(j)];
row = row + 1;
end
end
case 3
indvec3rd = zeros(n*(n+1)*(n+2)/6, 3);
for i = 1:n
for j = i:n
for k = j:n
indvec3rd(row, :) = [v(i) v(j) v(k)];
row = row + 1;
end
end
end
end
end
end
function powerNorm = calcPowerNormalization(~,v)
powerNorm(1) = sqrt(mean(abs(v ).^2));
powerNorm(2) = sqrt(mean(abs(v.^2).^2));
powerNorm(3) = sqrt(mean(abs(v.^3).^2));
end
end
end