New MPI mitigation schemes // Duobinary // Start of FTN schemes
This commit is contained in:
Silas Oettinghaus
296
Classes/04_DSP/Equalizer/VNLE.m
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296
Classes/04_DSP/Equalizer/VNLE.m
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classdef VNLE < handle
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% Implementation of plain and simple FFE.
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% 1) Training mode (stable performance when you use NLMS)
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% 2) Decision directed mode
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% Eq = VNLE("epochs_tr",5,"epochs_dd",5,"len_tr",4096*2,"mu_dd",[0.0004 0.0005 0.0006],"mu_tr",0,"order",[25,2,2],"sps",2,"decide",1);
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% Somehow it is not possible to use only 1 nonlinear order
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properties
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sps % usually 2
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order
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e
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error
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len_tr
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mu_tr
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epochs_tr
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mu_dd
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epochs_dd
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constellation
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decide
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x_norm
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ce
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ie2
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ie3
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end
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methods
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function obj = VNLE(options)
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arguments(Input)
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options.sps = 2;
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options.order = [15,2,2];
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options.len_tr = 4096;
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options.mu_tr = 0;
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options.epochs_tr = 5;
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options.mu_dd = 1e-5;
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options.epochs_dd = 5;
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options.decide = false;
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end
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fn = fieldnames(options);
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for n = 1:numel(fn)
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obj.(fn{n}) = options.(fn{n});
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end
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obj.error = 0;
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end
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function [X] = process(obj, X, D)
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% actual processing of the signal (steps 1. - 3.)
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% 1 normalize RMS
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X = X.normalize("mode","rms");
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obj.constellation = unique(D.signal);
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obj.x_norm = obj.calcPowerNormalization(X.signal);
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obj.ce = obj.calcVNLEMemoryLength(obj.order);
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[obj.ie2,obj.ie3] = obj.calcIndiceVectors(obj.order);
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obj.e = zeros( sum(obj.ce) ,1);
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% Training Mode
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training = 1;
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showviz = 0;
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obj.equalize(X.signal, D.signal,obj.mu_tr,obj.epochs_tr,obj.len_tr,training,showviz);
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% Decision Directed Mode
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N = X.length;
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training = 0;
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showviz = 0;
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[signal,decision]=obj.equalize(X.signal, D.signal,obj.mu_dd,obj.epochs_dd,N,training,showviz);
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% Output Signal
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if obj.decide
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X.signal = decision;
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else
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X.signal = signal;
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end
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X.fs = D.fs; %change sampling frequency of outgoing signal from fdac e.g. 2 sps to symbol spaced = fsym
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lbdesc = [num2str(obj.order),' tap FFE'];
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X = X.logbookentry(lbdesc); % append to logbook
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end
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function [y,d_hat] = equalize(obj,x,d,mu,epochs,N,training,showviz)
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arguments
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obj
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x
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d
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mu
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epochs
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N
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training
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showviz
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end
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if all(mu == mu(1))
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% mu = mu(1);
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mu = diag(ones(1,sum(obj.ce))*mu(1));
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else
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mu = diag([ones(1,obj.ce(1))*mu(1) ...
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ones(1,obj.ce(2))*mu(2) ...
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ones(1,obj.ce(3))*mu(3) ]);
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end
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x = [zeros(floor(obj.order(1)/2),1); x; zeros(obj.order(1),1)];
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if showviz
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f = figure(111);
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subplot(2,2,1:2);
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hold on
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a = scatter(1:numel(x),x,1,'.');
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a2 = scatter(1,1,1,'.');
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a3 = scatter(1,1,2,'.');
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a4 = xline(1);
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ylim([-3 3])
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xlim([0 length(x)]);
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subplot(2,2,3:4)
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c = stem(obj.e);
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ylim([-1 1])
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drawnow
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end
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for epoch = 1 : epochs
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symbol = 0;
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for sample = 1 : obj.sps : N
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symbol = symbol+1;
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% x_in = x(obj.order(1)+sample+(obj.sps-1):-1:sample+obj.sps);
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x_in = x(obj.order(1)+sample-1:-1:sample);
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x_in = obj.calcVNLENonlinVecs(x_in,obj.ie2,obj.ie3,obj.order,obj.x_norm);
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y(symbol,1) = obj.e.' * x_in; % Calculating output of LMS __ * |
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if training
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err(symbol) = y(symbol) - d(symbol); % Instantaneous error
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else
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[~,symbol_idx] = min(abs(y(symbol) - obj.constellation)); % decision for closest constellation point
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d_hat(symbol,1) = obj.constellation(symbol_idx);
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err(symbol) = y(symbol) - d_hat(symbol); % Instantaneous error
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end
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if ~all(mu==0,'all') %mu has not only zeros
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obj.e = obj.e - (mu * err(symbol) * x_in) ; % Weight update rule of LMS
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else
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normalizationfactor = (x_in.' * x_in);
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obj.e = obj.e - err(symbol) * x_in / normalizationfactor; % Weight update rule of NLMS
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end
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if mod(sample,100) == 1 && showviz
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a2.XData = 1:2*numel(y);
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a2.YData = repelem(y, 2);
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a3.XData = 1:2*numel(d_hat);
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a3.YData = repelem(d_hat, 2);
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a4.Value = sample;
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% b.YData = x(symbol:symbol+500);
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c.YData = obj.e;
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drawnow;
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end
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obj.error(epoch,symbol) = err(symbol) * err(symbol)'; % Instantaneous square error
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end
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end
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end
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%% Functions needed During Adaption
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function x_in_vnle_format = calcVNLENonlinVecs(~,x_in_block,I_2,I_3,N_,norm_)
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% These are the second and third order input signal products of the VNLE EQ
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% ∑ 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)
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l1=length(x_in_block);
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l2=length(I_2);
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l3=length(I_3);
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final_length = l1+l2+l3;
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x_in_vnle_format = zeros(final_length,1);
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idx = l1;
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x_in_vnle_format(1:idx) = x_in_block;
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if N_(2) > 0
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delta_2 = round((N_(1)-N_(2)) / 2);
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input_vec_se = x_in_block(delta_2:end) / norm_(2); %TODO normalization step
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% Extract columns from I_2
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col1 = input_vec_se(I_2(:,1));
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col2 = input_vec_se(I_2(:,2));
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x2 = col1 .* col2;
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x_in_vnle_format(idx+1:idx+l2) = x2;
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end
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if N_(3) > 0
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delta_3 = round((N_(1)-N_(3))/2);
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input_vec_th = x_in_block(delta_3:end) / norm_(3);
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% Extract columns from I_3
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col1 = input_vec_th(I_3(:,1));
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col2 = input_vec_th(I_3(:,2));
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col3 = input_vec_th(I_3(:,3));
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% Perform matrix multiplication
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x3 = col1 .* col2 .* col3;
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idx = idx+l2;
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x_in_vnle_format(idx+1:idx+l3) = x3;
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end
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end
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%% Functions needed for Preparation
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function [C] = calcVNLEMemoryLength(~,N)
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%calculates the memory length of VNLE
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C = zeros(size(N));
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for o = 1:numel(N)
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switch o
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case 1
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C(o) = N(o);
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case 2
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C(o) = N(o)*(N(o)+1) / 2;
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case 3
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C(o) = N(o)*(N(o)+1)*(N(o)+2) / 6;
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end
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end
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end
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function [indvec2nd, indvec3rd] = calcIndiceVectors(~,N)
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% Init vectors of 2nd and 3rd order coefficient indices ->
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% yield combination with
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indvec2nd=[];
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indvec3rd=[];
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for o = 2:numel(N)
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n = N(o);
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v = 1:n; % Ursprünglicher Vektor
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row = 1;
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% Schleifen zur Generierung des Indize Vektors
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switch o
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case 2
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indvec2nd = zeros(n*(n+1)/2, o);
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for i = 1:n
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for j = i:n
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indvec2nd(row, :) = [v(i) v(j)];
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row = row + 1;
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end
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end
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case 3
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indvec3rd = zeros(n*(n+1)*(n+2)/6, 3);
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for i = 1:n
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for j = i:n
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for k = j:n
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indvec3rd(row, :) = [v(i) v(j) v(k)];
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row = row + 1;
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end
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end
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end
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end
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end
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end
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function powerNorm = calcPowerNormalization(~,v)
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powerNorm(1) = sqrt(mean(abs(v ).^2));
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powerNorm(2) = sqrt(mean(abs(v.^2).^2));
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powerNorm(3) = sqrt(mean(abs(v.^3).^2));
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end
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end
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end
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