599 lines
21 KiB
Matlab
599 lines
21 KiB
Matlab
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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e_dc
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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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mu_dc
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constellation
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decide
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save_debug = 0;
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debug_struct
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optmize_mus = 0;
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mu_optimization
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mu_optimization_iter = 0;
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mu_optimization_len
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plot_mu_optimization = 0
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mu_optimization_fignum = 3020;
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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.mu_dc = 0;
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options.decide = false;
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options.save_debug = 0;
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options.optmize_mus = 0;
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options.mu_optimization_len = 2^15;
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options.plot_mu_optimization = 0;
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options.mu_optimization_fignum = 3020;
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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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obj.e_dc = 0;
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end
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function [X,N] = 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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obj.e_dc = 0;
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if obj.optmize_mus
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obj.optimizeMus(X.signal,D.signal);
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obj.e = zeros(sum(obj.ce),1);
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obj.e_dc = 0;
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end
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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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N = X - D;
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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 = x(:);
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d = d(:);
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x = [zeros(floor(obj.order(1)/2),1); x; zeros(obj.order(1),1)];
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n_symbols = floor(N / obj.sps);
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y = zeros(n_symbols,1);
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d_hat = zeros(n_symbols,1);
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if showviz
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figure(111);
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subplot(2,2,1:2);
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hold on
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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_dc + obj.e.' * x_in; % Calculating output of LMS __ * |
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if training
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err = 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 = 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 * x_in) * err ) ; % 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 * x_in / normalizationfactor; % Weight update rule of NLMS
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end
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if obj.mu_dc ~= 0
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obj.e_dc = obj.e_dc - obj.mu_dc * err;
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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 * err'; % Instantaneous square error
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if obj.save_debug
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obj.debug_struct.error(epoch,symbol) = err * err';
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if training
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obj.debug_struct.error_tr(epoch,symbol) = err * err';
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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 optimizeMus(obj,x,d)
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mu_range = [1e-5, 1e-2];
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mu_dc_range = [1e-5, 1e-1];
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[x_opt,d_opt,N_opt] = obj.optimizationSignals(x,d);
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vars = obj.muOptimizableVariables("mu_tr",mu_range);
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vars = [vars, obj.muOptimizableVariables("mu_dd",mu_range)];
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optimize_mu_dc = obj.mu_dc ~= 0;
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if optimize_mu_dc
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vars = [vars, optimizableVariable("mu_dc",mu_dc_range,"Transform","log")];
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end
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obj.mu_optimization_iter = 0;
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fprintf("VNLE mu opt uses %d samples / %d symbols\n",N_opt,numel(d_opt));
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obj.mu_optimization = bayesopt(@(p)obj.muObjective(p,x_opt,d_opt),vars, ...
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"MaxObjectiveEvaluations",20, ...
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"AcquisitionFunctionName","expected-improvement-plus", ...
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"IsObjectiveDeterministic",false, ...
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"Verbose",0, ...
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"PlotFcn",[]);
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obj.mu_tr = obj.muVectorFromParams(obj.mu_optimization.XAtMinObjective,"mu_tr");
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obj.mu_dd = obj.muVectorFromParams(obj.mu_optimization.XAtMinObjective,"mu_dd");
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if optimize_mu_dc
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obj.mu_dc = obj.mu_optimization.XAtMinObjective.mu_dc;
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end
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if optimize_mu_dc
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fprintf("\nVNLE mu opt done: mu_tr=[%s], mu_dd=[%s], mu_dc=%9.3e, BER=%9.3e\n", ...
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obj.formatMuVector(obj.mu_tr),obj.formatMuVector(obj.mu_dd), ...
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obj.mu_dc,obj.mu_optimization.MinObjective);
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else
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fprintf("\nVNLE mu opt done: mu_tr=[%s], mu_dd=[%s], BER=%9.3e\n", ...
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obj.formatMuVector(obj.mu_tr),obj.formatMuVector(obj.mu_dd), ...
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obj.mu_optimization.MinObjective);
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end
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if obj.plot_mu_optimization
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obj.plotMuOptimization();
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end
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end
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function objective = muObjective(obj,params,x,d)
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old_state = obj.captureObjectiveState();
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cleanup = onCleanup(@()obj.restoreObjectiveState(old_state));
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obj.save_debug = 0;
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optimize_mu_dc = ismember("mu_dc",string(params.Properties.VariableNames));
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if optimize_mu_dc
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obj.mu_dc = params.mu_dc;
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end
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obj.e = zeros(sum(obj.ce),1);
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obj.e_dc = 0;
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obj.debug_struct = struct();
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muTrCandidate = obj.muVectorFromParams(params,"mu_tr");
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muDdCandidate = obj.muVectorFromParams(params,"mu_dd");
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N_tr = min(obj.len_tr,numel(x));
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obj.equalize(x,d,muTrCandidate,obj.epochs_tr,N_tr,1,0);
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[signal,~] = obj.equalize(x,d,muDdCandidate,obj.epochs_dd,numel(x),0,0);
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[ber,errors] = obj.berObjective(signal,d);
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objective = ber;
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if ~isfinite(objective)
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objective = inf;
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end
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obj.mu_optimization_iter = obj.mu_optimization_iter + 1;
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if optimize_mu_dc
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fprintf("\rVNLE mu opt %02d: mu_tr=[%s], mu_dd=[%s], mu_dc=%9.3e, BER=%9.3e, errors=%d", ...
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obj.mu_optimization_iter,obj.formatMuVector(muTrCandidate), ...
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obj.formatMuVector(muDdCandidate),params.mu_dc,ber,errors);
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else
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fprintf("\rVNLE mu opt %02d: mu_tr=[%s], mu_dd=[%s], BER=%9.3e, errors=%d", ...
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obj.mu_optimization_iter,obj.formatMuVector(muTrCandidate), ...
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obj.formatMuVector(muDdCandidate),ber,errors);
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end
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clear cleanup
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end
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function [x_opt,d_opt,N_opt] = optimizationSignals(obj,x,d,opt_len)
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if nargin < 4
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opt_len = obj.mu_optimization_len;
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end
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N_available = min(numel(x),numel(d) * obj.sps);
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if isempty(opt_len) || opt_len <= 0 || isinf(opt_len)
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N_opt = N_available;
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else
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N_opt = min(N_available,max(obj.len_tr,opt_len));
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end
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N_opt = obj.sps * floor(N_opt / obj.sps);
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N_opt = max(obj.sps,N_opt);
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n_symbols = N_opt / obj.sps;
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x_opt = x(1:N_opt);
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d_opt = d(1:n_symbols);
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end
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function [ber,errors] = berObjective(~,signal,d)
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M = numel(unique(d));
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mapper = PAMmapper(M,0);
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eq_signal_sd = Signal(signal);
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eq_signal_hd = mapper.quantize(eq_signal_sd);
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tx_symbols = Signal(d);
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rx_bits = mapper.demap(eq_signal_hd);
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tx_bits = mapper.demap(tx_symbols);
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skip_front = min(1000,max(0,floor(numel(rx_bits.signal) / 4)));
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[~,errors,ber,~] = calc_ber(rx_bits.signal,tx_bits.signal, ...
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"skip_front",skip_front, ...
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"skip_end",0, ...
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"returnErrorLocation",1);
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end
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function vars = muOptimizableVariables(obj,prefix,mu_range)
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vars = optimizableVariable.empty;
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activeOrders = find(obj.order > 0);
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for idx = 1:numel(activeOrders)
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orderIdx = activeOrders(idx);
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varName = sprintf("%s_%d",prefix,orderIdx);
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vars = [vars, optimizableVariable(varName,mu_range,"Transform","log")]; %#ok<AGROW>
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end
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end
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function mu = muVectorFromParams(obj,params,prefix)
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mu = zeros(1,3);
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for orderIdx = 1:numel(mu)
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varName = sprintf("%s_%d",prefix,orderIdx);
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if ismember(varName,string(params.Properties.VariableNames))
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mu(orderIdx) = params.(varName);
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elseif numel(obj.(char(prefix))) >= orderIdx
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mu(orderIdx) = obj.(char(prefix))(orderIdx);
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else
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mu(orderIdx) = obj.(char(prefix))(1);
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end
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end
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end
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function plotMuOptimization(obj)
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if isempty(obj.mu_optimization)
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return
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end
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X = obj.mu_optimization.XTrace;
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objective = obj.mu_optimization.ObjectiveTrace;
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objective = objective(:);
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valid = isfinite(objective);
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if isempty(X) || ~any(valid)
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return
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end
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var_names = X.Properties.VariableNames;
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n_vars = numel(var_names);
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eval_idx = (1:numel(objective)).';
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objective_plot = obj.positiveObjectiveForLogPlot(objective);
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best_plot = obj.positiveObjectiveForLogPlot(cummin(objective));
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figure(obj.mu_optimization_fignum);
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clf;
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t = tiledlayout(2,2,"TileSpacing","compact","Padding","compact");
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title(t,"VNLE Bayesian mu optimization");
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nexttile;
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h_candidate = semilogy(eval_idx,objective_plot,"o-","DisplayName","candidate");
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obj.addOptimizationDataTips(h_candidate,X,objective,objective_plot,eval_idx,var_names);
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hold on;
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h_best_trace = semilogy(eval_idx,best_plot,"k-","LineWidth",1.2,"DisplayName","best so far");
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h_best_trace.DataTipTemplate.DataTipRows(end+1) = dataTipTextRow("Evaluation",eval_idx);
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h_best_trace.DataTipTemplate.DataTipRows(end+1) = dataTipTextRow("Best BER",best_plot);
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grid on;
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xlabel("Evaluation");
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ylabel("BER");
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legend("Location","best");
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if n_vars < 2
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return
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end
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pairs = nchoosek(1:n_vars,2);
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n_pair_plots = min(size(pairs,1),3);
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[~,best_idx] = min(objective);
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for pair_idx = 1:n_pair_plots
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nexttile;
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x_name = var_names{pairs(pair_idx,1)};
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y_name = var_names{pairs(pair_idx,2)};
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x_data = X.(x_name);
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y_data = X.(y_name);
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c_data = log10(objective_plot);
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h_scatter = scatter(log10(x_data),log10(y_data),35,c_data,"filled");
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obj.addOptimizationDataTips(h_scatter,X,objective,objective_plot,eval_idx,var_names);
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hold on;
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h_best = plot(log10(x_data(best_idx)),log10(y_data(best_idx)),"kp", ...
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"MarkerSize",12, ...
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"MarkerFaceColor","y", ...
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"DisplayName","best");
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obj.addOptimizationDataTips(h_best,X(best_idx,:),objective(best_idx),objective_plot(best_idx),eval_idx(best_idx),var_names);
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grid on;
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xlabel("log10(" + string(x_name) + ")");
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ylabel("log10(" + string(y_name) + ")");
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cb = colorbar;
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cb.Label.String = "log10(BER)";
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title(string(x_name) + " vs " + string(y_name));
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end
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end
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function addOptimizationDataTips(~,plot_handle,X,objective,objective_plot,eval_idx,var_names)
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plot_handle.DataTipTemplate.DataTipRows(end+1) = dataTipTextRow("Evaluation",eval_idx);
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plot_handle.DataTipTemplate.DataTipRows(end+1) = dataTipTextRow("BER",objective);
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plot_handle.DataTipTemplate.DataTipRows(end+1) = dataTipTextRow("BER shown",objective_plot);
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for var_idx = 1:numel(var_names)
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var_name = var_names{var_idx};
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plot_handle.DataTipTemplate.DataTipRows(end+1) = dataTipTextRow(var_name,X.(var_name));
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end
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end
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function objective_plot = positiveObjectiveForLogPlot(~,objective)
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objective_plot = objective;
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positive_values = objective(isfinite(objective) & objective > 0);
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if isempty(positive_values)
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floor_value = 1e-12;
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else
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floor_value = min(positive_values) / 10;
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end
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objective_plot(~isfinite(objective_plot) | objective_plot <= 0) = floor_value;
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end
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function state = captureObjectiveState(obj)
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state.e = obj.e;
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state.e_dc = obj.e_dc;
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state.error = obj.error;
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state.mu_dc = obj.mu_dc;
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state.save_debug = obj.save_debug;
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state.debug_struct = obj.debug_struct;
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end
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function restoreObjectiveState(obj,state)
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obj.e = state.e;
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obj.e_dc = state.e_dc;
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obj.error = state.error;
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obj.mu_dc = state.mu_dc;
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obj.save_debug = state.save_debug;
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obj.debug_struct = state.debug_struct;
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end
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function s = formatMuVector(~,mu)
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s = strtrim(sprintf("%9.3e ",mu));
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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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x_in_block = x_in_block(:);
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l1=length(x_in_block);
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l2=size(I_2,1);
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l3=size(I_3,1);
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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
|
|
|
|
case 2
|
|
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|
indvec2nd = zeros(n*(n+1)/2, o);
|
|
for i = 1:n
|
|
for j = i:n
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|
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
|
|
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|
function powerNorm = calcPowerNormalization(~,v)
|
|
v = v(:);
|
|
|
|
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
|
|
|
|
end
|
|
end
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