classdef FFE < handle % Implementation of plain and simple FFE. % 1) Training mode (stable performance when you use NLMS) % 2) Decision directed mode %LMS: mu in order of 0.001 for acceptable convergence speed %NLMS: mu in order of 0.01 for acceptable convergence speed %RLS: mu is lambda -> 0.99 -> 1 (has a strong dependency on this! use a loop to find out best values) % FFE("epochs_tr",5,"epochs_dd",2,"len_tr",2^13,"mu_dd",mu_dd,"mu_tr",mu_tr,"order",25,"sps",2,"decide",0, "adaption",adaption_method(adaption),"dd_mode",use_dd_mode); % eq_ = FFE("epochs_tr",5,"epochs_dd",5,"len_tr",len_tr, ... % "mu_dd",1e-1,"mu_tr",0.4,"order",50, ... % "sps",2,"decide",0,"optmize_mus",1,"dd_mode",1, ... % "adaption_technique","nlms","mu_dc",1.021e-05); properties sps % usually 2 order e e_tr error len_tr mu_tr epochs_tr adaption_technique % nlms, lms, rls dd_mode % 1 or 0 to set DD-mode on or off mu_dd %weight update in dd mode epochs_dd dd_len_fraction mu_dc adaptive_dc_enabled e_dc P % covariance matrix of rls constellation % symbol constellation decide %wether to return the (hard) decisions or the result after FFE (soft) save_debug = 0; debug_struct optmize_mus = 0; mu_optimization mu_optimization_iter = 0; mu_optimization_len plot_mu_optimization = 0; mu_optimization_fignum = 3010; optimize_dc_params = 0; dc_optimization dc_optimization_iter = 0; dc_optimization_len dc_optimization_max_evals dc_optimization_delay_weight dc_optimization_smoothing_len end properties (Access = private) dc_alpha = 0.98 dc_gamma = 1e-6 dc_mu_min = 1e-6 dc_mu_max = 3e-1 dc_mu_eff_min = 0 dc_mu_eff_max = inf dc_power_exponent = 1 end methods function obj = FFE(options) arguments(Input) options.sps = 2; options.order = 15; options.len_tr = 4096; options.mu_tr = 0; options.epochs_tr = 5; options.adaption_technique adaption_method = adaption_method.lms; options.dd_mode = 1; options.mu_dd = 1e-5; options.epochs_dd = 5; options.dd_len_fraction = 1; options.mu_dc = 0; options.adaptive_dc_enabled = false; options.decide = false; options.save_debug = 0; options.optmize_mus = 0; options.mu_optimization_len = 2^15; options.plot_mu_optimization = 0; options.mu_optimization_fignum = 3010; options.optimize_dc_params = 0; options.dc_optimization_len = 2^15; options.dc_optimization_max_evals = 20; options.dc_optimization_delay_weight = 1e-3; options.dc_optimization_smoothing_len = 501; end fn = fieldnames(options); for n = 1:numel(fn) obj.(fn{n}) = options.(fn{n}); end obj.e = zeros(obj.order,1); obj.e_dc = 0; obj.error = 0; end function [X,Noi] = process(obj, X, D) % actual processing of the signal (steps 1. - 3.) % 1 normalize RMS X = X.normalize("mode","rms"); obj.constellation = unique(D.signal); obj.e_dc = 0; delta = 0.05; obj.P = (1/delta) * eye(obj.order); if obj.optmize_mus obj.optimizeMus(X.signal,D.signal); obj.e = zeros(obj.order,1); obj.e_dc = 0; obj.P = (1/delta) * eye(obj.order); end if obj.optimize_dc_params obj.optimizeDcParams(X.signal,D.signal); obj.e = zeros(obj.order,1); obj.e_dc = 0; obj.P = (1/delta) * eye(obj.order); end % Training Mode training = 1; showviz = 0; obj.equalize(X.signal, D.signal,obj.mu_tr,obj.epochs_tr,obj.len_tr,training,showviz); obj.e_tr = obj.e; % Decision Directed Mode n = X.length; training = 0; showviz = 0; if obj.dd_mode [signal,decision] = obj.equalize(X.signal, D.signal,obj.mu_dd,obj.epochs_dd,n,training,showviz); else [signal,decision] = obj.equalize(X.signal, D.signal,0,1,n,training,showviz); end % Output Signal if obj.decide X.signal = decision; else X.signal = signal; end 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']; X = X.logbookentry(lbdesc); % append to logbook Noi = X; Noi = X - D; end function [y,d_hat] = equalize(obj,x,d,mu,epochs,N,training,showviz) arguments obj x d mu epochs N training showviz end x = [zeros(floor(obj.order/2),1); x; zeros(obj.order,1)]; lambda = mu; if training mask = ones(obj.order,1); else mask = zeros(obj.order,1); mask(900:end) = 1; mask(ceil(length(obj.e)/2)) = 1; end mask = ones(obj.order,1); maincursor_pos=ceil(length(obj.e)/2); always_ideal_decision = 0; grad =0; weight = 0; update = 0; if mu == 0 || (~obj.dd_mode && ~training) epochs = 1; end P_err = 0; err_prev = 0; dc_alpha = obj.dc_alpha; dc_gamma = obj.dc_gamma; dc_mu_min = obj.dc_mu_min; dc_mu_max = obj.dc_mu_max; dc_mu_eff_min = obj.dc_mu_eff_min; dc_mu_eff_max = obj.dc_mu_eff_max; dc_power_exponent = obj.dc_power_exponent; debug_enabled = obj.save_debug; if debug_enabled n_symbols_debug = ceil(N / obj.sps); obj.debug_struct.error = NaN(1,n_symbols_debug); obj.debug_struct.error_first_epoch = NaN(1,n_symbols_debug); obj.debug_struct.main_cursor = NaN(1,n_symbols_debug); obj.debug_struct.mu_nlms = NaN(1,n_symbols_debug); obj.debug_struct.update_gradient = NaN(1,n_symbols_debug); obj.debug_struct.mu_dc_eff = NaN(1,n_symbols_debug); obj.debug_struct.e_dc_eff = NaN(1,n_symbols_debug); if training obj.debug_struct.error_tr = NaN(1,n_symbols_debug); obj.debug_struct.update_tr = NaN(1,n_symbols_debug); else obj.debug_struct.error_dd = NaN(1,n_symbols_debug); obj.debug_struct.update = NaN(1,n_symbols_debug); end end for epoch = 1 : epochs symbol = 0; % obj.e_dc = 0; for sample = 1 : obj.sps : N symbol = symbol+1; mu_dc_eff = 0; U = x(obj.order+sample-1:-1:sample); y(symbol,1) = obj.e_dc + (obj.e.*mask).' * U; % Calculating output of LMS __ * | if training d_hat(symbol,1) = d(symbol); else if ~always_ideal_decision [~,symbol_idx] = min(abs(y(symbol) - obj.constellation)); % decision for closest constellation point d_hat(symbol,1) = obj.constellation(symbol_idx); else d_hat(symbol,1) = d(symbol); end end % err(symbol) = y(symbol) - d_hat(symbol); % Instantaneous error err(symbol) = d_hat(symbol) - y(symbol); % Instantaneous error true_err(symbol) = y(symbol) - d(symbol); % Instantaneous error if training || obj.dd_mode switch obj.adaption_technique case adaption_method.nlms % mu used as update weight (suggestion: 0.01-0.05; bit higher during tr) normU = ((U.'*U)) + eps; weight = mu / normU; grad = err(symbol) * U; update = grad * weight; obj.e = obj.e + update; case adaption_method.lms % mu used as update weight (suggestion: 0.001) weight = mu; grad = err(symbol) * U; update = grad * weight; obj.e = obj.e + update; case adaption_method.rls % RLS‐Gain: denom = lambda + U.' * obj.P * U; k = (obj.P * U) / denom; % Gewichtsupdate: update = k * err(symbol); obj.e = obj.e + update; % P-Matrix‐Update: obj.P = (1/lambda) * (obj.P - k * (U.' * obj.P)); end if obj.mu_dc ~= 0 if obj.adaptive_dc_enabled delta_mu = dc_gamma * err(symbol) * err_prev * (U.'*U); obj.mu_dc = min(max(obj.mu_dc + delta_mu,dc_mu_min),dc_mu_max); err_prev = err(symbol); P_err = dc_alpha*P_err + (1-dc_alpha)*err(symbol)^2; mu_dc_eff = obj.mu_dc / ((P_err + eps)^dc_power_exponent); else mu_dc_eff = obj.mu_dc; end mu_dc_eff = min(max(mu_dc_eff,dc_mu_eff_min),dc_mu_eff_max); obj.e_dc = obj.e_dc + mu_dc_eff * err(symbol); end end % % if debug_enabled && epoch == 1 % obj.debug_struct.error_first_epoch(1,symbol) = err(symbol) * err(symbol)'; % end if debug_enabled && epoch == epochs error_power = err(symbol) * err(symbol)'; update_power = update.'*update ./ (rms(obj.e) + eps); obj.debug_struct.error(1,symbol) = error_power; obj.debug_struct.main_cursor(1,symbol) = abs(obj.e(maincursor_pos)); obj.debug_struct.mu_nlms(1,symbol) = weight; obj.debug_struct.update_gradient(1,symbol) = grad.'*grad; obj.debug_struct.mu_dc_eff(1,symbol) = mu_dc_eff; obj.debug_struct.e_dc_eff(1,symbol) = obj.e_dc; if training obj.debug_struct.error_tr(1,symbol) = error_power; obj.debug_struct.update_tr(1,symbol) = update_power; else obj.debug_struct.error_dd(1,symbol) = error_power; obj.debug_struct.update(1,symbol) = update_power; end end end end end function optimizeMus(obj,x,d) [x_opt,d_opt,N_opt] = obj.optimizationSignals(x,d); switch obj.adaption_technique case adaption_method.lms mu_range = [1e-5, 1e-2]; case adaption_method.nlms mu_range = [1e-3, 5e-1]; case adaption_method.rls mu_range = [0.98, 0.99999]; end mu_dc_range = [1e-5, 1e-1]; mu_tr_var = optimizableVariable("mu_tr",mu_range,"Transform","log"); vars = mu_tr_var; if obj.dd_mode vars = [vars, optimizableVariable("mu_dd",mu_range,"Transform","log")]; end optimize_mu_dc = obj.mu_dc ~= 0; if optimize_mu_dc vars = [vars, optimizableVariable("mu_dc",mu_dc_range,"Transform","log")]; end obj.mu_optimization_iter = 0; fprintf("FFE mu opt uses %d samples / %d symbols\n",N_opt,numel(d_opt)); obj.mu_optimization = bayesopt(@(p)obj.muObjective(p,x_opt,d_opt),vars, ... "MaxObjectiveEvaluations",20, ... "AcquisitionFunctionName","expected-improvement-plus", ... "IsObjectiveDeterministic",false, ... "Verbose",0, ... "PlotFcn",[]); obj.mu_tr = obj.mu_optimization.XAtMinObjective.mu_tr; if obj.dd_mode obj.mu_dd = obj.mu_optimization.XAtMinObjective.mu_dd; end if optimize_mu_dc obj.mu_dc = obj.mu_optimization.XAtMinObjective.mu_dc; end if obj.dd_mode && optimize_mu_dc fprintf("\nFFE mu opt done: mu_tr=%9.3e, mu_dd=%9.3e, mu_dc=%9.3e, BER=%9.3e\n", ... obj.mu_tr,obj.mu_dd,obj.mu_dc,obj.mu_optimization.MinObjective); elseif obj.dd_mode fprintf("\nFFE mu opt done: mu_tr=%9.3e, mu_dd=%9.3e, BER=%9.3e\n", ... obj.mu_tr,obj.mu_dd,obj.mu_optimization.MinObjective); elseif optimize_mu_dc fprintf("\nFFE mu opt done: mu_tr=%9.3e, mu_dc=%9.3e, BER=%9.3e\n", ... obj.mu_tr,obj.mu_dc,obj.mu_optimization.MinObjective); else fprintf("\nFFE mu opt done: mu_tr=%9.3e, BER=%9.3e\n", ... obj.mu_tr,obj.mu_optimization.MinObjective); end if obj.plot_mu_optimization obj.plotMuOptimization(); end end function optimizeDcParams(obj,x,d) [x_opt,d_opt,N_opt] = obj.optimizationSignals(x,d,obj.dc_optimization_len); vars = optimizableVariable("mu_dc",[1e-5,1e-1],"Transform","log"); if obj.adaptive_dc_enabled vars = [vars, ... optimizableVariable("dc_alpha",[0.85,0.995]), ... optimizableVariable("dc_gamma",[1e-7,3e-5],"Transform","log"), ... optimizableVariable("dc_power_exponent",[0,1]), ... optimizableVariable("dc_mu_eff_max",[1e-3,3e-1],"Transform","log")]; end obj.dc_optimization_iter = 0; fprintf("FFE DC opt uses fixed mu_tr=%9.3e, mu_dd=%9.3e on %d samples / %d symbols\n", ... obj.mu_tr,obj.mu_dd,N_opt,numel(d_opt)); obj.dc_optimization = bayesopt(@(p)obj.dcObjective(p,x_opt,d_opt),vars, ... "MaxObjectiveEvaluations",obj.dc_optimization_max_evals, ... "AcquisitionFunctionName","expected-improvement-plus", ... "IsObjectiveDeterministic",false, ... "Verbose",0, ... "PlotFcn",[]); best = obj.dc_optimization.XAtMinObjective; obj.mu_dc = best.mu_dc; if obj.adaptive_dc_enabled obj.dc_alpha = best.dc_alpha; obj.dc_gamma = best.dc_gamma; obj.dc_power_exponent = best.dc_power_exponent; obj.dc_mu_eff_max = best.dc_mu_eff_max; fprintf("\nFFE DC opt done: mu_dc=%9.3e, alpha=%6.3f, gamma=%9.3e, p=%5.2f, mu_eff_max=%9.3e, objective=%9.3e\n", ... obj.mu_dc,obj.dc_alpha,obj.dc_gamma,obj.dc_power_exponent,obj.dc_mu_eff_max,obj.dc_optimization.MinObjective); else fprintf("\nFFE DC opt done: mu_dc=%9.3e, objective=%9.3e\n", ... obj.mu_dc,obj.dc_optimization.MinObjective); end end function [x_opt,d_opt,N_opt] = optimizationSignals(obj,x,d,opt_len) if nargin < 4 opt_len = obj.mu_optimization_len; end N_available = min(numel(x),numel(d) * obj.sps); if isempty(opt_len) || opt_len <= 0 || isinf(opt_len) N_opt = N_available; else N_opt = min(N_available,max(obj.len_tr,opt_len)); end N_opt = obj.sps * floor(N_opt / obj.sps); N_opt = max(obj.sps,N_opt); n_symbols = N_opt / obj.sps; x_opt = x(1:N_opt); d_opt = d(1:n_symbols); end function objective = muObjective(obj,params,x,d) old_debug = obj.save_debug; old_mu_dc = obj.mu_dc; obj.save_debug = 0; has_mu_dc = any(strcmp(params.Properties.VariableNames,"mu_dc")); if has_mu_dc obj.mu_dc = params.mu_dc; end obj.e = zeros(obj.order,1); obj.e_dc = 0; obj.P = (1/0.05) * eye(obj.order); obj.debug_struct = struct(); N_tr = min(obj.len_tr,numel(x)); [signal,~] = obj.equalize(x,d,params.mu_tr,obj.epochs_tr,N_tr,1,0); if obj.dd_mode [signal,~] = obj.equalize(x,d,params.mu_dd,obj.epochs_dd,numel(x),0,0); end [ber,errors] = obj.berObjective(signal,d); objective = ber; if ~isfinite(objective) objective = inf; end obj.mu_optimization_iter = obj.mu_optimization_iter + 1; if obj.dd_mode && has_mu_dc fprintf("\rFFE mu opt %02d: mu_tr=%9.3e, mu_dd=%9.3e, mu_dc=%9.3e, BER=%9.3e, errors=%d", ... obj.mu_optimization_iter,params.mu_tr,params.mu_dd,params.mu_dc,ber,errors); elseif obj.dd_mode fprintf("\rFFE mu opt %02d: mu_tr=%9.3e, mu_dd=%9.3e, BER=%9.3e, errors=%d", ... obj.mu_optimization_iter,params.mu_tr,params.mu_dd,ber,errors); elseif has_mu_dc fprintf("\rFFE mu opt %02d: mu_tr=%9.3e, mu_dc=%9.3e, BER=%9.3e, errors=%d", ... obj.mu_optimization_iter,params.mu_tr,params.mu_dc,ber,errors); else fprintf("\rFFE mu opt %02d: mu_tr=%9.3e, BER=%9.3e, errors=%d", ... obj.mu_optimization_iter,params.mu_tr,ber,errors); end obj.save_debug = old_debug; obj.mu_dc = old_mu_dc; end function objective = dcObjective(obj,params,x,d) state = obj.captureObjectiveState(); cleanup = onCleanup(@()obj.restoreObjectiveState(state)); obj.applyDcObjectiveParams(params); obj.save_debug = 1; obj.e = zeros(obj.order,1); obj.e_dc = 0; obj.P = (1/0.05) * eye(obj.order); obj.debug_struct = struct(); N_tr = min(obj.len_tr,numel(x)); [signal,~] = obj.equalize(x,d,obj.mu_tr,obj.epochs_tr,N_tr,1,0); if obj.dd_mode [signal,~] = obj.equalize(x,d,obj.mu_dd,obj.epochs_dd,numel(x),0,0); end [ber,errors] = obj.berObjective(signal,d); [delay_symbols,delay_corr] = obj.dcDelayObjective(signal,d); delay_penalty = obj.dc_optimization_delay_weight * abs(delay_symbols) / max(numel(d),1); objective = ber + delay_penalty; if ~isfinite(objective) objective = inf; end obj.dc_optimization_iter = obj.dc_optimization_iter + 1; if obj.adaptive_dc_enabled fprintf("\rFFE DC opt %02d: mu_dc=%9.3e, alpha=%6.3f, gamma=%9.3e, p=%5.2f, mu_eff_max=%9.3e, BER=%9.3e, delay=%7.0f, corr=%6.3f, obj=%9.3e, errors=%d", ... obj.dc_optimization_iter,params.mu_dc,params.dc_alpha,params.dc_gamma,params.dc_power_exponent,params.dc_mu_eff_max, ... ber,delay_symbols,delay_corr,objective,errors); else fprintf("\rFFE DC opt %02d: mu_dc=%9.3e, BER=%9.3e, delay=%7.0f, corr=%6.3f, obj=%9.3e, errors=%d", ... obj.dc_optimization_iter,params.mu_dc,ber,delay_symbols,delay_corr,objective,errors); end end function applyDcObjectiveParams(obj,params) var_names = string(params.Properties.VariableNames); if any(var_names == "mu_dc") obj.mu_dc = params.mu_dc; end if any(var_names == "dc_alpha") obj.dc_alpha = params.dc_alpha; end if any(var_names == "dc_gamma") obj.dc_gamma = params.dc_gamma; end if any(var_names == "dc_power_exponent") obj.dc_power_exponent = params.dc_power_exponent; end if any(var_names == "dc_mu_eff_max") obj.dc_mu_eff_max = params.dc_mu_eff_max; end end function state = captureObjectiveState(obj) state.e = obj.e; state.e_dc = obj.e_dc; state.P = obj.P; state.save_debug = obj.save_debug; state.debug_struct = obj.debug_struct; state.mu_dc = obj.mu_dc; state.dc_alpha = obj.dc_alpha; state.dc_gamma = obj.dc_gamma; state.dc_power_exponent = obj.dc_power_exponent; state.dc_mu_eff_max = obj.dc_mu_eff_max; end function restoreObjectiveState(obj,state) obj.e = state.e; obj.e_dc = state.e_dc; obj.P = state.P; obj.save_debug = state.save_debug; obj.debug_struct = state.debug_struct; obj.mu_dc = state.mu_dc; obj.dc_alpha = state.dc_alpha; obj.dc_gamma = state.dc_gamma; obj.dc_power_exponent = state.dc_power_exponent; obj.dc_mu_eff_max = state.dc_mu_eff_max; end function [ber,errors] = berObjective(~,signal,d) M = numel(unique(d)); mapper = PAMmapper(M,0); eq_signal_sd = Signal(signal); eq_signal_hd = mapper.quantize(eq_signal_sd); tx_symbols = Signal(d); rx_bits = mapper.demap(eq_signal_hd); tx_bits = mapper.demap(tx_symbols); [~,errors,ber,~] = calc_ber(rx_bits.signal,tx_bits.signal, ... "skip_front",10, ... "skip_end",10, ... "returnErrorLocation",1); end function [delay_symbols,delay_corr] = dcDelayObjective(obj,signal,d) delay_symbols = 0; delay_corr = 0; if ~isfield(obj.debug_struct,"e_dc_eff") || isempty(obj.debug_struct.e_dc_eff) return end smooth_len = obj.dc_optimization_smoothing_len; e_dc_eff_s = movmean(obj.debug_struct.e_dc_eff(:),smooth_len,"omitnan"); avg_lvl_dc = obj.averageLevelTrace(signal,d,smooth_len); xcorr_len = min(numel(e_dc_eff_s),numel(avg_lvl_dc)); if xcorr_len < 2 return end inv_dc_xcorr = -e_dc_eff_s(1:xcorr_len); avg_lvl_xcorr = avg_lvl_dc(1:xcorr_len); inv_dc_xcorr = fillmissing(inv_dc_xcorr,"linear","EndValues","nearest"); avg_lvl_xcorr = fillmissing(avg_lvl_xcorr,"linear","EndValues","nearest"); inv_dc_xcorr = inv_dc_xcorr - mean(inv_dc_xcorr,"omitnan"); avg_lvl_xcorr = avg_lvl_xcorr - mean(avg_lvl_xcorr,"omitnan"); if rms(inv_dc_xcorr) <= eps || rms(avg_lvl_xcorr) <= eps return end [dc_level_xcorr,dc_level_lags] = xcorr(inv_dc_xcorr,avg_lvl_xcorr,"coeff"); [delay_corr,delay_idx] = max(dc_level_xcorr); delay_symbols = dc_level_lags(delay_idx); if ~isfinite(delay_corr) delay_corr = 0; delay_symbols = 0; end end function avg_lvl_dc = averageLevelTrace(obj,signal,d,smooth_len) signal = signal(:); d = d(:); n_symbols = min(numel(signal),numel(d)); signal = signal(1:n_symbols); d = d(1:n_symbols); levels = unique(d); avg_for_lvl = NaN(numel(levels),n_symbols); for level_idx = 1:numel(levels) level_mask = d == levels(level_idx); level_samples = signal(level_mask); if isempty(level_samples) continue end smooth_window = min(smooth_len,numel(level_samples)); avg_for_lvl(level_idx,level_mask) = movmean(level_samples,smooth_window,"omitnan","Endpoints","shrink"); avg_for_lvl(level_idx,:) = obj.interpolateMissingAverage(avg_for_lvl(level_idx,:)); end avg_lvl_dc = mean(avg_for_lvl,1,"omitnan").'; end function level_average = interpolateMissingAverage(~,level_average) valid_samples = isfinite(level_average); if nnz(valid_samples) == 0 return elseif nnz(valid_samples) == 1 level_average(:) = level_average(valid_samples); return end t = 1:numel(level_average); level_average(~valid_samples) = interp1(t(valid_samples),level_average(valid_samples), ... t(~valid_samples),"linear","extrap"); end function plotMuOptimization(obj) if isempty(obj.mu_optimization) return end X = obj.mu_optimization.XTrace; objective = obj.mu_optimization.ObjectiveTrace; objective = objective(:); valid = isfinite(objective); if isempty(X) || ~any(valid) return end var_names = X.Properties.VariableNames; n_vars = numel(var_names); eval_idx = (1:numel(objective)).'; objective_plot = obj.positiveObjectiveForLogPlot(objective); best_plot = obj.positiveObjectiveForLogPlot(cummin(objective)); figure(obj.mu_optimization_fignum); clf; t = tiledlayout(2,2,"TileSpacing","compact","Padding","compact"); title(t,"FFE Bayesian mu optimization"); nexttile; h_candidate = semilogy(eval_idx,objective_plot,"o-","DisplayName","candidate"); obj.addOptimizationDataTips(h_candidate,X,objective,objective_plot,eval_idx,var_names); hold on; h_best_trace = semilogy(eval_idx,best_plot,"k-","LineWidth",1.2,"DisplayName","best so far"); h_best_trace.DataTipTemplate.DataTipRows(end+1) = dataTipTextRow("Evaluation",eval_idx); h_best_trace.DataTipTemplate.DataTipRows(end+1) = dataTipTextRow("Best BER",best_plot); grid on; xlabel("Evaluation"); ylabel("BER"); legend("Location","best"); if n_vars < 2 return end pairs = nchoosek(1:n_vars,2); n_pair_plots = min(size(pairs,1),3); [~,best_idx] = min(objective); for pair_idx = 1:n_pair_plots nexttile; x_name = var_names{pairs(pair_idx,1)}; y_name = var_names{pairs(pair_idx,2)}; x_data = X.(x_name); y_data = X.(y_name); c_data = log10(objective_plot); h_scatter = scatter(log10(x_data),log10(y_data),35,c_data,"filled"); obj.addOptimizationDataTips(h_scatter,X,objective,objective_plot,eval_idx,var_names); hold on; h_best = plot(log10(x_data(best_idx)),log10(y_data(best_idx)),"kp", ... "MarkerSize",12, ... "MarkerFaceColor","y", ... "DisplayName","best"); obj.addOptimizationDataTips(h_best,X(best_idx,:),objective(best_idx),objective_plot(best_idx),eval_idx(best_idx),var_names); grid on; xlabel("log10(" + string(x_name) + ")"); ylabel("log10(" + string(y_name) + ")"); cb = colorbar; cb.Label.String = "log10(BER)"; title(string(x_name) + " vs " + string(y_name)); end end function addOptimizationDataTips(~,plot_handle,X,objective,objective_plot,eval_idx,var_names) plot_handle.DataTipTemplate.DataTipRows(end+1) = dataTipTextRow("Evaluation",eval_idx); plot_handle.DataTipTemplate.DataTipRows(end+1) = dataTipTextRow("BER",objective); plot_handle.DataTipTemplate.DataTipRows(end+1) = dataTipTextRow("BER shown",objective_plot); for var_idx = 1:numel(var_names) var_name = var_names{var_idx}; plot_handle.DataTipTemplate.DataTipRows(end+1) = dataTipTextRow(var_name,X.(var_name)); end end function objective_plot = positiveObjectiveForLogPlot(~,objective) objective_plot = objective; positive_values = objective(isfinite(objective) & objective > 0); if isempty(positive_values) floor_value = 1e-12; else floor_value = min(positive_values) / 10; end objective_plot(~isfinite(objective_plot) | objective_plot <= 0) = floor_value; end end end