386 lines
14 KiB
Matlab
386 lines
14 KiB
Matlab
classdef FFE < 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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%LMS: mu in order of 0.001 for acceptable convergence speed
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%NLMS: mu in order of 0.01 for acceptable convergence speed
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%RLS: mu is lambda -> 0.99 -> 1 (has a strong dependency on this! use a loop to find out best values)
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% 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);
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% eq_ = FFE("epochs_tr",5,"epochs_dd",5,"len_tr",len_tr, ...
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% "mu_dd",1e-1,"mu_tr",0.4,"order",50, ...
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% "sps",2,"decide",0,"optmize_mus",1,"dd_mode",1, ...
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% "adaption_technique","nlms","mu_dc",1.021e-05);
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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_tr
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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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adaption_technique % nlms, lms, rls
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dd_mode % 1 or 0 to set DD-mode on or off
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mu_dd %weight update in dd mode
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epochs_dd
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dd_len_fraction
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mu_dc
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e_dc
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P % covariance matrix of rls
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constellation % symbol constellation
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decide %wether to return the (hard) decisions or the result after FFE (soft)
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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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end
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methods
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function obj = FFE(options)
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arguments(Input)
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options.sps = 2;
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options.order = 15;
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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.adaption_technique adaption_method = adaption_method.lms;
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options.dd_mode = 1;
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options.mu_dd = 1e-5;
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options.epochs_dd = 5;
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options.dd_len_fraction = 0.25;
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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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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.e = zeros(obj.order,1);
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obj.e_dc = 0;
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obj.error = 0;
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end
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function [X,Noi] = 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.e_dc = 0;
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delta = 0.05;
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obj.P = (1/delta) * eye(obj.order);
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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(obj.order,1);
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obj.e_dc = 0;
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obj.P = (1/delta) * eye(obj.order);
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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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obj.e_tr = obj.e;
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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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if obj.dd_mode
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n_dd = obj.ddLength(n);
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obj.equalize(X.signal, D.signal,obj.mu_dd,obj.epochs_dd,n_dd,training,showviz);
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end
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[signal,decision]=obj.applyCurrentTaps(X.signal,n);
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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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Noi = X;
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Noi = 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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x = [zeros(floor(obj.order/2),1); x; zeros(obj.order,1)];
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lambda = mu;
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if training
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mask = ones(obj.order,1);
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else
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mask = zeros(obj.order,1);
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mask(900:end) = 1;
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mask(ceil(length(obj.e)/2)) = 1;
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end
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mask = ones(obj.order,1);
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maincursor_pos=ceil(length(obj.e)/2);
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always_ideal_decision = 0;
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grad =0;
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weight = 0;
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update = 0;
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if mu == 0 || (~obj.dd_mode && ~training)
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epochs = 1;
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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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U = x(obj.order+sample-1:-1:sample);
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y(symbol,1) = obj.e_dc + (obj.e.*mask).' * U; % Calculating output of LMS __ * |
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if training
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d_hat(symbol,1) = d(symbol);
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else
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if ~always_ideal_decision
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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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else
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d_hat(symbol,1) = d(symbol);
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end
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end
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% err(symbol) = y(symbol) - d_hat(symbol); % Instantaneous error
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err(symbol) = d_hat(symbol) - y(symbol); % Instantaneous error
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true_err(symbol) = y(symbol) - d(symbol); % Instantaneous error
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if training || obj.dd_mode
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switch obj.adaption_technique
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case adaption_method.lms
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% mu used as update weight (suggestion: 0.001)
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weight = mu;
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grad = err(symbol) * U;
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update = grad * weight;
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obj.e = obj.e + update;
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case adaption_method.nlms
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% mu used as update weight (suggestion: 0.01-0.05; bit higher during tr)
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normU = ((U.'*U)) + eps;
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weight = mu / normU;
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grad = err(symbol) * U;
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update = grad * weight;
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obj.e = obj.e + update;
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case adaption_method.rls
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% RLS‐Gain:
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denom = lambda + U.' * obj.P * U;
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k = (obj.P * U) / denom;
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% Gewichtsupdate:
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update = k * err(symbol);
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obj.e = obj.e + update;
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% P-Matrix‐Update:
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obj.P = (1/lambda) * (obj.P - k * (U.' * obj.P));
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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(symbol);
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end
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end
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if obj.save_debug
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obj.debug_struct.error(epoch,symbol) = err(symbol) * err(symbol)'; % Instantaneous square error
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if training
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obj.debug_struct.error_tr(epoch,symbol) = err(symbol) * err(symbol)'; % Instantaneous square error
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obj.debug_struct.update_tr(epoch,symbol) = update.'*update ./ rms(obj.e);
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else
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% if symbol == length(d)
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% M = numel(unique(d));
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% bits_ref = PAMmapper(M,0).demap(d);
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% bits_eq = PAMmapper(M,0).demap(d_hat);
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% [~,~,obj.debug_struct.ber(epoch)] = calc_ber(bits_eq,bits_ref);
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% end
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end
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% obj.debug_struct.main_cursor(epoch,symbol) = abs(obj.e(maincursor_pos));
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% obj.debug_struct.mu_nlms(epoch,symbol) = weight;
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% obj.debug_struct.update_gradient(epoch,symbol) = grad.'*grad;
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% obj.debug_struct.update(epoch,symbol) = update.'*update ./ rms(obj.e);
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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 [y,d_hat] = applyCurrentTaps(obj,x,N)
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x = [zeros(floor(obj.order/2),1); x; zeros(obj.order,1)];
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for sample = 1 : obj.sps : N
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symbol = (sample - 1) / obj.sps + 1;
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U = x(obj.order+sample-1:-1:sample);
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y(symbol,1) = obj.e_dc + obj.e.' * U;
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[~,symbol_idx] = min(abs(y(symbol) - obj.constellation));
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d_hat(symbol,1) = obj.constellation(symbol_idx);
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end
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end
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function N_dd = ddLength(obj,N)
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if isempty(obj.dd_len_fraction) || obj.dd_len_fraction <= 0 || obj.dd_len_fraction >= 1
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N_dd = N;
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return
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end
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N_dd = floor(N * obj.dd_len_fraction);
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N_dd = max(obj.sps,N_dd);
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N_dd = min(N,N_dd);
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end
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function optimizeMus(obj,x,d)
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switch obj.adaption_technique
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case adaption_method.lms
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mu_range = [1e-5, 1e-2];
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case adaption_method.nlms
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mu_range = [1e-3, 5e-1];
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case adaption_method.rls
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mu_range = [0.98, 0.99999];
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end
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mu_dc_range = [1e-5, 1e-1];
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mu_tr_var = optimizableVariable("mu_tr",mu_range,"Transform","log");
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vars = mu_tr_var;
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if obj.dd_mode
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vars = [vars, optimizableVariable("mu_dd",mu_range,"Transform","log")];
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end
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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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obj.mu_optimization = bayesopt(@(p)obj.muObjective(p,x,d),vars, ...
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"MaxObjectiveEvaluations",10, ...
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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.mu_optimization.XAtMinObjective.mu_tr;
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if obj.dd_mode
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obj.mu_dd = obj.mu_optimization.XAtMinObjective.mu_dd;
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end
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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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objective_db = 10*log10(obj.mu_optimization.MinObjective);
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if obj.dd_mode && optimize_mu_dc
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fprintf("\nFFE mu opt done: mu_tr=%9.3e, mu_dd=%9.3e, mu_dc=%9.3e, MSE=%9.3e, MSE_dB=%7.2f dB\n", ...
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obj.mu_tr,obj.mu_dd,obj.mu_dc,obj.mu_optimization.MinObjective,objective_db);
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elseif obj.dd_mode
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fprintf("\nFFE mu opt done: mu_tr=%9.3e, mu_dd=%9.3e, MSE=%9.3e, MSE_dB=%7.2f dB\n", ...
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obj.mu_tr,obj.mu_dd,obj.mu_optimization.MinObjective,objective_db);
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elseif optimize_mu_dc
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fprintf("\nFFE mu opt done: mu_tr=%9.3e, mu_dc=%9.3e, MSE=%9.3e, MSE_dB=%7.2f dB\n", ...
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obj.mu_tr,obj.mu_dc,obj.mu_optimization.MinObjective,objective_db);
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else
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fprintf("\nFFE mu opt done: mu_tr=%9.3e, MSE=%9.3e, MSE_dB=%7.2f dB\n", ...
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obj.mu_tr,obj.mu_optimization.MinObjective,objective_db);
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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_debug = obj.save_debug;
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old_mu_dc = obj.mu_dc;
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obj.save_debug = 1;
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if isprop(params,"mu_dc")
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obj.mu_dc = params.mu_dc;
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end
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obj.e = zeros(obj.order,1);
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obj.e_dc = 0;
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obj.P = (1/0.05) * eye(obj.order);
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obj.debug_struct = struct();
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obj.equalize(x,d,params.mu_tr,obj.epochs_tr,obj.len_tr,1,0);
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if obj.dd_mode
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obj.equalize(x,d,params.mu_dd,obj.epochs_dd,obj.ddLength(numel(x)),0,0);
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objective = mean(obj.debug_struct.error(end,:),"omitnan");
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else
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objective = mean(obj.debug_struct.error_tr(end,:),"omitnan");
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end
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if ~isfinite(objective)
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objective = inf;
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end
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objective_db = 10*log10(objective);
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obj.mu_optimization_iter = obj.mu_optimization_iter + 1;
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optimize_mu_dc = isprop(params,"mu_dc");
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if obj.dd_mode && optimize_mu_dc
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fprintf("\rFFE mu opt %02d: mu_tr=%9.3e, mu_dd=%9.3e, mu_dc=%9.3e, MSE=%9.3e, MSE_dB=%7.2f dB", ...
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obj.mu_optimization_iter,params.mu_tr,params.mu_dd,params.mu_dc,objective,objective_db);
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elseif obj.dd_mode
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fprintf("\rFFE mu opt %02d: mu_tr=%9.3e, mu_dd=%9.3e, MSE=%9.3e, MSE_dB=%7.2f dB", ...
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obj.mu_optimization_iter,params.mu_tr,params.mu_dd,objective,objective_db);
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elseif optimize_mu_dc
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fprintf("\rFFE mu opt %02d: mu_tr=%9.3e, mu_dc=%9.3e, MSE=%9.3e, MSE_dB=%7.2f dB", ...
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obj.mu_optimization_iter,params.mu_tr,params.mu_dc,objective,objective_db);
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else
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fprintf("\rFFE mu opt %02d: mu_tr=%9.3e, MSE=%9.3e, MSE_dB=%7.2f dB", ...
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obj.mu_optimization_iter,params.mu_tr,objective,objective_db);
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end
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obj.save_debug = old_debug;
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obj.mu_dc = old_mu_dc;
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end
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end
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end
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