Gif stuff
nonlinear MLSE investigation trying hard to implment ML-based pre Equalization to find the branch metrics
This commit is contained in:
Silas Oettinghaus
@@ -131,7 +131,7 @@ classdef FFE < handle
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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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save_debug = 1;
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save_debug = 0;
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grad =0;
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weight = 0;
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update = 0;
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233
Classes/04_DSP/Equalizer/FFE_MLSE.m
Normal file
233
Classes/04_DSP/Equalizer/FFE_MLSE.m
Normal file
@@ -0,0 +1,233 @@
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classdef ML_MLSE < 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 0.0001 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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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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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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constellation
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L %viterbi memory length
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alpha
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DIR
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DIR_flip
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trellis_states
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traceback_depth
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end
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methods
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function obj = ML_MLSE(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.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.traceback_depth = 1024;
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options.L = 1
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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.error = 0;
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end
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function [X,X_viterbi] = 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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if length(X)/length(D) ~= obj.sps
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warning('Signal length does not fit to reference!');
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end
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% Training Mode
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n = obj.len_tr;
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training = 1;
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obj.equalize(X.signal, D.signal,obj.mu_tr,obj.epochs_dd,n,training);
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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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[y,y_vit]=obj.equalize(X.signal, D.signal,obj.mu_dd,obj.epochs_dd,n,training);
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X_viterbi = X;
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X.signal = y;
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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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X_viterbi.signal = y_vit;
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X_viterbi.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),'order FFE + PF + Viterbi'];
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X_viterbi = X_viterbi.logbookentry(lbdesc); % append to logbook
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end
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function [y,y_vit] = equalize(obj,x,d,mu,epochs,N,training)
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% ==============================================================
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% FFE + Whitening + Viterbi Equalizer (reference implementation)
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% ==============================================================
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% --- Input padding and preallocation
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x = [zeros(floor(obj.order/2),1); x; zeros(obj.order,1)];
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N_ = N / obj.sps;
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y = zeros(N_,1);
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y_white = zeros(N_,1);
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for epoch = 1:epochs
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% ==============================================================
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% INITIALIZATION (only before final epoch and detection mode)
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% ==============================================================
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if epoch == epochs && ~training
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% --- Parameters
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S = numel(unique(d));
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L = obj.L;
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nStates = S^L;
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nFeasible = S^(L-1)*S;
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% --- Trellis setup
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obj.DIR = arburg(y-d, L);
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obj.DIR_flip = flip(obj.DIR);
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obj.trellis_states = reshape(unique(d),1,[]);
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pre_comb_mat = repmat(obj.trellis_states, L, 1);
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pre_comb_cell = mat2cell(pre_comb_mat, ones(1,L), size(pre_comb_mat,2));
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combs = fliplr(combvec(pre_comb_cell{:}).');
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first_sym = combs(:,1);
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last_sym = combs(:,end);
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nStates = size(combs,1);
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noise_free_received = inf(nStates,nStates);
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valid = false(nStates);
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for from = 1:nStates
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for to = 1:nStates
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if all(combs(to,2:end) == combs(from,1:end-1))
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noise_free_received(to,from) = ...
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dot(combs(to,:), obj.DIR_flip(end:-1:2)) + last_sym(from)*obj.DIR_flip(1);
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valid(to,from) = true;
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end
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end
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end
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nf_vec = noise_free_received(valid);
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[valid_to, valid_from] = find(valid);
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from_per_to = arrayfun(@(to)find(valid(to,:)), 1:nStates, 'UniformOutput', false);
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% --- Noise stats
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y_ideal = conv(d(:), obj.DIR(:), "same");
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sigma2 = mean(abs(y - y_ideal).^2);
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inv2s2 = 1/(2*sigma2);
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% --- Vector initialization
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bm_vec = zeros(1,nFeasible);
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pm = zeros(nStates,1);
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pm_next = zeros(nStates,1);
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bm_fw = zeros(nStates,nStates,length(y));
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zi = zeros(max(numel(obj.DIR)-1,0),1);
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end
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% ==============================================================
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% RUNTIME LOOP (FFE update + Viterbi detection in last epoch)
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% ==============================================================
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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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% --- FFE output
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U = x(obj.order+sample-1:-1:sample);
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y(symbol,1) = obj.e.' * U;
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% --- Decision
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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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[~,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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% --- LMS weight update
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err(symbol) = d_hat(symbol) - y(symbol);
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obj.e = obj.e + mu * (err(symbol) * U);
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% --- Whitening + Viterbi (final epoch only)
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if epoch == epochs && ~training
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[y_white(symbol), zi] = filter(obj.DIR,1,y(symbol), zi);
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if symbol == 1
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pm = -inf(nStates,nStates);
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pm(:,1:nStates) = 0;
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else
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bm_vec = -(y_white(symbol) - nf_vec).^2 * inv2s2;
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bm_mat = -inf(nStates,nStates);
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bm_mat(valid) = bm_vec;
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pm_new = pm + bm_mat;
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[pm_survive(:,symbol), pm_survivor_fw_idx(:,symbol)] = max(pm_new,[],2);
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pm = repmat(pm_survive(:,symbol).', nStates,1);
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end
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% --- Traceback
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if mod(symbol,obj.traceback_depth) == 0
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[~,viterbi_path(symbol)] = max(pm_survive(:,symbol));
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for n = symbol:-1:symbol-obj.traceback_depth+2
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viterbi_path(n-1) = pm_survivor_fw_idx(viterbi_path(n),n);
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end
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end
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end
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end
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% --- Final reconstruction
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if epoch == epochs && ~training
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y_vit = first_sym(viterbi_path);
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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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246
Classes/04_DSP/Equalizer/ML_MLSE.m
Normal file
246
Classes/04_DSP/Equalizer/ML_MLSE.m
Normal file
@@ -0,0 +1,246 @@
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classdef ML_MLSE < 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 0.0001 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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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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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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constellation
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L %viterbi memory length
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alpha
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DIR
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DIR_flip
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trellis_states
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traceback_depth
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end
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methods
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function obj = ML_MLSE(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.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.traceback_depth = 1024;
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options.L = 1
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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.error = 0;
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end
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function [X,X_viterbi] = 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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if length(X)/length(D) ~= obj.sps
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warning('Signal length does not fit to reference!');
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end
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% Training Mode
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n = obj.len_tr;
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training = 1;
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obj.equalize(X.signal, D.signal,obj.mu_tr,obj.epochs_dd,n,training);
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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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[y,y_vit]=obj.equalize(X.signal, D.signal,obj.mu_dd,obj.epochs_dd,n,training);
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X_viterbi = X;
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X.signal = y;
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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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X_viterbi.signal = y_vit;
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X_viterbi.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),'order FFE + PF + Viterbi'];
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X_viterbi = X_viterbi.logbookentry(lbdesc); % append to logbook
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end
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function [y,y_vit] = equalize(obj,x,d,mu,epochs,N,training)
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% ==============================================================
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% FFE + Whitening + ML-Based Branch Metric Estimation + Viterbi
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% ==============================================================
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% --- Input padding and preallocation
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x = [zeros(floor(obj.order/2),1); x; zeros(obj.order,1)];
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N_ = N / obj.sps;
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y = zeros(N_,1);
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y_white = zeros(N_,1);
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for epoch = 1:epochs
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% ==============================================================
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% INITIALIZATION (only before final epoch and detection mode)
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% ==============================================================
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if epoch == epochs && ~training
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% --- Parameters
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S = numel(unique(d)); % alphabet size
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L = obj.L; % MLSE memory
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Nf = L; % filter length
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Delta = ceil(L/2); % delay parameter
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nStates = S^L;
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nFeasible = S^(L-1)*S;
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% --- Trellis mapping
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obj.DIR = arburg(y-d, L);
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obj.DIR_flip = flip(obj.DIR);
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obj.trellis_states = reshape(unique(d),1,[]);
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pre_comb_mat = repmat(obj.trellis_states, L, 1);
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pre_comb_cell = mat2cell(pre_comb_mat, ones(1,L), size(pre_comb_mat,2));
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combs = fliplr(combvec(pre_comb_cell{:}).');
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first_sym = combs(:,1);
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last_sym = combs(:,end);
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nStates = size(combs,1);
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% --- Valid transitions
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valid = false(nStates);
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for from = 1:nStates
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for to = 1:nStates
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if all(combs(to,2:end) == combs(from,1:end-1))
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valid(to,from) = true;
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end
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end
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end
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[valid_to, valid_from] = find(valid);
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% --- Noise estimation
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y_ideal = conv(d(:), obj.DIR(:), "same");
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sigma2 = mean(abs(y - y_ideal).^2);
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inv2s2 = 1/(2*sigma2);
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% --- Allocate vectors and weights
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pm = zeros(nStates,1);
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w = zeros(Nf,nFeasible); % filter weights per transition
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b = zeros(1,nFeasible); % bias terms
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v_hat = zeros(1,nFeasible);
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v_tilde = zeros(1,nFeasible);
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bm_vec = zeros(1,nFeasible);
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zi = zeros(max(numel(obj.DIR)-1,0),1);
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end
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% ==============================================================
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% RUNTIME LOOP
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% ==============================================================
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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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% --- FFE output
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U = x(obj.order+sample-1:-1:sample);
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y(symbol,1) = obj.e.' * U;
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% --- Decision / FFE adaptation
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if training
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d_hat = d(symbol);
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else
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[~,idx] = min(abs(y(symbol) - obj.constellation));
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d_hat = obj.constellation(idx);
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end
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err = d_hat - y(symbol);
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obj.e = obj.e + mu * (err * U);
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% --- Whitening + MLSE in last epoch
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if epoch == epochs && ~training
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[y_white(symbol), zi] = filter(obj.DIR,1,y(symbol), zi);
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k = symbol;
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% --- Build Δ-delayed observation window y_k
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i1 = k - Nf + 1 + Delta;
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i2 = k + Delta;
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buf = y_white(max(1,i1):min(length(y_white),i2));
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padL = max(0,1 - i1);
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padR = max(0,i2 - length(y_white));
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yk = [zeros(padL,1); buf(:); zeros(padR,1)]; % Nf×1
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% --- Predict branch metrics for all feasible transitions
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v_hat = (yk.' * w) + b; % [1×nFeasible]
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v_hat = v_hat.'; % [nFeasible×1]
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% --- Extended path metrics
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v_tilde = pm(valid_from) + v_hat; % [nFeasible×1]
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% --- Compute branch metrics (distance)
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bm_vec = -(y_white(k) - v_hat).^2 * inv2s2; % 1×nFeasible
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% --- Survivor selection (vector aggregation)
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pm_new_vec = pm(valid_from) + bm_vec.'; % nFeasible×1
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pm_next = -inf(nStates,1);
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surv_idx = zeros(nStates,1);
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for t = 1:nStates
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mask = (valid_to==t);
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[pm_next(t), arg] = max(pm_new_vec(mask));
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surv_idx(t) = valid_from(find(mask,1,'first')-1+arg);
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end
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pm = pm_next;
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% --- Traceback
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if mod(symbol,obj.traceback_depth) == 0
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[~,viterbi_path(symbol)] = max(pm);
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for n = symbol:-1:symbol-obj.traceback_depth+2
|
||||
viterbi_path(n-1) = surv_idx(viterbi_path(n));
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
% --- Output reconstructed path
|
||||
if epoch == epochs && ~training
|
||||
y_vit = first_sym(viterbi_path);
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
end
|
||||
end
|
||||
@@ -277,14 +277,107 @@ classdef MLSE < handle
|
||||
|
||||
|
||||
if debug
|
||||
alpha_ = alpha - min(alpha) + eps;
|
||||
figure();hold on;
|
||||
n = 10;
|
||||
scatter(1:n,obj.trellis_states(repmat([1:numel(obj.trellis_states)]',1,n)),abs(alpha_(:,end-n+1:end)),'Marker','o','LineWidth',1);
|
||||
scatter(1:n,obj.trellis_states(viterbi_path(end-n+1:end)),500,'Marker','x','LineWidth',1,'MarkerEdgeColor','green');
|
||||
% scatter(1:n,data_ref(end-n+1:end),500,'Marker','x','LineWidth',1,'MarkerEdgeColor','red');
|
||||
yticks(obj.trellis_states);
|
||||
ylim([min(obj.trellis_states)-1 max(obj.trellis_states)+1]);
|
||||
% alpha_ = alpha - min(alpha) + eps;
|
||||
% figure();hold on;
|
||||
% n = 10;
|
||||
% scatter(1:n,obj.trellis_states(repmat([1:numel(obj.trellis_states)]',1,n)),abs(alpha_(:,end-n+1:end)),'Marker','o','LineWidth',1);
|
||||
% scatter(1:n,obj.trellis_states(viterbi_path(end-n+1:end)),500,'Marker','x','LineWidth',1,'MarkerEdgeColor','green');
|
||||
% % scatter(1:n,data_ref(end-n+1:end),500,'Marker','x','LineWidth',1,'MarkerEdgeColor','red');
|
||||
% yticks(obj.trellis_states);
|
||||
% ylim([min(obj.trellis_states)-1 max(obj.trellis_states)+1]);
|
||||
|
||||
%% ----- Build true path from known sequence (data_ref) -----
|
||||
% Memory length used by VA (L = length(obj.DIR)-1 symbols stored in state)
|
||||
L = size(combs,2); % each row of combs is the L-tap state vector
|
||||
N = length(data_in);
|
||||
|
||||
% Map each trellis level to an index (1..M)
|
||||
[~, level_to_idx] = ismember(levels, levels); %#ok<ASGLU> % identity map
|
||||
[ok_ref, ref_idx] = ismember(data_ref(:).', levels);
|
||||
if ~all(ok_ref)
|
||||
warning('Some data_ref symbols are not in "levels". True-path build may fail.');
|
||||
end
|
||||
|
||||
% Precompute next_state(from_state, u_idx) LUT such that:
|
||||
% combs(next_state,:) == [ combs(from_state,2:end) , levels(u_idx) ]
|
||||
next_state = zeros(size(combs,1), numel(levels), 'uint32');
|
||||
for from = 1:size(combs,1)
|
||||
prefix = combs(from,2:end); % what must match in 'to' for a valid transition
|
||||
for ui = 1:numel(levels)
|
||||
target = [prefix, levels(ui)];
|
||||
% find the unique 'to' whose state vector equals target
|
||||
to = find(all(bsxfun(@eq, combs, target), 2), 1, 'first');
|
||||
if isempty(to), to = 0; end
|
||||
next_state(from, ui) = to;
|
||||
end
|
||||
end
|
||||
|
||||
% Initialize true path at n=1: pick any state with last_sym == data_ref(1)
|
||||
% Prefer one whose suffix matches the first available history if L>1.
|
||||
cand = find(last_sym == data_ref(1));
|
||||
if isempty(cand)
|
||||
% fallback: choose closest in amplitude (should not happen if levels match)
|
||||
[~,ix] = min(abs(last_sym - data_ref(1)));
|
||||
cand = ix;
|
||||
end
|
||||
true_state_path = zeros(1,N,'uint32');
|
||||
true_state_path(1) = cand(1);
|
||||
|
||||
% Propagate forward using the known inputs data_ref(n)
|
||||
for n = 2:N
|
||||
ui = ref_idx(n); % index of the actual transmitted level at time n
|
||||
from = true_state_path(n-1);
|
||||
if from==0 || ui==0
|
||||
true_state_path(n) = 0;
|
||||
else
|
||||
true_state_path(n) = next_state(from, ui);
|
||||
if true_state_path(n)==0
|
||||
% Safety fallback: if no valid transition found (should not happen)
|
||||
% choose any to-state whose vector matches shift+current symbol
|
||||
target = [combs(from,2:end), levels(ui)];
|
||||
to = find(all(bsxfun(@eq, combs, target), 2), 1, 'first');
|
||||
if isempty(to), to = from; end
|
||||
true_state_path(n) = to;
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
%% ----- Collect branch metrics along decoded vs. true path -----
|
||||
bm_decoded = nan(1,N);
|
||||
bm_true = nan(1,N);
|
||||
|
||||
% n=1 in your code stores pm into bm_fw(:,:,1); real BMs start at n>=2
|
||||
for n = 2:N
|
||||
% Decoded path: to = viterbi_path(n), from = survivor that fed it
|
||||
to_d = viterbi_path(n);
|
||||
from_d = pm_survivor_fw_idx(to_d, n);
|
||||
bm_decoded(n) = bm_fw(to_d, from_d, n);
|
||||
|
||||
% True path: transition true_state_path(n-1) -> true_state_path(n)
|
||||
to_t = true_state_path(n);
|
||||
from_t = true_state_path(n-1);
|
||||
if to_t>0 && from_t>0
|
||||
bm_true(n) = bm_fw(to_t, from_t, n);
|
||||
end
|
||||
end
|
||||
|
||||
% Convert to "cost" for intuitive plotting (your BM is a log-likelihood)
|
||||
cost_dec = -bm_decoded;
|
||||
cost_true= -bm_true;
|
||||
|
||||
%% ----- Plot a short window for clarity -----
|
||||
win = max(2, N-20000):N; % last 200 samples (adjust as needed)
|
||||
figure('Color','w'); hold on; grid on; box on;
|
||||
plot(win, cost_true(win), 'LineWidth',1.2, 'DisplayName','True path cost (−BM)');
|
||||
plot(win, cost_dec(win), 'LineWidth',1.2, 'DisplayName','Decoded path cost (−BM)');
|
||||
xlabel('Time index n'); ylabel('Branch cost'); title('Branch metrics along true vs decoded path');
|
||||
legend('Location','best');
|
||||
|
||||
%% ----- Optional: overlay symbol levels for the same window -----
|
||||
yyaxis right
|
||||
plot(win, data_in(win), ':', 'LineWidth',0.8, 'DisplayName','y(n)');
|
||||
ylabel('Amplitude');
|
||||
|
||||
end
|
||||
|
||||
VITERBI_ESTIMATION_SYMBOLS(1:length(data_in)) = first_sym(viterbi_path);
|
||||
@@ -564,11 +657,6 @@ classdef MLSE < handle
|
||||
|
||||
end
|
||||
|
||||
function s = logsumexp(a,dim)
|
||||
% returns log(sum(exp(a),dim)) safely
|
||||
amax = max(a,[],dim);
|
||||
s = amax + log(sum(exp(a - amax), dim));
|
||||
end
|
||||
|
||||
end
|
||||
end
|
||||
|
||||
Reference in New Issue
Block a user