356 lines
13 KiB
Matlab
356 lines
13 KiB
Matlab
classdef ML_MLSE < handle
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% ---------------------------------------------------------------------
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% W. Lanneer and Y. Lefevre,
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% “Machine Learning-Based Pre-Equalizers for Maximum Likelihood
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% Sequence Estimation in High-Speed PONs,” EUSIPCO 2023
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% ---------------------------------------------------------------------
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% This implementation reproduces the closed-loop ML-based
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% pre-equalizer training for MLSE, supporting both training and
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% detection (decision-directed) modes.
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% ---------------------------------------------------------------------
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properties
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sps
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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
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mu_dd
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epochs_dd
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adaptive_mu
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constellation
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L
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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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delta
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% Internal variables
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S
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Nf
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nStates
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nFeasible
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combs
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first_sym
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last_sym
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valid
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valid_to_idx
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valid_from_idx
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w
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% Fast lookup
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nSym
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key_table
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trans_index
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true_to_state_idx
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% Debug metrics
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ber = []
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ce = ones(1,1)
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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 = 0.001;
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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.adaptive_mu = 1;
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options.delta = 0;
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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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% ==============================================================
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% PROCESS
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% ==============================================================
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function [X,X_viterbi] = process(obj, X, D)
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% Normalize input RMS
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X = X.normalize("mode","rms");
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obj.constellation = sort(unique(D.signal),'ascend');
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obj.nSym = numel(obj.constellation);
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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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% --- Parameters
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obj.S = obj.nSym;
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obj.Nf = obj.order * obj.sps;
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obj.nStates = obj.S^obj.L;
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obj.nFeasible = obj.nStates * obj.S;
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% --- Trellis mapping
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obj.trellis_states = reshape(obj.constellation,1,[]);
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pre_comb_mat = repmat(obj.trellis_states, obj.L, 1);
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pre_comb_cell = mat2cell(pre_comb_mat, ones(1,obj.L), size(pre_comb_mat,2));
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obj.combs = fliplr(combvec(pre_comb_cell{:}).');
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obj.first_sym = obj.combs(:,1);
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obj.last_sym = obj.combs(:,end);
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obj.nStates = size(obj.combs,1);
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% --- Valid transitions
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obj.valid = false(obj.nStates);
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for from = 1:obj.nStates
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for to = 1:obj.nStates
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if all(obj.combs(to,2:end) == obj.combs(from,1:end-1))
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obj.valid(to,from) = true;
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end
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end
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end
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[obj.valid_to_idx,obj.valid_from_idx] = find(obj.valid);
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% --- Initialize weights
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if isempty(obj.w) || any(size(obj.w) ~= [obj.Nf+1,obj.nFeasible])
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obj.w = randn(obj.Nf+1,obj.nFeasible);
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end
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% --- Fast lookup tables
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[~, sym_idx_mat] = ismember(obj.combs, obj.constellation);
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key_vals = 1 + sum((sym_idx_mat - 1) .* (obj.nSym .^ (0:obj.L-1)), 2);
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max_key = obj.nSym^obj.L;
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obj.key_table = zeros(max_key,1,'uint32');
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obj.key_table(key_vals) = 1:obj.nStates;
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obj.trans_index = sparse(obj.nStates,obj.nStates);
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for i = 1:length(obj.valid_from_idx)
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f = obj.valid_from_idx(i);
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t = obj.valid_to_idx(i);
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obj.trans_index(t,f) = i;
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end
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% ==============================================================
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% TRAINING
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% ==============================================================
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fprintf('\n--- Training mode ---\n');
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obj.equalize(X.signal, D.signal, obj.mu_tr, obj.epochs_tr, obj.len_tr, true);
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obj.e_tr = obj.e;
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% ==============================================================
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% DECISION-DIRECTED / TESTING
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% ==============================================================
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fprintf('--- Decision-directed / detection mode ---\n');
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[y, y_vit] = obj.equalize(X.signal, D.signal, obj.mu_dd, obj.epochs_dd, X.length, false);
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X_viterbi = X;
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X.signal = y;
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X_viterbi.signal = y_vit;
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end
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% ==============================================================
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% EQUALIZE
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% ==============================================================
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function [y,y_ref] = equalize(obj,x,d,mu,epochs,N,training)
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debug = 0;
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showPlots = 0;
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y = zeros(N,1);
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nSymbols = ceil(N/obj.sps);
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for epoch = 1:epochs
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pm = zeros(obj.nStates,1);
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pred = zeros(nSymbols,obj.nStates,'uint32');
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pm_sto = nan(obj.nStates,nSymbols,'like',pm);
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CE_accum = 0;
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start_sample = 1;
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end_sample = N;
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start_symbol = 1 + floor((start_sample - 1)/obj.sps);
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% --- initialize true state
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if numel(d) >= obj.L && start_symbol >= obj.L
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init_seq = d(start_symbol-obj.L+1:start_symbol);
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key_init = obj.seq2key(init_seq);
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true_to_state_idx = obj.key_table(key_init);
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if true_to_state_idx==0, true_to_state_idx=1; end
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else
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true_to_state_idx = uint32(1);
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end
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for sample = start_sample:obj.sps:end_sample
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symbol = (sample - start_sample)/obj.sps + 1;
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sym_idx = start_symbol + (symbol - 1);
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% --- Observation window (with delta)
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i1 = sample - obj.Nf + 1 + obj.delta;
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i2 = sample + obj.delta;
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buf = x(max(1,i1):min(length(x),i2));
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padL = max(0,1 - i1);
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padR = max(0,i2 - length(x));
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yk = [zeros(padL,1); buf(:); zeros(padR,1)];
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yk = [yk;1];
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% --- Branch metrics
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c_hat = (yk.' * obj.w).';
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pm = pm - min(pm);
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v_tilde = pm(obj.valid_from_idx) + c_hat;
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% --- allocate once
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if epoch==1 && symbol==1
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obj.true_to_state_idx = ones(ceil(N/obj.sps),1,'uint32');
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end
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% --- previous "to" becomes "from"
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if symbol>1
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true_from_state_idx = obj.true_to_state_idx(symbol-1);
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else
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true_from_state_idx = 1;
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end
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% --- compute or reuse "to" state
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if epoch==1
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if sym_idx>=obj.L
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key_to = obj.seq2key(d(sym_idx-obj.L+1:sym_idx));
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state_idx = obj.key_table(key_to);
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if state_idx==0
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state_idx = true_from_state_idx;
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end
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obj.true_to_state_idx(symbol) = state_idx;
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else
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obj.true_to_state_idx(symbol) = true_from_state_idx;
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end
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end
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true_to_state_idx = obj.true_to_state_idx(symbol);
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% --- fast Dirac creation
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dirac = zeros(obj.nFeasible,1);
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trans_idx = obj.trans_index(true_to_state_idx,true_from_state_idx);
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if trans_idx~=0
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dirac(trans_idx)=1;
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end
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% ===================================================================
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% TRAINING MODE (weight update)
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% ===================================================================
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if training
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% --- Softmax and CE
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v_shift = -(v_tilde - min(v_tilde));
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v_shift = min(v_shift,100);
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expv = exp(v_shift);
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p = expv./(sum(expv)+eps);
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CE_symbol(symbol) = -log(p(dirac==1)+eps);
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% --- CE smoothing and adaptive μ
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if sym_idx>obj.L
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CE_smooth(symbol)=0.01*CE_symbol(symbol)+0.99*CE_symbol(symbol-1);
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else
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CE_smooth(symbol)=CE_symbol(symbol);
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end
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CE_accum=CE_accum+CE_symbol(symbol);
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% --- Gradient update
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dmp=(dirac-p)';
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dL_Dw=(yk).*dmp;
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if sym_idx>=obj.L
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if obj.adaptive_mu
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mu_eff=CE_smooth(symbol);
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mu_eff=max(min(mu_eff,0.2),1e-4);
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else
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mu_eff=mu;
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end
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obj.w=obj.w - mu_eff.*dL_Dw;
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end
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end
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% ===================================================================
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% DECODING MODE (Viterbi only)
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% ===================================================================
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% Compare-Select (always executed)
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vmat=inf(obj.nStates,obj.nStates);
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vmat(obj.valid)=v_tilde;
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[pm_next,pred(symbol,:)]=min(vmat,[],2);
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pm_next=pm_next-min(pm_next);
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pm=pm_next;
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pm_sto(:,symbol)=pm;
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end
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% --- Traceback
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[~,s_end]=min(pm);
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vpath=zeros(symbol,1,'uint32');
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vpath(symbol)=s_end;
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for n=symbol:-1:2
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vpath(n-1)=pred(n,vpath(n));
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end
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y_ref=d(start_symbol:end);
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y=obj.first_sym(vpath);
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% --- BER/CE reporting and plots
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if training
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err=sum(y~=y_ref(1:length(y)));
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ser=err/length(y);
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try
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ref_bits=PAMmapper(obj.S,0).demap(y_ref(1:length(y)));
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eq_bits=PAMmapper(obj.S,0).demap(y);
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[~,~,ber,~]=calc_ber(ref_bits,eq_bits,"skip_front",10,"skip_end",10,"returnErrorLocation",1);
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fprintf('Epoch %d - BER: %.2e\n',epoch,ber);
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obj.ber(epoch)=ber;
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catch
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fprintf('Epoch %d - SER: %.2e\n',epoch,ser);
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obj.ber(epoch)=ser;
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end
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obj.ce(epoch)=CE_accum/symbol;
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if debug && mod(epoch,10)==1 && showPlots
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figure(10);clf
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subplot(3,2,1:2);
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imagesc(obj.w);axis xy;colorbar;title('Filter W');
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subplot(3,2,3);
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vtilde_mat=NaN(obj.nStates,obj.nStates);
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vtilde_mat(obj.valid)=v_tilde;
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imagesc(vtilde_mat);axis xy;colorbar;title('Path Metrics (v\_tilde)');
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subplot(3,2,4);
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plot(1:symbol,pm_sto);title('Path Metric Evolution');
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subplot(3,2,5);hold on;
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scatter(1:symbol,CE_symbol,1,'.');
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scatter(1:symbol,CE_smooth,1,'.');
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title('Cross Entropy');
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subplot(3,2,6);hold on;
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yyaxis left
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scatter(1:length(obj.ce),obj.ce,10,'s','filled');
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ylabel('Cross Entropy');
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yyaxis right
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scatter(1:length(obj.ber),obj.ber,10,'d','filled');
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set(gca,'YScale','log');
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ylabel('BER (log)');
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xlabel('Epoch');grid on;
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title('Convergence');
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drawnow;
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end
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end
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end
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end
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% ==============================================================
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% Helper: Sequence → key (always scalar)
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% ==============================================================
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function key = seq2key(obj, seq)
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[~, idx] = ismember(flip(seq), obj.constellation);
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pow = (obj.nSym .^ (0:obj.L-1)).';
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key = 1 + sum((idx(:) - 1) .* pow);
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end
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end
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end
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