Many changes here and there. I lost track... :-(
Current work is on MLSE and SD Decoding etc. MLSE is currently not 100% working, the scalings are maybe off?!
This commit is contained in:
Silas Oettinghaus
@@ -83,6 +83,14 @@ classdef MLSE < handle
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% impulse respnse to remove from signal
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obj.DIR = flip(obj.DIR); %i.e. -0.2676 -0.0478 1.0000
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% % make the combined impulse-response have net gain = 1
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% h = obj.DIR(:);
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% h = h / sum(h);
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% obj.DIR = h.';
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% Normalize the Trellis states to =1 RMS
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obj.trellis_states = obj.trellis_states ./ rms(obj.trellis_states);
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% seems to be the only way to use combvec for a flexible amount
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% of vectors. 'combs' contains all trellis states
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pre_comb_mat = repmat(obj.trellis_states,length(obj.DIR)-1,1);
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@@ -116,6 +124,7 @@ classdef MLSE < handle
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% first: RMS normalization of input data (rms==1)
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data_in = data_in ./ rms(data_in);
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data_in = data_in - mean(data_in);
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% then, match amplitude levels of input signal to those of the calculated ideal symbols
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% i.e. match the rms values of data_in to noise_free_received (rms=1.xx)
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@@ -125,6 +134,10 @@ classdef MLSE < handle
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end
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end
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y_clean = conv( data_ref, flip(obj.DIR), "same" );
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sigma2 = var( data_in - y_clean );
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inv2s2 = 1/(2*sigma2);
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%% FORWARD PASS (VITERBI -Alpha's) %%%%%
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@@ -134,7 +147,7 @@ classdef MLSE < handle
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% first start is evaluated without ISI/ wihout the full Impulse response
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% so simply use the constellation here
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bm = -(data_in(1) - last_sym).^2 ;
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bm = -(data_in(1) - last_sym).^2 * inv2s2;
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pm = pm + bm;
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[alpha(:,1),pm_survivor_fw_idx(:,1)] = max(pm,[],2);
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pm = repmat(alpha(:,1).',nStates,1);
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@@ -143,10 +156,10 @@ classdef MLSE < handle
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% Forward Recursion (FSM Computation)
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for n = 2:length(data_in)
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bm = -(data_in(n) - noise_free_received).^2 ;
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bm = -(data_in(n) - noise_free_received).^2 * inv2s2;
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pm = pm + bm;
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[alpha(:,n),pm_survivor_fw_idx(:,n)] = max(pm,[],2); % choose lowest path metric as new state
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pm = repmat(alpha(:,n).',nStates,1); % update pm (chosen state to 2nd dimension -> FROM state)
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[alpha(:,n),pm_survivor_fw_idx(:,n)] = max(pm,[],2); % choose lowest path metric as new state
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pm = repmat(alpha(:,n).',nStates,1); % update pm (chosen state to 2nd dimension -> FROM state)
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bm_fw(:,:,n) = bm;
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@@ -177,7 +190,7 @@ classdef MLSE < handle
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% predecessor
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for h = length(data_in)-1:-1:1
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bm = -(data_in(h+1) - noise_free_received).^2 ;
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bm = -(data_in(h+1) - noise_free_received).^2 * inv2s2;
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pm = pm + bm.';
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[beta(:,h),pm_survivor_bw_idx(:,h)] = max(pm,[],2); % choose lowest path metric as new state
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pm = repmat(beta(:,h).',nStates,1); % update pm (chosen state to 2nd dimension -> FROM state)
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@@ -214,10 +227,22 @@ classdef MLSE < handle
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%% FORWARD PASS PAM2,4,8 %%%%%
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nml_LLP = LLP - max(LLP);
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expLLP = exp(nml_LLP); %subtract highst value for better numerical stability, LLP's are not always close to zero
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state_prob = expLLP ./ sum(expLLP);
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nml_LLP = LLP - max(LLP); %subtract highest value for better numerical stability, LLP's are not always close to zero
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expLLP = exp(nml_LLP);
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state_prob = expLLP ./ sum(expLLP); % sums to one (or numerically close to one)
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% compute symbol‐posteriors from LLP in the log‐domain:
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amax = max(LLP,[],1);
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logZ = amax + log(sum(exp(LLP - amax), 1));
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logPstate = LLP - logZ; % still in log‐domain
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state_prob = exp(logPstate); % exact, sums to 1
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% figure
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% hold on;
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% for i = 1:obj.M
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% scatter(1:length(expLLP),expLLP(i,:),1,'.');
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% end
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% scatter(1:length(expLLP),max(expLLP(:,:)),3,'.');
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if obj.M == 6
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@@ -305,8 +330,8 @@ classdef MLSE < handle
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% Number of symbols and bits per symbol
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num_bits = log2(length(obj.trellis_states)); % 2 bits per symbol
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bit_mapping = PAMmapper(length(obj.trellis_states),0,"eth_style",0).demap(first_sym./rms(first_sym));
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% bit_mapping = PAMmapper(length(obj.trellis_states),0,"eth_style",0).demap(first_sym./rms(first_sym));
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bit_mapping = PAMmapper(length(obj.trellis_states),0,"eth_style",0).showBitMapping;
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% Initialize LLR storage
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LLR_maxlogmap = zeros(length(data_in),num_bits);
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LLR_exact = zeros(length(data_in),num_bits);
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@@ -343,8 +368,8 @@ classdef MLSE < handle
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llr1 = LLR_exact(idx_bit_0,k);
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% Calculate mutual information for bit position k
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I0 = mean(log2(1 + exp(llr0(100:end-100)))); % exp(--LLR) = exp(positive) > 1
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I1 = mean(log2(1 + exp(-llr1(100:end-100)))); % exp(-+LLR) = exp(negative) < 1
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I0 = mean(log2(1 + exp(llr0))); % exp(--LLR) = exp(positive) > 1
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I1 = mean(log2(1 + exp(-llr1))); % exp(-+LLR) = exp(negative) < 1
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MI(k) = 1 - 0.5 * (I0 + I1);
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end
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@@ -354,8 +379,7 @@ classdef MLSE < handle
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VITERBI_ESTIMATION_SYMBOLS = VITERBI_ESTIMATION_SYMBOLS./rms(VITERBI_ESTIMATION_SYMBOLS);
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debug = 0;
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debug = 1;
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if debug
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%%% DEBUG PLOT LIKELIHOOD RATIOS %%%
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figure(115);clf
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@@ -380,6 +404,7 @@ classdef MLSE < handle
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if debug
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tx_bits = reshape(tx_bits',[],1);
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disp('Start DEBUG MLSE:')
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% DECIDE based on Viterbi traceback
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VITERBI_ESTIMATION_SYMBOLS = VITERBI_ESTIMATION_SYMBOLS./rms(VITERBI_ESTIMATION_SYMBOLS);
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rx_bits = PAMmapper(obj.M,0,"eth_style",0).demap(VITERBI_ESTIMATION_SYMBOLS');
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@@ -417,13 +442,19 @@ classdef MLSE < handle
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rx_bits = reshape(rx_bits',[],1);
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[~,~,ber_fw,~] = calc_ber(rx_bits,tx_bits,"skip_front",100,"skip_end",150,"returnErrorLocation",1);
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fprintf('FW BER: %.2e \n',ber_fw);
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disp('Stop DEBUG MLSE:')
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disp('')
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end
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end
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end
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methods (Access=private)
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function s = logsumexp(a,dim)
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% returns log(sum(exp(a),dim)) safely
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amax = max(a,[],dim);
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s = amax + log(sum(exp(a - amax), dim));
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end
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end
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end
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152
Classes/04_DSP/Sequence Detection/MLSE_new.m
Normal file
152
Classes/04_DSP/Sequence Detection/MLSE_new.m
Normal file
@@ -0,0 +1,152 @@
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classdef MLSE_new < handle
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%MLSE: BCJR‐based soft‐output for PAM‐M sequence estimation & GMI
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properties
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M % PAM order (e.g. 4)
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DIR % channel impulse response
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trellis_states % PAM constellation levels (e.g. [-3 -1 1 3])
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end
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methods
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function obj = MLSE_new(opts)
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arguments
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opts.M double = 4;
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opts.DIR double = 1;
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opts.trellis_states double = [-3 -1 1 3];
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end
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obj.M = opts.M;
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obj.DIR = opts.DIR;
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obj.trellis_states = opts.trellis_states;
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end
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function [hd_out, LLR, NGMI] = process(obj, signalclass,ref_symbolclass)
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% rx, tx: column vectors of equalized and reference symbols
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data_in = signalclass.signal;
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shape_in = size(data_in);
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data_ref = ref_symbolclass.signal;
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[data_out_hd,LLR,GMI] = obj.bcjr_soft(data_in,data_ref);
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try
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data_out_hd = reshape(data_out_hd,shape_in(1),shape_in(2));
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catch
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warning('output reshaping failed after MLSE');
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end
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signalclass_hd = signalclass;
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signalclass_hd.signal = data_out_hd;
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[hd_out, LLR, NGMI] = obj.bcjr_soft(rx, tx);
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end
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end
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methods (Access=private)
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function [hd_sym, LLR, NGMI] = bcjr_soft(obj, y, x)
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%--- build trellis states & branch outputs ---
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DIR = flip(obj.DIR(:));
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S = combvec(obj.trellis_states, obj.trellis_states)';
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prev = S(:,1); cur = S(:,2);
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branch_out = prev*DIR(1) + cur*DIR(2); % for 2‐tap
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N = numel(y);
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M = obj.M;
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m = log2(M);
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%--- forward/backward metrics (max‐log) ---
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nStates = numel(obj.trellis_states);
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alpha = -inf(nStates,N);
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beta = -inf(nStates,N);
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bm_fw = zeros(nStates,nStates,N);
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% branch metrics
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sigma2 = var(y - x);
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inv2sigma2 = 1/(2*sigma2);
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for n=1:N
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bm = -((y(n)-branch_out).^2)* inv2sigma2;
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bm = reshape(bm, nStates, nStates);
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bm_fw(:,:,n) = bm;
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end
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% forward
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alpha(:,1) = max(bm_fw(:,:,1),[],2);
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for n=2:N
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mat = alpha(:,n-1) + bm_fw(:,:,n);
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alpha(:,n) = max(mat,[],2);
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end
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% backward
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beta(:,N) = 0;
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for n=N-1:-1:1
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mat = beta(:,n+1).' + bm_fw(:,:,n+1);
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beta(:,n) = max(mat,[],2);
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end
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% Precompute the “zero‐th” forward metric
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alpha0 = zeros(nStates,1);
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LLP = -inf(nStates,nStates,N);
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for n = 1:N
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% Select the correct previous alpha column
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if n == 1
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a_prev = alpha0;
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else
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a_prev = alpha(:,n-1);
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end
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% Combine α, branch metric, and β
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mat = a_prev + bm_fw(:,:,n) + beta(:,n).';
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LLP(:,:,n) = mat;
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end
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%--- compute LLRs symbol‐wise via log‐sum‐exp over branches ---
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levels = obj.trellis_states;
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bit_map = PAMmapper(M,0).demap(levels');
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LLR = zeros(N,m);
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for n=1:N
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% sum branch posteriors per symbol
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llp_n = LLP(:,:,n);
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logZ = logsumexp(llp_n(:));
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post = exp(llp_n - logZ);
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% aggregate per symbol index
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Psym = zeros(M,1);
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for i=1:nStates
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for j=1:nStates
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% branch (i->j) emits symbol 'cur(j)'
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idx = find(levels==cur(j));
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Psym(idx) = Psym(idx) + post(i,j);
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end
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end
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% bit‐LLR from symbol posterior
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for k=1:m
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idx1 = bit_map(:,k)==1;
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idx0 = ~idx1;
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P1 = sum(Psym(idx1));
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P0 = sum(Psym(idx0));
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LLR(n,k) = log(P1/P0);
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end
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end
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%--- hard decisions ---
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[~,symIdx] = max(LLR,[],2);
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hd_sym = levels(symIdx);
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%--- GMI via Alvarado Eq.(30) ---
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tx_bits = PAMmapper(M,0).demap(x);
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MI = zeros(1,m);
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for k=1:m
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r0 = LLR(tx_bits(:,k)==0,k);
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r1 = LLR(tx_bits(:,k)==1,k);
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I0 = mean(log2(1+exp(-r0)));
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I1 = mean(log2(1+exp(+r1)));
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MI(k) = 1 - 0.5*(I0+I1);
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end
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GMI = sum(MI);
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NGMI = GMI/m;
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end
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end
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end
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function s = logsumexp(a)
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m = max(a(:));
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s = m + log(sum(exp(a-m), 'all'));
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end
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