420 lines
18 KiB
Matlab
420 lines
18 KiB
Matlab
classdef MLSE < handle
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%MLSE calculates the most probable sequence for an input signal with given/ known channel impulse response of any length
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properties(Access=public)
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M %PAM-M
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DIR
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trellis_states
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duobinary_output
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end
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methods (Access=public)
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function obj = MLSE(options)
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%NAME Construct an instance of this class
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% Detailed explanation goes here
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arguments
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options.M double = 4;
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options.DIR double = [1];
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options.trellis_states double = [-3 -1 1 3];
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options.duobinary_output logical = false;
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end
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%
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fn = fieldnames(options);
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for n = 1:numel(fn)
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try
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obj.(fn{n}) = options.(fn{n});
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end
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end
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% do more stuff
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end
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function [signalclass_hd,signalclass_sd] = process(obj,signalclass,ref_symbolclass)
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data_in = signalclass.signal;
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data_ref = ref_symbolclass.signal;
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[data_out_hd,data_out_sd] = obj.process_(data_in,data_ref);
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signalclass_hd = signalclass;
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signalclass_hd.signal = data_out_hd;
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signalclass_sd = signalclass;
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signalclass_sd.signal = data_out_sd;
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end
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function [VITERBI_ESTIMATION_SYMBOLS,soft_decisions] = process_(obj,data_in,data_ref)
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% remove unnecessary zeros at start of impulse response to keep
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% number of trellis states minimal
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DIR_nonzero = find(obj.DIR ~= 0);
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if DIR_nonzero(1) > 1
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obj.DIR(1:DIR_nonzero(1)-1) = [];
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end
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if isscalar(obj.DIR)
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obj.DIR = [0 obj.DIR];
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end
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%% PREPARATIONS %%%%%%%%
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%%%% Separate the equalized signal into the respective levels based on the actually transmitted level
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constellation = unique(data_ref);
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decisionLevels = (constellation(1:end-1) + constellation(2:end)) / 2;
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tx_bits = PAMmapper(numel(constellation),0).demap(data_ref);
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% impulse respnse i.e. [0.5, 1.0000]
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obj.DIR = flip(obj.DIR);
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% RMS normalization of input data
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data_in = data_in ./ rms(data_in);
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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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pre_comb_cell = mat2cell(pre_comb_mat,ones(1,size(pre_comb_mat,1)),size(pre_comb_mat,2));
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combs = fliplr(combvec(pre_comb_cell{:}).');
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% Save first and last symbol of each state
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first_sym = combs(:,1);
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last_sym = combs(:,end);
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states = sum(combs,2);
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% Calculate all possible input symbols for the desired impulse
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% response. Row number is the index of the previous state,
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% column number is the index of the next state
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% noise free received == branch metrics
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noise_free_received = zeros(length(states),length(states));
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count_row = 1;
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count_col = 1;
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for l1 = 1:length(states)
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for l2 = 1:length(states)
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if sum(combs(l2,2:end) == combs(l1,1:end-1)) == size(combs,2)-1
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noise_free_received(count_row,count_col) = sum(combs(l2,:).*obj.DIR(end:-1:2)) + last_sym(l1)*obj.DIR(1);
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else
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noise_free_received(count_row,count_col) = inf;
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end
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count_row = count_row + 1;
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end
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count_col = count_col + 1;
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count_row = 1;
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end
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% 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
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if isreal(data_in)
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if obj.M == round(obj.M)
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data_in = data_in * rms(noise_free_received(noise_free_received ~= inf),'all','omitnan');
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end
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end
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%% FORWARD PASS %%%%%
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% Initialize the output vector
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pm = zeros(length(states),length(states));
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bm_fw = zeros(length(states),length(states),length(data_in));
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% Forward Recursion (FSM Computation)
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for n = 1:length(data_in)
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bm = abs(data_in(n) - noise_free_received).^2;
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pm = pm + bm;
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[pm_survivor_fw(:,n),pm_survivor_fw_idx(:,n)] = min(pm,[],2); % choose lowest path metric as new state
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pm = repmat(pm_survivor_fw(:,n).',length(states),1); % update pm (chosen state to 2nd dimension -> FROM state)
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bm_fw(:,:,n) = bm;
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end
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% we can now get the best path as min
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best_fw_path = NaN(1,length(data_in)+1);
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% find ideal trellis path by going through the trellis backwards
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[~,best_fw_path(length(data_in)+1)] = min(pm_survivor_fw(:,length(data_in)));
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%% BACKWARD PASS %%%%%
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% Initialize the output vector
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pm = zeros(length(states),length(states));
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pm_survivor_bw = zeros(length(states),length(data_in)+1);
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pm_survivor_bw_idx = zeros(length(states),length(data_in)+1);
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bm_bw = zeros(length(states),length(states),length(data_in)+1);
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% starting with the state that has the lowest sum path
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% metric, follow the stored information about the
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% predecessor
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for h = length(data_in):-1:1
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best_fw_path(h) = pm_survivor_fw_idx(best_fw_path(h+1),h);
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bm = abs(data_in(h) - noise_free_received).^2;
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pm = pm + bm.';
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[pm_survivor_bw(:,h),pm_survivor_bw_idx(:,h)] = min(pm,[],2); % choose lowest path metric as new state
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pm = repmat(pm_survivor_bw(:,h).',length(states),1); % update pm (chosen state to 2nd dimension -> FROM state)
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bm_bw(:,:,h) = bm;
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end
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VITERBI_ESTIMATION_IDX(1:length(data_in)) = first_sym(best_fw_path(2:end));
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VITERBI_ESTIMATION_SYMBOLS(1:length(data_in)) = constellation(best_fw_path(2:end));
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%% FORWARD PASS %%%%%
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%calc the log probabilities (llp's)
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for k = 2:length(data_in)
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fsm = repmat(pm_survivor_fw(:,k-1)',[length(states),1]); %pm_survivor_fw size: length(states)xlength(sequence)
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bm = bm_fw(:,:,k); %bm_fw size: length(states)xlength(states)xlength(sequence)
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bsm = repmat(pm_survivor_bw(:,k)',[length(states),1]); %pm_survivor_bw size: length(states)xlength(sequence)+1
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llp(:,k) = min(fsm+bm+bsm,[],2);
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end
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% directly decide based on lowest LLP index
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[~,llp_based_state_seq]=min(llp);
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LLP_EST(1:length(data_in)) = constellation(llp_based_state_seq);
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rx_bits = PAMmapper(numel(constellation),0).demap(LLP_EST');
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[~,~,ber_llp,~] = calc_ber(rx_bits,tx_bits,"skip_front",100,"skip_end",150,"returnErrorLocation",1);
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fprintf('LLP BER : %.2e \n',ber_llp);
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% [~,~,ber_llp,~] = calc_ber(circshift(rx_bits,1),tx_bits,"skip_front",100,"skip_end",150,"returnErrorLocation",1);
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% fprintf('LLP BER +1: %.2e \n',ber_llp);
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% [~,~,ber_llp,~] = calc_ber(circshift(rx_bits,-1),tx_bits,"skip_front",100,"skip_end",150,"returnErrorLocation",1);
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% fprintf('LLP BER -1: %.2e \n',ber_llp);
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%%%% DECIDE based on Viterbi traceback
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rx_bits = PAMmapper(numel(constellation),0).demap(VITERBI_ESTIMATION_SYMBOLS');
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[~,~,ber_viterbi,~] = calc_ber(rx_bits,tx_bits,"skip_front",100,"skip_end",150,"returnErrorLocation",1);
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fprintf('Viterbi BER: %.2e \n',ber_viterbi);
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% [~,~,ber_viterbi,~] = calc_ber(circshift(rx_bits,1),tx_bits,"skip_front",100,"skip_end",150,"returnErrorLocation",1);
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% fprintf('Viterbi BER: %.2e \n',ber_viterbi);
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% directly decide based on the FW path metrics
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[~,fw_direct_state_seq]=min(pm_survivor_fw);
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FW_EST(1:length(data_in)) = constellation(fw_direct_state_seq);
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rx_bits = PAMmapper(numel(constellation),0).demap(FW_EST');
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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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% directly decide based on the BW path metrics
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[~,bw_direct_state_seq]=min(pm_survivor_bw);
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BW_EST(1:length(data_in)) = constellation(bw_direct_state_seq(2:end));
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rx_bits = PAMmapper(numel(constellation),0).demap(BW_EST');
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[~,~,ber_bw,~] = calc_ber(rx_bits,tx_bits,"skip_front",100,"skip_end",150,"returnErrorLocation",1);
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fprintf('BW BER: %.2e \n',ber_bw);
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% [~,~,ber_viterbi,~] = calc_ber(circshift(rx_bits,1),tx_bits,"skip_front",100,"skip_end",150,"returnErrorLocation",1);
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% fprintf('BW BER: %.2e \n',ber_viterbi);
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% [~,~,ber_viterbi,~] = calc_ber(circshift(rx_bits,-1),tx_bits,"skip_front",100,"skip_end",150,"returnErrorLocation",1);
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% fprintf('BW BER: %.2e \n',ber_viterbi);
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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tx_symbolpos = zeros(numel(constellation),length(data_ref));
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est_symbolpos = zeros(numel(constellation),length(data_ref));
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for lvl = 1:numel(constellation)
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tx_symbolpos(lvl,data_ref==constellation(lvl)) = 1;
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est_symbolpos(lvl,VITERBI_ESTIMATION_IDX==first_sym(lvl)) = 1;
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est_symbolpos_llm(lvl,llp_based_state_seq==lvl) = 1;
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end
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est_symbolpos= logical(est_symbolpos);
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tx_symbolpos = logical(tx_symbolpos);
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est_symbolpos_llm = logical(est_symbolpos_llm);
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figure(299);clf;hold on;
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llp_filt = NaN(length(states),length(data_in));
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llp_ = llp - min(llp,[],1);
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for c = 2%:numel(constellation)
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for c2 = 1:3%numel(constellation)
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idx = est_symbolpos_llm(c,:);
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llp_filt(c2,idx) = (llp(c2,idx));
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plotidx = 2:200000;
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scatter(plotidx,llp_filt(c2,plotidx),1,'o','LineWidth',1,'DisplayName',sprintf('LLP of Symbol %d | %d was transmitted',c2,c));
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end
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end
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% Assume llp is a 4 x N matrix (4 PAM-4 symbols, N time steps)
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[numSymbols, numTimeSteps] = size(llp);
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P_symbols = zeros(numSymbols, numTimeSteps); % To hold the soft output probabilities
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for k = 1:numTimeSteps
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% Compute the exponentials. (Use -llp_shifted if llp's are costs.)
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exponents = -llp_(:, k);
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% Normalize to form a probability vector.
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P_symbols(:, k) = exponents / sum(exponents);
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end
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% Optionally, if you prefer a single soft output value per symbol (an expectation),
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% define your PAM-4 constellation levels, e.g.:
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soft_output = sum(P_symbols .* constellation, 1); % 1 x N vector of soft outputs
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%%%% BITWISE LLR's ??? %%%%%
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figure(100);
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clf
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hold on
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title('LLR between inner and outer bits')
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bitmapping = PAMmapper(numel(constellation),0).demap(constellation);
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for bp = 1:size(bitmapping,2)
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pos_bitone = find(bitmapping(:,bp)==1);
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pos_bitzero = find(bitmapping(:,bp)~=1);
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llr_bits(bp,:) = min(llp(pos_bitone,:),[],1) - min(llp(pos_bitzero,:),[],1);
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subplot(size(bitmapping,2),1,bp)
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scatter(1:length(data_ref),llr_bits(bp,:),1,'.');
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end
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% From: Log-Likelihood Probabilities LLP --> To: Log-Likelihood Ratios LLR
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for s = 1:length(states)-1
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llr(s,:) = llp_(s,:) - llp_(s+1,:); % subtract llp's of successive const. points to get llr's
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end
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% Build Sets of LLR's that contain only those values at
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% timepoint k, where the symbols:
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% a) were actually transmitted: set "S"
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% b) were decoded by viterbi: set "SC"
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S = NaN(length(states)-1,length(data_in));
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SC = NaN(length(states)-1,length(data_in));
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llp_inf = llp_;
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llp_inf(llp_==0) = Inf;
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[~,scnd_idx] = min(llp_inf,[],1) ;
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for s = 1:length(states)-1
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%%% SET "S"
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% find all time indices k, where const point s was actually transmitted
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indice = tx_symbolpos(s,:)==1;
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S(s,indice) = llr(s,indice);
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%calc mean of all llr's where symbol s was transmitted
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K(s,1) = mean(S(s,indice),'omitnan');
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% find all time indices k, where const. point s+1 was actually transmitted
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indice_plusone = tx_symbolpos(s+1,:)==1;
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S(s,indice_plusone) = llr(s,indice_plusone);
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K(s,2) = mean(S(s,indice_plusone),'omitnan');
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%%% SET "SC"
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% find all time indices k, where symbol s was decoded
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% idx: find positions in time where a symbol s was decoded
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idx = est_symbolpos_llm(s,:);
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% idx 2: find positions where the strongest competitor is
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% s+1, i.e. the second best llp is at s+1
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idx2 = scnd_idx == s+1;
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SC(s,idx&idx2) = llr(s,idx&idx2);
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KC(s,1) = mean(SC(s,idx&idx2),'omitnan');
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% find all time indices k, where symbol s+1 was decoded
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% idx: find positions in time where a symbol s+1 was decoded
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idx = est_symbolpos_llm(s+1,:);
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idx2 = scnd_idx == s;
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% idx 2: find positions where the strongest competitor is
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% s, i.e. the second best llp is at s
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SC(s,idx&idx2) = llr(s,idx&idx2);
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KC(s,2) = mean(SC(s,idx&idx2),'omitnan');
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% scale the sets, using the average (?) of the
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llrcn(s,:) = SC(s,:) * ( constellation(s+1)-constellation(s) ) ./ ( K(s,2)-K(s,1)) + decisionLevels(s);
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end
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figure(111)
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title("Bla")
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clf
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for s = 1:length(states)-1
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figure(1111)
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hold on
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title(sprintf('llrcn = llp %d - llp %d',s, s+1,s, s+1));
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scatter(1:length(llrcn),llrcn(s,:),1,'.');
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% STUFENARTIGE LLR'S UND LLP'S %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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figure(111)
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subplot(1,length(states),s)
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hold on
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title(sprintf('llr = llp %d - llp %d \n SC=llr(tx sym = %d or %d)',s, s+1,s, s+1));
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scatter(1:length(llr),llr(s,:),1,'.');
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scatter(1:length(SC),SC(s,:),1,'.');
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yline([K(s,1),K(s,2)]);
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low = min(min(llr));
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hi = max(max(llr));
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ylim([low,hi]);
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subplot(1,length(states),length(states))
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hold on
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scatter(1:length(llr),llr(s,:),1,'.');
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ylim([low,hi]);
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% HISTOGRAMME %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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figure(112)
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subplot(length(states),1,s)
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hold on
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title(sprintf('histogram of llr; between const point %d - %d',s, s+1));
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histogram(llrcn(s,:),10000,'EdgeAlpha',0)
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% histogram(SC(s,:),10000,'EdgeAlpha',0)
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xlim([-20, 20]);
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subplot(length(states),1,length(states))
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hold on
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histogram(llrcn(s,:),10000,'EdgeAlpha',0)
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% histogram(SC(s,:),10000,'EdgeAlpha',0)
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% xlim([-20, 20]);
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end
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softdecisions = mean(llrcn,1,'omitnan');
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distance = abs(VITERBI_ESTIMATION_SYMBOLS-llrcn);
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[win_cost,win_idx] = min(distance,[],1);
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for i = 1:length(data_in)
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soft_decisions(i) = llrcn(win_idx(i),i);
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end
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soft_decisions = max(llrcn,[],1);
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showLevelHistogram(soft_decisions,data_ref)
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figure()
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% scatter(1:length(data_in),VITERBI_ESTIMATION_SYMBOLS,1,'.');
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scatter(1:length(data_in),soft_decisions,1,'.');
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MLM_ESTIMATION(1:length(data_in)) = PAMmapper(numel(constellation),0).quantize(soft_decisions)';
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rx_bits = PAMmapper(numel(constellation),0).demap(MLM_ESTIMATION');
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[~,~,ber_mlm,~] = calc_ber(rx_bits,tx_bits,"skip_front",100,"skip_end",150,"returnErrorLocation",1);
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fprintf('MLM BER: %.2e \n',ber_mlm);
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end
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end
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methods (Access=private)
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end
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end
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