Add new functions
This commit is contained in:
Silas Oettinghaus
156
Functions/Metrics/air_garcia_implementation.m
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156
Functions/Metrics/air_garcia_implementation.m
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@@ -0,0 +1,156 @@
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function air = air_garcia_implementation(x,r,idx_tx,Px,M_training)
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MAX_MEMORY = 200e6; % maximum allowed size for a matrix
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if nargin == 3
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Px = [];
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M_training = [];
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end
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if nargin == 4
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M_training = [];
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end
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% if input is complex, separate into real and imaginary parts
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if any(imag(x(:))~=0) || any(imag(r(:))~=0)
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x = [real(x); imag(x)];
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r = [real(r); imag(r)];
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end
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D = size(x, 1); % D = 2 if complex x
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N = size(x, 2); % number of constellation points
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M = size(r, 2); % number of samples
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% set default training set size
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if isempty(M_training)
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M_training = ceil(0.3*M);
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end
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M_testing = M - M_training;
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% Training: estimate parameters of the conditionally Gaussian model
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% sort according to transmit index
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[idx_tx_training, idx_sort] = sort(idx_tx(1:M_training));
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r_training = r(:, idx_sort);
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i_bounds = zeros(1, N+1);
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% compute conditional means and covariance matrices
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C_n = zeros(D, D, N);
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det_n = zeros(1, N);
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for n=1:N
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% find how many times x(:, n) was transmitted and update i_bounds
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N_current_x = find(idx_tx_training((i_bounds(n)+1):end)==n, 1, 'last');
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if isempty(N_current_x), N_current_x=0; end
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i_bounds(n+1) = i_bounds(n) + N_current_x;
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if N_current_x > 0
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% Compute mu_n=E[Y|X=x_n] according to Eq. (14) and store it in
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% x(:, n) to save space
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x(:, n) = sum(r_training(:, (i_bounds(n)+1):i_bounds(n+1)), 2)/(i_bounds(n+1)-i_bounds(n));
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% compute C_n=cov[Y|X=x_n] according to Eq. (15)
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r_meanfree = r_training(:, (i_bounds(n)+1):i_bounds(n+1)) - x(:, n);
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C_n(:, :, n) = (r_meanfree*r_meanfree')/(i_bounds(n+1)-i_bounds(n));
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% store also the determinant of C(:, :, n)
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det_n(n) = det(C_n(:, :, n));
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% if the determinant is 0, or if the matrix is badly conditioned,
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% regularize by adding a small identity matrix. Note that we do
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% need the check for 0 determinant, in case a cloud has exactly 0
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% variance according to the training set
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if det_n(n)==0 || cond(C_n(:, :, n))>1e16
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C_n(:, :, n) = C_n(:, :, n) + 5 * eps * eye(D);
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det_n(n) = (5*eps)^D;
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end
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end
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end
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% uniform input pmf Px if not provided
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if isempty(Px)
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Px = repmat(1/N, [1, N]);
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end
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% extract testing set and sort it according to transmit index
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[idx_tx_testing, idx_sort] = sort(idx_tx((M_training+1):M));
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r_testing = r(:, M_training+idx_sort);
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% computation of h(Y|X)
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h_Y_X = 0;
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i_bounds_testing = zeros(1, N+1);
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% loop over constellation points to compute h(Y|X)
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for n = 1:N
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% find how many times x(:, n) was transmitted and update
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% i_bounds_testing
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N_current_x = find(idx_tx_testing((i_bounds_testing(n)+1):end)==n, 1, 'last');
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if isempty(N_current_x), N_current_x=0; end
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i_bounds_testing(n+1) = i_bounds_testing(n) + N_current_x;
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% add the corresponding contribution to the mutual information (two
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% first lines of Eq. (17)). This, together with
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% D/2*log2(2*pi) after the end of the loop, gives h(Y|X)
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h_Y_X = h_Y_X + N_current_x * log2(det_n(n))/2+...
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sum(sum(conj(r_testing(:, (i_bounds_testing(n)+1):i_bounds_testing(n+1))-x(:, n)).*(C_n(:, :, n)\(r_testing(:, (i_bounds_testing(n)+1):i_bounds_testing(n+1))-x(:, n)))))/2/log(2);
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end
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h_Y_X = D/2*log2(2*pi) + h_Y_X/M_testing;
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% When computing log(py), we might run out of memory. If necessary, we
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% doe the computation in blocks
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logpy = zeros(1, M_testing);
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BLOCK_SIZE = floor(MAX_MEMORY/N);
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N_blocks = ceil(M_testing/BLOCK_SIZE);
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% loop over blocks of symbols. This loop can be replaced by parfor to allow
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% parallel computation
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for i_block = 1:N_blocks
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logpy_cur = zeros(1, M_testing);
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% beginning of block
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i_start = (i_block-1) * BLOCK_SIZE + 1;
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% end of block
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i_end = min(M_testing, i_block*BLOCK_SIZE);
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% block size
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current_block_size = i_end-i_start+1;
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% compute exponents of third line of (17)
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exponents = zeros(N, current_block_size);
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for n = 1:N
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exponents(n, :) = -log(det_n(n))/2-real(sum(conj(r_testing(:, i_start:i_end)-x(:, n)).*(C_n(:, :, n)\(r_testing(:, i_start:i_end)-x(:, n))), 1))/2;
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%sum über 2 einträge von r
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end
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% compute third line of Eq. (17). Use a custom function
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% that computes log(sum(exp(x))) avoiding overflow errors
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logpy_cur(i_start:i_end) = math_logsumexp(log(Px(:))+exponents, 1);
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logpy = logpy + logpy_cur;
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end
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% output entropy h(Y)
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h_Y = D/2*log2(2*pi) - mean(logpy)/log(2);%log basis change
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% compute mutual information
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air = h_Y - h_Y_X;
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end
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function [y] = math_logsumexp(x, dim)
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%[y] = math_logsumexp(x, dim)
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% Computes log(sum(exp(x), dim)), avoiding overflow errors when one of the
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% x is large.
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if nargin<2 || isempty(dim)
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m = max(x);
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y = m + log(sum(exp(x-m)));
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else
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m = max(x, [], dim);
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y = m + log(sum(exp(x-m), dim));
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end
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end
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48
Functions/Metrics/calc_air.m
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48
Functions/Metrics/calc_air.m
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function [ach_inf_rate] = calc_air(test_signal,reference_signal,options)
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% Calculation of AIR acc. to J. Kozesnik, „Numerically Computing Achievable Rates of Memoryless Channels“, Francisco Javier Garcıa-Gomez, doi: 10.1007/978-94-009-9857-5.
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% Implementation is not accessible, I mailed TUM to get the code...
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arguments(Input)
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test_signal;
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reference_signal;
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options.skip_front = 0;
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options.skip_end = 0;
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options.returnErrorLocation = 0;
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end
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options.skip_end = abs(options.skip_end);
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options.skip_front = abs(options.skip_front);
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assert((options.skip_end+options.skip_front)<length(test_signal),"You can not skip more bits than overall length of data! Set skip_front or skip_end to lower value or check data_in");
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if isa(reference_signal,'Signal')
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reference_signal = reference_signal.signal;
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end
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if isa(test_signal,'Signal')
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test_signal = test_signal.signal;
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end
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% TRIM
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[test_signal,reference_signal]=trimseq(test_signal,reference_signal,options.skip_front,options.skip_end);
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% CALC EVM
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%%% new implementation of AIR
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constellation = unique(reference_signal);
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reference_idx = arrayfun(@(x) find(constellation == x, 1), reference_signal);
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ach_inf_rate = air_garcia_implementation(constellation',test_signal',reference_idx');
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function [data_,reference_]=trimseq(data,reference,skipstart,skip_end)
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data_ = data(skipstart+1:end-skip_end,:);
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delta_bits = length(reference) - length(data);
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skip_end = delta_bits + skip_end;
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reference_ = reference(skipstart+1:end-skip_end,:);
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end
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end
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52
Functions/Metrics/calc_ber.m
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52
Functions/Metrics/calc_ber.m
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function [bits,errors,ber,errorIndice] = calc_ber(data_in,data_ref,options)
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arguments(Input)
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data_in;
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data_ref;
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options.skip_front = 0;
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options.skip_end = 0;
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options.returnErrorLocation = 0;
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end
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options.skip_end = abs(options.skip_end);
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options.skip_front = abs(options.skip_front);
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assert((options.skip_end+options.skip_front)<length(data_in),"You can not skip more bits than overall length of data! Set skip_front or skip_end to lower value or check data_in");
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errorIndice= [];
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% trim sequence to given start; stop. trim reference if signal is shorter
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[data_in,data_ref]=trimseq(data_in,data_ref,options.skip_front,options.skip_end);
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if length(data_ref) == length(data_in)
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bits = numel(data_in(:,options.skip_front+1:end));
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if options.returnErrorLocation == 0
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errors = sum( data_in ~= data_ref,"all" );
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else
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errorIndice = sum(data_in ~= data_ref,1);
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errors = sum(errorIndice ,"all" );
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[~,errorIndice] = find(errorIndice~=0);
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errorIndice = errorIndice+options.skip_front;
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end
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% Determine BER
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ber = sum(errors)/sum(bits);
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else
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error('Sequence length does not match');
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end
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function [data_,reference_]=trimseq(data,reference,skipstart,skip_end)
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data_ = logical(data(skipstart+1:end-skip_end,:))';
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delta_bits = length(reference) - length(data);
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skip_end = delta_bits + skip_end;
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reference_ = logical(reference(skipstart+1:end-skip_end,:))';
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end
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end
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66
Functions/Metrics/calc_evm.m
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66
Functions/Metrics/calc_evm.m
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@@ -0,0 +1,66 @@
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function [evm_total,evm_lvl] = calc_evm(test_signal,reference_signal,options)
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arguments(Input)
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test_signal;
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reference_signal;
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options.skip_front = 0;
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options.skip_end = 0;
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options.returnErrorLocation = 0;
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end
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options.skip_end = abs(options.skip_end);
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options.skip_front = abs(options.skip_front);
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assert((options.skip_end+options.skip_front)<length(test_signal),"You can not skip more bits than overall length of data! Set skip_front or skip_end to lower value or check data_in");
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if isa(reference_signal,'Signal')
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reference_signal = reference_signal.signal;
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end
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if isa(test_signal,'Signal')
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test_signal = test_signal.signal;
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end
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% TRIM
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[test_signal,reference_signal]=trimseq(test_signal,reference_signal,options.skip_front,options.skip_end);
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% CALC EVM
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[evm_total,evm_lvl] = calc_evm_(test_signal,reference_signal);
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function [evm_total,evm_lvl] = calc_evm_(test_signal,reference_signal)
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assert(length(test_signal) == length(reference_signal),"Sequence length does not match");
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error_vector = (test_signal-reference_signal);
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%%% Overall EVM
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evm_total = rms(error_vector);
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try
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%%% Per Level EVM
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k = unique(reference_signal);
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for lvl = 1:length(k)
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lvl_errors = error_vector(reference_signal==k(lvl));
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evm_lvl(lvl) = rms(lvl_errors);
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end
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catch
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evm_lvl = NaN;
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warning('No EVM per level calculated')
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end
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end
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function [data_,reference_]=trimseq(data,reference,skipstart,skip_end)
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data_ = data(skipstart+1:end-skip_end,:);
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delta_bits = length(reference) - length(data);
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skip_end = delta_bits + skip_end;
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reference_ = reference(skipstart+1:end-skip_end,:);
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end
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end
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123
Functions/Metrics/calc_ngmi.m
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123
Functions/Metrics/calc_ngmi.m
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@@ -0,0 +1,123 @@
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function [GMI,NGMI] = calc_ngmi(test_signal,reference_signal,options)
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% Silas implementation of (N)GMI calculation according to: J. Cho, L. Schmalen, und P. J. Winzer,
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% „Normalized Generalized Mutual Information as a Forward Error Correction Threshold for Probabilistically Shaped QAM“,
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% in 2017 European Conference on Optical Communication (ECOC), Sep. 2017, doi: 10.1109/ECOC.2017.8345872.
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% This implementation assumes the same normal distributed noise for each
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% channel (sigma2 is calculated once for the whole signal)
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arguments(Input)
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test_signal;
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reference_signal;
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options.skip_front = 0;
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options.skip_end = 0;
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options.returnErrorLocation = 0;
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end
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options.skip_end = abs(options.skip_end);
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options.skip_front = abs(options.skip_front);
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assert((options.skip_end+options.skip_front)<length(test_signal),"You can not skip more bits than overall length of data! Set skip_front or skip_end to lower value or check data_in");
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if isa(reference_signal,'Signal')
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reference_signal = reference_signal.signal;
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end
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if isa(test_signal,'Signal')
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test_signal = test_signal.signal;
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end
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% TRIM
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[test_signal,reference_signal]=trimseq(test_signal,reference_signal,options.skip_front,options.skip_end);
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% CALC EVM
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[GMI,NGMI] = calc_ngmi_(test_signal,reference_signal);
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function [GMI,NGMI] = calc_ngmi_(test_signal,reference_signal)
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assert(length(test_signal) == length(reference_signal),"Sequence length does not match");
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%%% implemented according to [1] J. Cho, L. Schmalen, und P. J. Winzer,
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% „Normalized Generalized Mutual Information as a Forward Error Correction Threshold for Probabilistically Shaped QAM“,
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% in 2017 European Conference on Optical Communication (ECOC), Sep. 2017, S. 1–3. doi: 10.1109/ECOC.2017.8345872.
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error_vector = (test_signal-reference_signal);
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sigma2 = var(error_vector); %noise variance
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%%% Separate Classes
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constellation = unique(reference_signal);
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received_sd = NaN(numel(constellation),length(reference_signal));
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lvlcol = cbrewer2('Set1',numel(constellation));
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for lvl = 1:numel(constellation)
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%Separate the equalized signal into the
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%respective levels based on the actually
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%transmitted level!
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received_sd(lvl,reference_signal==constellation(lvl)) = test_signal(reference_signal==constellation(lvl));
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end
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N = length(test_signal); % Number of received samples
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M = length(constellation); %P
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m = log2(M); %bits per symbol
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entries = sum(~isnan(received_sd),2)';
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P_X = entries./N;
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% Parameters
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symbols = constellation'; % PAM-4 symbols
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gray_bits = PAMmapper(M,0).demap_(constellation); % Gray coding (bits per symbol)
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% Conditional probability function for AWGN
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q_Y_given_X = @(y, x) (1 / sqrt(2 * pi * sigma2)) * exp(-(y - x).^2 / (2 * sigma2));
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% Entropy term
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H_X = -sum(P_X .* log2(P_X)); % Entropy of input distribution
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% GMI computation
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noise_impact_term = 0;
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for k = 1:N
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y_k = test_signal(k); % Current received sample
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[~, closest_symbol_idx] = min(abs(symbols - y_k)); % Closest symbol index
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closest_symbol = symbols(closest_symbol_idx); % Closest symbol
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for i = 1:m
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% Extract i-th bit for each symbol
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bit_mask = gray_bits(:, i); % Binary column for i-th bit of all symbols
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matching_symbols = symbols(bit_mask == gray_bits(closest_symbol_idx, i));
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% Numerator: Sum over x in x_{b_{k, i}}
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numerator = sum(q_Y_given_X(y_k, matching_symbols) .* P_X(ismember(symbols, matching_symbols)));
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% Denominator: Sum over all x
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denominator = sum(q_Y_given_X(y_k, symbols) .* P_X);
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% Logarithmic contribution
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noise_impact_term = noise_impact_term + log2(numerator / denominator);
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end
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end
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% Normalize the noise impact term by N
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noise_impact_term = noise_impact_term / N;
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% GMI
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GMI = H_X + noise_impact_term;
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NGMI = GMI / m;
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end
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function [data_,reference_]=trimseq(data,reference,skipstart,skip_end)
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data_ = data(skipstart+1:end-skip_end,:);
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|
||||
delta_bits = length(reference) - length(data);
|
||||
|
||||
skip_end = delta_bits + skip_end;
|
||||
|
||||
reference_ = reference(skipstart+1:end-skip_end,:);
|
||||
|
||||
end
|
||||
|
||||
end
|
||||
Reference in New Issue
Block a user