small updates from work pc
try to implement kalman filter for MPI mitigation
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sioe
245
Classes/04_DSP/Equalizer/FFE_Kalman.m
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245
Classes/04_DSP/Equalizer/FFE_Kalman.m
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classdef FFE_Kalman < handle
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% Implementation of plain and simple FFE.
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% 1) Training mode (stable performance when you use NLMS)
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% 2) Decision directed mode
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% Eq = FFE("epochs_tr",5,"epochs_dd",5,"len_tr",4096*2,"mu_dd",1e-4,"mu_tr",0,"order",25,"sps",2,"decide",0);
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properties
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sps % usually 2
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order
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e
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error
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len_tr
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mu_tr
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epochs_tr
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mu_dd
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epochs_dd
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constellation
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decide
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end
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methods
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function obj = FFE_Kalman(options)
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arguments(Input)
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options.sps = 2;
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options.order = 15;
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options.len_tr = 4096;
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options.mu_tr = 0;
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options.epochs_tr = 5;
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options.mu_dd = 1e-5;
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options.epochs_dd = 5;
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options.decide = false;
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end
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fn = fieldnames(options);
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for n = 1:numel(fn)
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obj.(fn{n}) = options.(fn{n});
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end
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obj.e = zeros(obj.order,1);
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obj.error = 0;
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end
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function [X,Noi] = process(obj, X, D)
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% actual processing of the signal (steps 1. - 3.)
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% 1 normalize RMS
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X = X.normalize("mode","rms");
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obj.constellation = unique(D.signal);
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% Training Mode
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training = 1;
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showviz = 0;
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obj.equalize(X.signal, D.signal,obj.mu_tr,obj.epochs_tr,obj.len_tr,training,showviz);
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% Decision Directed Mode
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n = X.length;
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training = 0;
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showviz = 0;
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[signal,decision]=obj.equalize(X.signal, D.signal,obj.mu_dd,obj.epochs_dd,n,training,showviz);
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% Output Signal
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if obj.decide
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X.signal = decision;
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else
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X.signal = signal;
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end
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X.fs = D.fs; %change sampling frequency of outgoing signal from fdac e.g. 2 sps to symbol spaced = fsym
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lbdesc = [num2str(obj.order),' tap FFE'];
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X = X.logbookentry(lbdesc); % append to logbook
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Noi = X;
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Noi = X - D;
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end
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function [y,d_hat] = equalize(obj,x,d,mio,epochs,N,training,showviz)
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arguments
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obj
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x
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d
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mio
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epochs
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N
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training
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showviz
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end
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x = [zeros(floor(obj.order/2),1); x; zeros(obj.order,1)];
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for epoch = 1 : epochs
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symbol = 0;
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% Initialization of Kalman filter variables
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A = 1; % State transition matrix
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H = 1; % Observation matrix
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Q = 1e-4; % Process noise covariance
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R = 1e-1; % Measurement noise covariance
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P = 1; % Initial error covariance
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mpi_est = 0; % Initial estimate for MPI noise
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K = 0; % Kalman gain
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subtract_mpi_est = 1;
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for sample = 1 : obj.sps : N
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symbol = symbol + 1;
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% Get the current input sample and the equalizer output
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U = x(obj.order + sample - 1 : -1 : sample);
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if subtract_mpi_est || ~training
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y(symbol,1) = (obj.e.' * U) - mpi_est .* 1 ; % Subtract MPI estimate
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else
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y(symbol,1) = obj.e.' * U;
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end
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% Decision and error calculation
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if training
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d_hat(symbol,1) = d(symbol);
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else
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[~, symbol_idx] = min(abs(y(symbol) - obj.constellation)); % Closest constellation point
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d_hat(symbol,1) = obj.constellation(symbol_idx);
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end
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err(symbol) = y(symbol) - d_hat(symbol); % Instantaneous residual error
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true_err(symbol) = y(symbol) - d(symbol);
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% Kalman filter update to track the MPI noise
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% Prediction step
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P = A * P * A' + Q; % Update error covariance
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K = P * H' / (H * P * H' + R); % Kalman gain
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% Update step
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mpi_est_new = mpi_est + K * (err(symbol) - H * mpi_est); % MPI noise estimation
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alpha=0;
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mpi_est = alpha * mpi_est + (1 - alpha) * mpi_est_new;
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P = (1 - K * H) * P; % Update error covariance
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% Subtract MPI noise from the signal
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if subtract_mpi_est || ~training
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y(symbol) = y(symbol);% - mpi_est;
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else
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end
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% Equalizer weight update (LMS or NLMS)
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if mio ~= 0
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obj.e = obj.e - (mio * err(symbol) * U); % LMS weight update
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else
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normalizationfactor = (U.' * U);
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obj.e = obj.e - err(symbol) * U / normalizationfactor; % NLMS weight update
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end
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% Store MPI estimate for visualization
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mpi_estimates(symbol) = mpi_est;
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Kgain(symbol) = K;
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P_(symbol) = P;
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H_(symbol) = H;
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end %symbols
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end %epoch
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if ~training
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if 1
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% figure;
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% subplot(2,2,1)
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% hold on
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% scatter(1:numel(y),y,1,'.');
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% plot(1:numel(mpi_estimates), mpi_estimates);
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% subplot(2,2,3)
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% plot(1:numel(true_err), true_err);
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% subplot(2,2,2)
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% scatter(1:numel(y),y'-mpi_estimates,1,'.');
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% xlabel('Sample Index');
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% ylabel('MPI Noise Estimate');
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% title('MPI Noise Estimation Over Time (Kalman Filter)');
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% grid on;
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figure(111);
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subplot(3,1,1)
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hold on
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cla
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scatter(1:numel(y),y,1,'.');
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plot(1:numel(mpi_estimates), mpi_estimates,'DisplayName','mpi est');
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ylim([-2,2]);
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subplot(3,1,2)
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cla
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plot(1:numel(true_err), true_err,'DisplayName','true err');
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ylim([-1,1]);
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subplot(3,1,3)
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plot(1:numel(true_err), true_err-mpi_estimates,'DisplayName',['diff rms: ',num2str(rms(true_err-mpi_estimates))]);
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ylim([-1,1]);
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legend
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figure(333)
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hold on
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von = 5000;
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bis = 15000;
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plot(von:bis,true_err(von:bis),'DisplayName','Error')
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plot(von:bis,movmean(true_err(von:bis), [30,30]),'DisplayName','Error')
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plot(von:bis,mpi_estimates(von:bis),'DisplayName','Est','LineWidth',2);
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legend
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figure(222)
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hold on
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crr = xcorr(mpi_estimates,true_err,'normalized');
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plot(crr);
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end
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% y = y-mpi_estimates';
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end
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end
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end
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end
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