+++ Changes +++
+ duobinary_target now supports memoryless decoding (FFE targets DB response without MLSE) + PAMmapper.quantize now supports custom constellations for quantization + Added a new folder 'Documentations' for pdfs, slides, etc. + Added new FSO evaluation scripts in projects/FSO transmission/Evaluation Scripts + Added ffe_db (rudimentary module, not important anymore)
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magf
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projects/ASTRO Electrical Link/Electrical_Link_GPT.m
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projects/ASTRO Electrical Link/Electrical_Link_GPT.m
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%==========================================================================
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% High-Speed Link Modell (Dispersion + Reflexionen + Crosstalk)
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% Eigenständiges MATLAB-Skript mit Testsequenz (PRBS), Kanalmodell im f-Bereich
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% und Auswertung (Eye + Spektren).
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%
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% Idee:
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% - Hauptkanal: H11(f) = exp(-gamma(f)*l)
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% - Crosstalk: H21(f) = k_xt * j*(f/fc) / (1 + j*(f/fc)) * exp(-gamma_xt(f)*l)
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% (Highpass-artig: typisches FEXT-ähnliches Verhalten; simpel aber nützlich)
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% - Reflexionen: optionaler 2-Tap Echo-Term (vereinfachtes Stub/Mismatch-Modell)
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%
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% Keine Toolboxes zwingend nötig (außer eye diagram -> optional).
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%==========================================================================
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clear; close all; clc;
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%% ----------------------- Simulationseinstellungen -----------------------
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Rb = 10e9; % Bitrate [b/s]
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UI = 1/Rb; % Unit Interval [s]
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os = 32; % Oversampling
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Fs = Rb*os; % Abtastrate [Hz]
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Ts = 1/Fs;
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Nbits = 4096; % Anzahl Bits pro Lane
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A = 1.0; % NRZ-Amplitude (0/1 -> +/-A)
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% PRBS-Seed
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rng(1);
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%% ----------------------- Testsequenzen (Aggressor + Victim) -------------
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% Victim-Lane Daten
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b_v = randi([0 1], Nbits, 1);
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x_v = A*(2*b_v - 1); % NRZ: -A/+A
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% Aggressor-Lane Daten (unabhängig)
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b_a = randi([0 1], Nbits, 1);
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x_a = A*(2*b_a - 1);
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% Upsampling (NRZ-Rechteck)
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x_v_up = upsample(x_v, os);
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x_a_up = upsample(x_a, os);
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% Simple Zero-Order Hold (rechteckig halten)
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x_v_up = filter(ones(os,1), 1, x_v_up);
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x_a_up = filter(ones(os,1), 1, x_a_up);
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% Am Anfang Filter-Transient entfernen / zentrieren
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x_v_up = x_v_up(os:end);
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x_a_up = x_a_up(os:end);
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% Signal-Länge
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N = length(x_v_up);
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% Optional: leichte TX-RiseTime-Abbildung (1st order LP)
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% (hilft, unrealistische unendliche Bandbreite zu vermeiden)
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f_tx_3dB = 0.35/(35e-12); % grob: 35ps 10-90% -> f3dB ~ 0.35/tr
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[x_v_up, x_a_up] = apply_1pole_lp(x_v_up, x_a_up, Fs, f_tx_3dB);
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%% ----------------------- Frequenzachse (FFT) ----------------------------
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% FFT-Länge als Power-of-two (schneller, weniger Circular-Artefakte)
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Nfft = 2^nextpow2(N*2);
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f = (0:Nfft-1).'*Fs/Nfft; % 0 ... Fs*(1-1/Nfft)
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% Für Transferfunktionen brauchen wir auch negative Frequenzen implizit:
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% MATLAB-FFT nutzt diese Darstellung automatisch, solange H hermitesch ist.
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% Wir definieren H für alle FFT-Bins konsistent mit reellen Signalen.
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%% ----------------------- RLGC-Modell (Dispersion & Loss) -----------------
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% Leitungslänge
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l = 0.40; % [m]
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% Per-unit-length Parameter (Beispielwerte, grob PCB-ähnlich)
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L = 3.2e-7; % [H/m]
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C = 1.6e-10; % [F/m]
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G0 = 0; % [S/m] (DC)
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tanD = 0.012; % Verlustfaktor (vereinfachtes Dielektrikum-Modell)
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% G(f) ~ omega*C*tanD
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omega = 2*pi*f;
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G = G0 + omega.*C*tanD;
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% Skin-Effekt / Rauheit: R(f) ~ Rdc + k*sqrt(f)
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Rdc = 0.05; % [Ohm/m]
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kR = 0.20; % [Ohm/m/sqrt(Hz)] * sqrt(Hz) -> Ohm/m
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R = Rdc + kR*sqrt(max(f,1)); % max(..,1) vermeidet sqrt(0)
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% gamma(f) und Z0(f)
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gamma = sqrt( (R + 1j*omega*L) .* (G + 1j*omega*C) ); % [1/m]
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Z0 = sqrt( (R + 1j*omega*L) ./ (G + 1j*omega*C) ); % [Ohm]
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% Hauptpfad-Transferfunktion (perfekt terminiert)
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H11 = exp(-gamma*l);
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%% ----------------------- Crosstalk-Modell (Aggressor -> Victim) ----------
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% Sehr vereinfachtes FEXT-ähnliches Modell: wächst mit f, sättigt
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k_xt = 0.04; % Crosstalk-Stärke (skalieren)
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fc = 8e9; % Eckfrequenz der Koppelcharakteristik
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% optional etwas andere Verluste auf dem Koppelpfad
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gamma_xt = gamma .* (1.05 + 0.00j);
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Hxt_shape = (1j*(f/fc)) ./ (1 + 1j*(f/fc)); % ~ Highpass
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H21 = k_xt .* Hxt_shape .* exp(-gamma_xt*l);
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%% ----------------------- Reflexions/Echo-Modell (optional) ---------------
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% Einfache 2-Tap-Approximation: Hecho = 1 + a*exp(-j*2*pi*f*tau)
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% (z.B. Stub/Via-Resonanz als Echo)
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useEcho = true;
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a_echo = 0.18; % Echo-Amplitude (|a|<1)
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tau = 120e-12; % Echo-Delay [s]
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if useEcho
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Hecho = 1 + a_echo*exp(-1j*2*pi*f*tau);
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H11 = H11 .* Hecho;
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end
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%% ----------------------- Kanal-Anwendung per FFT -------------------------
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% Zero-padding auf Nfft
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Xv = fft(x_v_up, Nfft);
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Xa = fft(x_a_up, Nfft);
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% Victim-Ausgang = Hauptpfad * Victim + Crosstalkpfad * Aggressor
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Yv = H11 .* Xv + H21 .* Xa;
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y_v = real(ifft(Yv, Nfft));
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y_v = y_v(1:N); % zurück auf Originallänge
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%% ----------------------- Auswertung: Eye Diagramm ------------------------
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% Eye über viele UIs (ohne Toolbox: eigene Darstellung)
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plot_eye(y_v, os, 2); % 2 UI Breite
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%% ----------------------- Auswertung: Frequenzgänge -----------------------
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figure('Name','Transferfunktionen');
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subplot(2,1,1);
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plot(f/1e9, 20*log10(abs(H11)+1e-15)); grid on;
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xlabel('f [GHz]'); ylabel('|H_{11}| [dB]');
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title('Hauptkanal (inkl. Dispersion/Loss + optional Echo)');
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subplot(2,1,2);
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plot(f/1e9, 20*log10(abs(H21)+1e-15)); grid on;
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xlabel('f [GHz]'); ylabel('|H_{21}| [dB]');
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title('Crosstalk-Pfad (Aggressor -> Victim)');
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%% ----------------------- Optional: Bitfehlersicht / Sampling -------------
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% Einfaches Sampling in der UI-Mitte (ohne Taktwiedergewinnung)
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% (nur grobe Demo, kein echter CDR)
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sampleOffset = round(os/2);
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idx = sampleOffset:os:(sampleOffset + (Nbits-2)*os);
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samples = y_v(idx);
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% Hard Decision
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bh = samples > 0;
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ber = mean(bh(:) ~= b_v(1:length(bh)));
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fprintf('--- Ergebnis ---\n');
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fprintf('Bitrate: %.2f Gb/s, Oversampling: %d, Fs: %.2f GHz\n', Rb/1e9, os, Fs/1e9);
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fprintf('Echo: %d (a=%.3f, tau=%.1f ps)\n', useEcho, a_echo, tau*1e12);
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fprintf('Crosstalk k_xt=%.3f, fc=%.2f GHz\n', k_xt, fc/1e9);
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fprintf('Grobe BER (ohne CDR/EQ): %.3e\n', ber);
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%==========================================================================
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% Lokale Hilfsfunktionen
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%==========================================================================
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function [x1o, x2o] = apply_1pole_lp(x1, x2, Fs, f3dB)
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% 1. Ordnung Tiefpass als TX-Bandbegrenzung (optional)
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if isempty(f3dB) || f3dB<=0
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x1o = x1; x2o = x2; return;
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end
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w = 2*pi*f3dB;
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a = exp(-w/Fs);
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b = 1-a;
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x1o = filter(b, [1 -a], x1);
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x2o = filter(b, [1 -a], x2);
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end
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function plot_eye(y, os, nUI)
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% Eye-Diagramm ohne Toolbox: Segmente von nUI*os sampeln und überlagern
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Lseg = nUI*os;
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nSeg = floor(length(y)/os) - nUI - 2;
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if nSeg < 10
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warning('Zu wenig Daten für Eye.');
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return;
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end
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figure('Name','Eye Diagramm');
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hold on; grid on;
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t = (0:Lseg-1)/os; % in UI
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for k = 1:nSeg
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i0 = (k-1)*os + 1;
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seg = y(i0:i0+Lseg-1);
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plot(t, seg);
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end
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xlabel('Zeit [UI]');
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ylabel('Amplitude [V (rel.)]');
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title(sprintf('Eye Diagramm (Breite = %d UI, Oversampling = %d)', nUI, os));
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end
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