Scattered stuff from Silas during Dissertation

projects/Diss/peak_distortion.m

@@ -0,0 +1,66 @@
+% Build convolution matrix and solve c such that conv(x,c) approx delta
+x = [0.05; -0.12; 0.3; 1; 0.25; -0.1; 0.04];  % channel pulse response
+Ntaps = 7;
+mu = 0.002;
+Nit = 500;
+
+[c, hhist] = peakDistEqualizer(x, Ntaps, mu, Nit);
+
+h_eff = conv(x,c);
+
+stem(h_eff)
+grid on
+xlabel('Sample index')
+ylabel('Combined impulse response')
+
+
+function [c, h_hist] = peakDistEqualizer(x, Ntaps, mu, Nit)
+% Peak-distortion / Lucky sign-gradient equalizer
+%
+% x     : sampled channel pulse response, main cursor should be near center
+% Ntaps : odd number of equalizer taps
+% mu    : step size
+% Nit   : number of training iterations
+%
+% c     : equalizer coefficients
+% h     : combined impulse response h = conv(x,c)
+
+    x = x(:);
+    assert(mod(Ntaps,2)==1, 'Ntaps must be odd');
+
+    midTap = (Ntaps+1)/2;
+    c = zeros(Ntaps,1);
+    c(midTap) = 1;              % start with through connection
+
+    h_hist = cell(Nit,1);
+
+    for it = 1:Nit
+        h = conv(x,c);
+        h_hist{it} = h;
+
+        % locate main cursor
+        [~, mainIdx] = max(abs(h));
+
+        % normalize main cursor conceptually
+        h = h / h(mainIdx);
+
+        % update non-center equalizer taps
+        for j = 1:Ntaps
+            if j == midTap
+                continue
+            end
+
+            % map equalizer tap j to corresponding ISI sample
+            isiIdx = mainIdx + (j - midTap);
+
+            if isiIdx >= 1 && isiIdx <= length(h)
+                c(j) = c(j) - mu * sign(h(isiIdx));
+            end
+        end
+
+        % optional: normalize center/main gain
+        h = conv(x,c);
+        [~, mainIdx] = max(abs(h));
+        c = c / h(mainIdx);
+    end
+end