% 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