GenerateProblem(channel_length, pilot_length, channel_sparsity, number_of_symbols, noise, cplx)

function [y, A, x, group, err] = GenerateProblem(channel_length, pilot_length, channel_sparsity, number_of_symbols, noise, cplx)

N = channel_length;
P = pilot_length;
n = number_of_symbols;
K = channel_sparsity;

k = randperm(N);
XPos = sort(k(1:K));
A = []; xreal = []; groupreal = []; D = dct(eye(N));

if cplx
    xcomplex = [];
    groupcomplex = [];
end

for i = 1:n
    m = randperm(N);
    W = D(m(1:P),:);
    A = blkdiag(A,W);
    Xreal = zeros(N,1);
    Xcomplex = zeros(N,1);
    Xreal(XPos) = randn(K,1);
    xreal = [xreal' Xreal']';
    groupreal = [groupreal 1:N];
    if cplx
        Xcomplex(XPos) = randn(K,1);
        xcomplex = [xcomplex' Xcomplex']';
        groupcomplex = [groupcomplex 1:N];
    end
end

x = xreal;
group = groupreal;
if cplx
    x = [x' xcomplex']';
    group = [group groupcomplex];
    A = blkdiag(A,A);
end

y = A*x + noise*randn(size(A,1),1);
err = noise*sqrt(length(y));