Heavy-Dense QCD (HDQCD) is a popular theory to investigate the sign problem in quantum field theory. Besides its physical applications,

HDQCD is relatively easy to implement numerically: the fermionic degrees of freedom are integrated out, and the fermion determinant factorises into local ones. The theory has a sign problem, the severeness of which depends on the value of the chemical potential, which makes this theory ideal to test the 'reach'of new algorithms.

We use the LLR approach to obtain the probability distribution of the

phase of the fermion determinant. Our goal is the calculation of the

phase factor expectation value, which appears as Fourier transform of

this probablity distribution. We here propose a new and systematic

moment expansion for this phase factor. We compare the answer from the

moment expansion order by order with the ``exact'' answer. We find

that this expansion converge quickly and works very well in the strong sign problem region.