Audio source separation comes with the need to devise mul-tichannel filters that can exploit priors about the target signals. In that context, experience shows that modeling magnitude spectra is effective. However, devising a probabilistic model on complex spectral data with a prior on magnitudes is non trivial, because it should both reflect the prior but also be tractable for easy inference. In this paper, we approximate the ideal donut-shaped distribution of a complex variable with approximately known magnitude as a Gaussian mixture model called BEADS (Bayesian Expansion Approximating the Donut Shape) and show that it permits straightforward inference and filtering while effectively constraining the magnitudes of the signals to comply with the prior. As a result, we demonstrate large improvements over the Gaussian baseline for multichannel audio coding when exploiting the BEADS model.