Gaussian approximation of the LLR distribution for the ML and partial marginalization MIMO detectors

We derive a Gaussian approximation of the LLR distribution conditioned on the transmitted signal and the channel matrix for the soft-output via partial marginalization MIMO detector. This detector performs exact ML as a special case. Our main results consist of discussing the operational meaning of this approximation and a proof that, in the limit of high SNR, the LLR distribution of interest converges in probability towards a Gaussian distribution.