  Compute-forward multiple access (CFMA) is a multiple access transmission
scheme based on Compute-and-Forward (CF) which allows the receiver to first
decode linear combinations of the transmitted signals and then solve for
individual messages. This paper extends the CFMA scheme to a two-user Gaussian
multiple-input multiple-output (MIMO) multiple access channel (MAC). We first
derive the expression of the achievable rate pair for MIMO MAC with CFMA. We
prove a general condition under which CFMA can achieve the sum capacity of the
channel. Furthermore, this result is specialized to SIMO and 2-by-2 diagonal
MIMO multiple access channels, for which more explicit sum capacity-achieving
conditions on power and channel matrices are derived. Numerical results are
also provided for the performance of CFMA on general MIMO multiple access
channels.
