  In this paper, we propose a low complexity graph-based linear minimum mean
square error (LMMSE) equalizer in order to remove inter-symbol and inter-stream
interference in multiple input multiple output (MIMO) communication. The
proposed state space representation inflicted on the graph provides linearly
increasing computational complexity with block length. Also, owing to the
Gaussian assumption used in the presented cycle-free factor graph, the
complexity of the suggested equalizer structure is not affected by the size of
the signalling space. In addition, we introduce an efficient way of computing
extrinsic bit log-likelihood ratio (LLR) values for LMMSE estimation compatible
with higher order alphabets which is shown to perform better than the other
methods in the literature. Overall, we provide an efficient receiver structure
reaching high data rates in frequency selective MIMO systems whose performance
is shown to be very close to a genie-aided matched filter bound through
extensive simulations.
