  Orthogonality is a much desired property for MIMO coding. It enables
symbol-wise decoding, where the errors in other symbol estimates do not affect
the result, thus providing an optimality that is worth pursuing. Another
beneficial property is a low complexity soft decision decoder, which for
orthogonal complex MIMO codes is known for two transmit (Tx) antennas i.e. for
the Alamouti code. We propose novel soft decision decoders for the orthogonal
complex MIMO codes on three and four Tx antennas and extend the old result of
maximal ratio combining (MRC) to cover all orthogonal codes up to four Tx
antennas.
  As a rule, a sophisticated transmission scheme encompasses forward error
correction (FEC) coding, and its performance is measured at the FEC decoder
instead of at the MIMO decoder. We introduce the receiver structure that
delivers the MIMO decoder's soft decisions to the demodulator, which in turn
cranks out the logarithm of likelihood ratio (LLR) of each bit and delivers
them to the FEC decoder. This makes a significant improvement on the receiver,
where a maximum likelihood (ML) MIMO decoder makes hard decisions at a too
early stage. Further, the additional gain is achieved with stunningly low
complexity.
