Using our bit synchronous formulation, we can immediately derive the
MMSE expression for 
making the following assumptions.
The source bits of one user are uncorrelated with the past and future bits
from itself and all bits from other users(i.e. 
).
The noise 
is white, and zero mean and uncorrelated with the source
(i.e. 
and 
). Thus,
where 
is the autocorrelation matrix of 
and
is an all zero vector of dimension matching the
stacked source vector with a one in the position
corresponding to 
in the stacked source
vector. 
The MMSE solution minimizes the squared error in the presence of
channel noise, and becomes the zero-forcing solution when no noise is present.
Performance is very similar to the zero forcing solution when the SNR
is relatively high, but is improved at low SNR's. Also,
the zero-forcing solution may not exist if
is not invertible,
but the MMSE solution will provided the noise is not zero
because (and thus
) is invertible.