In this case, the discrete time representation of the model is straightforward.
The discrete time output of the sampler synchronized to the kth user
following the chip-matched filter
is given by
since the pulse shaping filter 
has duration 
.
Given 
of length 
, we wish to represent the chip-spaced input
to the tapped-delay line as the -length vector
in order to express the output of the linear filter as
where 
is the delay in chips after the first chip in the
spreading sequence. If 
then 
. This means that the
first element of lines up with the first chip in the
spreading sequence. If 
, then may be negative and
if 
then may be positive. This makes the model more
general by not requiring the first element of to line up
with the first element of the spreading sequence of bit n.
In the discrete time model, we construct baud-spaced channel convolution
matrices of dimension 
for each user, i.e.,
of dimension 
which map the baud spaced symbols of the kth user
to the appropriate chip spaced sequences. Here, 
where he symbol 
represents the ceiling operation.
as determined by the
dimensions of . Define the kth user's baud spaced symbol vector
as 
, then it
follows that the chip spaced regressor vector may be expressed as
be a special ordering of all of the columns
in the 
matrices, defined as
