79)
(6.80)
where D is the operator which extracts the Dth column from the preceding matrix. The LMMSEbased
weights can be written as follows.
(6.81)
Note that the interference cancellation ability of this receiver is strictly related to including the
interference statistics into the calculation of the weights.
As we have discussed in the previous sections inverting the above matrix can be tedious and complex,
and alternative solutions exist. We will give a solution based on the LMS algorithm. The equalizer
weights are updated according to the following rule:
(6.82)
Here we see the update error vector has been slightly modified from previous discussions to
include the update dependent on the channel estimate. The original intent was to use this technique
without the use of a training sequence but nothing precludes the system designer form using a training
sequence to improve the channel estimates.
6.2.6 Maximum Likelihood Estimation (MLE)
In this section, we will present the STE solution from the ML perspective. The discussion begins with
the familiar ML metric and then shows how this metric changes as the channel conditions vary.
Assume the received signal on antenna #1 is
(6.83)
where we have generally assumed the desired signal contains delay spread components on the order
of J, and there are M interfering signals with each having I delay spread components.
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