mohatta2015.pdf

MORE DETAILS 175
8.2 MORE DETAILS
In this section, we will explore parameter estimation in more detail and examine
radio aspects.
8.2.1 Parameter estimation
In the previous section, we introduced the notion of indirect adaptation, in which
intermediate parameters are estimated and used to compute linear equalization
weights. Another option is to estimate the weights directly, referred to as direct
adaptation. One way to do this is with an adaptive filtering approach that adaptively
learns the best set of weights. An example is the least-mean squares (LMS)
algorithm. Using known or detected symbols, it forms an error signal at symbol
period m given by
em = s m -hHr m + i»i(m)r m _ 1 ], (8.6)
where we've added index m to the weights to show that they change in time. Ideally,
we would like this error to be as small as possible. This can be achieved by updating
the weights for the next symbol period using
w 2 (m+l) = w 2 {m) + ßr m e m (8.7)
wi(m+l) = wi(m)+ / ur rn _ie m . (8.8)
The quantity μ is a step size, which determines how fast we adapt the weights.
When we are tracking rapid changes, we want μ to be large. When the error is
mostly due to noise, we want μ to be small, to minimize changing the weights from
their optimum values.
Returning to indirect adaptation, there are actually two types. Consider again
MMSE LE. Recall that the weights can be obtained by solving a set of equations
Rw = h, where R can be interpreted as a data correlation matrix. With parametric
estimation of R, we estimate the channel response and noise power and use them
to form a data correlation matrix. The term parametric is used because we form
the data correlation values using a parametric model of the received samples and
estimate its parameters.
Another option is to estimate R directly form the received samples. For example,
E{rir 2 } « (1/4)(Γ!Γ 2 + r 2 r 3 + r 3 r 4 + r 4 r 5 ). (8.9)
This approach is also indirect adaptation, but it is nonparametric in the sense that
we do not need a model of the received samples to determine the data correlation
values.
Parametric and nonparametric approaches also exist for channel estimation. In
general, particular tracking approaches are based on a model of the channel coefficient's
behavior over time.
The overall set of design choices for adaptive MMSE LE is summarized in Figure
8.1. Note that the channel response h can also be computed using a parametric or
nonparametric approach.