mohatta2015.pdf
signal processing from power amplifier operation control point of view
signal processing from power amplifier operation control point of view
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MORE DETAILS 175<br />
8.2 MORE DETAILS<br />
In this section, we will explore parameter estimation in more detail and examine<br />
radio aspects.<br />
8.2.1 Parameter estimation<br />
In the previous section, we introduced the notion of indirect adaptation, in which<br />
intermediate parameters are estimated and used to compute linear equalization<br />
weights. Another option is to estimate the weights directly, referred to as direct<br />
adaptation. One way to do this is with an adaptive filtering approach that adaptively<br />
learns the best set of weights. An example is the least-mean squares (LMS)<br />
algorithm. Using known or detected symbols, it forms an error signal at symbol<br />
period m given by<br />
em = s m -hHr m + i»i(m)r m _ 1 ], (8.6)<br />
where we've added index m to the weights to show that they change in time. Ideally,<br />
we would like this error to be as small as possible. This can be achieved by updating<br />
the weights for the next symbol period using<br />
w 2 (m+l) = w 2 {m) + ßr m e m (8.7)<br />
wi(m+l) = wi(m)+ / ur rn _ie m . (8.8)<br />
The quantity μ is a step size, which determines how fast we adapt the weights.<br />
When we are tracking rapid changes, we want μ to be large. When the error is<br />
mostly due to noise, we want μ to be small, to minimize changing the weights from<br />
their optimum values.<br />
Returning to indirect adaptation, there are actually two types. Consider again<br />
MMSE LE. Recall that the weights can be obtained by solving a set of equations<br />
Rw = h, where R can be interpreted as a data correlation matrix. With parametric<br />
estimation of R, we estimate the channel response and noise power and use them<br />
to form a data correlation matrix. The term parametric is used because we form<br />
the data correlation values using a parametric model of the received samples and<br />
estimate its parameters.<br />
Another option is to estimate R directly form the received samples. For example,<br />
E{rir 2 } « (1/4)(Γ!Γ 2 + r 2 r 3 + r 3 r 4 + r 4 r 5 ). (8.9)<br />
This approach is also indirect adaptation, but it is nonparametric in the sense that<br />
we do not need a model of the received samples to determine the data correlation<br />
values.<br />
Parametric and nonparametric approaches also exist for channel estimation. In<br />
general, particular tracking approaches are based on a model of the channel coefficient's<br />
behavior over time.<br />
The overall set of design choices for adaptive MMSE LE is summarized in Figure<br />
8.1. Note that the channel response h can also be computed using a parametric or<br />
nonparametric approach.