lect9-10 - Kevin Buckley - 2007 1 ECE 8770 Topics in...

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Unformatted text preview: Kevin Buckley - 2007 1 ECE 8770 Topics in Digital Communications - Sp. 2007 Lecture 9,10 4 Channel Equalization 4.4 Adaptive Equalization Material in this Subsection of the course corresponds to Sections 11-1 and 11-2 of the course text. Our focus in this Subsection will be on both the linear equalizer and the DFE, on the Minimum Mean-Squared Error (MMSE) optimum design criterion, and on the Least Mean-Squared (LMS) adaptive algorithm. In Subsection 4.5 we will discuss alternative equalizer design criteria and adaptive algorithms. 4.4.1 MMSE & Adaptive Filters & Equalizers The principal motivation for extending optimum equalization to adaptive is that design of optimum equalizers requires information (i.e. received signal correlations or equivalently channel characteristics) that is note usually available. Adaptive equalizers are self designing, and thus do not require this information. The princi- pal concept involved in understanding and extending optimum equalization theory to adaptive equalization is that of searching a mean-squared error surface. We will explore this topic in more detail than covered in the course text. MMSE based equalizers, whether linear or DFE, are based on a formulation that assumes a desired signal (e.g. for equalizers the transmitted symbol se- quence). Consequently, optimum MMSE algorithms require the cross correlation between the desired and received signals. Adaptive implementations require the desired signal itself! At first glance, this would seem to render adaptive equalizers hideously impractical. There are two commonly employed techniques used, often in conjunction, to overcome this problem. These techniques are: 1) the use of training data ; and 2) decision directed implementation. Other less implemented techniques will be discussed in later Sections. Kevin Buckley - 2007 2 Figure 1(a) illustrates the standard linear MMSE filter structure. The data vector (a.k.a. the observation vector) x k is linearly combined using the coefficient vector w to generate the sequence d k which is an approximate of a desired signal d k . If x k is the vector of data in the delay line of an FIR filter, then w represents the coefficients of this FIR filter. However, Figure 1(a) represents a more general optimum filtering problem. The error signal is e k . For MMSE filtering, the coefficient vector w is designed to minimize E {| e k | 2 } , the mean squared error. We denote this vector w opt . We have already discussed the design of this coefficient vector within the context of linear equalizers and DFEs. We will revisit this issue a little later.At this point, just note that in a given optimum MMSE application, d k may or may not be accessible. That is, the specific structure surrounding the MMSE filter depends on the application....
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lect9-10 - Kevin Buckley - 2007 1 ECE 8770 Topics in...

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