lect11-12 - Kevin Buckley 2007 1 ECE 8770 Topics in Digital...

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Unformatted text preview: Kevin Buckley - 2007 1 ECE 8770 Topics in Digital Communications - Sp. 2007 Lecture 11-12 4 Channel Equalization 4.6 MLSE with Unknown Channels In the previous Subsection we considered several equalizer approaches that are effective when the ISI channel is unknown. For example, initializing an adaptive equalizer with training data followed by decision directed operation can be effective. This is not a blind approach, since blind processing implies that neither the channel nor the input is known. Two blind adaptive equalizers, CMA and its generalization Bussgang, were also introduced. Adaptive channel equalization, followed by symbol detection, is an effective approach to receiving digital communications signals transmitted through unknown ISI channels. Even so, for performance reasons maximum likelihood sequence estimation (MLSE), implemented using a Viterbi algorithm, is often preferred. In this Subsection we continue to address digital communications over an unknown ISI channel. This time we focus MLSE based symbol estimation. This principal challenge addressed here concerns the fact that the Viterbi algorithm, as described for ISI chan- nels in Section 3 of the Course, requires knowledge of the channel for the branch cost computations, since the MLSE cost is a function of the channel coefficients. Thus, for unknown channels, to implement MLSE, some auxiliary signal processing is required to provide or otherwise deal with this needed characterization of the channel. In this Section we overview variations of two basic approaches to MLSE with unknown channel: channel estimation prior to MLSE; and approaches based on some direct MLSE formulation. Below we look at the following topics: 1. For channel estimation prior to MLSE: – FIR system identification (ID) based on training data, – blind channel ID in conjunction with MLSE, – ML channel estimation with unknown symbols, and – blind linear algebra based approaches. 2. for approaches based on a direct MLSE formulation: – joint ML channel/sequence estimation; and – direct MLSE with unknown channel. Implicit in any blind approach to digital communications over unknown ISI channel is the exploitation of the known structure of the channel input (i.e. we know the input is a sequence of a limited set of symbols). Kevin Buckley - 2007 2 4.6.1 Channel Estimation Prior to MLSE FIR System Identification (ID) based on Training Data Figure 1 illustrates a basic system identification approach to channel estimation for a situation for which both the channel input and output are accessible (e.g. in training mode). As illustrated, the channel is assumed to be FIR with unknown impulse response vector f . The approach is to configure the system identification FIR filter in parallel with the channel to be identified, to input a common signal (e.g. a training sequence), and to select the ID filter so as to minimize the mean- squared error e k between the channel and ID filter outputs. This is just the MMSE filtering problem employed earlier to design the MMSE linear equalizer:...
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lect11-12 - Kevin Buckley 2007 1 ECE 8770 Topics in Digital...

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