This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Kevin Buckley  2007 1 ECE 8770 Topics in Digital Communications  Sp. 2007 Lecture 10a 4 Channel Equalization 4.4 Adaptive Equalization 4.5 Alternative Adaptation Schemes (continued) The Kalman Filter as an Adaptive Equalizer: In this Subsection we develop the Kalman filtering algorithm for adaptation of the coefficient vector of a linear equalizer or DFE. We start with the general Kalman fil tering problem formulation and solution, and we then discuss its application to channel equalization. 1. Kalman Filtering: The Kalman filter is popular as an effective estimator of the state of a random process because it is the minimum meansquared state estimator . It is also the conditional mean estimator of the state . We will see that it can also be used as an effective adaptive equalizer. The StateSpace Model or a Random Process: Consider the following general discretetime linear statespace model w k +1 = A k w k + G k v k (1) z k = H k w k + k (2) where z k is the L 1 dimensional observation (i.e. data) vector at time k , w k is the M 1 dimensional state vector, H k is the L L dimensional transition matrix from the state to the output at time k , k is the L 1 measurement noise vector, A k is the M M dimensional state transition matrix at time k , v k is the P 1 dimensional process noise vector, and G k is the M P dimensional transition matrix at time k from the state transition noise to the next state. We assume that k and v k are zeromean vector sequences, uncorrelated across time, with covariance matrices S k and Q k at time k , respectively. k and v n are assumed uncorrelated with one another for all k and n . Kevin Buckley  2007 2 Figure 1 illustrates this general discretetime linear statespace model. This canFigure 1 illustrates this general discretetime linear statespace model....
View
Full
Document
This document was uploaded on 10/12/2009.
 Spring '09

Click to edit the document details