Lesson plan
Adaptive equalizer
An adaptive equalizer is an equalizer that automatically adapts to time-varying properties of the communication channel. It is frequently used with coherent modulations such as phase-shift keying, mitigating the effects of multipath propagation and Doppler spreading. Adaptive equalizers are a subclass of adaptive filters. The central idea is altering the filter's coefficients to optimize a filter characteristic. For example, in case of linear discrete-time filters, the following equation can be used: : \mathbf{w}_{opt} = \mathbf{R}^{-1}\mathbf{p} where \mathbf{w}_{opt} is the vector of the filter's coefficients, \mathbf{R} is the received signal covariance matrix and \mathbf{p} is the cross-correlation vector between the tap-input vector and the desired response. In practice, the last quantities are not known and, if necessary, must be estimated during the equalization procedure either explicitly or implicitly. Many adaptation strategies exist. They include, e.g.: * Least mean squares filter (LMS) Note that the receiver does not have access to the transmitted signal x when it is not in training mode. If the probability that the equalizer makes a mistake is sufficiently small, the symbol decisions d(n) made by the equalizer may be substituted for x .…
Article summary
An adaptive equalizer is an equalizer that automatically adapts to time-varying properties of the communication channel. It is frequently used with coherent modulations such as phase-shift keying, mitigating the effects of multipath propagation and Doppler spreading. Adaptive equalizers are a subclass of adaptive filters. The central idea is altering the filter's coefficients to optimize a filter characteristic. For example, in case of linear discrete-time filters, the following equation can be used: : \mathbf{w}_{opt} = \mathbf{R}^{-1}\mathbf{p} where \mathbf{w}_{opt} is the vector of the filter's coefficients, \mathbf{R} is the received signal covariance matrix and \mathbf{p} is the cross-correlation vector between the tap-input vector and the desired response. In practice, the last quantities are not known and, if necessary, must be estimated during the equalization procedure either explicitly or implicitly. Many adaptation strategies exist. They include, e.g.: * Least mean squares filter (LMS) Note that the receiver does not have access to the transmitted signal x when it is not in training mode. If the probability that the equalizer makes a mistake is sufficiently small, the symbol decisions d(n) made by the equalizer may be substituted for x .…
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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