# Equalizer (communications)

In telecommunication, the equalizer is a device that attempts to reverse the distortion incurred by a signal transmitted through a channel.

## Digital communications

In digital communications, its purpose is to reduce intersymbol interference to allow recovery of the transmit symbols. It may be a simple linear filter or a complex algorithm. The following equalizer types are commonly used in digital communications:

• Linear Equalizer: processes the incoming signal with a linear filter
• MMSE equalizer: designs the filter to minimize E[|e|2], where e is the error signal, which is the filter output minus the transmitted signal.[1]
• Zero Forcing Equalizer: approximates the inverse of the channel with a linear filter.
• Decision Feedback Equalizer: augments a linear equalizer by adding a filtered version of previous symbol estimates to the original filter output.[2]
• Blind Equalizer: estimates the transmitted signal without knowledge of the channel statistics, using only knowledge of the transmitted signal's statistics.
• Adaptive Equalizer: is typically a linear equalizer or a DFE. It updates the equalizer parameters (such as the filter coefficients) as it is processes the data. Typically, it uses the MSE cost function; it assumes that it makes the correct symbol decisions, and uses its estimate of the symbols to compute e, which is defined above.
• Viterbi Equalizer: Finds the maximum likelihood (ML) optimal solution to the equalization problem. Its goal is to minimize the probability of making an error over the entire sequence.
• BCJR Equalizer: uses the BCJR algorithm (also called the Forward-backward algorithm) to find the maximum a posteriori (MAP) solution. Its goal is to minimize the probability that a given bit was incorrectly estimated.
• Turbo equalizer: applies turbo decoding while treating the channel as a convolutional code.

## Analogue communications

Below is a list of equalizers with applications in analogue communications: