Channel Equalization

Introduction

In digital communication systems, the data signals are transmitted through linearly analog channels with distortions, such as telephone lines, cables and wireless radios. In point to point communication two major sources of channel distortion in digital communication systems are multi-path propagation and limited band-width. Linear channel distortion leads to inter-symbol interference (ISI) at the receiver end, which generally leads to high error rate in symbol detection and estimation. The channel has to be estimated or equalized for the coherent detection of the transmitted signal. Channel equalization and channel estimation is used in this regard depending on the system model and feasibility.

typical communication system model

The main purpose of equalization is to reduce intersymbol interference to allow recovery of the transmit symbols. It may be a simple linear filter or a complex algorithm. Channel equalization is a simple way of mitigating the detrimental effects caused by a frequency-selective and/or dispersive communication link between sender and receiver. The equalizer is a transversal filter which tries to approximate an inverse channel so that it nullifies the effect of the channel when the received data passes through it. The ultimate goal of these techniques is to try to estimate or equalize within overhead, processing power and time. he 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.
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.
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.

Classification of Equalizers