Blind equalization on arvau

Wikipedia / Blind equalization

Blind equalization is a digital signal processing technique in which the transmitted signal is inferred (equalized) from the received signal, while making use only of the transmitted signal statistics. Hence, the use of the word blind in the name.

Blind equalization is essentially blind deconvolution applied to digital communications. Nonetheless, the emphasis in blind equalization is on online estimation of the equalization filter, which is the inverse of the channel impulse response, rather than the estimation of the channel impulse response itself. This is due to blind deconvolution common mode of usage in digital communications systems, as a means to extract the continuously transmitted signal from the received signal, with the channel impulse response being of secondary intrinsic importance.

The estimated equalizer is then convolved with the received signal to yield an estimation of the transmitted signal.

Problem statement

Noiseless model

Assuming a linear time invariant via

, called an equalization filter, such that

are Interchangeable.

Noisy model

, representing additive noise, is included. The model is therefore

Algorithms

, further restrictions must be imposed over the above models to render the blind equalization problem tractable. One such assumption, common to all algorithms described below is to assume that the channel has finite impulse response is an arbitrary natural number.

This assumption may be justified on physical grounds, since the energy of any real signal must be finite, and therefore its impulse response must tend to zero. Thus it may be assumed that all coefficients beyond a certain point are negligibly small.

Minimum phase

If the channel impulse response is assumed to be minimum phase, the problem becomes trivial.

Bussgang methods

Bussgang methods make use of the Least mean squares filter algorithm

with

is a suitable nonlinear function.

Polyspectra techniques

Polyspectra techniques utilize higher order statistics in order to compute the equalizer.