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.
Assuming a linear time invariant channel with impulse response
, the noiseless model relates the received signal
via The blind equalization problem can now be formulated as follows; Given the received signal
to the blind equalization problem is not unique.
In fact, it may be determined only up to a signed scale factor and an arbitrary time delay.
are estimates of the transmitted signal and channel impulse response, respectively, then
give rise to the same received signal
In the noisy model, an additional term,
, representing additive noise, is included.
The model is therefore Many algorithms for the solution of the blind equalization problem have been suggested over the years.
However, as one usually has access to only a finite number of samples from the received signal
, 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,
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.
If the channel impulse response is assumed to be minimum phase, the problem becomes trivial.
Bussgang methods make use of the Least mean squares filter algorithm with where
el., "Blind Equalization Using the Constant Modulus Criterion: A Review", PROCEEDINGS OF THE IEEE, VOL.