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.
Assuming a linear time invariant channel with impulse response
infty | |
\{h[n]\} | |
n=-infty |
r[k]
s[k]
infty | |
r[k]=\sum | |
n=-infty |
h[n]s[k-n]
The blind equalization problem can now be formulated as follows; Given the received signal
r[k]
w[k]
infty | |
\hat{s}[k]=\sum | |
n=-infty |
w[n]r[k-n]
where
\hat{s}
s
\hat{s}
\{\tilde{s}[n],\tilde{h}[n]\}
\{c\tilde{s}[n+d],\tilde{h}[n-d]/c\}
r
c
d
s
h
In the noisy model, an additional term,
n[k]
infty | |
r[k]=\sum | |
n=-infty |
h[n]s[k-n]+n[k]
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
r(t)
N | |
\{h[n]\} | |
n=-N |
N
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
wn+1[k]=
* | |
w | |
n[k]+\mue |
[n]r[n-k],k=-N,...N
with
e[n]=g(\hat{s}[n])-\hat{s}[n]
where
\mu
g
Polyspectra techniques utilize higher order statistics in order to compute the equalizer.
[1] C. RICHARD JOHNSON, JR., et. el., "Blind Equalization Using the Constant Modulus Criterion: A Review", PROCEEDINGS OF THE IEEE, VOL. 86, NO. 10, OCTOBER 1998.