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177:, 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.
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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.
1081:, 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
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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
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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.
644:
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. That is, if
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signal, while making use only of the transmitted signal statistics. Hence, the use of the word
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The blind equalization problem can now be formulated as follows; Given the received signal
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are estimates of the transmitted signal and channel impulse response, respectively, then
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with the received signal to yield an estimation of the transmitted signal.
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940:, representing additive noise, is included. The model is therefore
556:{\displaystyle {\hat {s}}=\sum _{n=-\infty }^{\infty }wr}
155:. Nonetheless, the emphasis in blind equalization is on
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1417:{\displaystyle e=\mathbf {g} ({\hat {s}})-{\hat {s}}}
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1323:{\displaystyle w_{n+1}=w_{n}+\mu \,e^{*}r,k=-N,...N}
46:. Unsourced material may be challenged and removed.
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1037:{\displaystyle r=\sum _{n=-\infty }^{\infty }hs+n}
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257:, the noiseless model relates the received signal
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1173:If the channel impulse response is assumed to be
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796:{\displaystyle \{c{\tilde {s}},{\tilde {h}}/c\}}
397:{\displaystyle r=\sum _{n=-\infty }^{\infty }hs}
1447:is an appropriate positive adaptation step and
705:{\displaystyle \{{\tilde {s}},{\tilde {h}}\}}
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250:{\displaystyle \{h\}_{n=-\infty }^{\infty }}
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465:, called an equalization filter, such that
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106:Learn how and when to remove this message
911:In the noisy model, an additional term,
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803:give rise to the same received signal
863:. In fact, by symmetry, the roles of
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44:adding citations to reliable sources
15:
1487:in order to compute the equalizer.
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1469:is a suitable nonlinear function.
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147:Blind equalization is essentially
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1185:Bussgang methods make use of the
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1161:is an arbitrary natural number.
1134:{\displaystyle \{h\}_{n=-N}^{N}}
180:The estimated equalizer is then
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1177:, the problem becomes trivial.
31:needs additional citations for
1497:Independent component analysis
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201:channel with impulse response
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1502:Principal components analysis
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1462:{\displaystyle \mathbf {g} }
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823:for any real scale factor
637:{\displaystyle {\hat {s}}}
588:{\displaystyle {\hat {s}}}
286:to the transmitted signal
1187:Least mean squares filter
123:digital signal processing
1535:Telecommunication theory
1512:Linear predictive coding
843:and integral time delay
1485:higher order statistics
1083:finite impulse response
125:technique in which the
1481:Polyspectra techniques
1476:Polyspectra techniques
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153:digital communications
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903:are Interchangeable.
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199:linear time invariant
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1440:{\displaystyle \mu }
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1074:{\displaystyle r(t)}
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595:is an estimation of
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55:"Blind equalization"
40:improve this article
1507:Blind deconvolution
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164:equalization filter
149:blind deconvolution
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119:Blind equalization
1540:Signal processing
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1154:{\displaystyle N}
933:{\displaystyle n}
896:{\displaystyle h}
876:{\displaystyle s}
856:{\displaystyle d}
836:{\displaystyle c}
816:{\displaystyle r}
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608:{\displaystyle s}
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458:{\displaystyle w}
429:{\displaystyle r}
308:{\displaystyle s}
279:{\displaystyle r}
188:Problem statement
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175:impulse response
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615:. The solution
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1175:minimum phase
1169:Minimum phase
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144:in the name.
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132:is inferred (
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57: –
56:
52:
51:Find sources:
45:
41:
35:
34:
29:This article
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1471:
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50:
38:Please help
33:verification
30:
907:Noisy model
197:Assuming a
151:applied to
136:) from the
127:transmitted
96:August 2016
1529:Categories
1518:References
1189:algorithm
1048:Algorithms
160:estimation
66:newspapers
1435:μ
1400:^
1391:−
1373:^
1300:−
1282:−
1259:∗
1250:μ
1119:−
1011:−
985:∞
980:∞
977:−
967:∑
774:−
762:~
732:~
685:~
661:~
629:^
580:^
545:−
519:∞
514:∞
511:−
501:∑
482:^
386:−
360:∞
355:∞
352:−
342:∑
243:∞
238:∞
235:−
182:convolved
134:equalized
1491:See also
1483:utilize
1141:, where
138:received
172:channel
170:of the
168:inverse
162:of the
80:scholar
1427:where
566:where
157:online
130:signal
82:
75:
68:
61:
53:
1333:with
142:blind
121:is a
87:JSTOR
73:books
883:and
315:via
59:news
42:by
1531::
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36:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
