Content deleted Content added
→top: ce lead, wikilink mathematical algorithm, wikilink noisy data, rm context notice |
Article use. |
||
| (2 intermediate revisions by 2 users not shown) | |||
Line 1:
{{Short description|Algorithm for analyzing noisy data streams}}
'''Maximum likelihood sequence estimation''' ('''MLSE''') is a [[mathematical algorithm]]
==Theory==
Line 7:
==Background==
Suppose that there is an underlying signal {''x''(''t'')}, of which an observed signal {''r''(''t'')} is available. The observed signal ''r'' is related to ''x'' via a transformation that may be nonlinear and may involve attenuation, and would usually involve the incorporation of [[random noise]]. The [[statistical parameter]]s of this transformation are assumed to be known. The problem to be solved is to use the observations {''r''(''t'')} to create a good estimate of {''x''(''t'')}.
Maximum likelihood sequence estimation is formally the application of [[maximum likelihood]] to this problem. That is, the estimate of {''x''(''t'')} is defined to be a sequence of values which maximize the functional
:<math>L(x)=p(r\mid x),</math>
where ''p''(''r'' | ''x'') denotes the conditional joint probability density function of the observed series {''r''(''t'')} given that the underlying series has the values {''x''(''t'')}.
In contrast, the related method of maximum a posteriori estimation is formally the application of the [[maximum a posteriori]] (MAP) estimation approach. This is more complex than maximum likelihood sequence estimation and requires a known distribution (in [[Bayesian inference|Bayesian terms]], a [[prior distribution]]) for the underlying signal. In this case the estimate of {''x''(''t'')} is defined to be a sequence of values which maximize the functional
:<math>P(x)=p(x\mid r),</math>
where ''p''(''x'' | ''r'') denotes the conditional joint probability density function of the underlying series {''x''(''t'')} given that the observed series has taken the values {''r''(''t'')}. [[Bayes' theorem]] implies that
Line 31:
* {{Cite book|title=Wireless Communications|author=Andrea Goldsmith|chapter=Maximum Likelihood Sequence Estimation|pages=362–364|publisher=Cambridge University Press|year=2005|isbn=9780521837163}}
* {{Cite book|pages=319–321|title=Fundamentals of DSL Technology|author1=Philip Golden |author2=Hervé Dedieu |author3=Krista S. Jacobsen |name-list-style=amp |publisher=CRC Press|year=2006|isbn=9780849319136}}
* Crivelli, D. E.; Carrer, H. S., Hueda, M. R. (2005) [http://www.scielo.org.ar/pdf/laar/v35n2/v35n2a04.pdf "Performance evaluation of maximum likelihood sequence estimation receivers in lightwave systems with optical amplifiers"], ''Latin American Applied Research'', 35 (2), 95–98.
* Katz, G., Sadot, D., Mahlab, U., and Levy, A.(2008) "Channel estimators for maximum-likelihood sequence estimation in direct-detection optical communications", ''Optical Engineering'' 47 (4), 045003. {{
==External links==
| |||