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Mean square error reduction by precoding of mixed Gaussian input
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Signal Processing.
KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
2012 (English)In: 2012 International Symposium on Information Theory and Its Applications, ISITA 2012, 2012, 81-85 p.Conference paper, Published paper (Refereed)
Abstract [en]

Suppose a vector of observations y = Hx + n stems from independent inputs x and n, both of which are Gaussian Mixture (GM) distributed, and that H is a fixed and known matrix. This work focuses on the design of a precoding matrix, F, such that the model modifies to z = HFx + n. The goal is to design F such that the mean square error (MSE) when estimating x from z is smaller than when estimating x from y. We do this under the restriction E[(Fx)TFx] ≤ PT, that is, the precoder cannot exceed an average power constraint. Although the minimum mean square error (MMSE) estimator, for any fixed F, has a closed form, the MMSE does not under these settings. This complicates the design of F. We investigate the effect of two different precoders, when used in conjunction with the MMSE estimator. The first is the linear MMSE (LMMSE) precoder. This precoder will be mismatched to the MMSE estimator, unless x and n are purely Gaussian variates. We find that it may provide MMSE gains in some setting, but be harmful in others. Because the LMMSE precoder is particularly simple to obtain, it should nevertheless be considered. The second precoder we investigate, is derived as the solution to a stochastic optimization problem, where the objective is to minimize the MMSE. As such, this precoder is matched to the MMSE estimator. It is derived using the KieferWolfowitz algorithm, which moves iteratively from an initially chosen F0 to a local minimizer F*. Simulations indicate that the resulting precoder has promising performance.

Place, publisher, year, edition, pages
2012. 81-85 p.
National Category
Signal Processing Telecommunications
Identifiers
URN: urn:nbn:se:kth:diva-109504Scopus ID: 2-s2.0-84873547730ISBN: 978-488552267-3 (print)OAI: oai:DiVA.org:kth-109504DiVA: diva2:582924
Conference
International Symposium on Information Theory and its Applications (ISITA2012), Honolulu, HI, USA, Oct. 28-31, 2012.
Funder
Swedish Research CouncilICT - The Next Generation
Note

QC 20130220

Available from: 2013-01-07 Created: 2013-01-07 Last updated: 2013-04-11Bibliographically approved

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Citation style
  • apa
  • harvard1
  • ieee
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More styles
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Output format
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