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The linear model under mixed gaussian inputs: Designing the transfer matrix
KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0003-2638-6047
2013 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 21, 5247-5259 p.Article in journal (Refereed) Published
Abstract [en]

Suppose a linear model Y = Hx+n, where inputs x, n are independent Gaussian mixtures. The problem is to design the transfer matrix so as to minimize the mean square error (MSE) when estimating x from . This problem has important applications, but faces at least three hurdles. Firstly, even for a fixed H, the minimum MSE (MMSE) has no analytical form. Secondly, theMMSE is generally not convex in . Thirdly, derivatives of the MMSEw.r.t. are hard to obtain. This paper casts theproblemas a stochastic program and invokes gradient methods. The study is motivated by two applications in signal processing. One concerns the choice of error-reducing precoders; the other deals with selection of pilot matrices for channel estimation. In either setting, our numerical results indicate improved estimation accuracy-markedly better than those obtained by optimal design based on standard linear estimators. Some implications of the non-convexities of the MMSE are noteworthy, yet, to our knowledge, not well known. For example, there are cases in which more pilot power is detrimental for channel estimation. This paper explains why.

Place, publisher, year, edition, pages
2013. Vol. 61, no 21, 5247-5259 p.
Keyword [en]
estimation, Gaussian mixtures, minimum mean square error (MMSE)
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:kth:diva-133159DOI: 10.1109/TSP.2013.2278812ISI: 000324934300008Scopus ID: 2-s2.0-84884804981OAI: oai:DiVA.org:kth-133159DiVA: diva2:660249
Funder
Swedish Research Council, 621-2011-1024
Note

QC 20131029

Available from: 2013-10-29 Created: 2013-10-28 Last updated: 2017-12-06Bibliographically approved

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Chatterjee, Saikat

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