Vector Precoding for Wireless MIMO Systems and its Replica Analysis

Müller, Ralf R.; Guo, Dongning; Moustakas, Aris L.

doi:10.1109/jsac.2008.080411

Cited by 93 publications

(111 citation statements)

References 35 publications

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“…In the context of communication and information theory, Takeda et al [16] utilized the asymptotic result in their analysis of a class of orthogonally-spread code-division multiple-access (CDMA) channels. Müller et al [17,18] discussed a problem of vector precoding in multi-antenna communications, in which the asymptotic exponent was used. Relation of the above result to our problem becomes evident if we identify A = UDU * and XX * = NE, that is, if the random matrix A has orthogonal (β = 1) or unitary (β = 2) invariance, our problem is reduced to the Itzykson-Zuber integral, so that the above-mentioned result by Guionnet and Maïda has solved our problem with the solution (6).…”

Section: Related Workmentioning

confidence: 99%

Asymptotics of Harish-Chandra-Itzykson-Zuber integrals and free probability theory

Tanaka¹

2008

J. Phys.: Conf. Ser.

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Abstract.We discuss an asymptotic exponent N −1 log EA[exp(β tr X * AX/2)] in the limit N → ∞, where β = 1 or 2, where A is an N -by-N real symmetric (β = 1) or complex Hermitian (β = 2) random matrix, and where X is an N -by-M real (β = 1) or complex (β = 2) matrix, with M being kept finite while taking the limit N → ∞. Relation of the problem to the so-called Harish-Chandra or Itzykson-Zuber integrals are also discussed. Assuming that the result is given in terms of limiting eigenvalues of Q = N −1 X * X, we show that the exponent is given by a sum of integrated R-transforms of the limiting eigenvalue distribution of A. We also provide some examples for which the same result holds without the above assumption.

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Section: Related Workmentioning

confidence: 99%

Asymptotics of Harish-Chandra-Itzykson-Zuber integrals and free probability theory

Tanaka¹

2008

J. Phys.: Conf. Ser.

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“…This triplet face of the posterior enables us to use the methods from one field to another, in our case tools developed from statistical mechanics to the asymptotic analysis of the CS reconstruction schemes. One finds several such works if the CS circle is replaced by neural systems [51], CDMA [61], MIMO [96] and so on. The performance analysis part of the thesis (Section 1.1.3 and Chapter 2) lies at the center while the application Chapters (3,4 and 5) totally reside in the region of the intersection of CS and Bayesian Statistics circles of the venn diagram.…”

Section: Scope and Contribution Of The Thesismentioning

confidence: 99%

“…al in [68], Ganguli and Sompolinsky in [104] and Takeda and Kabashima [70,105,106] have shown statistical mechanical analysis of the CS by considering the noiseless recovery problem and they indicated that RSB analysis is needed in the phase regimes where the RS solution is not stable. In this work, the performance of these CS estimators, considered as MAP estimator, is shown for the noisy problem by using the replica method including RS and RSB as in [54,55,96], where the RSB ansatz gives a better solution when the replica symmetry (RS) solution is unstable. This work is a kind of extension of [55], from MIMO systems to the CS systems.…”

Section: Introductionmentioning

confidence: 99%

Improved reconstruction in compressive sensing of clustered signals

Barzideh

Lundheim

2015

Africon 2015

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This thesis deals with an emerging area of signal processing, called Compressive Sensing (CS), that allows the reconstruction of sparse or compressible signals from fewer measurements than are used in traditional schemes. Like traditional signal representation schemes, CS follows a similar framework: encoding, transmission/storing, and decoding. The encoding part is done using random projection (RP) or random sensing, and the decoding is done via nonlinear reconstruction algorithms from a reduced amount of measurements. The performance of the reconstruction schemes used and the application of such paradigm are the two main focuses of the thesis. It has three parts: the introduction, performance analysis of recovery algorithms in CS and some applications of CS.The introductory part provides the background for the following four chapters. It begins by defining the basic concepts used in CS theory and presents the Bayesian framework. Further, an analytical tool from statistical mechanics for performance analysis of physical systems is introduced applied on a non-noisy CS problem. The Bayesian framework is given ample emphasis in the thesis for two reasons. First, it serves as a bridge between the recovery algorithms used in CS and a tool from the statistical mechanics, called the replica method. Second, it is used as main framework to incorporate different prior signal information, like sparsity and clusteredness. Furthermore, a short description of CS applications is given before the introduction concludes by presenting the scope and the contribution of the thesis.The second part of the thesis deals with the study of the performance of recovery methods in CS systems using the Replica Method. At the beginning, the study of the performance of the recovery algorithms in CS was focused on the ratio of the amount of measurement used, the sparsity level, and how accurate the recovered information is. However, there was a luck of universal performance analysis. The Replica method provides this by considering large size systems. This thesis contributes to such analysis via the Bayesian framework. In this work noisy CS systems are considered and the recovering algorithms are reinterpreted as a maximum a posteriori (MAP) estimator. It, therefore, provides replica analysis including one step replica breaking ansatz for CS systems as an extension of similar analysis done for other systems like multiple input/multiple output (MIMO).The CS application is the third part of the thesis. The theory of CS has been applied in many signal processing fields such as image processing, communication, networks and so on. There are hundreds, if not thousands of articles on this subject at present. In this thesis, there are novel results that contribute to the application of CS theory. The theory is applied to limited feedback in temporally correlated MIMO channels, where the sparsity property was used to reduce feedback overhead significantly while delivering the same performance. Further, including another assumption, i.e., more st...

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“…in the large-system limit, which is equal to the corresponding joint moment k∈K E[Xñ k k ] for the distribution defined as the right-hand side of (43).…”

Section: Proof Of Lemmamentioning

confidence: 99%

Large-System Analysis of Joint Channel and Data Estimation for MIMO DS-CDMA Systems

Takeuchi¹,

Vehkaperä²,

Tanaka³

et al. 2012

IEEE Trans. Inform. Theory

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This paper presents a large-system analysis of the performance of joint channel estimation, multiuser detection, and per-user decoding (CE-MUDD) for randomly-spread multiple-input multiple-output (MIMO) direct-sequence codedivision multiple-access (DS-CDMA) systems. A suboptimal receiver based on successive decoding in conjunction with linear minimum mean-squared error (LMMSE) channel estimation is investigated. The replica method, developed in statistical mechanics, is used to evaluate the performance in the large-system limit, where the number of users and the spreading factor tend to infinity while their ratio and the number of transmit and receive antennas are kept constant. The performance of the joint CE-MUDD based on LMMSE channel estimation is compared to the spectral efficiencies of several receivers based on one-shot LMMSE channel estimation, in which the decoded data symbols are not utilized to refine the initial channel estimates. The results imply that the use of joint CE-MUDD significantly reduces rate loss due to transmission of pilot signals, especially for multiple-antenna systems. As a result, joint CE-MUDD can provide significant performance gains, compared to the receivers based on one-shot channel estimation.

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Vector Precoding for Wireless MIMO Systems and its Replica Analysis

Cited by 93 publications

References 35 publications

Asymptotics of Harish-Chandra-Itzykson-Zuber integrals and free probability theory

Asymptotics of Harish-Chandra-Itzykson-Zuber integrals and free probability theory

Improved reconstruction in compressive sensing of clustered signals

Large-System Analysis of Joint Channel and Data Estimation for MIMO DS-CDMA Systems

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