Applications of Large Random Matrices in Communications Engineering

Müller, Ralf R.; Alfano, Giusi; Zaidel, Benjamin M.; de Miguel, Rodrigo

doi:10.48550/arxiv.1310.5479

Cited by 9 publications

(17 citation statements)

References 100 publications

(181 reference statements)

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“…This paper is organized as follows: Section 2 briefly presents the concept of "asymptotic freeness" (in the almost sure sense) in random matrix theory, see [26] for a detailed exposition. Section 3 presents a more explicit form of the fixed-point equations in (3) for the diagonal-and scalar-EP methods.…”

Section: B Outlinementioning

confidence: 99%

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Expectation Propagation for Approximate Inference: Free Probability Framework

Çakmak

Opper

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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We study asymptotic properties of expectation propagation (EP) -a method for approximate inference originally developed in the field of machine learning. Applied to generalized linear models, EP iteratively computes a multivariate Gaussian approximation to the exact posterior distribution. The computational complexity of the repeated update of covariance matrices severely limits the application of EP to large problem sizes. In this study, we present a rigorous analysis by means of free probability theory that allows us to overcome this computational bottleneck if specific data matrices in the problem fulfill certain properties of asymptotic freeness. We demonstrate the relevance of our approach on the gene selection problem of a microarray dataset.

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Section: B Outlinementioning

confidence: 99%

“…This gives the highest degree of non-commutativity in the definition of asymptotic freeness. We next present the concept of asymptotic freeness in a more general and formal setup [26]. To this end we define a non-commutative polynomial set in p matrices of order n:…”

Section: Asymptotic Freenessmentioning

confidence: 99%

Expectation Propagation for Approximate Inference: Free Probability Framework

Çakmak

Opper

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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“…Thus, the multiplexing rate is obtained by replacing the term (1−η H ) in (28) with α H (due to Theorem 1). This leads to (29). Finally, we note that if α H < 1 the S-transform S H (z) diverges as z → (−α H ), see Lemma 5.…”

Section: Appendix D Proof Of Examplementioning

confidence: 83%

Capacity Scaling in MIMO Systems With General Unitarily Invariant Random Matrices

Çakmak

Müller

Fleury³

2018

IEEE Trans. Inform. Theory

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We investigate the capacity scaling of MIMO systems with the system dimensions. To that end we quantify how the mutual information varies when the number of antennas (at either the receiver or transmitter side) is altered. For a system comprising R receive and T transmit antennas with R > T , we find the following: By removing as many receive antennas as needed to obtain a square system (provided the channel matrices before and after the removal have full rank) the maximum resulting loss of mutual information over all signal-to-noise ratios (SNRs) depends only on R, T and the matrix of left-singular vectors of the initial channel matrix, but not on its singular values. In particular, if the latter matrix is Haar distributed the ergodic rate loss is given by T t=1 R r=T +1 1 r−t nats. Under the same assumption, if T, R → ∞ with the ratio φ T /R fixed, the rate loss normalized by R converges almost surely to H(φ) bits with H(·) denoting the binary entropy function. We also quantify and study how the mutual information as a function of the system dimensions deviates from the traditionally assumed linear growth in the minimum of the system dimensions at high SNR.

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“…zero-mean random variables with variance n −1 . In this case, p D follows Marcenko-Pastur law [16], and therefore, the R-transform reads…”

Section: Applications Of the Resultsmentioning

confidence: 99%

Nonlinear Precoders for Massive MIMO Systems with General Constraints

Bereyhi¹,

Sedaghat²,

Asaad³

et al. 2017

Preprint

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We introduce a class of nonlinear least square error precoders with a general penalty function for multiuser massive MIMO systems. The generality of the penalty function allows us to consider several hardware limitations including transmitters with a predefined constellation and restricted number of active antennas. The large-system performance is then investigated via the replica method under the assumption of replica symmetry. It is shown that the least square precoders exhibit the "marginal decoupling property" meaning that the marginal distributions of all precoded symbols converge to a deterministic distribution. As a result, the asymptotic performance of the precoders is described by an equivalent single-user system. To address some applications of the results, we further study the asymptotic performance of the precoders when both the peak-to-average power ratio and number of active transmit antennas are constrained. Our numerical investigations show that for a desired distortion at the receiver side, proposed forms of the least square precoders need to employ around 35% fewer number of active antennas compared to cases with random transmit antenna selection.

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Applications of Large Random Matrices in Communications Engineering

Cited by 9 publications

References 100 publications

Expectation Propagation for Approximate Inference: Free Probability Framework

Expectation Propagation for Approximate Inference: Free Probability Framework

Capacity Scaling in MIMO Systems With General Unitarily Invariant Random Matrices

Nonlinear Precoders for Massive MIMO Systems with General Constraints

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