On the Ergodic Mutual Information of Multiple Cluster Scattering MIMO Channels

Wei, Lu; Zheng, Zhong; Tirkkonen, Olav; Hämäläinen, Jyri

doi:10.1109/lcomm.2013.071813.131137

Cited by 12 publications

(6 citation statements)

References 14 publications

(16 reference statements)

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“…The idea to investigate the dynamical correlation functions comes naturally from considering the signal model of the MIMO system described in Wei, Zheng, Tirkkonen, and Hamalainen [32]. In this model the products of independent complex Ginibre matrices arise, and the results of Section 2.2 seem to be relevant in the MIMO communication setting.…”

Section: 3mentioning

confidence: 99%

“…In this problem the transmission of a vector-valued signal between two adjacent clusters of scatterers is modeled by a random matrix, and the transmission of a vector-valued signal through a sequence of clusters of scatterers is modeled by the corresponding product of random independent matrices. Exact solvability of the relevant random matrix ensemble enables to give formulae for the expectation of the mutual information, which is an important quantity in wireless telecommunication, see Akemann, Ipsen, and Kieburg [5], and Wei, Zheng, Tirkkonen, and Hamalainen [32].…”

Section: Introductionmentioning

confidence: 99%

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Dynamical correlation functions for products of random matrices

Strahov

2015

Random Matrices: Theory Appl.

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We introduce and study a family of random processes with a discrete time related to products of random matrices. Such processes are formed by singular values of random matrix products, and the number of factors in a random matrix product plays a role of a discrete time. We consider in detail the case when the (squared) singular values of the initial random matrix form a polynomial ensemble, and the initial random matrix is multiplied by standard complex Gaussian matrices. In this case, we show that the random process is a discrete-time determinantal point process. For three special cases (the case when the initial random matrix is a standard complex Gaussian matrix, the case when it is a truncated unitary matrix, or the case when it is a standard complex Gaussian matrix with a source) we compute the dynamical correlation functions explicitly, and find the hard edge scaling limits of the correlation kernels. The proofs rely on the Eynard-Mehta theorem, and on contour integral representations for the correlation kernels suitable for an asymptotic analysis.Let us mention that recent works on products of random matrices (in particular, the works mentioned above) deal with the situation when the number of matrices in products under consideration is fixed. In this paper, we propose to consider sequences of products of random matrices instead of fixed products. The main idea behind this work is rather similar to that of Johansson and Nordenstam [21]. Johansson and Nordenstam [21] start with an infinite random matrix picked from the Gaussian Unitary Ensemble (GUE), and consider the eigenvalues of its minors. They show that all such eigenvalues form a determinantal process on N × R. Such determinantal processes are called the minor processes. Here we can start from a matrix product G m · · · G 1 , and consider squared singular values of subproducts G k · · · G 1 , k = 1, . . . , m. As a result we arrive to a family of determinantal processes on {1, . . . , m} × R >0 , which can be understood as time-dependent extensions of the processes studied previously.The minor processes and their generalizations are of great interest in Random Matrix Theory, and are closely related to random tiling models, and to certain percolation models on the Z + × Z + lattice. In particular, it was observed by Johansson and Nordenstam [21] (see also [28]) that the spectra of the principal minors of a GUE matrix behave as domino tilings of large size Aztec diamonds. We refer the reader to [3, 1, 2] and references therein for a description of these connections, and for recent results in this area of research. Many other time-dependent determinantal point processes appeared over the past decade in the context of growth models, and were applied to different problems in numerative combinatorics and statistical physics, see, for example, [11,10].The novelty of this paper is in the very observation that products of random matrices also lead to time-dependent determinantal point processes. These processes are rather different from those formed by eigenv...

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Section: 3mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamical correlation functions for products of random matrices

Strahov

2015

Random Matrices: Theory Appl.

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“…As an instance of application of such spectral statistics, [1] provides a closed-form expression for the mutual information conveyed by a MIMO multiple scattering channel [1,Formula (82)] when Channel State Information (CSI) is available at the receiver. Using the result in [1], Wei et al [7] present the first exact analysis of the above system in the case of orthogonal space-time block coding, while an approximate analysis for an arbitrary number of matrix factors and in a more general scenario is given in [15].…”

Section: Introductionmentioning

confidence: 99%

Information-Theoretic Characterization of MIMO Systems With Multiple Rayleigh Scattering

Alfano

Chiasserini

Nordio

et al. 2018

IEEE Trans. Inform. Theory

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We present an information-theoretic analysis of a point-to-point Multiple-Input-Multiple-Output (MIMO) link affected by Rayleigh fading and multiple scattering, under perfect channel state information at the receiver. Unlike previous work addressing this setting, we investigate the Random Coding Error Exponent, its associated cutoff rate and the Expurgated Error Exponent, and derive closed-form expressions for them. Moreover, leveraging the average mutual information expression presented in [1], we derive another important metric, namely, the sum rate, under linear receive processing and independent stream decoding. In particular, we characterize the performance of the Minimum Mean Squared Error receiver in closed form, and that of the Zero Forcing receiver by resorting to bounding techniques. The bulk of the work relies on results about finite-dimensional random matrix products, a number of which are novel and detailed in the Appendices. The analysis, validated through numerical results, highlights the severe degradation in the performance of linear receivers due to multi-fold scattering. It also unveils the performance trend of multiple scattering MIMO channels as a function of the number of antennas and the number of scattering stages.

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“…Recently, an asymptotic expression for ergodic capacity of the double-scattering channels was derived in [8]. Moreover, authors in [9]- [11] derived the ergodic mutual information for finite dimensional channel matrices. However, all the above results are valid for ergodic channels, where each codeword has infinite length.…”

mentioning

confidence: 99%

Asymptotic Analysis of Rayleigh Product Channels: A Free Probability Approach

Zheng

Wei

Speicher

et al. 2017

IEEE Trans. Inform. Theory

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The Rayleigh product channel model is useful in capturing the performance degradation due to rank deficiency of MIMO channels. In this paper, such a performance degradation is investigated via the channel outage probability assuming slowly varying channel with delay-constrained decoding. Using techniques of free probability theory, the asymptotic variance of channel capacity is derived when the dimensions of the channel matrices approach infinity. In this asymptotic regime, the channel capacity is rigorously proven to be Gaussian distributed. Using the obtained results, a fundamental tradeoff between multiplexing gain and diversity gain of Rayleigh product channels can be characterized by closed-form expression at any finite signal-to-noise ratio. Numerical results are provided to compare the relative outage performance between Rayleigh product channels and conventional Rayleigh MIMO channels. Index TermsCentral limit theorem; finite-SNR diversity-multiplexing tradeoff; free probability theory; MIMO; outage capacity; Rayleigh product channels.

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On the Ergodic Mutual Information of Multiple Cluster Scattering MIMO Channels

Cited by 12 publications

References 14 publications

Dynamical correlation functions for products of random matrices

Dynamical correlation functions for products of random matrices

Information-Theoretic Characterization of MIMO Systems With Multiple Rayleigh Scattering

Asymptotic Analysis of Rayleigh Product Channels: A Free Probability Approach

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