Statistical mechanical analysis of the linear vector channel in digital communication

Takeda, Kenta; Hatabu, Atsushi; Kabashima, Yoshiyuki

doi:10.1088/1751-8113/40/47/004

Cited by 18 publications

(29 citation statements)

References 29 publications

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“…Later, Guo and Verdú generalized the approach to CDMA with arbitrary signaling [31]. Meanwhile, in [7] and [32] the method was applied to spatially correlated MIMO channels with binary inputs. These works were further generalized in [33] to the analysis of the sum-rate of a MIMO-MAC.…”

Section: Psfrag Replacementsmentioning

confidence: 99%

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Large-System Analysis of Correlated MIMO Multiple Access Channels with Arbitrary Signaling in the Presence of Interference

Girnyk

Vehkaperä

Rasmussen

2014

IEEE Trans. Wireless Commun.

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Presence of multiple antennas on both sides of a communication channel promises significant improvements in system throughput and power efficiency. In effect, a new class of large multiple-input multiple-output (MIMO) communication systems has recently emerged and attracted both scientific and industrial attention. To analyze these systems in realistic scenarios, one has to include such aspects as co-channel interference, multiple access and spatial correlation. In this paper, we study the properties of correlated MIMO multiple-access channels in the presence of external interference. Using the replica method from statistical physics, we derive the ergodic sum-rate of the communication for arbitrary signal constellations when the numbers of antennas at both ends of the channel grow large. Based on these asymptotic expressions, we also address the problem of sum-rate maximization using statistical channel information and linear precoding. The numerical results demonstrate that when the interfering terminals use discrete constellations, the resulting interference becomes easier to handle compared to Gaussian signals. Thus, it may be possible to accommodate more interfering transmitter-receiver pairs within the same area as compared to the case of Gaussian signals. In addition, we demonstrate numerically for the Gaussian and QPSK signaling schemes that it is possible to design precoder matrices that significantly improve the achievable rates at low-to-mid range of signal-to-noise ratios when compared to isotropic precoding.

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Section: Psfrag Replacementsmentioning

confidence: 99%

“…Corollary 1. In the LSL, the asymptotic average sum-rate of an uncorrelated MIMO-MAC given in (4) in the presence of interference is given by (32) on the top of the page, where parameters ε s,k , ξ s,k , ε i,ℓ , ξ i,ℓ , ε i,ℓ and ξ i,ℓ satisfy the following set of fixed-point equations…”

Section: B Uncorrelated Channelsmentioning

confidence: 99%

Large-System Analysis of Correlated MIMO Multiple Access Channels with Arbitrary Signaling in the Presence of Interference

Girnyk

Vehkaperä

Rasmussen

2014

IEEE Trans. Wireless Commun.

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“…For our system that we address, which is given by (2.3.10) or equivalently by (2.3.2), the Hamiltonian becomes [105,106]. That is, we use fixed states y = Ax 0 + w instead of y for the large system limit, as N, M → ∞, while maintaining N/M fixed.…”

Section: Discussionmentioning

confidence: 99%

“…where R(v) is the R-transform of the limiting eigenvalue distribution of the matrix J( see, definition 1 in [96] of R-transform or in [53] for better understanding of R-transform) and {λ a } denote the eigenvalues of L(n) as explained in [55,96,109].…”

Section: Discussionmentioning

confidence: 99%

“…Kabashima et. 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.…”

Section: Introductionmentioning

confidence: 99%

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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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Inference from correlated patterns: a unified theory for perceptron learning and linear vector channels

Kabashima

2008

J. Phys.: Conf. Ser.

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A framework to analyze inference performance in densely connected single-layer feed-forward networks is developed for situations where a given data set is composed of correlated patterns. The framework is based on the assumption that the left and right singular value bases of the given pattern matrix are generated independently and uniformly from Haar measures. This assumption makes it possible to characterize the objective system by a single function of two variables which is determined by the eigenvalue spectrum of the cross-correlation matrix of the pattern matrix. Links to existing methods for analysis of perceptron learning and Gaussian linear vector channels and an application to a simple but nontrivial problem are also shown.

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Statistical mechanical analysis of the linear vector channel in digital communication

Cited by 18 publications

References 29 publications

Large-System Analysis of Correlated MIMO Multiple Access Channels with Arbitrary Signaling in the Presence of Interference

Large-System Analysis of Correlated MIMO Multiple Access Channels with Arbitrary Signaling in the Presence of Interference

Improved reconstruction in compressive sensing of clustered signals

Inference from correlated patterns: a unified theory for perceptron learning and linear vector channels

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