Vector Precoding for Gaussian MIMO Broadcast Channels: Impact of Replica Symmetry Breaking

Zaidel, Benjamin M.; Mueller, Ralf S.; Moustakas, Aris L.; Miguel, Rodrigo de

doi:10.48550/arxiv.1001.3790

Cited by 1 publication

(15 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…x∈χ n e −u( Whether these minimization problems are solvable or not the replica analysis results can provide the asymptotic performances of all the above estimators via replica method as showed in [10], [14], [22], [23] and [24]. We apply RS ansatz as used by Müller and et al in [27] and RSB ansatz as used by Zaidel and et al [29] on vector precoding for MIMO. Actually, this work is an extension of the RSB analysis to MIMO systems done in [29] to the CS system.…”

Section: Bayesian Framework For Sparse Signalmentioning

confidence: 99%

“…We apply RS ansatz as used by Müller and et al in [27] and RSB ansatz as used by Zaidel and et al [29] on vector precoding for MIMO. Actually, this work is an extension of the RSB analysis to MIMO systems done in [29] to the CS system.…”

Section: Bayesian Framework For Sparse Signalmentioning

confidence: 99%

“…The inner expectation in (3.12) is the Harish -Chandra -Itzykoson-Zuber integral (again see in [27] and [29] and the references therein). The plan here is to evaluate the fixed-rank matrices L(n) as N → ∞.…”

Section: A Statistical Physics Analysismentioning

confidence: 99%

“…Kabashima and et. al in [22], Ganguli and Sompolinsky in [23] and Takeda and Kabashima [24] - [26] 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 paper the performance of those CS estimators, considered as MAP estimator, is shown for the noisy problem by using the replica method including RS and RSB as in [27] - [29], where the RSB ansatz gives better solution when the replica symmetry (RS) solution is unstable. This work is kind of an extension of [29] from MIMO systems to the CS systems.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper the performance of those CS estimators, considered as MAP estimator, is shown for the noisy problem by using the replica method including RS and RSB as in [27] - [29], where the RSB ansatz gives better solution when the replica symmetry (RS) solution is unstable. This work is kind of an extension of [29] from MIMO systems to the CS systems.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Compressed Sensing Performance Analysis via Replica Method Using Bayesian Framework

Godana

2015

2015 17th UKSim-AMSS International Conference on Modelling and Simulation (UKSim)

View full text Add to dashboard Cite

Compressive sensing (CS) is a new methodology to capture signals at lower rate than the Nyquist sampling rate when the signals are sparse or sparse in some domain. The performance of CS estimators is analyzed in this paper using tools from statistical mechanics, especially called replica method. This method has been used to analyze communication systems like Code Division Multiple Access (CDMA) and multiple input multiple output (MIMO) systems with large size. Replica analysis, now days rigorously proved, is an efficient tool to analyze large systems in general. Specifically, we analyze the performance of some of the estimators used in CS like LASSO (the Least Absolute Shrinkage and Selection Operator) estimator and Zero-Norm regularizing estimator as a special case of maximum a posteriori (MAP) estimator by using Bayesian framework to connect the CS estimators and replica method. We use both replica symmetric (RS) ansatz and one-step replica symmetry breaking (1RSB) ansatz, clamming the latter is efficient when the problem is not convex. This work is more analytical in its form. It is deferred for next step to focus on the numerical results.

show abstract