• Corpus ID: 2495820

On the Convexity of log det (I + K X^{-1})

  title={On the Convexity of log det (I + K X^\{-1\})},
  author={Young-Han Kim and Seung-Jean Kim},
A simple proof is given for the convexity of log det (I+K X^{-1}) in the positive definite matrix variable X with a given positive semidefinite K. 

A Note on the Convexity of $\log \det ( I + KX^{-1} )$ and its Constrained Optimization Representation

This note provides another proof for the convexity of $\log \det ( I + KX^{-1} )$ over the positive definite cone for any given positive semidefinite matrix $K \succeq 0$.

On the Ergodic Capacity Region of the Separately Correlated Rician Fading Multiple Access MIMO Channel

It is shown by numerical results that this asymptotic approach to the ergodic capacity region of a multiple access separately-correlated Rician fading MIMO channel is very accurate even when the number of antennas is as low as a few units.

Wireless Powered Information Transfer Based on Zero-Forcing for Multiuser MIMO Systems

Through complexity analysis and simulations, it is shown that the proposed ZF-based transmission method can reduce at least 92% of the computation load in terms of runtime with moderate achievable rate loss, compared to the optimal method obtained by the interior-point method.

Caching Gaussians: Minimizing total correlation on the Gray-Wyner network

  • G. VeldM. Gastpar
  • Computer Science
    2016 Annual Conference on Information Science and Systems (CISS)
  • 2016
This work extends known results for 2 Gaussians to multivariates by showing that common information is a simple linear program, which can be solved analytically for circulant correlation matrices and total correlation in a Gaussian setting is captured in the dominant eigenvalue of the correlation matrix.

Stability of transmitter cooperation over a multiple access channel

This paper addresses the stability of cooperation between rational transmitters (TXs) signaling over a multiple access channel (MAC) using the framework of cooperation game theory and finds the core of the TX game cooperation game in partition form to be non-emptiness.

Coalition games for transmitter cooperation in wireless networks

Cooperation between rational users has emerged as a new networking paradigm to improve the performance of wireless networks. In this paper, transmitter cooperation between wireless nodes in a

Coalitional Games for Transmitter Cooperation in MIMO Multiple Access Channels

It is shown using an approximate lower bound to the utility function that TX cooperation is also stable at high SNRs when time sharing is allowed between decoding orders, and demonstrates that ideal zero cost TX cooperation over a MAC is stable and improves achievable rates for each individual user.

Wireless Backhaul Networks: Capacity Bound, Scalability Analysis and Design Guidelines

The main goal is to study the per-BS antenna requirement that ensures scalability of this network, i.e., its ability to deliver nonvanishing rate to each source-destination pair and construct a scalable short hop strategy that does not violate any fundamental limits on the spatial degrees of freedom.

A Gaussian Source Coding Perspective on Caching and Total Correlation

Caching is a tool to balance traffic without compromising the ‘on-demand’ aspect of content delivery; by sending data in advance a server can avoid peak traffic and a discussion on challenges to be overcome for generalizing such algorithms is provided.



Convex analysis and nonlinear optimization : theory and examples

Background * Inequality constraints * Fenchel duality * Convex analysis * Special cases * Nonsmooth optimization * The Karush-Kuhn-Tucker Theorem * Fixed points * Postscript: infinite versus finite

Convex Optimization

A comprehensive introduction to the subject of convex optimization shows in detail how such problems can be solved numerically with great efficiency.

The worst additive noise under a covariance constraint

The problem becomes one of extremizing the mutual information over all noise processes with covariances satisfying the correlation constraints R/sub 0/,..., R/ sub p/ for high signal powers, the worst additive noise is Gauss-Markov of order p as expected.

Comments on "Correlated Jamming on MIMO Gaussian Fading Channels"

It is shown here that while the lemma itself is correct, the derivation of the proof is subject to a major defect, and the full and correct derivation using the same approach is given.

Correlated jamming on MIMO Gaussian fading channels

A zero-sum mutual information game on MIMO Gaussian Rayleigh fading channels is considered, and it is proved that the knowledge of the channel input is useless to the jammer.

All convex invariant functions of hermitian matrices