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

@article{Kim2006OnTC, title={On the Convexity of log det (I + K X^\{-1\})}, author={Young-Han Kim and Seung-Jean Kim}, journal={ArXiv}, year={2006}, volume={abs/cs/0611043} }

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.

## 9 Citations

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

- MathematicsArXiv
- 2015

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 $K \succeq 0$.

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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

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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

- Computer Science2016 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

- Computer Science2012 International Conference on Signal Processing and Communications (SPCOM)
- 2012

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

- Computer Science2011 IEEE International Symposium on Information Theory Proceedings
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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

- Computer ScienceIEEE Transactions on Signal Processing
- 2014

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

- Computer ScienceIEEE Transactions on Wireless Communications
- 2015

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

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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.

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