Delay Constrained Throughput Analysis of a Correlated MIMO Wireless Channel

The maximum traffic arrival rate at the network for a given delay guarantee (delay constrained throughput) has been well studied for wired channels. However, few results are available for wireless channels, especially when multiple antennas are employed at the transmitter and receiver. In this work, we analyze the network delay constrained throughput of a multiple input multiple output (MIMO) wireless channel with time-varying spatial correlation. The MIMO channel is modeled via its virtual representation, where the individual spatial paths between the antenna pairs are Gilbert-Elliot channels. The whole system is then described by a K-State Markov chain, where K depends upon the degree of freedom (DOF) of the channel. We prove that the DOF based modeling is indeed accurate. Furthermore, we study the impact of the delay requirements at the network layer, violation probability and the number of antennas on the throughput under different fading speeds and signal strength.Comment: Submitted to ICCCN 2011, 8 pages, 5 figure

Gossip Algorithms for Distributed Signal Processing

Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This article presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmitted messages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page

Measuring edge importance: a quantitative analysis of the stochastic shielding approximation for random processes on graphs

Mathematical models of cellular physiological mechanisms often involve random walks on graphs representing transitions within networks of functional states. Schmandt and Gal\'{a}n recently introduced a novel stochastic shielding approximation as a fast, accurate method for generating approximate sample paths from a finite state Markov process in which only a subset of states are observable. For example, in ion channel models, such as the Hodgkin-Huxley or other conductance based neural models, a nerve cell has a population of ion channels whose states comprise the nodes of a graph, only some of which allow a transmembrane current to pass. The stochastic shielding approximation consists of neglecting fluctuations in the dynamics associated with edges in the graph not directly affecting the observable states. We consider the problem of finding the optimal complexity reducing mapping from a stochastic process on a graph to an approximate process on a smaller sample space, as determined by the choice of a particular linear measurement functional on the graph. The partitioning of ion channel states into conducting versus nonconducting states provides a case in point. In addition to establishing that Schmandt and Gal\'{a}n's approximation is in fact optimal in a specific sense, we use recent results from random matrix theory to provide heuristic error estimates for the accuracy of the stochastic shielding approximation for an ensemble of random graphs. Moreover, we provide a novel quantitative measure of the contribution of individual transitions within the reaction graph to the accuracy of the approximate process.Comment: Added one reference, typos corrected in Equation 6 and Appendix C, added the assumption that the graph is irreducible to the main theorem (results unchanged

Robust Power Allocation and Outage Analysis for Secrecy in Independent Parallel Gaussian Channels

This letter studies parallel independent Gaussian channels with uncertain eavesdropper channel state information (CSI). Firstly, we evaluate the probability of zero secrecy rate in this system for (i) given instantaneous channel conditions and (ii) a Rayleigh fading scenario. Secondly, when non-zero secrecy is achievable in the low SNR regime, we aim to solve a robust power allocation problem which minimizes the outage probability at a target secrecy rate. We bound the outage probability and obtain a linear fractional program that takes into account the uncertainty in eavesdropper CSI while allocating power on the parallel channels. Problem structure is exploited to solve this optimization problem efficiently. We find the proposed scheme effective for uncertain eavesdropper CSI in comparison with conventional power allocation schemes.Comment: 4 pages, 2 figures. Author version of the paper published in IEEE Wireless Communications Letters. Published version is accessible at http://dx.doi.org/10.1109/LWC.2015.249734