Ergodic capacity of the exponentially correlated slotted amplify and forward relay channel

In this paper we analyze the performance degradation of slotted amplify-and-forward protocol in wireless environments with high node density where the number of relays grows asymptotically large. Channel gains between source-destination pairs in such networks can no longer be independent. We analyze the degradation of performance in such wireless environments where channel gains are exponentially correlated by looking at the capacity per channel use. Theoretical results for eigenvalue distribution and the capacity are derived and compared with the simulation results. Both analytical and simulated results show that the capacity given by the asymptotic mutual information decreases with the network density.

Ergodic capacity of the slotted amplify and forward relay channel with finite relays

Abstract—In this paper we investigate the capacity of a general class of the slotted amplify and forward (SAF) relaying protocol where multiple, though a finite number of relays may transmit in a given cooperative slot and the relay terminals being half-duplex have a finite slot memory capacity. We derive an expression for the capacity per channel use of this generalized SAF channel assuming all source to relay, relay to destination and source to destination channel gains are independent and modeled as complex Gaussian. We show through the analysis of eigenvalue distributions that the increase in limiting capacity per channel use is marginal with the increase of relay terminals.

Ergodic capacity and outage performance of amplify-and-forward protocols

This thesis analyses the performance bounds of amplify-and-forward relay channels which are becoming increasingly popular in wireless communication applications. The statistics of cascaded Nakagami-m fading model which is a major obstacle in evaluating the outage of wireless networks is analysed using Mellin transform. Furthermore, the upper and the lower bounds for the ergodic capacity of the slotted amplify-and-forward relay channel, for finite and infinite number of relays are derived using random matrix theory. The results obtained will enable wireless network designers to optimize the network resources, benefiting the consumers.

Ergodic control of partially observed Markov chains

The ergodic or long-run average cost control problem for a partially observed finite-state Markov chain is studied via the associated fully observed separated control problem for the nonlinear filter. Dynamic programming equations for the latter are derived, leading to existence and characterization of optimal stationary policies.

Risk-Sensitive Ergodic Control of Continuous Time Markov Processes With Denumerable State Space

In this article, we study risk-sensitive control problem with controlled continuous time Markov chain state dynamics. Using multiplicative dynamic programming principle along with the atomic structure of the state dynamics, we prove the existence and a characterization of optimal risk-sensitive control under geometric ergodicity of the state dynamics along with a smallness condition on the running cost.

Descriptive set theory and the ergodic theory of countable groups

The primary focus of this thesis is on the interplay of descriptive set theory and the ergodic theory of group actions. This incorporates the study of turbulence and Borel reducibility on the one hand, and the theory of orbit equivalence and weak equivalence on the other. Chapter 2 is joint work with Clinton Conley and Alexander Kechris; we study measurable graph combinatorial invariants of group actions and employ the ultraproduct construction as a way of constructing various measure preserving actions with desirable properties. Chapter 3 is joint work with Lewis Bowen; we study the property MD of residually finite groups, and we prove a conjecture of Kechris by showing that under general hypotheses property MD is inherited by a group from one of its co-amenable subgroups. Chapter 4 is a study of weak equivalence. One of the main results answers a question of Abért and Elek by showing that within any free weak equivalence class the isomorphism relation does not admit classification by countable structures. The proof relies on affirming a conjecture of Ioana by showing that the product of a free action with a Bernoulli shift is weakly equivalent to the original action. Chapter 5 studies the relationship between mixing and freeness properties of measure preserving actions. Chapter 6 studies how approximation properties of ergodic actions and unitary representations are reflected group theoretically and also operator algebraically via a group's reduced C^*-algebra. Chapter 7 is an appendix which includes various results on mixing via filters and on Gaussian actions.

Characteristic Functions for Ergodic Tuples

Gohm, Rolf; Dey, S., 'Characteristic function for ergodic tuples', Integral Equations and Operator Theory 58(1) pp.43-63 RAE2008

Generic Ergodic Capacity Bounds for Fixed-Gain AF Dual-Hop Relaying Systems

This paper elaborates on the ergodic capacity of fixed-gain amplify-and-forward (AF) dual-hop systems, which have recently attracted considerable research and industry interest. In particular, two novel capacity bounds that allow for fast and efficient computation and apply for nonidentically distributed hops are derived. More importantly, they are generic since they apply to a wide range of popular fading channel models. Specifically, the proposed upper bound applies to Nakagami-m, Weibull, and generalized-K fading channels, whereas the proposed lower bound is more general and applies to Rician fading channels. Moreover, it is explicitly demonstrated that the proposed lower and upper bounds become asymptotically exact in the high signal-to-noise ratio (SNR) regime. Based on our analytical expressions and numerical results, we gain valuable insights into the impact of model parameters on the capacity of fixed-gain AF dual-hop relaying systems. © 2011 IEEE.