1,262 research outputs found
Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion
In this paper, we consider the stochastic optimal control problems under
G-expectation. Based on the theory of backward stochastic differential
equations driven by G-Brownian motion, which was introduced in [10.11], we can
investigate the more general stochastic optimal control problems under
G-expectation than that were constructed in [28]. Then we obtain a generalized
dynamic programming principle and the value function is proved to be a
viscosity solution of a fully nonlinear second-order partial differential
equation.Comment: 25 page
Outage Capacity and Optimal Transmission for Dying Channels
In wireless networks, communication links may be subject to random fatal
impacts: for example, sensor networks under sudden power losses or cognitive
radio networks with unpredictable primary user spectrum occupancy. Under such
circumstances, it is critical to quantify how fast and reliably the information
can be collected over attacked links. For a single point-to-point channel
subject to a random attack, named as a \emph{dying channel}, we model it as a
block-fading (BF) channel with a finite and random delay constraint. First, we
define the outage capacity as the performance measure, followed by studying the
optimal coding length such that the outage probability is minimized when
uniform power allocation is assumed. For a given rate target and a coding
length , we then minimize the outage probability over the power allocation
vector \mv{P}_{K}, and show that this optimization problem can be cast into a
convex optimization problem under some conditions. The optimal solutions for
several special cases are discussed.
Furthermore, we extend the single point-to-point dying channel result to the
parallel multi-channel case where each sub-channel is a dying channel, and
investigate the corresponding asymptotic behavior of the overall outage
probability with two different attack models: the independent-attack case and
the -dependent-attack case. It can be shown that the overall outage
probability diminishes to zero for both cases as the number of sub-channels
increases if the \emph{rate per unit cost} is less than a certain threshold.
The outage exponents are also studied to reveal how fast the outage probability
improves over the number of sub-channels.Comment: 31 pages, 9 figures, submitted to IEEE Transactions on Information
Theor
On Design of Collaborative Beamforming for Two-Way Relay Networks
We consider a two-way relay network, where two source nodes, S1 and S2,
exchange information through a cluster of relay nodes. The relay nodes receive
the sum signal from S1 and S2 in the first time slot. In the second time slot,
each relay node multiplies its received signal by a complex coefficient and
retransmits the signal to the two source nodes, which leads to a collaborative
two-way beamforming system. By applying the principle of analog network coding,
each receiver at S1 and S2 cancels the "self-interference" in the received
signal from the relay cluster and decodes the message. This paper studies the
2-dimensional achievable rate region for such a two-way relay network with
collaborative beamforming. With different assumptions of channel reciprocity
between the source-relay and relay-source channels, the achievable rate region
is characterized under two setups. First, with reciprocal channels, we
investigate the achievable rate regions when the relay cluster is subject to a
sum-power constraint or individual-power constraints. We show that the optimal
beamforming vectors obtained from solving the weighted sum inverse-SNR
minimization (WSISMin) problems are sufficient to characterize the
corresponding achievable rate region. Furthermore, we derive the closed form
solutions for those optimal beamforming vectors and consequently propose the
partially distributed algorithms to implement the optimal beamforming, where
each relay node only needs the local channel information and one global
parameter. Second, with the non-reciprocal channels, the achievable rate
regions are also characterized for both the sum-power constraint case and the
individual-power constraint case. Although no closed-form solutions are
available under this setup, we present efficient numerical algorithms.Comment: new version of the previously posted, single column double spacing,
24 page
Dynamic Resource Allocation in Cognitive Radio Networks: A Convex Optimization Perspective
This article provides an overview of the state-of-art results on
communication resource allocation over space, time, and frequency for emerging
cognitive radio (CR) wireless networks. Focusing on the
interference-power/interference-temperature (IT) constraint approach for CRs to
protect primary radio transmissions, many new and challenging problems
regarding the design of CR systems are formulated, and some of the
corresponding solutions are shown to be obtainable by restructuring some
classic results known for traditional (non-CR) wireless networks. It is
demonstrated that convex optimization plays an essential role in solving these
problems, in a both rigorous and efficient way. Promising research directions
on interference management for CR and other related multiuser communication
systems are discussed.Comment: to appear in IEEE Signal Processing Magazine, special issue on convex
optimization for signal processin
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