27,207 research outputs found
Monodromies of Algebraic Connections on the Trivial Bundle
In this note, we study monodromies of algebraic connections on the trivial
vector bundle. We prove that on a smooth complex affine curve, any monodromy
arises as the underlying local system of an algebraic connection on the trivial
bundle. We give a generalization of this for rank one monodromies in higher
dimension.Comment: 6 page
A Conversation with Eric Ghysels
Published in Econometric Theory, 2012, https://doi.org/10.1017/S026646661100017X</p
Comment on "Realized Variance and Market Microstructure Noise" by Peter R. Hansen and Asger Lunde
Training Optimization for Energy Harvesting Communication Systems
Energy harvesting (EH) has recently emerged as an effective way to solve the
lifetime challenge of wireless sensor networks, as it can continuously harvest
energy from the environment. Unfortunately, it is challenging to guarantee a
satisfactory short-term performance in EH communication systems because the
harvested energy is sporadic. In this paper, we consider the channel training
optimization problem in EH communication systems, i.e., how to obtain accurate
channel state information to improve the communication performance. In contrast
to conventional communication systems, the optimization of the training power
and training period in EH communication systems is a coupled problem, which
makes such optimization very challenging. We shall formulate the optimal
training design problem for EH communication systems, and propose two solutions
that adaptively adjust the training period and power based on either the
instantaneous energy profile or the average energy harvesting rate. Numerical
and simulation results will show that training optimization is important in EH
communication systems. In particular, it will be shown that for short block
lengths, training optimization is critical. In contrast, for long block
lengths, the optimal training period is not too sensitive to the value of the
block length nor to the energy profile. Therefore, a properly selected fixed
training period value can be used.Comment: 6 pages, 5 figures, Globecom 201
Scalable Coordinated Beamforming for Dense Wireless Cooperative Networks
To meet the ever growing demand for both high throughput and uniform coverage
in future wireless networks, dense network deployment will be ubiquitous, for
which co- operation among the access points is critical. Considering the
computational complexity of designing coordinated beamformers for dense
networks, low-complexity and suboptimal precoding strategies are often adopted.
However, it is not clear how much performance loss will be caused. To enable
optimal coordinated beamforming, in this paper, we propose a framework to
design a scalable beamforming algorithm based on the alternative direction
method of multipliers (ADMM) method. Specifically, we first propose to apply
the matrix stuffing technique to transform the original optimization problem to
an equivalent ADMM-compliant problem, which is much more efficient than the
widely-used modeling framework CVX. We will then propose to use the ADMM
algorithm, a.k.a. the operator splitting method, to solve the transformed
ADMM-compliant problem efficiently. In particular, the subproblems of the ADMM
algorithm at each iteration can be solved with closed-forms and in parallel.
Simulation results show that the proposed techniques can result in significant
computational efficiency compared to the state- of-the-art interior-point
solvers. Furthermore, the simulation results demonstrate that the optimal
coordinated beamforming can significantly improve the system performance
compared to sub-optimal zero forcing beamforming
Optimal Scheduling and Power Allocation for Two-Hop Energy Harvesting Communication Systems
Energy harvesting (EH) has recently emerged as a promising technique for
green communications. To realize its potential, communication protocols need to
be redesigned to combat the randomness of the harvested energy. In this paper,
we investigate how to apply relaying to improve the short-term performance of
EH communication systems. With an EH source and a non-EH half-duplex relay, we
consider two different design objectives: 1) short-term throughput
maximization; and 2) transmission completion time minimization. Both problems
are joint scheduling and power allocation problems, rendered quite challenging
by the half-duplex constraint at the relay. A key finding is that directional
water-filling (DWF), which is the optimal power allocation algorithm for the
single-hop EH system, can serve as guideline for the design of two-hop
communication systems, as it not only determines the value of the optimal
performance, but also forms the basis to derive optimal solutions for both
design problems. Based on a relaxed energy profile along with the DWF
algorithm, we derive key properties of the optimal solutions for both problems
and thereafter propose efficient algorithms. Simulation results will show that
both scheduling and power allocation optimizations are necessary in two-hop EH
communication systems.Comment: Submitted to IEEE Transaction on Wireless Communicatio
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