52,619 research outputs found
Weighted (Co)homology and Weighted Laplacian
In this paper, we generalize the combinatorial Laplace operator of Horak and
Jost by introducing the -weighted coboundary operator induced by a weight
function . Our weight function is a generalization of Dawson's
weighted boundary map. We show that our above-mentioned generalizations include
new cases that are not covered by previous literature. Our definition of
weighted Laplacian for weighted simplicial complexes is also applicable to
weighted/unweighted graphs and digraphs.Comment: 22 page
Multi-Pair Two-Way Relay Network with Harvest-Then-Transmit Users: Resolving Pairwise Uplink-Downlink Coupling
While two-way relaying is a promising way to enhance the spectral efficiency
of wireless networks, the imbalance of relay-user distances may lead to
excessive wireless power at the nearby-users. To exploit the excessive power,
the recently proposed harvest-then-transmit technique can be applied. However,
it is well-known that harvest-then-transmit introduces uplink-downlink coupling
for a user. Together with the co-dependent relationship between paired users
and interference among multiple user pairs, wirelessly powered two-way relay
network suffers from the unique pairwise uplink-downlink coupling, and the
joint uplink-downlink network design is nontrivial. To this end, for the one
pair users case, we show that a global optimal solution can be obtained. For
the general case of multi-pair users, based on the rank-constrained difference
of convex program, a convergence guaranteed iterative algorithm with an
efficient initialization is proposed. Furthermore, a lower bound to the
performance of the optimal solution is derived by introducing virtual receivers
at relay. Numerical results on total transmit power show that the proposed
algorithm achieves a transmit power value close to the lower bound
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