14,733 research outputs found
A Two-Phase Power Allocation Scheme for CRNs Employing NOMA
In this paper, we consider the power allocation (PA) problem in cognitive
radio networks (CRNs) employing nonorthogonal multiple access (NOMA) technique.
Specifically, we aim to maximize the number of admitted secondary users (SUs)
and their throughput, without violating the interference tolerance threshold of
the primary users (PUs). This problem is divided into a two-phase PA process:
a) maximizing the number of admitted SUs; b) maximizing the minimum throughput
among the admitted SUs. To address the first phase, we apply a sequential and
iterative PA algorithm, which fully exploits the characteristics of the
NOMA-based system. Following this, the second phase is shown to be quasiconvex
and is optimally solved via the bisection method. Furthermore, we prove the
existence of a unique solution for the second phase and propose another PA
algorithm, which is also optimal and significantly reduces the complexity in
contrast with the bisection method. Simulation results verify the effectiveness
of the proposed two-phase PA scheme
A finite field approach to solving the Bethe Salpeter equation
We present a method to compute optical spectra and exciton binding energies
of molecules and solids based on the solution of the Bethe-Salpeter equation
(BSE) and the calculation of the screened Coulomb interaction in finite field.
The method does not require the explicit evaluation of dielectric matrices nor
of virtual electronic states, and can be easily applied without resorting to
the random phase approximation. In addition it utilizes localized orbitals
obtained from Bloch states using bisection techniques, thus greatly reducing
the complexity of the calculation and enabling the efficient use of hybrid
functionals to obtain single particle wavefunctions. We report exciton binding
energies of several molecules and absorption spectra of condensed systems of
unprecedented size, including water and ice samples with hundreds of atoms
Power minimization for OFDM Transmission with Subcarrier-pair based Opportunistic DF Relaying
This paper develops a sum-power minimized resource allocation (RA) algorithm
subject to a sum-rate constraint for cooperative orthogonal frequency division
modulation (OFDM) transmission with subcarrier-pair based opportunistic
decode-and-forward (DF) relaying. The improved DF protocol first proposed in
[1] is used with optimized subcarrier pairing. Instrumental to the RA algorithm
design is appropriate definition of variables to represent source/relay power
allocation, subcarrier pairing and transmission-mode selection elegantly, so
that after continuous relaxation, the dual method and the Hungarian algorithm
can be used to find an (at least approximately) optimum RA with polynomial
complexity. Moreover, the bisection method is used to speed up the search of
the optimum Lagrange multiplier for the dual method. Numerical results are
shown to illustrate the power-reduction benefit of the improved DF protocol
with optimized subcarrier pairing.Comment: 4 pages, accepted by IEEE Communications Letter
Computing Nearest Gcd with Certification
International audienceA bisection method, based on exclusion and inclusion tests, is used to address the nearest univariate gcd problem formulated as a bivariate real minimization problem of a rational fraction. The paper presents an algorithm, a first implementation and a complexity analysis relying on Smale's -theory. We report its behavior on an illustrative example
Multicast Multigroup Beamforming for Per-antenna Power Constrained Large-scale Arrays
Large in the number of transmit elements, multi-antenna arrays with
per-element limitations are in the focus of the present work. In this context,
physical layer multigroup multicasting under per-antenna power constrains, is
investigated herein. To address this complex optimization problem
low-complexity alternatives to semi-definite relaxation are proposed. The goal
is to optimize the per-antenna power constrained transmitter in a maximum
fairness sense, which is formulated as a non-convex quadratically constrained
quadratic problem. Therefore, the recently developed tool of feasible point
pursuit and successive convex approximation is extended to account for
practical per-antenna power constraints. Interestingly, the novel iterative
method exhibits not only superior performance in terms of approaching the
relaxed upper bound but also a significant complexity reduction, as the
dimensions of the optimization variables increase. Consequently, multicast
multigroup beamforming for large-scale array transmitters with per-antenna
dedicated amplifiers is rendered computationally efficient and accurate. A
preliminary performance evaluation in large-scale systems for which the
semi-definite relaxation constantly yields non rank-1 solutions is presented.Comment: submitted to IEEE SPAWC 2015. arXiv admin note: substantial text
overlap with arXiv:1406.755
SqFreeEVAL: An (almost) optimal real-root isolation algorithm
Let f be a univariate polynomial with real coefficients, f in R[X].
Subdivision algorithms based on algebraic techniques (e.g., Sturm or Descartes
methods) are widely used for isolating the real roots of f in a given interval.
In this paper, we consider a simple subdivision algorithm whose primitives are
purely numerical (e.g., function evaluation). The complexity of this algorithm
is adaptive because the algorithm makes decisions based on local data. The
complexity analysis of adaptive algorithms (and this algorithm in particular)
is a new challenge for computer science. In this paper, we compute the size of
the subdivision tree for the SqFreeEVAL algorithm.
The SqFreeEVAL algorithm is an evaluation-based numerical algorithm which is
well-known in several communities. The algorithm itself is simple, but prior
attempts to compute its complexity have proven to be quite technical and have
yielded sub-optimal results. Our main result is a simple O(d(L+ln d)) bound on
the size of the subdivision tree for the SqFreeEVAL algorithm on the benchmark
problem of isolating all real roots of an integer polynomial f of degree d and
whose coefficients can be written with at most L bits.
Our proof uses two amortization-based techniques: First, we use the algebraic
amortization technique of the standard Mahler-Davenport root bounds to
interpret the integral in terms of d and L. Second, we use a continuous
amortization technique based on an integral to bound the size of the
subdivision tree. This paper is the first to use the novel analysis technique
of continuous amortization to derive state of the art complexity bounds
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