9,766 research outputs found

    Bound-intersection detection for multiple-symbol differential unitary space-time modulation

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    This paper considers multiple-symbol differential detection (MSD) of differential unitary space-time modulation (DUSTM) over multiple-antenna systems. We derive a novel exact maximum-likelihood (ML) detector, called the bound-intersection detector (BID), using the extended Euclidean algorithm for single-symbol detection of diagonal constellations. While the ML search complexity is exponential in the number of transmit antennas and the data rate, our algorithm, particularly in high signal-to-noise ratio, achieves significant computational savings over the naive ML algorithm and the previous detector based on lattice reduction. We also develop four BID variants for MSD. The first two are ML and use branch-and-bound, the third one is suboptimal, which first uses BID to generate a candidate subset and then exhaustively searches over the reduced space, and the last one generalizes decision-feedback differential detection. Simulation results show that the BID and its MSD variants perform nearly ML, but do so with significantly reduced complexity

    New results on the generalized frequency response functions of nonlinear volterra systems described by NARX model

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    In order that the nth-order Generalized Frequency Response Function (GFRF) for nonlinear systems described by a NARX model can be directly written into a more straightforward and meaningful form in terms of the first order GFRF and model parameters, the nth-order GFRF is now determined by a new mapping function based on a parametric characteristic. This can explicitly unveil the linear and nonlinear factors included in the GFRFs, reveal clearly the relationship between the nth-order GFRF and the model parameters, and also the relationship between the nth-order GFRF and the first order GFRF. Some new properties of the GFRFs can consequently be developed. These new results provide a novel and useful insight into the frequency domain analysis of nonlinear systems

    Nonlinear output frequency response functions for multi-input nonlinear volterra systems

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    The concept of Nonlinear Output Frequency Response Functions (NOFRFs) is extended to the nonlinear systems that can be described by a multi-input Volterra series model. A new algorithm is also developed to determine the output frequency range of nonlinear systems from the frequency range of the inputs. These results allow the concept of NOFRFs to be applied to a wide range of engineering systems. The phenomenon of the energy transfer in a two degree of freedom nonlinear system is studied using the new concepts to demonstrate the significance of the new results

    New Notions and Constructions of Sparsification for Graphs and Hypergraphs

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    A sparsifier of a graph GG (Bencz\'ur and Karger; Spielman and Teng) is a sparse weighted subgraph G~\tilde G that approximately retains the cut structure of GG. For general graphs, non-trivial sparsification is possible only by using weighted graphs in which different edges have different weights. Even for graphs that admit unweighted sparsifiers, there are no known polynomial time algorithms that find such unweighted sparsifiers. We study a weaker notion of sparsification suggested by Oveis Gharan, in which the number of edges in each cut (S,Sˉ)(S,\bar S) is not approximated within a multiplicative factor (1+ϵ)(1+\epsilon), but is, instead, approximated up to an additive term bounded by ϵ\epsilon times dS+vol(S)d\cdot |S| + \text{vol}(S), where dd is the average degree, and vol(S)\text{vol}(S) is the sum of the degrees of the vertices in SS. We provide a probabilistic polynomial time construction of such sparsifiers for every graph, and our sparsifiers have a near-optimal number of edges O(ϵ2npolylog(1/ϵ))O(\epsilon^{-2} n {\rm polylog}(1/\epsilon)). We also provide a deterministic polynomial time construction that constructs sparsifiers with a weaker property having the optimal number of edges O(ϵ2n)O(\epsilon^{-2} n). Our constructions also satisfy a spectral version of the ``additive sparsification'' property. Our construction of ``additive sparsifiers'' with Oϵ(n)O_\epsilon (n) edges also works for hypergraphs, and provides the first non-trivial notion of sparsification for hypergraphs achievable with O(n)O(n) hyperedges when ϵ\epsilon and the rank rr of the hyperedges are constant. Finally, we provide a new construction of spectral hypergraph sparsifiers, according to the standard definition, with poly(ϵ1,r)nlogn{\rm poly}(\epsilon^{-1},r)\cdot n\log n hyperedges, improving over the previous spectral construction (Soma and Yoshida) that used O~(n3)\tilde O(n^3) hyperedges even for constant rr and ϵ\epsilon.Comment: 31 page

    Geodesic continued fractions and LLL

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    We discuss a proposal for a continued fraction-like algorithm to determine simultaneous rational approximations to dd real numbers α1,,αd\alpha_1,\ldots,\alpha_d. It combines an algorithm of Hermite and Lagarias with ideas from LLL-reduction. We dynamically LLL-reduce a quadratic form with parameter tt as t0t\downarrow0. The new idea in this paper is that checking the LLL-conditions consists of solving linear equations in tt
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