15,600 research outputs found
Dynamical System of Scalar Field from 2-Dimension to 3-D and its Cosmological Implication
We give the three-dimensional dynamical autonomous systems for most of the
popular scalar field dark energy models including (phantom) quintessence,
(phantom) tachyon, k-essence and general non-canonical scalar field models,
change the dynamical variables from variables to observable
related variables , and show the intimate
relationships between those scalar fields that the three-dimensional system of
k-essence can reduce to (phantom) tachyon, general non-canonical scalar field
can reduce to (phantom) quintessence and k-essence can also reduce to (phantom)
quintessence for some special cases. For the applications of the
three-dimensional dynamical systems, we investigate several special cases and
give the exactly dynamical solutions in detail. In the end of this paper, we
argue that, it is more convenient and also has more physical meaning to express
the differential equations of dynamical systems in instead of variables and to investigate the
dynamical system in 3-Dimension instead of 2-Dimension. We also raise a
question about the possibility of the chaotic behavior in the spatially flat
single scalar field FRW cosmological models in the presence of ordinary matter.Comment: 20 pages, 8 figures,some references added. Minor changes according to
the suggestions from referee
Codebook Based Hybrid Precoding for Millimeter Wave Multiuser Systems
In millimeter wave (mmWave) systems, antenna architecture limitations make it
difficult to apply conventional fully digital precoding techniques but call for
low cost analog radio-frequency (RF) and digital baseband hybrid precoding
methods. This paper investigates joint RF-baseband hybrid precoding for the
downlink of multiuser multi-antenna mmWave systems with a limited number of RF
chains. Two performance measures, maximizing the spectral efficiency and the
energy efficiency of the system, are considered. We propose a codebook based RF
precoding design and obtain the channel state information via a beam sweep
procedure. Via the codebook based design, the original system is transformed
into a virtual multiuser downlink system with the RF chain constraint.
Consequently, we are able to simplify the complicated hybrid precoding
optimization problems to joint codeword selection and precoder design (JWSPD)
problems. Then, we propose efficient methods to address the JWSPD problems and
jointly optimize the RF and baseband precoders under the two performance
measures. Finally, extensive numerical results are provided to validate the
effectiveness of the proposed hybrid precoders.Comment: 35 pages, 9 figures, to appear in Trans. on Signal Process, 201
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