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Studies have indicated that the distributed compressed sensing based (DCS-based) channel estimation can decrease the length of the reference signals effectively. In block transmission, a unique word (UW) can be used as a cyclic prefix and reference signal. However, the DCS-based channel estimation requires diversity sequences instead of UW. In this paper, we proposed a novel method that employs a training sequence (TS) whose duration time is slightly longer than the maximum delay spread time. Based on proposed TS, the DCS approach perform perfectly in multipath channel estimation. Meanwhile, a cyclic prefix construct could be formed, which reduces the complexity of the frequency domain equalization (FDE) directly. Simulation results demonstrate that, by using the method of simultaneous orthogonal matching pursuit (SOMP), the required channel overhead has been reduced thanks to the proposed TS.

Abstract: Real fluid phenomena often present multi-scale behavior, such as tiny splashes and foams in the ocean and small vortexes near the bank of a wide river, which requires sufficiently fine grids and long computational time in the simulation to get adequately resolved solution. We present a new method to address this issue by solving Navier-Stokes equation on multiple layers of grids with different resolutions or categories. The governing equations are solved on different layers in successive passes. And the velocity and pressure fields are synchronized between adjacent layers through the processes of prolongation and restriction. The multi-layer approach enables combining the respective advantages of various grid types, catching the multi-scale behavior of fluids and optimizing the computational resources. Two simple examples, the regular-tetrahedral and the coarse-fine bi-layer grids, are given to illustrate the powerfulness of the multi-layer framework.

We propose the concepts of generalized null-additivity and of generalized autocontinuity from below (resp. from above) relating to a pair of fuzzy measures, and discuss the relationship among these new concepts, and null-additivity and autocontinuity (concerning a single fuzzy measure). By means of these structure characteristics of fuzzy measures we establish the generalized dominated convergence theorem and the generalized Vitali convergence theorem for Choquet integral in the framework involving an ordered pair of fuzzy measures. The previous related versions of dominated convergence theorem and of Vitali-like convergence theorem of Choquet integral are recovered by these generalized versions, respectively. In such a framework, the standard-type and pseudo-type of dominated convergence theorems (resp. Vitali-like convergence theorem) of Choquet integral are unified. [ABSTRACT FROM AUTHOR]