18,393 research outputs found
Monte Carlo construction of cubature on Wiener space
In this paper, we investigate application of mathematical optimization to
construction of a cubature formula on Wiener space, which is a weak
approximation method of stochastic differential equations introduced by Lyons
and Victoir (Cubature on Wiener Space, Proc. R. Soc. Lond. A 460, 169--198).
After giving a brief review of the cubature theory on Wiener space, we show
that a cubature formula of general dimension and degree can be obtained through
a Monte Carlo sampling and linear programming. This paper also includes an
extension of stochastic Tchakaloff's theorem, which technically yields the
proof of our main result.Comment: 24 pages; the organization is modified and Proposition 13 is newly
adde
A Generalized Framework on Beamformer Design and CSI Acquisition for Single-Carrier Massive MIMO Systems in Millimeter Wave Channels
In this paper, we establish a general framework on the reduced dimensional
channel state information (CSI) estimation and pre-beamformer design for
frequency-selective massive multiple-input multiple-output MIMO systems
employing single-carrier (SC) modulation in time division duplex (TDD) mode by
exploiting the joint angle-delay domain channel sparsity in millimeter (mm)
wave frequencies. First, based on a generic subspace projection taking the
joint angle-delay power profile and user-grouping into account, the reduced
rank minimum mean square error (RR-MMSE) instantaneous CSI estimator is derived
for spatially correlated wideband MIMO channels. Second, the statistical
pre-beamformer design is considered for frequency-selective SC massive MIMO
channels. We examine the dimension reduction problem and subspace (beamspace)
construction on which the RR-MMSE estimation can be realized as accurately as
possible. Finally, a spatio-temporal domain correlator type reduced rank
channel estimator, as an approximation of the RR-MMSE estimate, is obtained by
carrying out least square (LS) estimation in a proper reduced dimensional
beamspace. It is observed that the proposed techniques show remarkable
robustness to the pilot interference (or contamination) with a significant
reduction in pilot overhead
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