This paper addresses the problem of downlink channel estimation in frequency-division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems. The existing methods usually exploit hidden sparsity under a discrete Fourier transform (DFT) basis to estimate the downlink channel. However, there are at least two shortcomings of these DFT-based methods: 1) they are applicable to uniform linear arrays (ULAs) only, since the DFT basis requires a special structure of ULAs; and 2) they always suffer from a performance loss due to the leakage of energy over some DFT bins. To deal with the above shortcomings, we introduce an off-grid model for downlink channel sparse representation with arbitrary 2D-array antenna geometry, and propose an efficient sparse Bayesian learning (SBL) approach for the sparse channel recovery and off-grid refinement. The main idea of the proposed off-grid method is to consider the sampled grid points as adjustable parameters. Utilizing an in-exact block majorization-minimization (MM) algorithm, the grid points are refined iteratively to minimize the off-grid gap. Finally, we further extend the solution to uplinkaided channel estimation by exploiting the angular reciprocity between downlink and uplink channels, which brings enhanced recovery performance.
The performance of the existing sparse Bayesian learning (SBL) methods for
off-gird DOA estimation is dependent on the trade off between the accuracy and
the computational workload. To speed up the off-grid SBL method while remain a
reasonable accuracy, this letter describes a computationally efficient root SBL
method for off-grid DOA estimation, where a coarse refinable grid, whose
sampled locations are viewed as the adjustable parameters, is adopted. We
utilize an expectation-maximization (EM) algorithm to iteratively refine this
coarse grid, and illustrate that each updated grid point can be simply achieved
by the root of a certain polynomial. Simulation results demonstrate that the
computational complexity is significantly reduced and the modeling error can be
almost eliminated.Comment: 4 pages, 4 figure
This study investigated the effect of silane and surfactant treatments of graphene nanoplatelets (GnPs) on the mechanical and thermal properties of silicone rubber (SR) composites. GnPs were modified with aminopropyltriethoxysilane (APTES), vinyltrimethoxysilane (VTMS), and Triton X-100, and then the pristine GnPs and functionalized GnPs were individually incorporated into the SR. Compared with the pristine GnP/SR composite, the composites reinforced with modified GnP showed better tensile strength, elongation at break, and thermal conductivity properties due to better dispersion of modified GnPs and stronger interfacial interactions between the modified GnPs and matrix. The mechanical properties and thermal conductivity of the VTMS-GnP/SR composite were comparable to the properties of the Triton-GnP counterpart, but better than that of the APTES-GnP/SR composite. In addition, the VTMS-GnP/SR composite demonstrated the highest thermal stability and crystallization temperature among the four types of composites. The remarkable improvement of mechanical and thermal properties of the VTMS-GnP/SR composite was mainly due to the covalent linkage of VTMS-GnP with SR. The VTMS treatment was a more appropriate modification of GnP particles to improve the multifunctional properties of SR.
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