Approximate Random Matrix Models for Generalized Fading MIMO Channels

Approximate random matrix models for $\kappa-\mu$ and $\eta-\mu$ faded multiple input multiple output (MIMO) communication channels are derived in terms of a complex Wishart matrix. The proposed approximation has the least Kullback-Leibler (KL) divergence from the original matrix distribution. The utility of the results are demonstrated in a) computing the average capacity/rate expressions of $\kappa-\mu$/$\eta-\mu$ MIMO systems b) computing outage probability (OP) expressions for maximum ratio combining (MRC) for $\kappa-\mu$/$\eta-\mu$ faded MIMO channels c) ergodic rate expressions for zero-forcing (ZF) receiver in an uplink single cell massive MIMO scenario with low resolution analog-to-digital converters (ADCs) in the antennas. These approximate expressions are compared with Monte-Carlo simulations and a close match is observed

Analysis of Optimal Combining in Rician Fading with Co-channel Interference

Approximate Symbol error rate (SER), outage probability and rate expressions are derived for receive diversity system employing optimum combining when both the desired and the interfering signals are subjected to Rician fading, for the cases of a) equal power uncorrelated interferers b) unequal power interferers c) interferer correlation. The derived expressions are applicable for an arbitrary number of receive antennas and interferers and for any quadrature amplitude modulation (QAM) constellation. Furthermore, we derive a simple closed form expression for SER in the interference-limited regime, for the special case of Rayleigh faded interferers. A close match is observed between the SER, outage probability and rate results obtained through the derived analytical expressions and the ones obtained from Monte-Carlo simulations

Analysis of Outage Probability of MRC with η−μ\eta-\mu co-channel interference

Approximate outage probability expressions are derived for systems employing maximum ratio combining, when both the desired signal and the interfering signals are subjected to $\eta-\mu$ fading, with the interferers having unequal power. The approximations are in terms of the Appell Function and Gauss hypergeometric function. A close match is observed between the outage probability result obtained through the derived analytical expression and the one obtained through Monte-Carlo simulations

Unified geometric multigrid algorithm for hybridized high-order finite element methods

We consider a standard elliptic partial differential equation and propose a geometric multigrid algorithm based on Dirichlet-to-Neumann (DtN) maps for hybridized high-order finite element methods. The proposed unified approach is applicable to any locally conservative hybridized finite element method including multinumerics with different hybridized methods in different parts of the domain. For these methods, the linear system involves only the unknowns residing on the mesh skeleton, and constructing intergrid transfer operators is therefore not trivial. The key to our geometric multigrid algorithm is the physics-based energy-preserving intergrid transfer operators which depend only on the fine scale DtN maps. Thanks to these operators, we completely avoid upscaling of parameters and no information regarding subgrid physics is explicitly required on coarse meshes. Moreover, our algorithm is agglomeration-based and can straightforwardly handle unstructured meshes. We perform extensive numerical studies with hybridized mixed methods, hybridized discontinuous Galerkin method, weak Galerkin method, and a hybridized version of interior penalty discontinuous Galerkin methods on a range of elliptic problems including subsurface flow through highly heterogeneous porous media. We compare the performance of different smoothers and analyze the effect of stabilization parameters on the scalability of the multigrid algorithm

Joint power and resource allocation of D2D communication with low-resolution ADC

This paper considers the joint power control and resource allocation for a device-to-device (D2D) underlay cellular system with a multi-antenna BS employing ADCs with different resolutions. We propose a four-step algorithm that optimizes the ADC resolution profile at the base station (BS) to reduce the energy consumption and perform joint power control and resource allocation of D2D communication users (DUEs) and cellular users (CUEs) to improve the D2D reliability

Asymptotic maximum order statistic for SIR in κ−μ\kappa-\mu shadowed fading

Using tools from extreme value theory (EVT), it is proved that, when the user signal and the interferer signals undergo independent and non-identically distributed (i.n.i.d.) $\kappa-\mu$ shadowed fading, the limiting distribution of the maximum of $L$ independent and identically distributed (i.i.d.) signal-to-interference ratio (SIR) random variables (RVs) is a Frechet distribution. It is observed that this limiting distribution is close to the true distribution of maximum, for maximum SIR evaluated over moderate $L$. Further, moments of the maximum RV is shown to converge to the moments of the Frechet RV. Also, the rate of convergence of the actual distribution of the maximum to the Frechet distribution is derived and is analyzed for different $\kappa$ and $\mu$ parameters. Finally, results from stochastic ordering are used to analyze the variation in the limiting distribution with respect to the variation in source fading parameters. These results are then used to derive upper bound for the rate in Full Array Selection (FAS) schemes for antenna selection and the asymptotic outage probability and the ergodic rate in maximum-sum-capacity (MSC) scheduling systems

Airfoil wake modification with Gurney flap at Low-Reynolds number

The complex wake modifications produced by a Gurney flap on symmetric NACA airfoils at low Reynolds number are investigated. Two-dimensional incompressible flows over NACA 0000 (flat plate), 0006, 0012 and 0018 airfoils at a Reynolds number of $Re = 1000$ are analyzed numerically to examine the flow modifications generated by the flaps for achieving lift enhancement. While high lift can be attained by the Gurney flap on airfoils at high angles of attack, highly unsteady nature of the aerodynamic forces are also observed. Analysis of the wake structures along with the lift spectra reveals four characteristic wake modes (steady, 2S, P and 2P), influencing the aerodynamic performance. The effects of the flap over wide range of angles of attack and flap heights are considered to identify the occurrence of these wake modes, and are encapsulated in a wake classification diagram. Companion three-dimensional simulations are also performed to examine the influence of three-dimensionality on the wake regimes. The spanwise instabilities that appear for higher angles of attack are found to suppress the emergence of the 2P mode. The use of the wake classification diagram as a guidance for Gurney flap selection at different operating conditions to achieve the required aerodynamic performance is discussed

eHDG:An Exponentially Convergent Iterative Solver for HDG Discretizations of Hyperbolic Partial Differential Equations

We present a scalable and efficient iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of hyperbolic partial differential equations. It is an interplay between domain decomposition methods and HDG discretizations. In particular, the method is a fixed-point approach that requires only independent element-by-element local solves in each iteration. As such, it is well-suited for current and future computing systems with massive concurrencies. We rigorously show that the proposed method is exponentially convergent in the number of iterations for transport and linearized shallow water equations. Furthermore, the convergence is independent of the solution order. Various 2D and 3D numerical results for steady and time-dependent problems are presented to verify our theoretical findings.Comment: 10 pages, 5 figures, submitted to 14th Copper mountain conference on iterative methods (student paper competition

An Improved Iterative HDG Approach for Partial Differential Equations

We propose and analyze an iterative high-order hybridized discontinuous Galerkin (iHDG) discretization for linear partial differential equations. We improve our previous work (SIAM J. Sci. Comput. Vol. 39, No. 5, pp. S782--S808) in several directions: 1) the improved iHDG approach converges in a finite number of iterations for the scalar transport equation; 2) it is unconditionally convergent for both the linearized shallow water system and the convection-diffusion equation; 3) it has improved stability and convergence rates; 4) we uncover a relationship between the number of iterations and time stepsize, solution order, meshsize and the equation parameters. This allows us to choose the time stepsize such that the number of iterations is approximately independent of the solution order and the meshsize; and 5) we provide both strong and weak scalings of the improved iHDG approach up to $16,384$ cores. A connection between iHDG and time integration methods such as parareal and implicit/explicit methods are discussed. Extensive numerical results are presented to verify the theoretical findings.Comment: arXiv admin note: text overlap with arXiv:1605.0322

A Multilevel Approach for Trace System in HDG Discretizations

We propose a multilevel approach for trace systems resulting from hybridized discontinuous Galerkin (HDG) methods. The key is to blend ideas from nested dissection, domain decomposition, and high-order characteristic of HDG discretizations. Specifically, we first create a coarse solver by eliminating and/or limiting the front growth in nested dissection. This is accomplished by projecting the trace data into a sequence of same or high-order polynomials on a set of increasingly $h-$coarser edges/faces. We then combine the coarse solver with a block-Jacobi fine scale solver to form a two-level solver/preconditioner. Numerical experiments indicate that the performance of the resulting two-level solver/preconditioner depends only on the smoothness of the solution and is independent of the nature of the PDE under consideration. While the proposed algorithms are developed within the HDG framework, they are applicable to other hybrid(ized) high-order finite element methods. Moreover, we show that our multilevel algorithms can be interpreted as a multigrid method with specific intergrid transfer and smoothing operators. With several numerical examples from Poisson, pure transport, and convection-diffusion equations we demonstrate the robustness and scalability of the algorithms