Inner Bound on the GDOF of the K-User MIMO Gaussian Symmetric Interference Channel

The K-user multiple input multiple output (MIMO) Gaussian symmetric interference channel where each transmitter has M antennas and each receiver has N antennas is studied from a generalized degrees of freedom (GDOF) perspective. An inner bound on the GDOF is derived using a combination of techniques such as treating interference as noise, zero forcing (ZF) at the receivers, interference alignment (IA), and extending the Han-Kobayashi (HK) scheme to K users, as a function of the number of antennas and the log INR/log SNR level. Several interesting conclusions are drawn from the derived bounds. It is shown that when K > N/M + 1, a combination of the HK and IA schemes performs the best among the schemes considered. When N/M < K <= N/M + 1, the HK-scheme outperforms other schemes and is found to be GDOF optimal in many cases. In addition, when the SNR and INR are at the same level, ZF-receiving and the HK-scheme have the same GDOF performance.

Outer Bounds on the Sum Rate of the K-User MIMO Gaussian Interference Channel

This paper derives outer bounds on the sum rate of the K-user MIMO Gaussian interference channel (GIC). Three outer bounds are derived, under different assumptions of cooperation and providing side information to receivers. The novelty in the derivation lies in the careful selection of side information, which results in the cancellation of the negative differential entropy terms containing signal components, leading to a tractable outer bound. The overall outer bound is obtained by taking the minimum of the three outer bounds. The derived bounds are simplified for the MIMO Gaussian symmetric IC to obtain outer bounds on the generalized degrees of freedom (GDOF). The relative performance of the bounds yields insight into the performance limits of multiuser MIMO GICs and the relative merits of different schemes for interference management. These insights are confirmed by establishing the optimality of the bounds in specific cases using an inner bound on the GDOF derived by the authors in a previous work. It is also shown that many of the existing results on the GDOF of the GIC can be obtained as special cases of the bounds, e. g., by setting K = 2 or the number of antennas at each user to 1.

Effect of catchment characteristics on the relationship between past discharge and the power law recession coefficient

This study concerns the relationship between the power law recession coefficient k (in - dQ/dt = kQ(alpha), Q being discharge at the basin outlet) and past average discharge Q(N) (where N is the temporal distance from the center of the selected time span in the past to the recession peak), which serves as a proxy for past storage state of the basin. The strength of the k-Q(N) relationship is characterized by the coefficient of determination R-N(2), which is expected to indicate the basin's ability to hold water for N days. The main objective of this study is to examine how R-N(2) value of a basin is related with its physical characteristics. For this purpose, we use streamflow data from 358 basins in the United States and selected 18 physical parameters for each basin. First, we transform the physical parameters into mutually independent principal components. Then we employ multiple linear regression method to construct a model of R-N(2) in terms of the principal components. Furthermore, we employ step-wise multiple linear regression method to identify the dominant catchment characteristics that influence R-N(2) and their directions of influence. Our results indicate that R-N(2) is appreciably related to catchment characteristics. Particularly, it is noteworthy that the coefficient of determination of the relationship between R-N(2) and the catchment characteristics is 0.643 for N = 45. We found that topographical characteristics of a basin are the most dominant factors in controlling the value of R-N(2). Our results may be suggesting that it is possible to tell about the water holding capacity of a basin by just knowing about a few of its physical characteristics. (C) 2015 Elsevier B.V. All rights reserved.

Relationship between entropy and diffusion: A statistical mechanical derivation of Rosenfeld expression for a rugged energy landscape

Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by studying diffusion of a point Brownian particle on a model potential energy surface characterized by ruggedness. If we assume that the ruggedness has a Gaussian distribution, then for this model, one can obtain the excess entropy exactly for any dimension. By using the expression for the mean first passage time, we present a statistical mechanical derivation of the well-known and well-tested scaling relation proposed by Rosenfeld between diffusion and excess entropy. In anticipation that Rosenfeld diffusion-entropy scaling (RDES) relation may continue to be valid in higher dimensions (where the mean first passage time approach is not available), we carry out an effective medium approximation (EMA) based analysis of the effective transition rate and hence of the effective diffusion coefficient. We show that the EMA expression can be used to derive the RDES scaling relation for any dimension higher than unity. However, RDES is shown to break down in the presence of spatial correlation among the energy landscape values. (C) 2015 AIP Publishing LLC.

Structure-rheology relationship in a sheared lamellar fluid

The structure-rheology relationship in the shear alignment of a lamellar fluid is studied using a mesoscale model which provides access to the lamellar configurations and the rheology. Based on the equations and free energy functional, the complete set of dimensionless groups that characterize the system are the Reynolds number (rho gamma L-2/mu), the Schmidt number (mu/rho D), the Ericksen number (mu(gamma)/B), the interface sharpness parameter r, the ratio of the viscosities of the hydrophilic and hydrophobic parts mu(r), and the ratio of the system size and layer spacing (L/lambda). Here, rho and mu are the fluid density and average viscosity, (gamma) over dot is the applied strain rate, D is the coefficient of diffusion, B is the compression modulus, mu(r) is the maximum difference in the viscosity of the hydrophilic and hydrophobic parts divided by the average viscosity, and L is the system size in the cross-stream direction. The lattice Boltzmann method is used to solve the concentration and momentum equations for a two dimensional system of moderate size (L/lambda = 32) and for a low Reynolds number, and the other parameters are systematically varied to examine the qualitative features of the structure and viscosity evolution in different regimes. At low Schmidt numbers where mass diffusion is faster than momentum diffusion, there is fast local formation of randomly aligned domains with ``grain boundaries,'' which are rotated by the shear flow to align along the extensional axis as time increases. This configuration offers a high resistance to flow, and the layers do not align in the flow direction even after 1000 strain units, resulting in a viscosity higher than that for an aligned lamellar phase. At high Schmidt numbers where momentum diffusion is fast, the shear flow disrupts layers before they are fully formed by diffusion, and alignment takes place by the breakage and reformation of layers by shear, resulting in defects (edge dislocations) embedded in a background of nearly aligned layers. At high Ericksen number where the viscous forces are large compared to the restoring forces due to layer compression and bending, shear tends to homogenize the concentration field, and the viscosity decreases significantly. At very high Ericksen number, shear even disrupts the layering of the lamellar phase. At low Ericksen number, shear results in the formation of well aligned layers with edge dislocations. However, these edge dislocations take a long time to anneal; the relatively small misalignment due to the defects results in a large increase in viscosity due to high layer stiffness and due to shear localization, because the layers between defects get pinned and move as a plug with no shear. An increase in the viscosity contrast between the hydrophilic and hydrophobic parts does not alter the structural characteristics during alignment. However, there is a significant increase in the viscosity, due to pinning of the layers between defects, which results in a plug flow between defects and a localization of the shear to a part of the domain.