Eigenvalue Dynamics of a Central Wishart Matrix with Application to MIMO Systems

We investigate the dynamic behavior of the stationary random process defined by a central complex Wishart (CW) matrix ${\bf{W}}(t)$ as it varies along a certain dimension $t$. We characterize the second-order joint cdf of the largest eigenvalue, and the second-order joint cdf of the smallest eigenvalue of this matrix. We show that both cdfs can be expressed in exact closed-form in terms of a finite number of well-known special functions in the context of communication theory. As a direct application, we investigate the dynamic behavior of the parallel channels associated with multiple-input multiple-output (MIMO) systems in the presence of Rayleigh fading. Studying the complex random matrix that defines the MIMO channel, we characterize the second-order joint cdf of the signal-to-noise ratio (SNR) for the best and worst channels. We use these results to study the rate of change of MIMO parallel channels, using different performance metrics. For a given value of the MIMO channel correlation coefficient, we observe how the SNR associated with the best parallel channel changes slower than the SNR of the worst channel. This different dynamic behavior is much more appreciable when the number of transmit ($N_T$) and receive ($N_R$) antennas is similar. However, as $N_T$ is increased while keeping $N_R$ fixed, we see how the best and worst channels tend to have a similar rate of change.Comment: 15 pages, 9 figures and 1 table. This work has been accepted for publication at IEEE Trans. Inf. Theory. Copyright (c) 2014 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]

A MATLAB program for the computation of the confluent hypergeometric function Φ2

We here present a sample MATLAB program for the numerical evaluation of the confluent hypergeometric function Φ2. This program is based on the calculation of the inverse Laplace transform using the algorithm suggested by Simon and Alouini in their reference textbook [1]

2D kinematics of the edge-on spiral galaxy ESO 379-G006

We present a kinematical study of the nearly edge-on galaxy ESO 379-G006 that shows the existence of extraplanar ionized gas. With Fabry-Perot spectroscopy at H-alpha, we study the kinematics of ESO 379-G006 using velocity maps and position-velocity diagrams parallel to the major and to the minor axis of the galaxy. We build the rotation curve of the disk and discuss the role of projection effects due to the fact of viewing this galaxy nearly edge-on. The twisting of the isovelocities in the radial velocity field of the disk of ESO 379-G006 as well as the kinematic asymmetries found in some position-velocity diagrams parallel to the minor axis of the galaxy suggest the existence of deviations to circular motions in the disk that can be modeled and explained with the inclusion of a radial inflow probably generated by a bar or by spiral arms. We succeeded in detecting extraplanar Diffuse Ionized Gas in this galaxy. At the same time, from the analysis of position-velocity diagrams, we found some evidence that the extraplanar gas could lag in rotation velocity with respect to the midplane rotation.Comment: 61 pages, 15 figures. Accepted for publication in A

Distribution pattern and population structure of Calanus australis Brodsky, 1959 over the southern Patagonian Shelf off Argentina in summer

In the southwest Atlantic Ocean, Calanus australis is widely distributed in waters of the inner and middle shelf off Argentina. Along the coast of southern Patagonia it is the most abundant large copepod through all seasons, typically occurring at higher densities over the inner shelf < 100 m deep. Its concentration decreases offshore as it is replaced by Calanus simillimus and Neocalanus tonsus. The abundance, vertical distribution, and population structure of Calanus australis off Patagonia were examined during a summer survey (March 1998) in order to study the ecological response of the copepod to hydrographic conditions. Differences in population densities were related to geographical difference in water-column stability. Higher numbers were recorded inshore at 51°S in strongly stratified coastal waters, where a well developed thermocline was present at 50 m. A sharp decline in abundance was evident southwards, coinciding with the occurrence of highly mixed, coastal, isothermal, and isohaline waters. Very low concentrations were also found at the most offshore, thermally stratified stations influenced by transitional waters between shelf and Malvinas waters. The population consisted mainly of stage 5 copepodites and fewer adult females. The scarcity or absence of younger stages cannot be attributed to the mesh size employed (150μm). The population dynamics of Calanus australis are discussed and compared with other Calanus species. © 2000 International Council For the Exploration of the Sea.Fil: Sabatini, Marina Elena. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Mar del Plata. Instituto de Investigaciones Marinas y Costeras. Subsede Instituto Nacional de Investigación y Desarrollo Pesquero; ArgentinaFil: Ramírez, F. Instituto Nacional de Investigaciones y Desarrollo Pesquero; ArgentinaFil: Martos, Patricia. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias Marinas; Argentin

A Tractable Line-of-Sight Product Channel Model: Application to Wireless Powered Communications

We here present a general and tractable fading model for line-of-sight (LOS) scenarios, which is based on the product of two independent and non-identically distributed κ- μ shadowed random variables. Simple closed-form expressions for the probability density function and cumulative distribution function are derived, which are as tractable as the corresponding expressions derived from a product of Nakagami-m random variables. This newly proposed model simplifies the challenging characterization of LOS product channels, as well as combinations of LOS channels with non-LOS ones. Results are used to analyze performance measures of interest in the context of wireless powered communications.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

The dynamics of user channels in massive MIMO systems

The SNR associated with the different users in large-scale MIMO systems depends on the magnitude of the eigenvalues of the channel power matrix HH H. While it is known that the spread between the best and worst channels is reduced when the number of antennas N at the BS grows, there is little known about how these channels change due to the user mobility. Do all parallel channels change at the same rate, or conversely is their dynamic behavior different for the best and worst channels? We evaluate the interplay between the number of BS antennas N and the number of (single-antenna) users K in MIMO systems, and investigate the effect of letting N grow on the dynamics of the best and worst channels in this multiuser set-up.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Errors in kinematic distances and our image of the Milky Way Galaxy

Errors in the kinematic distances, under the assumption of circular gas orbits, were estimated by performing synthetic observations of a model disk galaxy. It was found that the error is < 0.5 kpc for most of the disk when the measured rotation curve was used, but larger if the real rotation curve is applied. In both cases, the error is significantly larger at the positions of the spiral arms. The error structure is such that, when kinematic distances are used to develope a picture of the large scale density distribution, the most significant features of the numerical model are significantly distorted or absent, while spurious structure appears. By considering the full velocity field in the calculation of the kinematic distances, most of the original density structures can be recovered.Comment: Accepted for publication in A