Applications of Stochastic Ordering to Wireless Communications

Stochastic orders are binary relations defined on probability distributions which capture intuitive notions like being larger or being more variable. This paper introduces stochastic ordering of instantaneous SNRs of fading channels as a tool to compare the performance of communication systems over different channels. Stochastic orders unify existing performance metrics such as ergodic capacity, and metrics based on error rate functions for commonly used modulation schemes through their relation with convex, and completely monotonic (c.m.) functions. Toward this goal, performance metrics such as instantaneous error rates of M-QAM and M-PSK modulations are shown to be c.m. functions of the instantaneous SNR, while metrics such as the instantaneous capacity are seen to have a completely monotonic derivative (c.m.d.). It is shown that the commonly used parametric fading distributions for modeling line of sight (LoS), exhibit a monotonicity in the LoS parameter with respect to the stochastic Laplace transform order. Using stochastic orders, average performance of systems involving multiple random variables are compared over different channels, even when closed form expressions for such averages are not tractable. These include diversity combining schemes, relay networks, and signal detection over fading channels with non-Gaussian additive noise, which are investigated herein. Simulations are also provided to corroborate our results.Comment: 25 pages, 10 figures, Submitted to the IEEE transactions on wireless communication

Finite Element Study on the Effect of Geometrical Parameters on the Mechanical Behavior of 3D Reentrant Auxetic Honeycombs.

Abstract Auxetic materials are a special case of cellular materials, which exhibit a negative Poisson’s ratio. This in fact is the reason behind their peculiar behavior i.e. lateral shrinkage under longitudinal compression and vice versa. Since these materials do not obey the laws of “normal” materials and go beyond common sense, they are still an emerging class which can be put to use for various purposes like self-locking reinforcing fibers in composites, controlled release media, self-healing films, piezoelectric sensors, and also be used in biomedical engineering. Their stress-strain behavior, Poisson’s ratio and impact energy absorption are controlled by bulk material as well as the unit cell geometry. Among many forms of auxetic structures available, we have chosen a three-dimensional reentrant auxetic honeycomb unit cell. The unit cell geometrical parameters were taken from literature. In this study, we try to understand the effects of strut angle through finite element simulations while keeping the bulk material, unit cell size, strut thickness and number of repetitions constant. A total of three different angles were tested, based on which we conclude that as angle increases, the Poisson’s ratio increases and Energy absorption is maximum at 30 deg

Revealing the higher-order spin nature of the Hall effect in non-collinear antiferromagnet Mn3Ni0.35Cu0.65N\mathrm{Mn_3Ni_{0.35}Cu_{0.65}N}

Ferromagnets generate an anomalous Hall effect even without the presence of a magnetic field, something that conventional antiferromagnets cannot replicate but noncollinear antiferromagnets can. The anomalous Hall effect governed by the resistivity tensor plays a crucial role in determining the presence of time reversal symmetry and the topology present in the system. In this work we reveal the complex origin of the anomalous Hall effect arising in noncollinear antiferromagnets by performing Hall measurements with fields applied in selected directions in space with respect to the crystalline axes. Our coplanar magnetic field geometry goes beyond the conventional perpendicular field geometry used for ferromagnets and allows us to suppress any magnetic dipole contribution. It allows us to map the in-plane anomalous Hall contribution and we demonstrate a 120$^\circ$ symmetry which we find to be governed by the octupole moment at high fields. At low fields we subsequently discover a surprising topological Hall-like signature and, from a combination of theoretical techniques, we show that the spins can be recast into dipole, emergent octupole and noncoplanar effective magnetic moments. These co-existing orders enable magnetization dynamics unachievable in either ferromagnetic or conventional collinear antiferromagnetic materials

Summer program Report : Quality control and Aging study for the GE1/1 detectors in CMS Muon endcap upgrade

In this report, I summarize the work I did during my tenure in the Summer program. The project started with conducting three quality controls -- gas leak test, High Voltage test and Gas gain test. These are necessary to check if the GE1/1 detectors pass the requirements necessary for its deployment in the CMS. Then, I explain how aging study of the detectors was conducted and how the data was analyzed to ascertain if the detector has undergone aging. Lastly, the ongoing process of setting up a further accelerated aging study within the GEM lab is explained, with some potential difficulties associated with it