Nonclassical Paths in Quantum Interference Experiments

In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well-known text books in quantum mechanics implicitly and/or explicitly use this assumption that is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from nonclassical paths in quantum interference experiments that provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these nonclassical paths is difficult to present. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.

On Precoding for Constant K-User MIMO Gaussian Interference Channel With Finite Constellation Inputs

This paper considers linear precoding for the constant channel-coefficient K-user MIMO Gaussian interference channel (MIMO GIC) where each transmitter-i (Tx-i) requires the sending of d(i) independent complex symbols per channel use that take values from fixed finite constellations with uniform distribution to receiver-i (Rx-i) for i = 1, 2, ..., K. We define the maximum rate achieved by Tx-i using any linear precoder as the signal-to-noise ratio (SNR) tends to infinity when the interference channel coefficients are zero to be the constellation constrained saturation capacity (CCSC) for Tx-i. We derive a high-SNR approximation for the rate achieved by Tx-i when interference is treated as noise and this rate is given by the mutual information between Tx-i and Rx-i, denoted as I(X) under bar (i); (Y) under bar (i)]. A set of necessary and sufficient conditions on the precoders under which I(X) under bar (i); (Y) under bar (i)] tends to CCSC for Tx-i is derived. Interestingly, the precoders designed for interference alignment (IA) satisfy these necessary and sufficient conditions. Furthermore, we propose gradient-ascentbased algorithms to optimize the sum rate achieved by precoding with finite constellation inputs and treating interference as noise. A simulation study using the proposed algorithms for a three-user MIMO GIC with two antennas at each node with d(i) = 1 for all i and with BPSK and QPSK inputs shows more than 0.1-b/s/Hz gain in the ergodic sum rate over that yielded by precoders obtained from some known IA algorithms at moderate SNRs.

Interference Alignment With Diversity for the 2 x 2 X-Network With Four Antennas

A transmission scheme based on the Alamouti code, which we call the Li-Jafarkhani-Jafar (LJJ) scheme, was recently proposed for the 2 x 2 X-network i.e., two-transmitter (Tx) two-receiver X-network] with two antennas at each node. This scheme was claimed to achieve a sum degrees of freedom (DoF) of 8/3 and also a diversity gain of two when fixed finite constellations are employed at each Tx. Furthermore, each Tx required the knowledge of only its own channel unlike the Jafar-Shamai scheme which required global CSIT to achieve the maximum possible sum DoF of 8/3. In this paper, we extend the LJJ scheme to the 2 x 2 X-network with four antennas at each node. The proposed scheme also assumes only local channel knowledge at each Tx. We prove that the proposed scheme achieves the maximum possible sum DoF of 16/3. In addition, we also prove that, using any fixed finite constellation with appropriate rotation at each Tx, the proposed scheme achieves a diversity gain of at least four.

Optimal Binary Power Control for Underlay CR With Different Interference Constraints and Impact of Channel Estimation Errors

Adapting the power of secondary users (SUs) while adhering to constraints on the interference caused to primary receivers (PRxs) is a critical issue in underlay cognitive radio (CR). This adaptation is driven by the interference and transmit power constraints imposed on the secondary transmitter (STx). Its performance also depends on the quality of channel state information (CSI) available at the STx of the links from the STx to the secondary receiver and to the PRxs. For a system in which an STx is subject to an average interference constraint or an interference outage probability constraint at each of the PRxs, we derive novel symbol error probability (SEP)-optimal, practically motivated binary transmit power control policies. As a reference, we also present the corresponding SEP-optimal continuous transmit power control policies for one PRx. We then analyze the robustness of the optimal policies when the STx knows noisy channel estimates of the links between the SU and the PRxs. Altogether, our work develops a holistic understanding of the critical role played by different transmit and interference constraints in driving power control in underlay CR and the impact of CSI on its performance.

Electromagnetic interference shielding through MWNT grafted Fe3O4 nanoparticles in PC/SAN blends

In this study, multiwall carbon nanotubes (MWNTs) were chemically grafted onto dopamine anchored iron oxide (Fe3O4) nanoparticles via diazotization reaction to design electromagnetic (EM) shielding materials based on PC (polycarbonate)/SAN poly (styrene-co-acrylonitrile)] blends. A two step mixing protocol was adopted to selectively localize the nanoparticles in a given phase of the blends. In the first step, MWNT-g-Fe3O4 nanoparticles were solution blended with PC, followed by dilution with SAN during melt mixing in the subsequent step. This strategy, besides improving the quality of dispersion of MWNTs in the blends, facilitated enhanced EM interference shielding effectiveness (SE). Both, the MWNTs and the modified MWNTs, selectively localized in the PC phase and led to high electrical conductivity, in striking contrast to PC filled MWNT composites. The SE was measured on toroidal samples over a broad range of frequencies; X-band (8.2-12 GHz) and K-u-band (12-18 GHz). It was observed that the shielding mechanism mostly involved reflection in the blends with MWNTs, whereas absorption dominated in the case of blends with MWNT-g-Fe3O4. To realize the efficacy of this strategy, a few compositions were prepared by physical mixing MWNTs with Fe3O4 nanoparticles. Intriguingly, blends with MWNT-g-Fe3O4 nanoparticles manifested enhanced microwave absorption over physically mixed nanoparticles. An SE of -32.5 dB was observed (at 18 GHz) for MWNT (3 wt%)-g-Fe3O4 (3 vol%) in PC/SAN blends.

Ecology of acoustic signalling and the problem of masking interference in insects

The efficiency of long-distance acoustic signalling of insects in their natural habitat is constrained in several ways. Acoustic signals are not only subjected to changes imposed by the physical structure of the habitat such as attenuation and degradation but also to masking interference from co-occurring signals of other acoustically communicating species. Masking interference is likely to be a ubiquitous problem in multi-species assemblages, but successful communication in natural environments under noisy conditions suggests powerful strategies to deal with the detection and recognition of relevant signals. In this review we present recent work on the role of the habitat as a driving force in shaping insect signal structures. In the context of acoustic masking interference, we discuss the ecological niche concept and examine the role of acoustic resource partitioning in the temporal, spatial and spectral domains as sender strategies to counter masking. We then examine the efficacy of different receiver strategies: physiological mechanisms such as frequency tuning, spatial release from masking and gain control as useful strategies to counteract acoustic masking. We also review recent work on the effects of anthropogenic noise on insect acoustic communication and the importance of insect sounds as indicators of biodiversity and ecosystem health.

Spatial filter based light-sheet laser interference technique for three-dimensional nanolithography

We propose a laser interference technique for the fabrication of 3D nano-structures. This is possible with the introduction of specialized spatial filter in a 2 pi cylindrical lens system (consists of two opposing cylindrical lens sharing a common geometrical focus). The spatial filter at the back-aperture of a cylindrical lens gives rise to multiple light-sheet patterns. Two such interfering counter-propagating light-sheet pattern result in periodic 3D nano-pillar structure. This technique overcomes the existing slow point-by-point scanning, and has the ability to pattern selectively over a large volume. The proposed technique allows large-scale fabrication of periodic structures. Computational study shows a field-of-view (patterning volume) of approximately 12: 2mm(3) with the pillar-size of 80 nm and inter-pillar separation of 180 nm. Applications are in nano-waveguides, 3D nano-electronics, photonic crystals, and optical microscopy. (C) 2015 AIP Publishing LLC.

Tailoring the dispersion of multiwall carbon nanotubes in co-continuous PVDF/ABS blends to design materials with enhanced electromagnetic interference shielding

Highly conducting composites were derived by selectively localizing multiwall carbon nanotubes (MWNTs) in co-continuous PVDF/ABS (50/50, wt/wt) blends. The electrical percolation threshold was obtained between 0.5 and 1 wt% MWNTs as manifested by a dramatic increase in the electrical conductivity by about six orders of magnitude with respect to the neat blends. In order to further enhance the electrical conductivity of the blends, the MWNTs were modified with amine terminated ionic liquid (IL), which, besides enhancing the interfacial interaction with PVDF, facilitated the formation of a network like structure of MWNTs. This high electrical conductivity of the blends, at a relatively low fraction (1 wt%), was further explored to design materials that can attenuate electromagnetic (EM) radiation. More specifically, to attenuate the EM radiation by absorption, a ferroelectric phase was introduced. To accomplish this, barium titanate (BT) nanoparticles chemically stitched onto graphene oxide (GO) sheets were synthesized and mixed along with MWNTs in the blends. Intriguingly, the total EM shielding effectiveness (SE) was enhanced by ca. 10 dB with respect to the blends with only MWNTs. In addition, the effect of introducing a ferromagnetic phase (Fe3O4) along with IL modified MWNTs was also investigated. This study opens new avenues in designing materials that can attenuate EM radiation by selecting either a ferroelectric (BT-GO) or a ferromagnetic phase (Fe3O4) along with intrinsically conducting nanoparticles (MWNTs).

PERCOLATION ON THE INFORMATION-THEORETICALLY SECURE SIGNAL TO INTERFERENCE RATIO GRAPH

We consider a continuum percolation model consisting of two types of nodes, namely legitimate and eavesdropper nodes, distributed according to independent Poisson point processes in R-2 of intensities lambda and lambda(E), respectively. A directed edge from one legitimate node A to another legitimate node B exists provided that the strength of the signal transmitted from node A that is received at node B is higher than that received at any eavesdropper node. The strength of the signal received at a node from a legitimate node depends not only on the distance between these nodes, but also on the location of the other legitimate nodes and an interference suppression parameter gamma. The graph is said to percolate when there exists an infinitely connected component. We show that for any finite intensity lambda(E) of eavesdropper nodes, there exists a critical intensity lambda(c) < infinity such that for all lambda > lambda(c) the graph percolates for sufficiently small values of the interference parameter. Furthermore, for the subcritical regime, we show that there exists a lambda(0) such that for all lambda < lambda(0) <= lambda(c) a suitable graph defined over eavesdropper node connections percolates that precludes percolation in the graphs formed by the legitimate nodes.

On the superposition principle in interference experiments

The superposition principle is usually incorrectly applied in interference experiments. This has recently been investigated through numerics based on Finite Difference Time Domain (FDTD) methods as well as the Feynman path integral formalism. In the current work, we have derived an analytic formula for the Sorkin parameter which can be used to determine the deviation from the application of the principle. We have found excellent agreement between the analytic distribution and those that have been earlier estimated by numerical integration as well as resource intensive FDTD simulations. The analytic handle would be useful for comparing theory with future experiments. It is applicable both to physics based on classical wave equations as well as the non-relativistic Schrodinger equation.

Outer Bounds on the Secrecy Rate of the 2-User Symmetric Deterministic Interference Channel with Transmitter Cooperation

This paper derives outer bounds for the 2-user symmetric linear deterministic interference channel (SLDIC) with limited-rate transmitter cooperation and perfect secrecy constraints at the receivers. Five outer bounds are derived, under different assumptions of providing side information to receivers and partitioning the encoded message/output depending on the relative strength of the signal and the interference. The usefulness of these outer bounds is shown by comparing the bounds with the inner bound on the achievable secrecy rate derived by the authors in a previous work. Also, the outer bounds help to establish that sharing random bits through the cooperative link can achieve the optimal rate in the very high interference regime.

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.

Novel Relay Selection Rules for Average Interference-Constrained Cognitive AF Relay Networks

Cooperative relaying combined with selection exploits spatial diversity to significantly improve the performance of interference-constrained secondary users in an underlay cognitive radio (CR) network. However, unlike conventional relaying, the state of the links between the relay and the primary receiver affects the choice of the relay. Further, while the optimal amplify-and-forward (AF) relay selection rule for underlay CR is well understood for the peak interference-constraint, this is not so for the less conservative average interference constraint. For the latter, we present three novel AF relay selection (RS) rules, namely, symbol error probability (SEP)-optimal, inverse-of-affine (IOA), and linear rules. We analyze the SEPs of the IOA and linear rules and also develop a novel, accurate approximation technique for analyzing the performance of AF relays. Extensive numerical results show that all the three rules outperform several RS rules proposed in the literature and generalize the conventional AF RS rule.

Tailor-Made Distribution of Nanoparticles in Blend Structure toward Outstanding Electromagnetic Interference Shielding

Engineering blend structure with tailor-made distribution of nanoparticles is the prime requisite to obtain materials with extraordinary properties. Herein, a unique strategy of distributing nanoparticles in different phases of a blend structure has resulted in >99% blocking of incoming electromagnetic (EM) radiation. This is accomplished by designing a ternary polymer blend structure using polycarbonate (PC), poly(vinylidene fluoride) (PVDF), and poly(methyl methacrylate) (PMMA) to simultaneously improve the structural, electrical, and electromagnetic interference shielding (EMI). The blend structure was made conducting by preferentially localizing the multi-wall nanotubes (MWNTs) in the PVDF phase. By taking advantage of pp stacking MWNTs was noncovalently modified with an imidazolium based ionic liquid (IL). Interestingly, the enhanced dispersion of IL-MWNTs in PVDF improved the electrical conductivity of the blends significantly. While one key requisite to attenuate EM radiation (i.e., electrical conductivity) was achieved using MWNTs, the magnetic properties of the blend structure was tuned by introducing barium ferrite (BaFe) nanoparticles, which can interact with the incoming EM radiation. By suitably modifying the surface of BaFe nanoparticles, we can tailor their localization under the macroscopic processing condition. The precise localization of BaFe nanoparticles in the PC phase, due to nucleophilic substitution reaction, and the MWNTs in the PVDF phase not only improved the conductivity but also facilitated in absorption of the incoming microwave radiation due to synergetic effect from MWNT and BaFe. The shielding effectiveness (SE) was measured in X and K-u band, and an enhanced SE of -37 dB was noted at 18 GHz frequency. PMMA, which acted as an interfacial modifier in PC/PVDF blends further, resulting in a significant enhancement in the mechanical properties besides retaining high SE. This study opens a new avenue in designing mechanically strong microwave absorbers with a suitable combination of materials.