End-to-End BER Analysis of Space Shift Keying in Decode-and-Forward Cooperative Relaying

Space shift keying (SSK) is a special case of spatial modulation (SM), which is a relatively new modulation technique that is getting recognized to be attractive in multi-antenna communications. Our new contribution in this paper is an analytical derivation of exact closed-form expression for the end-to-end bit error rate (BER) performance of SSK in decode-and-forward (1)1,) cooperative relaying. An incremental relaying (IR) scheme with selection combining (SC) at the destination is considered. In SSK, since the information is carried by the transmit antenna index, traditional selection combining methods based on instantaneous SNRs can not be directly used. To overcome this problem, we propose to do selection between direct and relayed paths based on the Euclidean distance between columns of the channel matrix. With this selection metric, an exact analytical expression for the end-to-end BER is derived in closed-form. Analytical results are shown to match with simulation results.

Mahogany seed - a step forward in deciphering autorotation

This article presents an experimental approach for evaluating the various flight characteristics of a mahogany seed in its autorotative descent. Analytical formulae proposed by Yasuda and Azuma are used to interpret the results. The findings are used in the development of a sophisticated blade element computational model, primarily to analyse planar autorotating systems. This approximate computational approach is then used to predict the flight performance of mahogany seeds and the results are compared with experimental data. The potential use of the computational model in the design of autorotating systems is then brought to light.

Biogenic nanosilver incorporated reverse osmosis membrane for antibacterial and antifungal activities against selected pathogenic strains: An enhanced eco-friendly water disinfection approach

Reverse osmosis (RO) membranes have been used extensively in water desalination plants, waste water treatment in industries, agricultural farms and drinking water production applications. The objective of this work is to impart antibacterial and antifungal activities to commercially available RO membrane used in water purification systems by incorporating biogenic silver nanoparticles (AgNPs) synthesized using Rosa indica wichuriana hybrid leaf extract. The morphology and surface topography of uncoated and AgNPs-coated RO membrane were studied using Scanning Electron Microscopy (SEM) and Atomic Force Microscopy (AFM). Elemental composition of the AgNPs-coated RO membrane was analyzed by energy-dispersive X-ray spectroscopy (EDAX). The functional groups were identified by Fourier Transform Infrared spectroscopy (FT-IR). Hydrophilicity of the uncoated and AgNPs-coated RO membrane was analyzed using water contact angle measurements. The thermal properties were studied by thermogravimetric analysis (TGA). The AgNPs incorporated RO membrane exhibited good antibacterial and antifungal activities against pathogenic bacterial strains such as E. coli, S. aureus, M. luteus, K. pneumoniae, and P. aeruginosa and fungal strains such as Candida tropicalis, C. krusei, C. glabrata, and C. albicans.

Interference-Constrained Optimal Power-Adaptive Amplify-and-Forward Relaying and Selection for Underlay Cognitive Radios

In an underlay cognitive radio (CR) system, a secondary user can transmit when the primary is transmitting but is subject to tight constraints on the interference it causes to the primary receiver. Amplify-and-forward (AF) relaying is an effective technique that significantly improves the performance of a CR by providing an alternate path for the secondary transmitter's signal to reach the secondary receiver. We present and analyze a novel optimal relay gain adaptation policy (ORGAP) in which the relay is interference aware and optimally adapts both its gain and transmit power as a function of its local channel gains. ORGAP minimizes the symbol error probability at the secondary receiver subject to constraints on the average relay transmit power and on the average interference caused to the primary. It is different from ad hoc AF relaying policies and serves as a new and fundamental theoretical benchmark for relaying in an underlay CR. We also develop a near-optimal and simpler relay gain adaptation policy that is easy to implement. An extension to a multirelay scenario with selection is also developed. Our extensive numerical results for single and multiple relay systems quantify the power savings achieved over several ad hoc policies for both MPSK and MQAM constellations.

Linear Transceiver Design for an Amplify-and-Forward Relay Based on the MBER Criterion

A design methodology based on the Minimum Bit Error Ratio (MBER) framework is proposed for a non-regenerative Multiple-Input Multiple-Output (MIMO) relay-aided system to determine various linear parameters. We consider both the Relay-Destination (RD) as well as the Source-Relay-Destination (SRD) link design based on this MBER framework, including the pre-coder, the Amplify-and-Forward (AF) matrix and the equalizer matrix of our system. It has been shown in the previous literature that MBER based communication systems are capable of reducing the Bit-Error-Ratio (BER) compared to their Linear Minimum Mean Square Error (LMMSE) based counterparts. We design a novel relay-aided system using various signal constellations, ranging from QPSK to the general M-QAM and M-PSK constellations. Finally, we propose its sub-optimal versions for reducing the computational complexity imposed. Our simulation results demonstrate that the proposed scheme indeed achieves a significant BER reduction over the existing LMMSE scheme.

Performance Analysis of Space-Shift Keying in Decode-and-Forward Multihop MIMO Networks

In this paper, space-shift keying (SSK) is considered for multihop multiple-input-multiple-output (MIMO) networks. In SSK, only one among n(s) = 2(m) available transmit antennas, chosen on the basis of m information bits, is activated during transmission. We consider two different systems of multihop co-operation, where each node has multiple antennas and employs SSK. In system I, a multihop diversity relaying scheme is considered. In system II, a multihop multibranch relaying scheme is considered. In both systems, we adopt decode-and-forward (DF) relaying, where each relay forwards the signal only when it correctly decodes. We analyze the end-to-end bit error rate (BER) and diversity order of both the systems with SSK. For binary SSK (n(s) = 2), our analytical BER expression is exact, and our numerical results show that the BERs evaluated through the analytical expression overlap with those obtained through Monte Carlo simulations. For nonbinary SSK (n(s) > 2), we derive an approximate BER expression, where the analytically evaluated BER results closely follow the simulated BER results. We show the comparison of the BERs of SSK and conventional phase-shift keying (PSK) and also show the instances where SSK outperforms PSK. We also present the diversity analyses for SSK in systems I and II, which predict the achievable diversity orders as a function of system parameters.

Secure Compute-and-Forward in a Bidirectional Relay

We consider the basic bidirectional relaying problem, in which two users in a wireless network wish to exchange messages through an intermediate relay node. In the compute-and-forward strategy, the relay computes a function of the two messages using the naturally occurring sum of symbols simultaneously transmitted by user nodes in a Gaussian multiple-access channel (MAC), and the computed function value is forwarded to the user nodes in an ensuing broadcast phase. In this paper, we study the problem under an additional security constraint, which requires that each user's message be kept secure from the relay. We consider two types of security constraints: 1) perfect secrecy, in which the MAC channel output seen by the relay is independent of each user's message and 2) strong secrecy, which is a form of asymptotic independence. We propose a coding scheme based on nested lattices, the main feature of which is that given a pair of nested lattices that satisfy certain goodness properties, we can explicitly specify probability distributions for randomization at the encoders to achieve the desired security criteria. In particular, our coding scheme guarantees perfect or strong secrecy even in the absence of channel noise. The noise in the channel only affects reliability of computation at the relay, and for Gaussian noise, we derive achievable rates for reliable and secure computation. We also present an application of our methods to the multihop line network in which a source needs to transmit messages to a destination through a series of intermediate relays.

MIMO Decode-and-Forward Relay Beamforming for Secrecy with Cooperative Jamming

In this paper, we consider decode-and-forward (DF) relay beamforming for secrecy with cooperative jamming (CJ) in the presence of multiple eavesdroppers. The communication between a source-destination pair is aided by a multiple-input multiple-output (MIMO) relay. The source has one transmit antenna and the destination and eavesdroppers have one receive antenna each. The source and the MIMO relay are constrained with powers P-S and P-R, respectively. We relax the rank-1 constraint on the signal beamforming matrix and transform the secrecy rate max-min optimization problem to a single maximization problem, which is solved by semidefinite programming techniques. We obtain the optimum source power, signal relay weights, and jamming covariance matrix. We show that the solution of the rank-relaxed optimization problem has rank-1. Numerical results show that CJ can improve the secrecy rate.

MIMO Decode-and-Forward Relay Beamforming for Secrecy with Cooperative Jamming

In this paper, we consider decode-and-forward (DF) relay beamforming for secrecy with cooperative jamming (CJ) in the presence of multiple eavesdroppers. The communication between a source-destination pair is aided by a multiple-input multiple-output (MIMO) relay. The source has one transmit antenna and the destination and eavesdroppers have one receive antenna each. The source and the MIMO relay are constrained with powers P-S and P-R, respectively. We relax the rank-1 constraint on the signal beamforming matrix and transform the secrecy rate max-min optimization problem to a single maximization problem, which is solved by semidefinite programming techniques. We obtain the optimum source power, signal relay weights, and jamming covariance matrix. We show that the solution of the rank-relaxed optimization problem has rank-1. Numerical results show that CJ can improve the secrecy rate.

Minimization Problems Based on Relative alpha-Entropy I: Forward Projection

Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative alpha-entropies (denoted I-alpha), arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (Kullback-Leibler divergence). Just like relative entropy, these relative alpha-entropies behave like squared Euclidean distance and satisfy the Pythagorean property. Minimizers of these relative alpha-entropies on closed and convex sets are shown to exist. Such minimizations generalize the maximum Renyi or Tsallis entropy principle. The minimizing probability distribution (termed forward I-alpha-projection) for a linear family is shown to obey a power-law. Other results in connection with statistical inference, namely subspace transitivity and iterated projections, are also established. In a companion paper, a related minimization problem of interest in robust statistics that leads to a reverse I-alpha-projection is studied.

Homogeneous isotropic superfluid turbulence in two dimensions: Inverse and forward cascades in the Hall-Vinen-Bekharevich-Khalatnikov model

We present the first direct-numerical-simulation study of the statistical properties of two-dimensional superfluid turbulence in the simplified, Hall-Vinen-Bekharevich-Khalatnikov two-fluid model. We show that both normalfluid and superfluid energy spectra can exhibit two power-law regimes, the first associated with an inverse cascade of energy and the second with the forward cascade of enstrophy. We quantify the mutual-friction-induced alignment of normal and superfluid velocities by obtaining probability distribution functions of the angle between them and the ratio of their moduli.

QEP Based Solution for Power Allocation in Amplify and Forward Networks

The problem of cooperative beamforming for maximizing the achievable data rate of an energy constrained two-hop amplify-and-forward (AF) network is considered. Assuming perfect channel state information (CSI) of all the nodes, we evaluate the optimal scaling factor for the relay nodes. Along with individual power constraint on each of the relay nodes, we consider a weighted sum power constraint. The proposed iterative algorithm initially solves a set of relaxed problems with weighted sum power constraint and then updates the solution to accommodate individual constraints. These relaxed problems in turn are solved using a sequence of Quadratic Eigenvalue Problems (QEP). The key contribution of this letter is the generalization of cooperative beamforming to incorporate both the individual and weighted sum constraint. Furthermore, we have proposed a novel algorithm based on Quadratic Eigenvalue Problem (QEP) and discussed its convergence.

Secure Communication in Amplify-and-Forward Networks with Multiple Eavesdroppers: Decoding with SNR Thresholds

The problem of secure unicast communication over a two hop Amplify-and-Forward wireless relay network with multiple eavesdroppers is considered. Assuming that a receiver (destination or eavesdropper) can decode a message only if the received SNR is above a predefined threshold, we consider this problem in two scenarios. In the first scenario, we maximize the SNR at the legitimate destination, subject to the condition that the received SNR at each eavesdropper is below the target threshold. Due to the non-convex nature of the objective function and eavesdroppers' constraints, we transform variables and obtain a quadratically constrained quadratic program (QCQP) with convex constraints, which can be solved efficiently. When the constraints are not convex, we consider a semidefinite relaxation (SDR) to obtain computationally efficient approximate solution. In the second scenario, we minimize the total power consumed by all relay nodes, subject to the condition that the received SNR at the legitimate destination is above the threshold and at every eavesdropper, it is below the corresponding threshold. We propose a semidefinite relaxation of the problem in this scenario and also provide an analytical lower bound.

Wireless Network-Coded Accumulate-Compute-and-Forward Two-Way Relaying

For the physical-layer network-coded wireless two-way relaying, it was observed by Koike-Akino et al. that adaptively changing the network coding map used at the relay according to channel conditions greatly reduces the impact of multiple-access interference, which occurs at the relay, and all these network coding maps should satisfy a requirement called exclusive law. We extend this approach to an accumulate-compute-and-forward protocol, which employs two phases: a multiple access (MA) phase consisting of two channel uses with independent messages in each channel use and a broadcast (BC) phase having one channel use. Assuming that the two users transmit points from the same 4-phase-shift keying (PSK) constellation, every such network coding map that satisfies the exclusive law can be represented by a Latin square of side 16, and conversely, this relationship can be used to get the network coding maps satisfying the exclusive law. Two methods of obtaining this network coding map to be used at the relay are discussed. Using the structural properties of the Latin squares for a given set of parameters, the problem of finding all the required maps is reduced to finding a small set of maps for the case. Having obtained all the Latin squares, a criterion is provided to select a Latin square for a given realization of fade state. This criterion turns out to be the same as the one used byMuralidharan et al. for two-stage bidirectional relaying.