Distributed Space Time Coding for Wireless Two-Way Relaying

We consider the wireless two-way relay channel, in which two-way data transfer takes place between the end nodes with the help of a relay. For the Denoise-And-Forward (DNF) protocol, it was shown by Koike-Akino et al. that adaptively changing the network coding map used at the relay greatly reduces the impact of Multiple Access Interference at the relay. The harmful effect of the deep channel fade conditions can be effectively mitigated by proper choice of these network coding maps at the relay. Alternatively, in this paper we propose a Distributed Space Time Coding (DSTC) scheme, which effectively removes most of the deep fade channel conditions at the transmitting nodes itself without any CSIT and without any need to adaptively change the network coding map used at the relay. It is shown that the deep fades occur when the channel fade coefficient vector falls in a finite number of vector subspaces of, which are referred to as the singular fade subspaces. DSTC design criterion referred to as the singularity minimization criterion under which the number of such vector subspaces are minimized is obtained. Also, a criterion to maximize the coding gain of the DSTC is obtained. Explicit low decoding complexity DSTC designs which satisfy the singularity minimization criterion and maximize the coding gain for QAM and PSK signal sets are provided. Simulation results show that at high Signal to Noise Ratio, the DSTC scheme provides large gains when compared to the conventional Exclusive OR network code and performs better than the adaptive network coding scheme.

Trellis coded modulation scheme for the fading relay channel

A decode and forward protocol based Trellis Coded Modulation (TCM) scheme for the half-duplex relay channel, in a Rayleigh fading environment, is presented. The proposed scheme can achieve any spectral efficiency greater than or equal to one bit per channel use (bpcu). A near-ML decoder for the suggested TCM scheme is proposed. It is shown that the high Signal to Noise Ratio (SNR) performance of this near-ML decoder approaches the performance of the optimal ML decoder. Based on the derived Pair-wise Error Probability (PEP) bounds, design criteria to maximize the diversity and coding gains are obtained. Simulation results show a large gain in SNR for the proposed TCM scheme over uncoded communication as well as the direct transmission without the relay.

Wireless Network Coding for MIMO Two-Way Relaying

The design of modulation schemes for the physical layer network-coded two-way MIMO relaying scenario is considered, with the denoise-and-forward protocol which employs two phases: Multiple Access phase and Broadcast phase. It is shown that for MIMO two-way relaying, the minimum distance of the effective constellation at the relay becomes zero when all the rows of the channel fade coefficient matrix belong to a finite number of vector subspaces referred to as the singular fade subspaces. The singular fade subspaces can be classified into two kinds based on whether their harmful effects can be removed or not: (i) the removable and (ii) the non-removable singular fade subspaces. It is shown that network coding maps obtained by the completion of appropriate partially filled Latin Rectangles can remove the harmful effects of all the removable singular fade subspaces. For 2(lambda)-PSK signal set, the removable and non-removable singular fade subspaces are characterized and, it is shown that the number of non-removable singular fade subspaces is a small fraction of the total number of singular fade subspaces and this fraction tends to zero as the constellation size tends to infinity. The Latin Rectangles for the case when the end nodes use different number of antennas are shown to be obtainable from the Latin Squares for the case when they use the same number of antennas. Also, the network coding maps which remove all the removable singular singular fade subspaces are shown to be obtainable from a small set of Latin Squares. The removal of all the singular fade subspaces by properly choosing the network coding map, provides a gain of 5.5 dB over the conventional Exclusive-OR network coding, in a Rayleigh fading scenario with 2 antennas at the end nodes and one antenna at the relay node, for 4-PSK signal set.

Optimal capacity relay node placement in a multi-hop network on a line

We use information theoretic achievable rate formulas for the multi-relay channel to study the problem of optimal placement of relay nodes along the straight line joining a source node and a destination node. The achievable rate formulas that we utilize are for full-duplex radios at the relays and decode-and-forward relaying. For the single relay case, and individual power constraints at the source node and the relay node, we provide explicit formulas for the optimal relay location and the optimal power allocation to the source-relay channel, for the exponential and the power-law path-loss channel models. For the multiple relay case, we consider exponential path-loss and a total power constraint over the source and the relays, and derive an optimization problem, the solution of which provides the optimal relay locations. Numerical results suggest that at low attenuation the relays are mostly clustered close to the source in order to be able to cooperate among themselves, whereas at high attenuation they are uniformly placed and work as repeaters. We also prove that a constant rate independent of the attenuation in the network can be achieved by placing a large enough number of relay nodes uniformly between the source and the destination, under the exponential path-loss model with total power constraint.

BER Analysis of Space Shift Keying in Cooperative Multi-hop Multi-branch DF Relaying

Space shift keying (SSK) is an attractive modulation technique for multi-antenna communications. In SSK, only one among the available transmit antennas is activated during one channel use, and the index of the chosen transmit antenna conveys information. In this paper, we analyze the performance of SSK in multi-hop, multi-branch cooperative relaying systems. We consider the decode-and-forward relaying protocol, where a relay forwards the decoded symbol if it decodes the symbol correctly from the received signal. We derive closed-form expressions for the end-to-end bit error rate of SSK in this system. Analytical and simulation results match very well.

Secure Transmission in Cooperative Networks with Weak Eavesdroppers

In this letter, we propose a scheme to improve the secrecy rate of cooperative networks using Analog Network Coding (ANC). ANC mixes the signals in the air; the desired signal is then separated out, from the mixed signals, at the legitimate receiver using techniques like self interference subtraction and signal nulling, thereby achieving better secrecy rates. Assuming global channel state information, memoryless adversaries and the decode-and-forward strategy, we seek to maximize the average secrecy rate between the source and the destination, subject to an overall power budget. Then, exploiting the structure of the optimization problem, we compute its optimal solution. Finally, we use numerical evaluations to compare our scheme with the conventional approaches.

Optimal power allocation for protective jamming in wireless networks: A flow based model

We address the problem of passive eavesdroppers in multi-hop wireless networks using the technique of friendly jamming. The network is assumed to employ Decode and Forward (DF) relaying. Assuming the availability of perfect channel state information (CSI) of legitimate nodes and eavesdroppers, we consider a scheduling and power allocation (PA) problem for a multiple-source multiple-sink scenario so that eavesdroppers are jammed, and source-destination throughput targets are met while minimizing the overall transmitted power. We propose activation sets (AS-es) for scheduling, and formulate an optimization problem for PA. Several methods for finding AS-es are discussed and compared. We present an approximate linear program for the original nonlinear, non-convex PA optimization problem, and argue that under certain conditions, both the formulations produce identical results. In the absence of eavesdroppers' CSI, we utilize the notion of Vulnerability Region (VR), and formulate an optimization problem with the objective of minimizing the VR. Our results show that the proposed solution can achieve power-efficient operation while defeating eavesdroppers and achieving desired source-destination throughputs simultaneously. (C) 2015 Elsevier B.V. All rights reserved.

Two-dimensional homogeneous isotropic fluid turbulence with polymer additives

We carry out an extensive and high-resolution direct numerical simulation of homogeneous, isotropic turbulence in two-dimensional fluid films with air-drag-induced friction and with polymer additives. Our study reveals that the polymers (a) reduce the total fluid energy, enstrophy, and palinstrophy; (b) modify the fluid energy spectrum in both inverse-and forward-cascade regimes; (c) reduce small-scale intermittency; (d) suppress regions of high vorticity and strain rate; and (e) stretch in strain-dominated regions. We compare our results with earlier experimental studies and propose new experiments.

Relay Selection with Channel Probing in Sleep-Wake Cycling Wireless Sensor Networks

In geographical forwarding of packets in a large wireless sensor network (WSN) with sleep-wake cycling nodes, we are interested in the local decision problem faced by a node that has ``custody'' of a packet and has to choose one among a set of next-hop relay nodes to forward the packet toward the sink. Each relay is associated with a ``reward'' that summarizes the benefit of forwarding the packet through that relay. We seek a solution to this local problem, the idea being that such a solution, if adopted by every node, could provide a reasonable heuristic for the end-to-end forwarding problem. Toward this end, we propose a local relay selection problem consisting of a forwarding node and a collection of relay nodes, with the relays waking up sequentially at random times. At each relay wake-up instant, the forwarder can choose to probe a relay to learn its reward value, based on which the forwarder can then decide whether to stop (and forward its packet to the chosen relay) or to continue to wait for further relays to wake up. The forwarder's objective is to select a relay so as to minimize a combination of waiting delay, reward, and probing cost. The local decision problem can be considered as a variant of the asset selling problem studied in the operations research literature. We formulate the local problem as a Markov decision process (MDP) and characterize the solution in terms of stopping sets and probing sets. We provide results illustrating the structure of the stopping sets, namely, the (lower bound) threshold and the stage independence properties. Regarding the probing sets, we make an interesting conjecture that these sets are characterized by upper bounds. Through simulation experiments, we provide valuable insights into the performance of the optimal local forwarding and its use as an end-to-end forwarding heuristic.

Dynamic response of a piezoelectric flapping wing

Piezo-composite membranes have advantages over motorized flapping where frequencies are high and certain coupling between bending and twisting is useful to generate lift and forward flight. We draw examples of fruit fly and bumble bee. Wings with Piezo ceramic PZT coating are realized. The passive mechanical response of the wing is characterized experimentally and validated using finite element simulation. Piezoelectric actuation with uniform electrode coating is characterized and optimal frequencies for flapping are identified. The experimental data are used in an empirical model and advanced ratio for a flapping insect like condition for various angular orientations is estimated.

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.

Sum Secrecy Rate in Multicarrier DF Relay Beamforming

In this paper, we study sum secrecy rate in multicarrier decode-and-forward relay beamforming. We obtain the optimal source power and relay weights on each subcarrier which maximize the sum secrecy rate. For a given total power on a given subcarrier k, P-0(k), we reformulate the optimization problem by relaxing the rank-1 constraint on the complex positive semidefinite relay weight matrix, and solve using semidefinite programming. We analytically prove that the solution to the relaxed optimization problem is indeed rank 1. We show that the subcarrier secrecy rate, R-s (P-0(k)), is a concave function in total power P-0(k) if R-s (P-0(k)) > 0 for any P-0(k) > 0. Numerical results show that the sum secrecy rate with optimal power allocation across subcarriers is more than the sum secrecy rate with equal power allocation. We also propose a low complexity suboptimal power allocation scheme which outperforms equal power allocation scheme.

Direct Link-Aware Relay Selection for Average Interference-Constrained Underlay Cognitive Radio

Cooperative relaying combined with selection exploits spatial diversity to significantly improve the performance of interference-constrained secondary users in an underlay cognitive radio network. We present a novel and optimal relay selection (RS) rule that minimizes the symbol error probability (SEP) of an average interference-constrained underlay secondary system that uses amplify-and-forward relays. A key point that the rule highlights for the first time is that, for the average interference constraint, the signal-to-interference-plus-noise-ratio (SINR) of the direct source-to-destination (SI)) link affects the choice of the optimal relay. Furthermore, as the SINR increases, the odds that no relay transmits increase. We also propose a simpler, more practical, and near-optimal variant of the optimal rule that requires just one bit of feedback about the state of the SD link to the relays. Compared to the SD-unaware ad hoc RS rules proposed in the literature, the proposed rules markedly reduce the SEP by up to two orders of magnitude.

A Jacobian-Based Algorithm for Planning Attitude Maneuvers Using Forward and Reverse Rotations

Algorithms for planning quasistatic attitude maneuvers based on the Jacobian of the forward kinematic mapping of fully-reversed (FR) sequences of rotations are proposed in this paper. An FR sequence of rotations is a series of finite rotations that consists of initial rotations about the axes of a body-fixed coordinate frame and subsequent rotations that undo these initial rotations. Unlike the Jacobian of conventional systems such as a robot manipulator, the Jacobian of the system manipulated through FR rotations is a null matrix at the identity, which leads to a total breakdown of the traditional Jacobian formulation. Therefore, the Jacobian algorithm is reformulated and implemented so as to synthesize an FR sequence for a desired rotational displacement. The Jacobian-based algorithm presented in this paper identifies particular six-rotation FR sequences that synthesize desired orientations. We developed the single-step and the multiple-step Jacobian methods to accomplish a given task using six-rotation FR sequences. The single-step Jacobian method identifies a specific FR sequence for a given desired orientation and the multiple-step Jacobian algorithm synthesizes physically feasible FR rotations on an optimal path. A comparison with existing algorithms verifies the fast convergence ability of the Jacobian-based algorithm. Unlike closed-form solutions to the inverse kinematics problem, the Jacobian-based algorithm determines the most efficient FR sequence that yields a desired rotational displacement through a simple and inexpensive numerical calculation. The procedure presented here is useful for those motion planning problems wherein the Jacobian is singular or null.

Top polarization, forward-backward asymmetry, and new physics

We consider how the measurement of top polarization at the Tevatron can be used to characterize and discriminate among different new physics models that have been suggested to explain the anomalous top forward-backward asymmetry reported at the Tevatron. This has the advantage of catching the essence of the parity-violating effect characteristic to the different suggested new physics models. Other observables constructed from these asymmetries are shown to be useful in discriminating between the models, even after taking into account the statistical errors. Finally, we discuss some signals at the 7 TeV LHC.