Generalizing the Amplify-and-Forward Relay Gain Model: An Optimal SEP Perspective

Two models for AF relaying, namely, fixed gain and fixed power relaying, have been extensively studied in the literature given their ability to harness spatial diversity. In fixed gain relaying, the relay gain is fixed but its transmit power varies as a function of the source-relay channel gain. In fixed power relaying, the relay transmit power is fixed, but its gain varies. We revisit and generalize the fundamental two-hop AF relaying model. We present an optimal scheme in which an average power constrained AF relay adapts its gain and transmit power to minimize the symbol error probability (SEP) at the destination. Also derived are insightful and practically amenable closed-form bounds for the optimal relay gain. We then analyze the SEP of MPSK, derive tight bounds for it, and characterize the diversity order for Rayleigh fading. Also derived is an SEP approximation that is accurate to within 0.1 dB. Extensive results show that the scheme yields significant energy savings of 2.0-7.7 dB at the source and relay. Optimal relay placement for the proposed scheme is also characterized, and is different from fixed gain or power relaying. Generalizations to MQAM and other fading distributions are also discussed.

Fidelity susceptibility of one-dimensional models with twisted boundary conditions

Recently it has been shown that the fidelity of the ground state of a quantum many-body system can be used todetect its quantum critical points (QCPs). If g denotes the parameter in the Hamiltonian with respect to which the fidelity is computed, we find that for one-dimensional models with large but finite size, the fidelity susceptibility chi(F) can detect a QCP provided that the correlation length exponent satisfies nu < 2. We then show that chi(F) can be used to locate a QCP even if nu >= 2 if we introduce boundary conditions labeled by a twist angle N theta, where N is the system size. If the QCP lies at g = 0, we find that if N is kept constant, chi(F) has a scaling form given by chi(F) similar to theta(-2/nu) f (g/theta(1/nu)) if theta << 2 pi/N. We illustrate this both in a tight-binding model of fermions with a spatially varying chemical potential with amplitude h and period 2q in which nu = q, and in a XY spin-1/2 chain in which nu = 2. Finally we show that when q is very large, the model has two additional QCPs at h = +/- 2 which cannot be detected by studying the energy spectrum but are clearly detected by chi(F). The peak value and width of chi(F) seem to scale as nontrivial powers of q at these QCPs. We argue that these QCPs mark a transition between extended and localized states at the Fermi energy. DOI: 10.1103/PhysRevB.86.245424

Optimal Linear Codes with a Local-Error-Correction Property

Motivated by applications to distributed storage, Gopalan et al recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check equation associated with small Hamming weight, thereby enabling recovery of the message symbol by examining a small number of other code symbols. This notion is expanded to the case when all code symbols, not just the message symbols, are covered by such ``local'' parity. In this paper, we extend the results of Gopalan et. al. so as to permit recovery of an erased code symbol even in the presence of errors in local parity symbols. We present tight bounds on the minimum distance of such codes and exhibit codes that are optimal with respect to the local error-correction property. As a corollary, we obtain an upper bound on the minimum distance of a concatenated code.

Electrophile-Induced C-C Bond Activation of Vinylcyclopropanes for the Synthesis of Z-Alkylidenetetrahydrofurans

We present a detailed study on the behavior of vinylcyclopropanes as masked donor acceptor system toward the stereoselective synthesis of Z-alkylidenetetrahydrofurans. Results of bromenium catalyzed indirect activation of C-C bond of vinylcyclopropanes and concomitant cyclization to alkylidenetetrahydrofuran and other heterocycles have been discussed. The stereoselective formation of the Z-isomer is strongly controlled by the extent of destabilization of one of the gauche conformers of the vinylcyclopropane. The ring-opening/cyclization step was found to be stereospecific as in the case of DA cyclopropanes. The activation of the C-C bond leads to a tight-carbocation intermediate, which is evident from the complete retention of the stereochemistry. The retention of configuration has been established by a necessary control experiment that rules out the possibility of a double inversion pathway. The present results serve as direct stereochemical evidence in support of a tight ion-pair intermediate versus the controversial S(N)2 pathway. A 2D potential energy scan has been carried out at B3LYP/6-31G(d) level theory to obtain the relative energies of the conformers. The Z-selectivity observed has been explained on the basis of the relative population of the conformers and modeling the intermediate and transition state involved in the reaction at M06-2x/6-31+G(d) level. Energy profile for the cyclization step was modeled considering various possible pathways through which cyclization can happen. The methodology has been successfully demonstrated on vinylcyclobutanes as well.

Cubicity, degeneracy, and crossing number

A $k$-box $B=(R_1,...,R_k)$, where each $R_i$ is a closed interval on the real line, is defined to be the Cartesian product $R_1\times R_2\times ...\times R_k$. If each $R_i$ is a unit length interval, we call $B$ a $k$-cube. Boxicity of a graph $G$, denoted as $\boxi(G)$, is the minimum integer $k$ such that $G$ is an intersection graph of $k$-boxes. Similarly, the cubicity of $G$, denoted as $\cubi(G)$, is the minimum integer $k$ such that $G$ is an intersection graph of $k$-cubes. It was shown in [L. Sunil Chandran, Mathew C. Francis, and Naveen Sivadasan: Representing graphs as the intersection of axis-parallel cubes. MCDES-2008, IISc Centenary Conference, available at CoRR, abs/cs/ 0607092, 2006.] that, for a graph $G$ with maximum degree $\Delta$, $\cubi(G)\leq \lceil 4(\Delta +1)\log n\rceil$. In this paper, we show that, for a $k$-degenerate graph $G$, $\cubi(G) \leq (k+2) \lceil 2e \log n \rceil$. Since $k$ is at most $\Delta$ and can be much lower, this clearly is a stronger result. This bound is tight. We also give an efficient deterministic algorithm that runs in $O(n^2k)$ time to output a $8k(\lceil 2.42 \log n\rceil + 1)$ dimensional cube representation for $G$. An important consequence of the above result is that if the crossing number of a graph $G$ is $t$, then $\boxi(G)$ is $O(t^{1/4}{\lceil\log t\rceil}^{3/4})$ . This bound is tight up to a factor of $O((\log t)^{1/4})$. We also show that, if $G$ has $n$ vertices, then $\cubi(G)$ is $O(\log n + t^{1/4}\log t)$. Using our bound for the cubicity of $k$-degenerate graphs we show that cubicity of almost all graphs in $\mathcal{G}(n,m)$ model is $O(d_{av}\log n)$, where $d_{av}$ denotes the average degree of the graph under consideration. model is O(davlogn).

Another look at tightness

We examine a natural, but non-tight, reductionist security proof for deterministic message authentication code (MAC) schemes in the multi-user setting. If security parameters for the MAC scheme are selected without accounting for the non-tightness in the reduction, then the MAC scheme is shown to provide a level of security that is less than desirable in the multi-user setting. We find similar deficiencies in the security assurances provided by non-tight proofs when we analyze some protocols in the literature including ones for network authentication and aggregate MACs. Our observations call into question the practical value of non-tight reductionist security proofs. We also exhibit attacks on authenticated encryption schemes, disk encryption schemes, and stream ciphers in the multi-user setting.

A multi-layer ultra wide band power splitter

This paper presents analysis and design of multilayer ultra wide band (UWB) power splitter suitable for wireless communications. An UWB power splitter is designed in suspended substrate stripline medium. The quarter wave transformer in the conventional Wilkinson power divider is replaced by broadside coupled lines to achieve tight coupling for broadband operation. The UWB power splitter is analyzed using circuit models of coupled lines and full wave simulator. Experimental results of 3dB power splitter designed using the proposed structure have been verified against the results from circuit simulation and full wave simulation. The return loss is better than 12 dB across the band 3.1GHz to 10.6GHz. Size of the power splitter is 30mm× 20mm×6.38mm.

Performance analysis of fixed gain amplify-and-forward relaying with time-efficient cascaded channel estimation

In a cooperative system with an amplify-and-forward relay, the cascaded channel training protocol enables the destination to estimate the source-destination channel gain and the product of the source-relay (SR) and relay-destination (RD) channel gains using only two pilot transmissions from the source. Notably, the destination does not require a separate estimate of the SR channel. We develop a new expression for the symbol error probability (SEP) of AF relaying when imperfect channel state information (CSI) is acquired using the above training protocol. A tight SEP upper bound is also derived; it shows that full diversity is achieved, albeit at a high signal-to-noise ratio (SNR). Our analysis uses fewer simplifying assumptions, and leads to expressions that are accurate even at low SNRs and are different from those in the literature. For instance, it does not approximate the estimate of the product of SR and RD channel gains by the product of the estimates of the SR and RD channel gains. We show that cascaded channel estimation often outperforms a channel estimation protocol that incurs a greater training overhead by forwarding a quantized estimate of the SR channel gain to the destination. The extent of pilot power boosting, if allowed, that is required to improve performance is also quantified.

Antenna Selection in Interference-Constrained Underlay Cognitive Radios: SEP-Optimal Rule and Performance Benchmarking

In the underlay mode of cognitive radio, secondary users are allowed to transmit when the primary is transmitting, but under tight interference constraints that protect the primary. However, these constraints limit the secondary system performance. Antenna selection (AS)-based multiple antenna techniques, which exploit spatial diversity with less hardware, help improve secondary system performance. We develop a novel and optimal transmit AS rule that minimizes the symbol error probability (SEP) of an average interference-constrained multiple-input-single-output secondary system that operates in the underlay mode. We show that the optimal rule is a non-linear function of the power gain of the channel from the secondary transmit antenna to the primary receiver and from the secondary transmit antenna to the secondary receive antenna. We also propose a simpler, tractable variant of the optimal rule that performs as well as the optimal rule. We then analyze its SEP with L transmit antennas, and extensively benchmark it with several heuristic selection rules proposed in the literature. We also enhance these rules in order to provide a fair comparison, and derive new expressions for their SEPs. The results bring out new inter-relationships between the various rules, and show that the optimal rule can significantly reduce the SEP.

k.p based closed form energy band gap and transport electron effective mass model for 100] and 110] relaxed and strained Silicon nanowire

In this paper, we address a physics based closed form model for the energy band gap (E-g) and the transport electron effective mass in relaxed and strained 100] and 110] oriented rectangular Silicon Nanowire (SiNW). Our proposed analytical model along 100] and 110] directions are based on the k.p formalism of the conduction band energy dispersion relation through an appropriate rotation of the Hamiltonian of the electrons in the bulk crystal along 001] direction followed by the inclusion of a 4 x 4 Luttinger Hamiltonian for the description of the valance band structure. Using this, we demonstrate the variation in Eg and the transport electron effective mass as function of the cross-sectional dimensions in a relaxed 100] and 110] oriented SiNW. The behaviour of these two parameters in 100] oriented SiNW has further been studied with the inclusion of a uniaxial strain along the transport direction and a biaxial strain, which is assumed to be decomposed from a hydrostatic deformation along 001] with the former one. In addition, the energy band gap and the effective mass of a strained 110] oriented SiNW has also been formulated. Using this, we compare our analytical model with that of the extracted data using the nearest neighbour empirical tight binding sp(3)d(5)s* method based simulations and has been found to agree well over a wide range of device dimensions and applied strain. (C) 2012 Elsevier Ltd. All rights reserved.

Performance analysis of adaptive physical layer network coding for wireless two-way relaying

The performance analysis of adaptive physical layer network-coded two-way relaying scenario is presented which employs two phases: Multiple access (MA) phase and Broadcast (BC) phase. The deep channel fade conditions which occur at the relay referred as the singular fade states fall in the following two classes: (i) removable and (ii) non-removable singular fade states. With every singular fade state, we associate an error probability that the relay transmits a wrong network-coded symbol during the BC phase. It is shown that adaptive network coding provides a coding gain over fixed network coding, by making the error probabilities associated with the removable singular fade states contributing to the average Symbol Error Rate (SER) fall as SNR-2 instead of SNR-1. A high SNR upper-bound on the average end-to-end SER for the adaptive network coding scheme is derived, for a Rician fading scenario, which is found to be tight through simulations. Specifically, it is shown that for the adaptive network coding scheme, the probability that the relay node transmits a wrong network-coded symbol is upper-bounded by twice the average SER of a point-to-point fading channel, at high SNR. Also, it is shown that in a Rician fading scenario, it suffices to remove the effect of only those singular fade states which contribute dominantly to the average SER.

Channel training signal design for reciprocal multiple antenna systems with beamforming

Fast and efficient channel estimation is key to achieving high data rate performance in mobile and vehicular communication systems, where the channel is fast time-varying. To this end, this work proposes and optimizes channel-dependent training schemes for reciprocal Multiple-Input Multiple-Output (MIMO) channels with beamforming (BF) at the transmitter and receiver. First, assuming that Channel State Information (CSI) is available at the receiver, a channel-dependent Reverse Channel Training (RCT) signal is proposed that enables efficient estimation of the BF vector at the transmitter with a minimum training duration of only one symbol. In contrast, conventional orthogonal training requires a minimum training duration equal to the number of receive antennas. A tight approximation to the capacity lower bound on the system is derived, which is used as a performance metric to optimize the parameters of the RCT. Next, assuming that CSI is available at the transmitter, a channel-dependent forward-link training signal is proposed and its power and duration are optimized with respect to an approximate capacity lower bound. Monte Carlo simulations illustrate the significant performance improvement offered by the proposed channel-dependent training schemes over the existing channel-agnostic orthogonal training schemes.

Accurate performance analysis of single and opportunistic AF relay cooperation with imperfect cascaded channel estimates

Given the significant gains that relay-based cooperation promises, the practical problems of acquisition of channel state information (CSI) and the characterization and optimization of performance with imperfect CSI are receiving increasing attention. We develop novel and accurate expressions for the symbol error probability (SEP) for fixed-gain amplify-and-forward relaying when the destination acquires CSI using the time-efficient cascaded channel estimation (CCE) protocol. The CCE protocol saves time by making the destination directly estimate the product of the source-relay and relay-destination channel gains. For a single relay system, we first develop a novel SEP expression and a tight SEP upper bound. We then similarly analyze an opportunistic multi-relay system, in which both selection and coherent demodulation use imperfect estimates. A distinctive aspect of our approach is the use of as few simplifying approximations as possible, which results in new results that are accurate at signal-to-noise-ratios as low as 1 dB for single and multi-relay systems. Using insights gleaned from an asymptotic analysis, we also present a simple, closed-form, nearly-optimal solution for allocation of energy between pilot and data symbols at the source and relay(s).

Selenium adsorption on Au(111) and Ag(111) surfaces: adsorbed selenium and selenide films

Results of a high resolution photoemission and electrochemistry study of Se adsorption Au(111) and Ag(111) surfaces performed by immersion of pristine samples into an aqeuous solution of Na2Se are presented. Cyclic voltammetry on Au shows formation of selenium adsorbed species and the structures observed in reductive desorption are to the atomic and polymeric species observed in XPS. In the case of Au(111) XPS spectra in the Se(3d) region indeed show two main features attributed to Se chemisorbed atomically and polymeric Se-8 features.' Smaller structures due to other types of Se conformations were also observed. The Au(4f) peak line, shape does not show core level, shifts: indicative of Au selenide formation the case of silver, XPS spectra for the Ag(3d) show a broadening of the peak and a deconvolution into Ag-B bulk like Ag-Se components shows that the Ag-Se is located at a lower binding energy, an effect similar to oxidation and sulfidation of Ag. The Se(3d) XPS spectrum is found to be substantially different from the Au case and dominated by atomic type Se due to the selenide, though a smaller intensity Se structure at an energy similar to the Se-8 structure for Au is also observed. Changes in the valence band region. related to Se adsorption are reported.

Low order anti-aliasing filters for sparse signals in embedded applications

Major emphasis, in compressed sensing (CS) research, has been on the acquisition of sub-Nyquist number of samples of a signal that has a sparse representation on some tight frame or an orthogonal basis, and subsequent reconstruction of the original signal using a plethora of recovery algorithms. In this paper, we present compressed sensing data acquisition from a different perspective, wherein a set of signals are reconstructed at a sampling rate which is a multiple of the sampling rate of the ADCs that are used to measure the signals. We illustrate how this can facilitate usage of anti-aliasing filters with relaxed frequency specifications and, consequently, of lower order.