High-rate, Double-Symbol-Decodable STBCs from Clifford Algebras

For the number of transmit antennas N = 2(a) the maximum rate (in complex symbols per channel use) of all the Quasi-Orthogonal Designs (QODs) reported in the literature is a/2(a)-1. In this paper, we report double-symbol-decodable Space-Time Block Codes with rate a-1/2(a)-2 for N = 2(a) transmit antennas. In particular, our code for 8 and 16 transmit antennas offer rates 1 and 3/4 respectively, the known QODs offer only 3/4 and 1/2 respectively. Our construction is based on the representations of Clifford algebras and applicable for any number of transmit antennas. We study the diversity sum and diversity product of our codes. We show that our diversity sum is larger than that of all known QODs and hence our codes perform better than the comparable QODs at low SNRs for identical spectral efficiency. We provide simulation results for various spectral efficiencies.

On the improvement of diversity-multiplexing gain tradeoff in a training based TDD-simo system

This paper investigates the diversity-multiplexing gain tradeoff (DMT) of a time-division duplex (TDD) single-input multiple-output (SIMO) system with perfect channel state information (CSI) at the receiver (CSIR) and partial CSI at the transmitter (CSIT). The partial CSIT is acquired through a training sequence from the receiver to the transmitter. The training sequence is chosen in an intelligent manner based on the CSIR, to reduce the training length by a factor of r, the number of receive antennas. We show that, for the proposed training scheme and a given channel coherence time, the diversity order increases linearly with r for nonzero multiplexing gain. This is a significant improvement over conventional orthogonal training schemes.

Low-Complexity Detection and Performance in Multi-Gigabit High Spectral Efficiency Wireless Systems

Recently, we reported a low-complexity likelihood ascent search (LAS) detection algorithm for large MIMO systems with several tens of antennas that can achieve high spectral efficiencies of the order of tens to hundreds of bps/Hz. Through simulations, we showed that this algorithm achieves increasingly near SISO AWGN performance for increasing number of antennas in Lid. Rayleigh fading. However, no bit error performance analysis of the algorithm was reported. In this paper, we extend our work on this low-complexity large MIMO detector in two directions: i) We report an asymptotic bit error probability analysis of the LAS algorithm in the large system limit, where N-t, N-r -> infinity keeping N-t = N-r, where N-t and N-r are the number of transmit and receive antennas, respectively. Specifically, we prove that the error performance of the LAS detector for V-BLAST with 4-QAM in i.i.d. Rayleigh fading converges to that of the maximum-likelihood (ML) detector as N-t, N-r -> infinity keeping N-t = N-r ii) We present simulated BER and nearness to capacity results for V-BLAST as well as high-rate non-orthogonal STBC from Division Algebras (DA), in a more realistic spatially correlated MIMO channel model. Our simulation results show that a) at an uncoded BER of 10(-3), the performance of the LAS detector in decoding 16 x 16 STBC from DA with N-t = = 16 and 16-QAM degrades in spatially correlated fading by about 7 dB compared to that in i.i.d. fading, and 19) with a rate-3/4 outer turbo code and 48 bps/Hz spectral efficiency, the performance degrades by about 6 dB at a coded BER of 10(-4). Our results further show that providing asymmetry in number of antennas such that N-r > N-t keeping the total receiver array length same as that for N-r = N-t, the detector is able to pick up the extra receive diversity thereby significantly improving the BER performance.

Robust/Optimal Temperature Profile Control of a High-Speed Aerospace Vehicle Using Neural Networks

An approximate dynamic programming (ADP)-based suboptimal neurocontroller to obtain desired temperature for a high-speed aerospace vehicle is synthesized in this paper. A I-D distributed parameter model of a fin is developed from basic thermal physics principles. "Snapshot" solutions of the dynamics are generated with a simple dynamic inversion-based feedback controller. Empirical basis functions are designed using the "proper orthogonal decomposition" (POD) technique and the snapshot solutions. A low-order nonlinear lumped parameter system to characterize the infinite dimensional system is obtained by carrying out a Galerkin projection. An ADP-based neurocontroller with a dual heuristic programming (DHP) formulation is obtained with a single-network-adaptive-critic (SNAC) controller for this approximate nonlinear model. Actual control in the original domain is calculated with the same POD basis functions through a reverse mapping. Further contribution of this paper includes development of an online robust neurocontroller to account for unmodeled dynamics and parametric uncertainties inherent in such a complex dynamic system. A neural network (NN) weight update rule that guarantees boundedness of the weights and relaxes the need for persistence of excitation (PE) condition is presented. Simulation studies show that in a fairly extensive but compact domain, any desired temperature profile can be achieved starting from any initial temperature profile. Therefore, the ADP and NN-based controllers appear to have the potential to become controller synthesis tools for nonlinear distributed parameter systems.

On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)

By using the strain smoothing technique proposed by Chen et al. (Comput. Mech. 2000; 25: 137-156) for meshless methods in the context of the finite element method (FEM), Liu et al. (Comput. Mech. 2007; 39(6): 859-877) developed the Smoothed FEM (SFEM). Although the SFEM is not yet well understood mathematically, numerical experiments point to potentially useful features of this particularly simple modification of the FEM. To date, the SFEM has only been investigated for bilinear and Wachspress approximations and is limited to linear reproducing conditions. The goal of this paper is to extend the strain smoothing to higher order elements and to investigate numerically in which condition strain smoothing is beneficial to accuracy and convergence of enriched finite element approximations. We focus on three widely used enrichment schemes, namely: (a) weak discontinuities; (b) strong discontinuities; (c) near-tip linear elastic fracture mechanics functions. The main conclusion is that strain smoothing in enriched approximation is only beneficial when the enrichment functions are polynomial (cases (a) and (b)), but that non-polynomial enrichment of type (c) lead to inferior methods compared to the standard enriched FEM (e.g. XFEM). Copyright (C) 2011 John Wiley & Sons, Ltd.

Optimal management of beaver population using a reduced-order distributed parameter model and single network adaptive critics

Beavers are often found to be in conflict with human interests by creating nuisances like building dams on flowing water (leading to flooding), blocking irrigation canals, cutting down timbers, etc. At the same time they contribute to raising water tables, increased vegetation, etc. Consequently, maintaining an optimal beaver population is beneficial. Because of their diffusion externality (due to migratory nature), strategies based on lumped parameter models are often ineffective. Using a distributed parameter model for beaver population that accounts for their spatial and temporal behavior, an optimal control (trapping) strategy is presented in this paper that leads to a desired distribution of the animal density in a region in the long run. The optimal control solution presented, imbeds the solution for a large number of initial conditions (i.e., it has a feedback form), which is otherwise nontrivial to obtain. The solution obtained can be used in real-time by a nonexpert in control theory since it involves only using the neural networks trained offline. Proper orthogonal decomposition-based basis function design followed by their use in a Galerkin projection has been incorporated in the solution process as a model reduction technique. Optimal solutions are obtained through a "single network adaptive critic" (SNAC) neural-network architecture.

Reduced Order Suboptimal Control Design for a Class of Nonlinear Distributed Parameter Systems Using POD and /spl thetas/-D Techniques

A new computational tool is presented in this paper for suboptimal control design of a class of nonlinear distributed parameter systems. First proper orthogonal decomposition based problem-oriented basis functions are designed, which are then used in a Galerkin projection to come up with a low-order lumped parameter approximation. Next, a suboptimal controller is designed using the emerging /spl thetas/-D technique for lumped parameter systems. This time domain sub-optimal control solution is then mapped back to the distributed domain using the same basis functions, which essentially leads to a closed form solution for the controller in a state feedback form. Numerical results for a real-life nonlinear temperature control problem indicate that the proposed method holds promise as a good suboptimal control design technique for distributed parameter systems.

Linear and nonlinear optical properties of cumulenes and polyenynes: a model exact study

Model exact static and frequency-dependent polarizabilities, static second hyperpolarizabilities and THG coefficents of cumulenes and polyenynes, calculated within the correlated Pariser-Parr-Pople (PPP) model defined over the pi-framework are reported and compared with the results for the polyenes. It is found that for the same chain length, the polarizabilities and THG coefficients of the cumulenes are largest and those of the polyenynes smallest with the polyenes having an intermediate value. The optical gap of the infinite cumulene is lowest (0.75 eV) and is associated with a low transition dipole moment for an excitation involving transfer of an electron between the two orthogonal conjugated pi-systems. The polyenynes have the largest optical gap (4.37 eV), with the magnitude being nearly independent of the chain length. This excitation involves charge transfer between the conjugated bonds in the terminal triple bond. Chain length and frequency dependence of alpha(ij) and gamma(ijkl) of these systems are also reported. The effect of a heteroatom on the polarizability and THG coefficients of acetylenic systems is also reported. It has been found that the presence of the heteroatom reduces the polarizability and THG coefficients of these systems, an effect opposite to that found in the polyenes and cyanine dyes. This result has been associated with the different nature of the charge transfer in the acetylenic systems.

Nonlinear static and dynamic damped response of a composite rectangular plate resting on a two-parameter elastic foundation

Nonlinear static and dynamic response analyses of a clamped. rectangular composite plate resting on a two-parameter elastic foundation have been studied using von Karman's relations. Incorporating the material damping, the governing coupled, nonlinear partial differential equations are obtained for the plate under step pressure pulse load excitation. These equations have been solved by a one-term solution and by applying Galerkin's technique to the deflection equation. This yields an ordinary nonlinear differential equation in time. The nonlinear static solution is obtained by neglecting the time-dependent variables. Thc nonlinear dynamic damped response is obtained by applying the ultraspherical polynomial approximation (UPA) technique. The influences of foundation modulus, shear modulus, orthotropy, etc. upon the nonlinear static and dynamic responses have been presented.

Hierarchies of circuit classes that are closed under complement

We examine three hierarchies of circuit classes and show they are closed under complementation. (1) The class of languages recognized by a family of polynomial size skew circuits with width O(w), are closed under complement. (2) The class of languages recognized by family of polynomial size circuits with width O(w) and polynomial tree-size, are closed under complement. (3) The class of languages recognized by a family of polynomial size, O(log(n)) depth, bounded AND fan-in with OR fan-in f (f⩾log(n)) circuits are closed under complement. These improve upon the results of (i) Immerman (1988) and Szelepcsenyi (1988), who show that 𝒩L𝒪𝒢 is closed under complementation, and (ii) Borodin et al. (1989), who show that L𝒪𝒢𝒞ℱL is closed under complement

Fast computation of Legendre and Zernike moments

This paper presents recursive algorithms for fast computation of Legendre and Zernike moments of a grey-level image intensity distribution. For a binary image, a contour integration method is developed for the evaluation of Legendre moments using only the boundary information. A method for recursive calculation of Zernike polynomial coefficients is also given. A square-to-circular image transformation scheme is introduced to minimize the computation involved in Zernike moment functions. The recursive formulae can also be used in inverse moment transforms to reconstruct the original image from moments. The mathematical framework of the algorithms is given in detail, and illustrated with binary and grey-level images.

Photochemical intramolecular gamma-hydrogen abstraction in a ketone and an alkene and the role of tunneling of hydrogen

Intramolecular gamma-hydrogen abstraction reactions were examined in pentane-2-one and 2-methyl-1-pentene in their lowest triplet states using the AM1 semi-empirical molecular orbital method with the complete geometry optimization in the unrestricted Hartree-Fock frame. The results reveal that the oxygen atom of the carbonyl group and the end carbon atom of the olefinic bond acquire high free valence and spin density indices in their respective lowest triplet states, leading to abstraction of hydrogen from the gamma-position relative to the carbonyl and olefinic bonds. The theoretical energy profiles fit with a polynomial and the probability of tunneling of hydrogen was estimated by the WKB (Wentzel, Kramer and Brillouin) method. The results, after thermal averaging of the rate constants, reveal that tunneling of hydrogen is significant at room temperature.

Simulation of ENSO-Related Surface Winds in the Tropical Pacific by an Atmospheric General Circulation Model Forced by Observed Sea Surface Temperatures

The authors present the simulation of the tropical Pacific surface wind variability by a low-resolution (R15 horizontal resolution and 18 vertical levels) version of the Center for Ocean-Land-Atmosphere Interactions, Maryland, general circulation model (GCM) when forced by observed global sea surface temperature. The authors have examined the monthly mean surface winds acid precipitation simulated by the model that was integrated from January 1979 to March 1992. Analyses of the climatological annual cycle and interannual variability over the Pacific are presented. The annual means of the simulated zonal and meridional winds agree well with observations. The only appreciable difference is in the region of strong trade winds where the simulated zonal winds are about 15%-20% weaker than observed, The amplitude of the annual harmonics are weaker than observed over the intertropical convergence zone and the South Pacific convergence zone regions. The amplitudes of the interannual variation of the simulated zonal and meridional winds are close to those of the observed variation. The first few dominant empirical orthogonal functions (EOF) of the simulated, as well as the observed, monthly mean winds are found to contain a targe amount of high-frequency intraseasonal variations, While the statistical properties of the high-frequency modes, such as their amplitude and geographical locations, agree with observations, their detailed time evolution does not. When the data are subjected to a 5-month running-mean filter, the first two dominant EOFs of the simulated winds representing the low-frequency EI Nino-Southern Oscillation fluctuations compare quite well with observations. However, the location of the center of the westerly anomalies associated with the warm episodes is simulated about 15 degrees west of the observed locations. The model simulates well the progress of the westerly anomalies toward the eastern Pacific during the evolution of a warm event. The simulated equatorial wind anomalies are comparable in magnitude to the observed anomalies. An intercomparison of the simulation of the interannual variability by a few other GCMs with comparable resolution is also presented. The success in simulation of the large-scale low-frequency part of the tropical surface winds by the atmospheric GCM seems to be related to the model's ability to simulate the large-scale low-frequency part of the precipitation. Good correspondence between the simulated precipitation and the highly reflective cloud anomalies is seen in the first two EOFs of the 5-month running means. Moreover, the strong correlation found between the simulated precipitation and the simulated winds in the first two principal components indicates the primary role of model precipitation in driving the surface winds. The surface winds simulated by a linear model forced by the GCM-simulated precipitation show good resemblance to the GCM-simulated winds in the equatorial region. This result supports the recent findings that the large-scale part of the tropical surface winds is primarily linear.

Some Algorithms for Eigensubspace Estimation

An important tool in signal processing is the use of eigenvalue and singular value decompositions for extracting information from time-series/sensor array data. These tools are used in the so-called subspace methods that underlie solutions to the harmonic retrieval problem in time series and the directions-of-arrival (DOA) estimation problem in array processing. The subspace methods require the knowledge of eigenvectors of the underlying covariance matrix to estimate the parameters of interest. Eigenstructure estimation in signal processing has two important classes: (i) estimating the eigenstructure of the given covariance matrix and (ii) updating the eigenstructure estimates given the current estimate and new data. In this paper, we survey some algorithms for both these classes useful for harmonic retrieval and DOA estimation problems. We begin by surveying key results in the literature and then describe, in some detail, energy function minimization approaches that underlie a class of feedback neural networks. Our approaches estimate some or all of the eigenvectors corresponding to the repeated minimum eigenvalue and also multiple orthogonal eigenvectors corresponding to the ordered eigenvalues of the covariance matrix. Our presentation includes some supporting analysis and simulation results. We may point out here that eigensubspace estimation is a vast area and all aspects of this cannot be fully covered in a single paper. (C) 1995 Academic Press, Inc.

Uniform algebras generated by holomorphic and close-to-harmonic functions

The initial motivation for this paper is to discuss a more concrete approach to an approximation theorem of Axler and Shields, which says that the uniform algebra on the closed unit disc (D) over bar generated by z and h, where h is a nowhere-holomorphic harmonic function on D that is continuous up to partial derivative D, equals C((D) over bar). The abstract tools used by Axler and Shields make harmonicity of h an essential condition for their result. We use the concepts of plurisubharmonicity and polynomial convexity to show that, in fact, the same conclusion is reached if h is replaced by h + R, where R is a non-harmonic perturbation whose Laplacian is ``small'' in a certain sense.