Benoit Champagne

Parametric localization of distributed sources

Most array processing algorithms are based on the assumption that the signals are generated by point sources. This is a mathematical constraint that is not satisfied in many applications. In this paper, we consider situations where the sources are distributed in space with a parametric angular cross-correlation kernel. We propose an algorithm that estimates the parameters of this model using a generalization of the MUSIC algorithm. The method involves maximizing a cost function that depends on a matrix array manifold and the noise eigenvectors. We study two particular cases: coherent and incoherent spatial source distributions. The spatial correlation function for a uniformly distributed signal is derived. From this, we find the array gain and show that (in contrast to point sources) it does not increase linearly with the number of sources. We compare our method to the conventional (point source) MUSIC algorithm. The simulation studies show that the new method outperforms the MUSIC algorithm by reducing the estimation bias and the standard deviation for scenarios with distributed sources. It is also shown that the threshold signal-to-noise ratio required for resolving two closely spaced distributed sources is considerably smaller for the new method. >

Performance of time-delay estimation in the presence of room reverberation

Synthetic microphone signals generated with the image model technique are used to study the effects of room reverberation on the performance of the maximum likelihood (ML) estimator of the time delay, in which the estimate is obtained by maximizing the cross correlation between filtered versions of the microphone signals. The results underscore the adverse effects of reverberation on the bias, variance and probability of anomaly of the ML estimator. Explanations of these effects are provided.

Incorporating the human hearing properties in the signal subspace approach for speech enhancement

The major drawback of most noise reduction methods in speech applications is the annoying residual noise known as musical noise. A potential solution to this artifact is the incorporation of a human hearing model in the suppression filter design. However, since the available models are usually developed in the frequency domain, it is not clear how they can be applied in the signal subspace approach for speech enhancement. In this paper, we present a Frequency to Eigendomain Transformation (FET) which permits to calculate a perceptually based eigenfilter. This filter yields an improved result where better shaping of the residual noise, from a perceptual perspective, is achieved. The proposed method can also be used with the general case of colored noise. Spectrogram illustrations and listening test results are given to show the superiority of the proposed method over the conventional signal subspace approach.

Nonlinear Optical Molecular Switches as Selective Cation Sensors

This work demonstrates that the recognition of cations by molecular switches can give rise to large contrasts of the second-order nonlinear optical (NLO) properties, which can therefore be used as a powerful and multi-usage detection tool. The proof of concept is given by evidencing, by means of ab initio calculations, the ability of spiropyran/merocyanine systems to selectively detect alkali, alkaline earth, and transition-metal cations.

The computer calculation of Lie point symmetries of large systems of differential equations

Abstract A MACSYMA program is presented that greatly helps in the calculation of Lie symmetry groups of large systems of differential equations. The program calculates the determining equations for systems of m differential equations of order k , with p independent and q dependent variables, where m , k , p and q are arbitrary positive integers. The program automatically produces a list of determining equations for the coefficients of the vector field. This list has been parsed so that it is free of duplicate equations and trivial differential redundancies. Numerical factors and non-zero parameters occurring as factors are also removed. From the solution of these determining equations one can construct the Lie symmetry group. An example shows the use of the program in batch mode. It also illustrates a feedback mechanism, that not only allows the treatment of a large number of complicated partial differential equations but also aids in solving the determining equations step by step.

Nonlinear optical properties of quasilinear conjugated oligomers, polymers and organic molecules

Recent developments concerning the nonlinear optical (NLO) properties of quasilinear conjugated oligomers, polymers and organic molecules are reviewed. Although our approach is from a theoretical perspective, it is oriented towards the practical design of both second- and third-order NLO materials. Since the field is relatively new, we critically assess the current state of knowledge and indicate where further investigations are needed. Some of the topics covered, which have received limited attention in the past, are vibrational hyperpolarizabilities, the potential for enhancement of NLO response due to formation of charged structures, and the quantitative role of the solid-state medium. After the introduction there is a section on the theoretical background which presents the formal expressions that are needed, introduces the available computational methodology and points out its limitations especially when applied to large systems. Then we discuss the results that have been obtained, starting with some...

Relay-Selection Improves the Security-Reliability Trade-Off in Cognitive Radio Systems

We consider a cognitive radio (CR) network consisting of a secondary transmitter (ST), a secondary destination (SD) and multiple secondary relays (SRs) in the presence of an eavesdropper, where the ST transmits to the SD with the assistance of SRs, while the eavesdropper attempts to intercept the secondary transmission. We rely on careful relay selection for protecting the ST-SD transmission against the eavesdropper with the aid of both single-relay and multi-relay selection. To be specific, only the “best” SR is chosen in the single-relay selection for assisting the secondary transmission, whereas the multi-relay selection invokes multiple SRs for simultaneously forwarding the STs transmission to the SD. We analyze both the intercept probability and outage probability of the proposed single-relay and multi-relay selection schemes for the secondary transmission relying on realistic spectrum sensing. We also evaluate the performance of classic direct transmission and artificial noise based methods for the purpose of comparison with the proposed relay selection schemes. It is shown that as the intercept probability requirement is relaxed, the outage performance of the direct transmission, the artificial noise based and the relay selection schemes improves, and vice versa. This implies a trade-off between the security and reliability of the secondary transmission in the presence of eavesdropping attacks, which is referred to as the security-reliability trade-off (SRT). Furthermore, we demonstrate that the SRTs of the single-relay and multi-relay selection schemes are generally better than that of classic direct transmission, explicitly demonstrating the advantage of the proposed relay selection in terms of protecting the secondary transmissions against eavesdropping attacks. Moreover, as the number of SRs increases, the SRTs of the proposed single-relay and multi-relay selection approaches significantly improve. Finally, our numerical results show that as expected, the multi-relay selection scheme achieves a better SRT performance than the single-relay selection.

Recursive least squares constant modulus algorithm for blind adaptive array

We consider the problem of blind adaptive signal separation with an antenna array, based on the constant modulus (CM) criterion. An approximation to the CM cost function is proposed, which allows the use of the recursive least squares (RLS) optimization technique. A novel RLS constant modulus algorithm (RLS-CMA) is derived, where the modulus power of the array output can take on arbitrary positive real values (i.e., fractional values allowed). Simulations are performed to compare the performance of the proposed RLS-CMA to other well-known algorithms for blind adaptive beamforming. Results indicate that the RLS-CMA has a significantly faster convergence rate and better tracking ability.

Calculation of electric dipole (hyper)polarizabilities by long-range-correction scheme in density functional theory: A systematic assessment for polydiacetylene and polybutatriene oligomers

The long-range correction (LC) for treating electron exchange in density functional theory, combined with the Becke-Lee-Yang-Parr (BLYP) exchange-correlation functional, was used to determine (hyper)polarizabilities of polydiacetylene/polybutatriene oligomers. In comparison with coupled-cluster calculations including single and double excitations as well as a perturbative treatment of triple excitations, our values indicate that the tendency of conventional functionals to result in a catastrophic overshoot for these properties is alleviated but not eliminated. No clear-cut preference for LC-BLYP over Hartree-Fock values is obtained. This analysis is consistent with the calculations of Sekino et al. [J. Chem. Phys. 126, 014107 (2007)] on polyacetylene and molecular hydrogen oligomers. Thus, the performance of LC-BLYP with regard to (hyper)polarizabilities of quasilinear conjugated systems is now well characterized.

Adaptive eigendecomposition of data covariance matrices based on first-order perturbations

In this paper, new algorithms for adaptive eigendecomposition of time-varying data covariance matrices are presented. The algorithms are based on a first-order perturbation analysis of the rank-one update for covariance matrix estimates with exponential windows. Different assumptions on the eigenvalue structure lead to three distinct algorithms with varying degrees of complexity. A stabilization technique is presented and both issues of initialization and computational complexity are discussed. Computer simulations indicate that the new algorithms can achieve the same performance as a direct approach in which the exact eigendecomposition of the updated sample covariance matrix is obtained at each iteration. Previous algorithms with similar performance require O(LM/sup 2/) complex operations per iteration, where L and M respectively denote the data vector and signal-subspace dimensions, and involve either some form of Gram-Schmidt orthogonalization or a nonlinear eigenvalue search. The new algorithms have parallel structures, sequential operation counts of order O(LM) or less, and do not involve any of the above steps. One particular algorithm can be used to update the complete signal-subspace eigenstructure in 5LM complex operations. This represents an order of magnitude improvement in computational complexity over existing algorithms with similar performance. Finally, a simplified local convergence analysis of one of the algorithms shows that it is stable and converges in the mean to the true eigendecomposition. The convergence is geometrical and is characterized by a single time constant. >