Arnab K. Shaw

An algorithm for pole-zero modeling and spectral analysis

An explicit connection between fitting exponential models and pole-zero models to observed data is made. The fitting problem is formulated as a constrained nonlinear minimization problem. This problem is then solved using a simplified iterative algorithm. The algorithm is applied to simulated data, and the performance of the algorithm is compared to previous results.

Cognitive radio - an adaptive waveform with spectral sharing capability

The growth of wireless applications and spectral limitations are serious concerns for both the military and civilian communities. Cognitive radio (CR) technologies expand spectrum efficiency using elements of space, time and frequency diversity that up to now have not been exploited. An adaptive waveform (AW) generation technique is presented which adapts to the changing electromagnetic environment and synthesizes waveform features in the frequency domain. Spectral coexistence with other applications is also addressed and can be accomplished in both static and dynamic environments. Bit error rate (BER) serves as the primary performance metric for evaluating and comparing AW processing with other waveforms and systems.

Superresolution by structured matrix approximation

The bearing estimation problem is formulated as a matrix-approximation problem. The columns of a matrix X are formed by the snapshot vectors from an N-element array. The matrix X is then approximated by a matrix in the least-square sense. The rank as well as the partial structure of the space spanned by the columns of the approximated X matrix are prespecified. After the approximated X matrix is computed, the bearings of the sources and, consequently, the spatial correlation of the source signals are estimated. The performance of the proposed technique is compared with two existing methods using simulation. The comparison is made in terms of bias, mean-squared error, failure rates, and confidence intervals for the mean and the variance estimates for all three methods at different signal-to-noise ratios. When the sources are moving slowly and the number of snapshot vectors available for processing is large, a simple online adaptive algorithm is suggested. >

A general overlay/underlay analytic expression representing cognitive radio waveform

Several studies have revealed that spectrum congestion is primarily due to the inefficient use of spectrum versus unavailability. Cognitive radio (CR) and ultra wide band (UWB) technologies have been proposed as candidates to address this problem. Currently, a CR determines unused frequency bands and transmits overlay waveforms in these bands, while UWB transmits underlay waveforms that span the entire frequency band while coexisting with primary users. This suggests that most of the spectrum occupied by primary users is underused. This work proposes a general soft decision cognitive radio (SDCR) framework, based on a previous developed spectrally modulated, spectrally modulated (SMSE) framework, to combine benefits of overlay/underlay techniques while maximizing channel capacity. We also show that current CR and UWB implementations represent two extreme SDCR cases and that current overlay/underlay waveforms are two special cases of the general waveform platform.

Frequency estimation by principal component AR spectral estimation method without eigendecomposition

An eigenvalue filtering method is proposed that applies a transformation to an autocorrelation matrix, which has the effect of truncating the undesired eigenvalues so that the corresponding matrix function closely approximates the pseudoinverse. It is shown using a computer simulation that compared to the forward-backward method, the proposed method enhances the threshold in SNR by about 6-8 dB. Further improvement is obtained by a simple subset selection method and a second eigenvalue filtering iteration. >

Optimal identification of discrete-time systems from impulse response data

An optimal method (OM) for estimation of the parameters of rational transfer functions from prescribed impulse response data is presented. The multidimensional nonlinear fitting error minimization problem has been theoretically decoupled into two subproblems of reduced computational complexities. The proposed approach is applicable for identifying rational models with arbitrary numbers of poles and zeros. The nonlinear denominator subproblem possesses weighted-quadratic structure which is utilized to formulate an efficient iterative minimization algorithm. The optimal numerator is found noniteratively with a linear least-squares approach that utilizes the optimized denominator. Both the decoupled subcriteria of OM posses global optimality properties. The Steiglitz-McBride (1960, SM) method is also decoupled for arbitrary numbers of poles and zeros (DSM-G). It is demonstrated that the denominator subproblem of DSM-G is theoretically optimal. For another existing decoupled SM method (DSM-J), it has been shown that only the numerator is theoretically optimal. >

Estimation of angles of arrivals of broadband signals

A high resolution one-step algorithm for estimating the angles of arrivals of multiple wideband sources is proposed. For a dense and equally spaced array structure, a bilinear transformation is utilized in frequency domain for coherent signal subspace processing. When compared with existing coherent approaches, the proposed algorithm is noniterative and does not need knowledge of initial estimates of the arrival angles. The performance of the algorithm is presented using simulated data.

Improved automatic target recognition using singular value decomposition

A new algorithm is presented for automatic target recognition (ATR) where the templates are obtained via singular value decomposition (SVD) of high range resolution (HRR) profiles. SVD analysis of a large class of HRR data reveals that the range-space eigenvectors corresponding to the largest singular value accounts for more than 90% of the target energy. Hence, it is proposed that the range-space eigenvectors be used as templates for classification. The effectiveness of data normalization and Gaussianization of profile data for improved classification performance is also studied. With extensive simulation studies it is shown that the proposed eigen-template based ATR approach provides consistent superior performance with the recognition rate reaching 99.5% for the four class XPATCH database.

Automatic target recognition using Eigen templates

This paper presents ATR results with High Range Resolution (HRR) profiles used for classification. It is shown that effective HRR-ATR performance can be achieved if the templates are formed via Singular Value Decomposition (SVD) of detected HRR profiles. It is demonstrated theoretically that in the mean-squared sense, the eigen-vectors represent the optimal feature set. SVD analysis of a large class of XPATCH and MSTAR HRR-data clearly indicates that significant proportion (> 90%) of target energy is accounted for by the eigen-vectors of range correlation matrix, corresponding to only the largest singular value. The SV Decomposition also decouples the range and angle basis spaces. Furthermore, it is shown that significant clutter reduction can be achieved if HRR data is reconstructed using only the significant eigenvectors. ATR results with eigen-templates are compared with those based on mean-templates. Results are included for both XPATCH and MSTAR data using linear least- squares and matched-filter based classifiers.

Some structured matrix approximation problems

An improved structured matrix approximation approach for simultaneous estimation of frequencies and wavenumbers from 2-D array data is proposed. A quasi-linear relationship of the error with the polynomial coefficients of both the spatial and temporal domains is derived. This leads to an iterative optimization of the error criterion simultaneously in both the domains. By performing simulations it is shown that the method is capable of resolving signals closely spaced in frequency and wavenumber at low SNR. Next, the extendibility of the method for least-squares fitting of Toeplitz/Hankel/data matrix to a given non-Toeplitz/Hankel/data matrix is also discussed.<<ETX>>