[Show abstract][Hide abstract] ABSTRACT: In this correspondence, we provide a multiple hypothesis test to detect the number of latent noncircular signals in a complex Gaussian random vector. Our method sequentially tests the results of individual generalized likelihood ratio test (GLRT) statistics with known asymptotic distributions to form the multiple hypothesis detector. Specifically, we are able to set a threshold yielding a precise probability of error. This test can be used to statistically determine if a given complex observation is circular Gaussian, and if not, how many latent signals in the observation are noncircular. Simulations are used to quantify the performance of the detector as compared to a detector based on the minimum description length (MDL) criterion. The utility of the detector is shown by applying it to a beamforming application using independent component analysis (ICA).
IEEE Transactions on Signal Processing 12/2011; DOI:10.1109/TSP.2011.2162951 · 3.20 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The generalized Gaussian distribution (GGD) provides a flexible and suitable tool for data modeling and simulation, however the characterization of the complex-valued GGD, in particular generation of samples from a complex GGD have not been well defined in the literature. In this correspondence, we provide a thorough presentation of the complex-valued GGD by: (i) constructing the probability density function (pdf); (ii) defining a procedure for generating random numbers from the complex-valued GGD; and (iii) implementing a maximum likelihood estimation (MLE) procedure for the shape and covariance parameters in the complex domain. We quantify the performance of the MLE with simulations and actual radar data.
IEEE Transactions on Signal Processing 04/2010; 58(3-58):1427 - 1433. DOI:10.1109/TSP.2009.2036049 · 3.20 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Knowing the statistical properties of a complex-valued signal is important in many signal processing applications by providing the necessary information for choosing the appropriate algorithm. In this paper, we provide generalized likelihood ratio tests (GLRT), based on the complex generalized Gaussian distribution (CGGD), for detecting two important signal properties: 1) the circularity of a complex random variable, not constrained to the Gaussian case and 2) whether a complex random variable is complex Gaussian. These tests can be combined to statistically determine if a complex random variable is, the often assumed, circular Gaussian. Simulations are used to quantify the performance of the detectors followed by application to communication signals and actual radar data.
[Show abstract][Hide abstract] ABSTRACT: Target detection in sea clutter is a challenging problem in radar detection, specifically, when the Doppler return of the target and clutter are collocated. Polarization diverse radars provide additional information that enhances target detection. In this paper, we use an effective independent component analysis (ICA) approach, adaptive complex maximization of non-Gaussianity (A-CMN), to efficiently combine polarimetric radar data prior to detection. We show that A-CMN estimates the polarimetric scatter coefficients for the single target in clutter case, thereby providing matched-filter performance without the need for clutter or target models. The detection performance using ICA is evaluated with sea clutter collected with the McMaster IPIX radar off the coast of Canada. We also demonstrates the ability of this approach to adapt to the changing sea clutter conditions using simulation results.
Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009, 19-24 April 2009, Taipei, Taiwan; 01/2009
[Show abstract][Hide abstract] ABSTRACT: We introduce a framework based on Wirtinger calculus for nonlinear complex-valued signal processing such that all computations can be directly carried out in the complex domain. The two main approaches for performing independent component analysis, maximum likelihood, and maximization of non-Gaussianity-which are intimately related to each other-are studied using this framework. The main update rules for the two approaches are derived, their properties and density matching strategies are discussed along with numerical examples to highlight their relationships.
IEEE Transactions on Signal Processing 10/2008; 56(9-56):4536 - 4544. DOI:10.1109/TSP.2008.926104 · 3.20 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The complex fast independent component analysis (c-FastICA) algorithm is one of the most ubiquitous methods for solving the ICA problems with complex-valued data. In this study, we extend the work of Bingham and Hyvarinen to the more general case of noncircular sources by deriving a new fixed-point algorithm that uses the information in the pseudo-covariance matrix. This modification provides significant improvement in performance when confronted with noncircular sources, specifically with sub-Gaussian noncircular signals such as binary phase-shift keying (BPSK) signals, where c-FastICA fails to achieve separation. We also present a rigorous local stability analysis that we use to quantify the effects of noncircularity on performance. Simulations are presented to demonstrate the effectiveness of our method.
IEEE Transactions on Signal Processing 06/2008; 56(5-56):2148 - 2154. DOI:10.1109/TSP.2007.911278 · 3.20 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The complex fast independent component analysis (c-FastICA) algorithm is one of the most popular methods for solving the ICA problem with complex-valued data. In this study, we extend the work of Bingham and Hyvarinen  by deriving conditions for local stability for the more general case of noncircular sources. We use the results of the analysis to quantify the effects of noncircularity on the performance of the algorithm using various nonlinearities and source distributions. Simulations are presented to demonstrate the results of our analysis.
Acoustics, Speech and Signal Processing, 2008. ICASSP 2008. IEEE International Conference on; 05/2008
[Show abstract][Hide abstract] ABSTRACT: In this paper, we use complex analytic functions to achieve independent component analysis (ICA) by maximization of non-Gaussianity and introduce the complex maximization of non-Gaussianity (CMN) algorithm. We derive both a gradient-descent and a quasi-Newton algorithm that use the full second-order statistics providing superior performance with circular and noncircular sources as compared to existing methods. We show the connection among ICA methods through maximization of non-Gaussianity, mutual information, and maximum likelihood (ML) for the complex case, and emphasize the importance of density matching for all three cases. Local stability conditions are derived for the CMN cost function that explicitly show the effects of noncircularity on convergence and demonstrated through simulation examples.
[Show abstract][Hide abstract] ABSTRACT: We introduce a fixed-point algorithm, the complex QAM (C-QAM) algorithm, for separation of quadrature amplitude modulated (QAM) sources through independent component analysis. The algorithm matches the input QAM distribution through a mixture of Gaussian kernels and uses fixed-point updates that fully take advantage of complex domain processing. We demonstrate the performance of the C-QAM algorithm through simulations and note that it provides improved performance over a wide range of operating conditions such as low signal-to-noise ratio, small sample sizes, and large number of sources
Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on; 05/2007
[Show abstract][Hide abstract] ABSTRACT: Complex maximization of nonGaussianity (CMN) has been shown to provide reliable separation of both circular and non-circular sources using a class of complex functions in the non-linearity. In this paper, we derive a fixed-point algorithm for blind separation of noncircular sources using CMN. We also introduce the adaptive CMN (A-CMN) algorithm that provides significant performance improvement by adapting the nonlinearity to the source distribution. The ability of A-CMN to adapt to a wide range of source statistics is demonstrated by simulation results.
Machine Learning for Signal Processing, 2006. Proceedings of the 2006 16th IEEE Signal Processing Society Workshop on; 10/2006
[Show abstract][Hide abstract] ABSTRACT: Complex maximization of nongaussianity (CMN) has been shown to provide reliable separation of both circular and noncircular sources. It is also shown that the algorithm converges to the principal component of the source distribution when studied in the estimation direction. In this paper, we study the local stability of the CMN algorithm and determine the conditions under which local stability is achieved by extending our previous work to all dimensions of the weight vector. We use these conditions of stability to quantify convergence performance for a number of complex nonlinear functions, and present simulation results to demonstrate the effectiveness of these functions.
Acoustics, Speech and Signal Processing, 2006. ICASSP 2006 Proceedings. 2006 IEEE International Conference on; 06/2006
[Show abstract][Hide abstract] ABSTRACT: We use complex, hence analytic, functions to achieve independent component analysis (ICA) by maximization of nonGaussianity and introduce the complex maximization of nonGaussianity (CMN) algorithm. We show that CMN converges to the principal component of the source distribution and that the algorithm provides robust performance for both circular and non-circular sources
Machine Learning for Signal Processing, 2005 IEEE Workshop on; 10/2005