Robust Nonlinear Array Interpolation for Direction of Arrival Estimation of Highly Correlated Signals

Abstract Important signal processing techniques need that the response of the different elements of a sensor array have specific characteristics. For physical systems this often is not achievable as the array elements’ responses are affected by mutual coupling or other effects. In such cases, it is necessary to apply array interpolation to allow the application of ESPRIT, Forward Backward Averaging (FBA), and Spatial Smoothing (SPS). Array interpolation provides a model or transformation between the true and a desired array response. If the true response of the array becomes more distorted with respect to the desired one or the considered region of the field of view of the array increases, nonlinear approaches become necessary. This work presents two novel methods for sector discretization. An Unscented Transform (UT) based method and a principal component analysis (PCA) based method are discussed. Additionally, two novel nonlinear interpolation methods are developed based on the nonlinear regression schemes Multivariate Adaptive Regression Splines (MARS) and Generalized Regression Neural Networks (GRNNs). These schemes are extended and applied to the array interpolation problem. The performance of the proposed methods is examined using simulated and measured array responses of a physical system used for research on mutual coupling in antenna arrays.

[1]  T. P. Bronez Sector interpolation of non-uniform arrays for efficient high resolution bearing estimation , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[2]  Achim Dreher,et al.  Miniaturized DRA array for GNSS applications , 2015, 2015 9th European Conference on Antennas and Propagation (EuCAP).

[3]  Marius Pesavento,et al.  Virtual array design for array interpolation using differential geometry , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[4]  Donald F. Specht,et al.  A general regression neural network , 1991, IEEE Trans. Neural Networks.

[5]  Benjamin Friedlander,et al.  The root-MUSIC algorithm for direction finding with interpolated arrays , 1993, Signal Process..

[6]  Alfred O. Hero,et al.  Space-alternating generalized expectation-maximization algorithm , 1994, IEEE Trans. Signal Process..

[7]  André Lima Férrer de Almeida,et al.  Multidimensional Array Interpolation Applied to Direction of Arrival Estimation , 2015, WSA.

[8]  Marius Pesavento,et al.  A new approach to array interpolation by generation of artificial shift invariances: interpolated ESPRIT , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[9]  Yoram Bresler,et al.  Exact maximum likelihood estimation of superimposed exponential signals in noise , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[10]  Tuomas Virtanen,et al.  Monaural Sound Source Separation by Nonnegative Matrix Factorization With Temporal Continuity and Sparseness Criteria , 2007, IEEE Transactions on Audio, Speech, and Language Processing.

[11]  Florian Roemer,et al.  Multi-dimensional model order selection , 2011, EURASIP J. Adv. Signal Process..

[12]  Thomas Kailath,et al.  Detection of signals by information theoretic criteria , 1985, IEEE Trans. Acoust. Speech Signal Process..

[13]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[14]  André Lima Férrer de Almeida,et al.  Array interpolation based on multivariate adaptive regression splines , 2016, 2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM).

[15]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[16]  M. S. Babtlett Smoothing Periodograms from Time-Series with Continuous Spectra , 1948, Nature.

[17]  B. Friedlander,et al.  Direction finding using spatial smoothing with interpolated arrays , 1992 .

[18]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[19]  Thomas Kailath,et al.  ESPRIT-estimation of signal parameters via rotational invariance techniques , 1989, IEEE Trans. Acoust. Speech Signal Process..

[20]  J. Freidman,et al.  Multivariate adaptive regression splines , 1991 .

[21]  Erik G. Larsson,et al.  Massive MIMO for next generation wireless systems , 2013, IEEE Communications Magazine.

[22]  Charles Elkan,et al.  Expectation Maximization Algorithm , 2010, Encyclopedia of Machine Learning.

[23]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[24]  P. Stoica,et al.  Novel eigenanalysis method for direction estimation , 1990 .

[25]  Z. Luo,et al.  Robust array interpolation using second-order cone programming , 2002, IEEE Signal Processing Letters.

[26]  Buon Kiong Lau,et al.  An improved array interpolation approach to DOA estimation in correlated signal environments , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[27]  Josef A. Nossek,et al.  A signal adaptive array interpolation approach with reduced transformation bias for DOA estimation of highly correlated signals , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[28]  Arthur Jay Barabell,et al.  Improving the resolution performance of eigenstructure-based direction-finding algorithms , 1983, ICASSP.

[29]  M. Haardt,et al.  Enhanced Model Order Estimation using Higher-Order Arrays , 2007, 2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers.

[30]  João Paulo Carvalho Lustosa da Costa,et al.  Unscented Transformation based array interpolation , 2015, 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[31]  Buon Kiong Lau,et al.  Data-adaptive array interpolation for DOA estimation in correlated signal environments , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[32]  P. P. Vaidyanathan,et al.  Coprime coarray interpolation for DOA estimation via nuclear norm minimization , 2016, 2016 IEEE International Symposium on Circuits and Systems (ISCAS).

[33]  Björn E. Ottersten,et al.  Analysis of subspace fitting and ML techniques for parameter estimation from sensor array data , 1992, IEEE Trans. Signal Process..

[34]  Mohammad Ali Sebt,et al.  Array Interpolation Using Covariance Matrix Completion of Minimum-Size Virtual Array , 2017, IEEE Signal Processing Letters.

[35]  S. Unnikrishna Pillai,et al.  Forward/backward spatial smoothing techniques for coherent signal identification , 1989, IEEE Trans. Acoust. Speech Signal Process..

[36]  André Quinquis,et al.  A New Method for Estimating the Number of Harmonic Components in Noise with Application in High Resolution Radar , 2004, EURASIP J. Adv. Signal Process..

[37]  Bjorn Ottersten,et al.  Exact and Large Sample ML Techniques for Parameter Estimation and Detection in Array Processing , 1993 .

[38]  James E. Evans,et al.  Application of Advanced Signal Processing Techniques to Angle of Arrival Estimation in ATC Navigation and Surveillance Systems , 1982 .

[39]  Josef A. Nossek,et al.  The Extended Invariance Principle for Signal Parameter Estimation in an Unknown Spatial Field , 2011, IEEE Transactions on Signal Processing.

[40]  Michael I. Miller,et al.  Maximum-likelihood narrow-band direction finding and the EM algorithm , 1990, IEEE Trans. Acoust. Speech Signal Process..