Algebraic Algorithms to Separate Overlapping Secondary Surveillance Radar Replies

The secondary surveillance radar (SSR) is a transponder system used in air-traffic control (ATC). Due to growing traffic densities, it is increasingly likely that a ground station receives a mixture of responses of various aircraft, partly overlapping in frequency and time. Currently such "collisions" are disregarded, at a loss of system performance and reliability. In this paper, we propose to equip the ground station with an antenna array, and investigate techniques to blindly separate such a mixture based on source waveform properties. At baseband, a received SSR signal consists of a binary sequence with alphabet {0,1}, modulated by a complex exponential due to the residual carrier frequency. We present three algebraic algorithms to compute the separating beamformers by taking into account the particular modulation format of the received signal. The Cramer-Rao bound (CRB) is derived, extensive simulations are presented, and an experimental platform has been built to collect measurement data and demonstrate the algorithms.

[1]  D. Lawley.  TESTS OF SIGNIFICANCE FOR THE LATENT ROOTS OF COVARIANCE AND CORRELATION MATRICES , 1956 .

[2]  L. Lathauwer,et al.  Signal Processing based on Multilinear Algebra , 1997 .

[3]  Phillip A. Regalia,et al.  On the behavior of information theoretic criteria for model order selection , 2001, IEEE Trans. Signal Process..

[4]  G. Galati,et al.  Analysis of SSR signals by super resolution algorithms , 2004, Proceedings of the Fourth IEEE International Symposium on Signal Processing and Information Technology, 2004..

[5]  Nicolas Petrochilos,et al.  Algorithms for Separation of Secondary Surveillance Radar Replies , 2002 .

[6]  Alle-Jan van der Veen,et al.  Joint diagonalization via subspace fitting techniques , 2001, ICASSP.

[7]  Alle-Jan van der Veen,et al.  Algorithms to separate overlapping secondary surveillance radar replies , 2004, ICASSP.

[8]  Ed F. Deprettere,et al.  Analysis of joint angle-frequency estimation using ESPRIT , 2003, IEEE Trans. Signal Process..

[9]  Erkki Oja,et al.  Efficient Variant of Algorithm FastICA for Independent Component Analysis Attaining the CramÉr-Rao Lower Bound , 2006, IEEE Transactions on Neural Networks.

[10]  P. Comon,et al.  ICA-based technique for radiating sources estimation: application to airport surveillance , 1993 .

[11]  Nikos D. Sidiropoulos,et al.  Parallel factor analysis in sensor array processing , 2000, IEEE Trans. Signal Process..

[12]  Arie Yeredor,et al.  Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separation , 2002, IEEE Trans. Signal Process..

[13]  Pierre Comon,et al.  ML estimation of SSR signals, identifiability, and Cramer-Rao Bounds , 2000, 2000 10th European Signal Processing Conference.

[14]  Antoine Souloumiac,et al.  Jacobi Angles for Simultaneous Diagonalization , 1996, SIAM J. Matrix Anal. Appl..

[15]  J. Cardoso,et al.  Blind beamforming for non-gaussian signals , 1993 .

[16]  Karim Abed-Meraim,et al.  A least-squares approach to joint Schur decomposition , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[17]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[18]  Pierre Comon,et al.  Separation de signaux ZCM: application en radar SSR , 2003 .

[19]  P. Dooren,et al.  An improved algorithm for the computation of Kronecker's canonical form of a singular pencil , 1988 .

[20]  Eric Moulines,et al.  A blind source separation technique using second-order statistics , 1997, IEEE Trans. Signal Process..

[21]  Michael C. Stevens,et al.  Secondary Surveillance Radar , 1988 .

[22]  Pierre Comon,et al.  A zero-cumulant random variable and its applications , 2006, Signal Process..

[23]  Alle-Jan van der Veen,et al.  Asymptotic properties of the algebraic constant modulus algorithm , 2001, IEEE Trans. Signal Process..

[24]  Alle-Jan van der Veen,et al.  Separation of zero/constant modulus signals , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[25]  R. M. Trim.  Mode S: an introduction and overview , 1990 .

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

[27]  P. Tichavský,et al.  Efficient variant of algorithm fastica for independent component analysis attaining the cramer-RAO lower bound , 2005, IEEE/SP 13th Workshop on Statistical Signal Processing, 2005.

[28]  Y. Selen,et al.  Model-order selection: a review of information criterion rules , 2004, IEEE Signal Processing Magazine.

[29]  G. Galati,et al.  Separation of multiple secondary surveillance radar sources in a real environment by a novel projection algorithm , 2005, Proceedings of the Fifth IEEE International Symposium on Signal Processing and Information Technology, 2005..

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

[31]  Arogyaswami Paulraj,et al.  An analytical constant modulus algorithm , 1996, IEEE Trans. Signal Process..

[32]  A. Leshem,et al.  Finite sample identifiability of multiple constant modulus sources , 2002, Sensor Array and Multichannel Signal Processing Workshop Proceedings, 2002.