GLRT-based array receivers for the detection of a known signal with unknown parameters corrupted by noncircular interferences

The detection of a known signal with unknown parameters in the presence of noise plus interferences (called total noise) whose covariance matrix is unknown is an important problem which has received much attention these last decades for applications such as radar, satellite localization or time acquisition in radio communications. However, most of the available receivers assume a second order (SO) circular (or proper) total noise and become suboptimal in the presence of SO noncircular (or improper) interferences, potentially present in the previous applications. The scarce available receivers which take the potential SO noncircularity of the total noise into account have been developed under the restrictive condition of a known signal with known parameters or under the assumption of a random signal. For this reason, following a generalized likelihood ratio test (GLRT) approach, the purpose of this paper is to introduce and to analyze the performance of different array receivers for the detection of a known signal, with different sets of unknown parameters, corrupted by an unknown noncircular total noise. To simplify the study, we limit the analysis to rectilinear known useful signals for which the baseband signal is real, which concerns many applications.

[1]  Gonzalo Seco Granados,et al.  ML estimator and hybrid beamformer for multipath and interference mitigation in GNSS receivers , 2005 .

[2]  Michael S. Braasch,et al.  GPS receiver architectures and measurements , 1999, Proc. IEEE.

[3]  Gonzalo Seco-Granados,et al.  ML estimator and hybrid beamformer for multipath and interference mitigation in GNSS receivers , 2005, IEEE Transactions on Signal Processing.

[4]  Louis L. Scharf,et al.  Detection and estimation of improper complex random signals , 2005, IEEE Transactions on Information Theory.

[5]  Harry L. Van Trees,et al.  Detection, Estimation, and Modulation Theory, Part I , 1968 .

[6]  John D Mallett,et al.  Convergence Rate in Adaptive Arrays. , 1978 .

[7]  Pascal Chevalier,et al.  Second-Order Optimal Array Receivers for Synchronization of BPSK, MSK, and GMSK Signals Corrupted by Noncircular Interferences , 2007, EURASIP J. Adv. Signal Process..

[8]  P. Stoica,et al.  Maximum likelihood methods in radar array signal processing , 1998, Proc. IEEE.

[9]  Pascal Chevalier,et al.  Extensions of the minimum variance method , 1996, Signal Process..

[10]  Daniel R. Fuhrmann,et al.  A CFAR adaptive matched filter detector , 1992 .

[11]  Pascal Chevalier,et al.  Widely linear estimation with complex data , 1995, IEEE Trans. Signal Process..

[12]  Pierre-Olivier Amblard,et al.  Filtrage adapte dans le cas gaussien complexe non circulaire , 1995 .

[13]  Hai Deng,et al.  Effective CLEAN algorithms for performance-enhanced detection of binary coding radar signals , 2004, IEEE Transactions on Signal Processing.

[14]  Jean Pierre Delmas,et al.  Performance analysis of LRT/GLRT-based array receivers for the detection of a known real-valued signal corrupted by noncircular interferences , 2011, Signal Process..

[15]  P. M. Grant,et al.  Digital communications. 3rd ed , 2009 .

[16]  Jean Pierre Delmas,et al.  Asymptotic distribution of GLR for impropriety of complex signals , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[17]  Robert A. Scholtz,et al.  Acquisition of Spread Spectrum Signals by an Adaptive Array , 1986 .

[18]  I. Reed,et al.  Rapid Convergence Rate in Adaptive Arrays , 1974, IEEE Transactions on Aerospace and Electronic Systems.

[19]  L.E. Brennan,et al.  Theory of Adaptive Radar , 1973, IEEE Transactions on Aerospace and Electronic Systems.

[20]  N. L. Johnson,et al.  Multivariate Analysis , 1958, Nature.

[21]  E. J. Kelly.  An Adaptive Detection Algorithm , 1986, IEEE Transactions on Aerospace and Electronic Systems.

[22]  Bernard C. Picinbono,et al.  Second-order complex random vectors and normal distributions , 1996, IEEE Trans. Signal Process..

[23]  John G. Proakis,et al.  Digital Communications , 1983 .

[24]  Adriaan van den Bos,et al.  The multivariate complex normal distribution-a generalization , 1995, IEEE Trans. Inf. Theory.

[25]  William M. Brown,et al.  Conjugate linear filtering , 1969, IEEE Trans. Inf. Theory.

[26]  Randy L. Haupt,et al.  Introduction to Adaptive Arrays , 1980 .

[27]  Harry Leib,et al.  Maximizing SNR in improper complex noise and applications to CDMA , 1997, IEEE Communications Letters.

[28]  Irving Reed,et al.  An Adaptive Array Signal Processing Algorithm for Communications , 1982, IEEE Transactions on Aerospace and Electronic Systems.

[29]  Pascal Chevalier,et al.  GLRT-based array receivers to detect a known signal corrupted by noncircular interferences , 2007, 2007 15th European Signal Processing Conference.

[30]  Alfred Hanssen,et al.  A generalized likelihood ratio test for impropriety of complex signals , 2006, IEEE Signal Processing Letters.

[31]  Pascal Chevalier,et al.  New insights into optimal widely linear array receivers for the demodulation of BPSK, MSK, and GMSK signals corrupted by noncircular interferences-application to SAIC , 2006, IEEE Transactions on Signal Processing.

[32]  Bernard C. Picinbono,et al.  On circularity , 1994, IEEE Trans. Signal Process..

[33]  Pascal Chevalier,et al.  Widely Linear MVDR Beamformers for the Reception of an Unknown Signal Corrupted by Noncircular Interferences , 2007, IEEE Transactions on Signal Processing.

[34]  A. Zoubir,et al.  EURASIP Journal on Advances in Signal Processing , 2011 .

[35]  James L. Massey,et al.  Proper complex random processes with applications to information theory , 1993, IEEE Trans. Inf. Theory.

[36]  Jean Pierre Delmas,et al.  On the asymptotic distribution of GLR for impropriety of complex signals , 2011, Signal Process..

[37]  H. V. Trees.  Detection, Estimation, And Modulation Theory , 2001 .