Adaptive detection using low rank approximation to a data matrix

Using an accurate formula for the error in approximating a low rank component, we calculate the performance of adaptive detection based on reduced-rank nulling. In this principal component inverse (PCI) method, one temporarily regards the interference as a strong signal to be enhanced. The resulting estimate of the interference waveform is subtracted from the observed data, and matched filtering is used to detect signal components in the residual waveform. We also present a generalized likelihood-ratio test (GLRT) for adaptively detecting a low rank signal in the presence of low rank interference. This approach leads to a test which is closely related to the PCI method and extends the PCI method to the case where strong signal components are present in the data. A major accomplishment of the work is our calculation of the statistics of the output of the matched filter for the case in which interference cancellation and signal detection are carried out on the same observed data matrix. That is, no separate data is used for adaptation. Examples are presented using both simulated data and real, active-sonar reverberation data from the ARSRP, the Acoustic Reverberation Special Research Program of the Office of Naval Research. >

[1]  C. Eckart,et al.  The approximation of one matrix by another of lower rank , 1936 .

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

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

[4]  S. Applebaum,et al.  Adaptive arrays , 1976 .

[5]  Loren W. Nolte,et al.  Performance evaluation of array processors for detecting Gaussian acoustic signals , 1977 .

[6]  T. T. Kadota,et al.  Efficient approximation of a family of noises for application in adaptive spatial processing for signal detection , 1980, IEEE Trans. Inf. Theory.

[7]  R. Kumaresan,et al.  Data adaptive signal estimation by singular value decomposition of a data matrix , 1982, Proceedings of the IEEE.

[8]  R. Kumaresan,et al.  Data-Adaptive Detection of a Weak Signal , 1983, IEEE Transactions on Aerospace and Electronic Systems.

[9]  I. P. Kirsteins.  On the Probability Density of Signal-to-Noise Ratio in an Improved Detector , 1985 .

[10]  I. Kirsteins,et al.  On the probability density of signal-to-noise ratio in an improved adaptive detector , 1984, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

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

[12]  Benjamin Friedlander,et al.  On the accuracy of the Kumaresan-Tufts method for estimating complex damped exponentials , 1987, IEEE Trans. Acoust. Speech Signal Process..

[13]  Louis L. Scharf,et al.  Rank reduction for modeling stationary signals , 1987, IEEE Trans. Acoust. Speech Signal Process..

[14]  Richard J. Vaccaro,et al.  The threshold analysis of SVD-based algorithms , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[15]  D. W. Tufts,et al.  Rapidly adaptive nulling of interference , 1989, IEEE 1989 International Conference on Systems Engineering.

[16]  Donald W. Tufts,et al.  Advances in principal component signal processing , 1989 .

[17]  Fu Li,et al.  Min-norm linear prediction for arbitrary sensor arrays , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[18]  Alex C. Kot,et al.  Analysis of estimation of signal parameters by linear-prediction at high SNR using matrix approximation , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[19]  Fu Li,et al.  Unified performance analysis of subspace-based estimation algorithms , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[20]  F. Li,et al.  Analysis of Min-Norm and MUSIC with arbitrary array geometry , 1990 .

[21]  D. Tufts,et al.  The effects of perturbations on matrix-based signal processing , 1990, Fifth ASSP Workshop on Spectrum Estimation and Modeling.

[22]  Donald W. Tufts,et al.  Estimation of the signal component of a data vector , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[23]  A Reduced-Rank Generalized Likelihood-Ratio Test , 1993 .