Abstract
We add to the many results on sample covariance matrix (SCM) dependent array processors by (i) weakening the traditional assumption of Gaussian data and (ii) providing for a class of array processors additional performance measures that are of value in practice. The data matrix is assumed drawn from a class of multivariate elliptically contoured (MEC) distributions. The performance measures include the exact probability density functions (PDFs), confidence regions, and moments of the weight vector (matrix), beam response, and beamformer output of certain SCM-based (SCB) array processors. The array processors considered include the SCB: (i) maximum-likelihood (ML) signal vector estimator, (ii) linearly constrained minimum variance beamformer (LCMV), (iii) minimum variance distortionless response beamformer (MVDR), and (iv) generalized sidelobe canceller (GSC) implementation of the LCMV beamformer. It is shown that the exact joint PDFs for the weight vectors/matrices of the aforementioned SCB array processors are a linear transformation from a complex multivariate extension of the standardized t-distribution. The SCB beam responses are generalized t-distributed, and the PDFs of the SCB beamformer outputs are given by Kummer's function. All but the beamformer outputs are shown to be completely invariant statistics over the class of MECs considered.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.