Scale-invariant subspace detectors based on first- and second-order statistical models

Abstract: The problem is to detect a multi-dimensional source transmitting an unknown sequence of complex-valued symbols to a multi-sensor array. In some cases the channel subspace is known, and in others only its dimension is known. Should the unknown transmissions be treated as unknowns in a first-order statistical model, or should they be assigned a prior distribution that is then used to marginalize a first-order model for a second-order statistical model? This question motivates the derivation of subspace detectors for cases where the subspace is known, and for cases where only the dimension of the subspace is known. For three of these four models the GLR detectors are known, and they have been reported in the literature. But the GLR detector for the case of a known subspace and a second-order model for the measurements is derived for the first time in this paper. When the subspace is known, second-order generalized likelihood ratio (GLR) tests outperform first-order GLR tests when the spread of subspace eigenvalues is large, while first-order GLR tests outperform second-order GLR tests when the spread is small. When only the dimension of the subspace is known, second-order GLR tests outperform first-order GLR tests, regardless of the spread of signal subspace eigenvalues. For a dimension-1 source, first-order and second-order statistical models lead to equivalent GLR tests. This is a new finding.

 Autoría: Santamaria I., Scharf L.L., Ramirez D.,

 Fuente: IEEE Transactions on Signal Processing, 2020, 68, 6432-6443

Editorial: Institute of Electrical and Electronics Engineers, Inc.

 Año de publicación: 2020

Nº de páginas: 12

Tipo de publicación: Artículo de Revista

DOI: 10.1109/TSP.2020.3036725

ISSN: 1053-587X,1941-0476

Proyecto español: TEC2016-75067-C4-4-R ; PID2019-104958RB-C43 ; TEC2017-92552-EXP ; TEC2017-86921-C2-2-R

Url de la publicación: https://doi.org/10.1109/TSP.2020.3036725