A Multifamily GLRT for CFAR Detection of Signals in a Union of Subspaces

You are here

Top Reasons to Join SPS Today!

1. IEEE Signal Processing Magazine
2. Signal Processing Digital Library*
3. Inside Signal Processing Newsletter
4. SPS Resource Center
5. Career advancement & recognition
6. Discounts on conferences and publications
7. Professional networking
8. Communities for students, young professionals, and women
9. Volunteer opportunities
10. Coming soon! PDH/CEU credits
Click here to learn more.

A Multifamily GLRT for CFAR Detection of Signals in a Union of Subspaces

Francois-Xavier Socheleau

Testing whether a signal lies within a known subspace is a well-studied problem in the framework of matched-subspace detectors [1][2][3][4][5][6]. However, in practice, signals are often generated by multimodal processes so that there is not one but several possible subspace models. Among the set of possible models, the active subspace that generated the observed signal may be unknown a priori. This kind of signals complies with what is referred to as the UoS model. More precisely, xRN is an unknown signal belonging to some union of M known subspaces, i.e., xMi=1Si, if and only if there exists i0 such that xSi0 [7]. In other words, x belongs to one of the subspace Si, but we do not know a priori to which one. UoS examples include signals with unknown spectral support [7], spectral signatures of radar targets [8] or sparse representations [9].

Signal detection under the UoS model has been partly addressed in the literature in the specific case where all subspaces are distinct, i. e., there are no subspaces in the union such that SiS, for i [8][9][10]. All these works resort to the GLRT and estimate the active subspace index i0 as the one that maximizes the likelihood functions. By assuming distinct subspaces, these methods fail to handle nested models properly. In our UoS context, nesting occurs when the signal can be expressed as the sum of an unknown number of basis vectors so that SiS, for 1i<M. Examples include signals of unknown duration, periodic signal with an unknown number of harmonics, signals transmitted through an unknown multipath channel, etc. In that case, the GLRT always chooses the subspace model with the largest dimension leading to possible detection losses. More generally, problems arise with the GLRT when subspaces are of different dimensions and are not pairwise disjoint.

In [11], the MFLRT has been introduced as a general solution to accommodate nested signal models. The idea is to add a penalty term to the GLR statistic to counteract its tendency to increase with the model order. More recently, a new normalizing transformation has been introduced in [12]. It generalizes the results of [11] and relies on the Legendre transform of the cumulant generating function (LT-CGF) of the test statistic. Although effective for various applications [13][14], these results are not directly applicable to our context since the GLR statistic involved in our problem does not satisfy the required properties.

SPS on Twitter

  • DEADLINE EXTENDED: There's still time to submit your proposal to host the 2023 IEEE International Symposium on Biom… https://t.co/IyGtA3abJj
  • The 35th Picture Coding Symposium is heading to Bristol, UK and is now accepting papers for their June event! Head… https://t.co/sn8KNrKrBA
  • Deadline to submit to has been extended to 25 January! https://t.co/INpP2KrzoH
  • CALL FOR PAPERS: The 2021 IEEE International Conference on Autonomous Systems is now accepting papers for their Aug… https://t.co/IodWdsdLKc
  • The Brain Space Initiative Talk Series continues Friday, 15 January at 11:00 AM EST when Dr. Eva Dyer presents "Rep… https://t.co/fHP98guH0Z

SPS Videos

Signal Processing in Home Assistants


Multimedia Forensics

Careers in Signal Processing             


Under the Radar