Analysis of the conjugate gradient matched filter

Chaoshu Jiang, Hongbin Li, Muralidhar Rangaswamy

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

We consider the conjugate gradient (CG) algorithm for the calculation of the weight vector of the optimum matched filter (MF). As an iterative algorithm, it produces a series of approximations to the optimum MF weight vector, each of which can be used to filter the test signal and form a test statistic. This effectively leads to a family of detectors, referred to as the CG-MF detectors, which are indexed by k the number of iterations incurred. We first consider a general case involving an arbitrary covariance matrix of the disturbance (including interference, noise, etc.) and show that all CG-MF detectors attain constant false alarm rate (CFAR) and, furthermore, are optimum in the sense that the k-th CG-MF detector yields the highest output signal-to-interference-and- noise ratio (SINR) among all linear detectors within the k-th Krylov subspace. We then consider a structured case frequently encountered in practice, where the covariance matrix of the disturbance contains a low-rank component (rank-r) due to dominant interference sources, a scaled identity due to the presence of a white noise, and a perturbation component containing the residual interference and/or due to the estimation error. We show that the (r + 1)-st CG-MF detector achieves CFAR and an output SINR nearly identical to that of the optimum MF detector which requires complete iterations of the CG algorithm till reaching convergence. Hence, the (r + 1)-st CG-MF detector can be used in place of the MF detector for significant computational saving when r is small.

Original languageEnglish
Title of host publicationRadarCon'11 - In the Eye of the Storm
Subtitle of host publication2011 IEEE Radar Conference
Pages480-485
Number of pages6
DOIs
StatePublished - 2011
Event2011 IEEE Radar Conference: In the Eye of the Storm, RadarCon'11 - Kansas City, MO, United States
Duration: 23 May 201127 May 2011

Publication series

NameIEEE National Radar Conference - Proceedings
ISSN (Print)1097-5659

Conference

Conference2011 IEEE Radar Conference: In the Eye of the Storm, RadarCon'11
Country/TerritoryUnited States
CityKansas City, MO
Period23/05/1127/05/11

Keywords

  • Krylov subspace
  • Space-time adaptive processing (STAP)
  • conjugate gradient method
  • matched filter

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