On the conjugate gradient matched filter

Chaoshu Jiang, Hongbin Li, Muralidhar Rangaswamy

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

The conjugate gradient (CG) algorithm is an efficient method for the calculation of the weight vector of the matched filter (MF). As an iterative algorithm, it produces a series of approximations to the 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 kth 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. We show that the (r+1)st CG-MF detector achieves CFAR and an output SINR nearly identical to that of the 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. Numerical results are presented to verify the accuracy of our analysis for the CG-MF detectors.

Original languageEnglish
Article number6146461
Pages (from-to)2660-2666
Number of pages7
JournalIEEE Transactions on Signal Processing
Volume60
Issue number5
DOIs
StatePublished - May 2012

Keywords

  • Conjugate gradient method
  • Krylov subspace
  • matched filter
  • space-time adaptive processing (STAP)

Fingerprint

Dive into the research topics of 'On the conjugate gradient matched filter'. Together they form a unique fingerprint.

Cite this