TY - JOUR
T1 - On the conjugate gradient matched filter
AU - Jiang, Chaoshu
AU - Li, Hongbin
AU - Rangaswamy, Muralidhar
PY - 2012/5
Y1 - 2012/5
N2 - 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.
AB - 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.
KW - Conjugate gradient method
KW - Krylov subspace
KW - matched filter
KW - space-time adaptive processing (STAP)
UR - http://www.scopus.com/inward/record.url?scp=84859977218&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84859977218&partnerID=8YFLogxK
U2 - 10.1109/TSP.2012.2187200
DO - 10.1109/TSP.2012.2187200
M3 - Article
AN - SCOPUS:84859977218
SN - 1053-587X
VL - 60
SP - 2660
EP - 2666
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 5
M1 - 6146461
ER -