TY - GEN
T1 - Analysis of the conjugate gradient matched filter
AU - Jiang, Chaoshu
AU - Li, Hongbin
AU - Rangaswamy, Muralidhar
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
KW - Krylov subspace
KW - Space-time adaptive processing (STAP)
KW - conjugate gradient method
KW - matched filter
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U2 - 10.1109/RADAR.2011.5960584
DO - 10.1109/RADAR.2011.5960584
M3 - Conference contribution
AN - SCOPUS:80052472977
SN - 9781424489022
T3 - IEEE National Radar Conference - Proceedings
SP - 480
EP - 485
BT - RadarCon'11 - In the Eye of the Storm
T2 - 2011 IEEE Radar Conference: In the Eye of the Storm, RadarCon'11
Y2 - 23 May 2011 through 27 May 2011
ER -