Conjugate gradient adaptive matched filter

We consider an adaptive reduced-rank detector, referred to as the CG-AMF detector, which is obtained by using the conjugate gradient (CG) algorithm to solve for the weight vector of the adaptive matched filter (AMF). The CG is a computationally efficient iterative algorithm, which finds the projection of the AMF weight vector to the Krylov subspace with a dimension growing with the CG iterations. This effectively leads to a family of reduced-rank detectors indexed by the number of CG iterations. The main purpose of this paper is to examine the output signal-to-interference-and-noise ratio (SINR) of the CG-AMF detector in the presence of strong clutter/interference. Specifically, by exploiting a connection between the CG algorithm and the Lanczos algorithm, we show the output SINR can be asymptotically expressed in a simple form involving a Ritz vector of the sample covariance matrix. The probability density function (pdf) and expected value of the output SINR are then obtained based on this approximation. Our theoretical analysis of the CG-AMF detector is verified by computer simulation. Numerical comparisons are also made with several popular reduced-rank detectors using either data-independent or data-dependent rank reduction approaches. Our results show that for a fixed training size, the CG-AMF detector often reaches its peak output SINR with a lower rank compared with the other reduced-rank detectors, which implies that the CG-AMF detector has lower computational complexity and less training requirement.