Adaptive Channel Assignment for Maneuvering Target Tracking in Multistatic Passive Radar

Abstract

In this paper, two adaptive channel assignment (CA) schemes are proposed for maneuvering target tracking (MTT) in multistatic passive radar. For a predetermined total number of channels w.r.t. each receiver, (a) the first scheme selects <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> channels to achieve the highest MTT accuracy; (b) the second scheme minimizes the number of channels while guaranteeing a required MTT performance. By utilizing the best-fitting Gaussian approximation, we derive the predicted conditional Cramér-Rao lower bound to evaluate the impact of CA on MTT performance, and formulate CA schemes as convex integer program problems, since channel variables are in binary form. The objective in the first CA problem is smooth, so we apply the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{2}$</tex-math></inline-formula> -box alternating direction method of multipliers to divide it into several simple subproblems and alternatively solve them in continuous domains without the introduction of relaxation error. The second CA problem may be infeasible when the required accuracy cannot be met with available channels. To tackle it, we introduce a linear rectification function w.r.t the performance constraint, and equivalently reformulate it as a feasible one. Then, a fast multi-start add-one-channel policy is designed to minimize the gap between the actual accuracy and the accuracy requirement. These algorithms offer considerable reductions in computational complexity compared with the branch and bound method and may achieve near-optimal performance. Simulation results demonstrate that these schemes can either achieve the highest MTT accuracy with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> channels or reduce the number of channels while guaranteeing MTT performance, compared with the traditional random channel allocation scheme.