Adaptive Subspace Signal Detection With Uncertain Partial Prior Knowledge: Off-Grid Problem and Efficient Implementation

Abstract

We consider signal detection in subspace interference with partial prior knowledge of the subspace. The problem was recently considered by Li et al. , where a subspace knowledge with learning (SKL) Bayesian model was proposed to leverage partial and uncertain knowledge of the subspace bases. The SKL, however, is based on the assumption that the subspace bases are a subset of a known overdetermined dictionary defined on a densely sampled frequency grid. Due to the so-called grid mismatch problem, i.e., the subspace bases may not be exactly on the frequency grid, there is a need to develop solutions that can exploit approximate prior knowledge, i.e., knowledge of frequency grid points close to the true frequencies but the latter themselves. In this paper, we extend the work by Li et al. and develop a modified SKL (mSKL) algorithm to exploit partial, approximate, and uncertain prior knowledge for subspace estimation and target detection. The mSKL is a Bayesian inference algorithm that can reject incorrect subspace bases, recover missing bases, and benefit approximately correct bases in the prior knowledge set. For computational efficiency, the recently introduced generalized approximate message passing (GAMP) is employed in the mSKL for efficient update of some posteriors. The resulting scheme, referred to as the mSKL-GAMP, is shown to offer competitive subspace recovery and target detection performance over a range of alternative methods in various scenarios with different grid mismatch levels.