Ginibre sampling and signal reconstruction

Abstract

The spatial distribution of sensing nodes plays a crucial role in signal sampling and reconstruction via wireless sensor networks. Although homogeneous Poisson point process (PPP) model is widely adopted for its analytical tractability, it cannot be considered a proper model for all experiencing nodes. The Ginibre point process (GPP) is a class of determinantal point processes that has been recently proposed for wireless networks with repulsiveness between nodes. A modified GPP can be considered an intermediate class between the PPP (fully random) and the GPP (relatively regular) that can be derived as limiting cases. In this paper we analyze sampling and reconstruction of finite-energy signals in ℝd when samples are gathered in space according to a determinantal point process whose second order product density function generalizes to ℝd that of a modified GPP in ℝ2. We derive closed form expressions for sampled signal energy spectral density (ESD) and for signal reconstruction mean square error (MSE). Results known in the literature are shown to be sub-cases of the proposed framework. The proposed analysis is also able to answer to the fundamental question: does the higher regularity of GPP also imply an higher signal reconstruction accuracy, according to the intuition? Theoretical results are illustrated through a simple case study