Nonparametric Radio Maps Reconstruction Via Elastic Net Regularization with Multi-Kernels

Radio maps can provide insightful information about the wireless environment to improve flexibility and intelligence of wireless networks. Channel gain cartography aims at reconstructing the path loss of any two points in space given a finite number of measurements. In this paper, a linear tomographic projection method is used to model the shadowing attenuation between any two points in a map. More specifically, the shadowing attenuation is considered to be the weighted integral of an underlying spatial loss field (SLF). The learning process is nonparametric in the sense that no model for the associated weights function of the SLF is assumed. The problem is posed as a regression problem with elastic nets regularization, i.e., a linear combination of ℓ
₁
and ℓ
₂
regularization terms. Further, the multi-kernel framework is used as a nonlinear approach and an algorithm that addresses a non-convex problem by iterating between two convex ones is proposed. The algorithm relies on the alternating direction method of multipliers (ADMM) to iteratively find a solution. Numerical evaluation with synthetic data shows great potential and outperforms state of the art approaches.