Compressive-Domain Interference Cancellation via Orthogonal Projection: How Small the Restricted Isometry Constant of the Effective Sensing Matrix Can Be?

Abstract

Knowledge of the achievable restricted isometry constant (RIC) of the sensing matrix is crucial for assessing the signal reconstruction performance of compressive sensing systems. In this paper we consider compressive-domain interference cancellation via orthogonal projection, and study the achievable RIC of the effective sensing matrix, namely, the product of the orthogonal projection matrix and the original sensing matrix. While existing algebraic based methods resorted to the polarization identity to find an upper bound of the considered RIC, motivated by geometric interpretations of the orthogonal projection and the restricted isometry property we derive an improved RIC in a closed form. The proposed solution is shown to be tighter than the existing upper bound. Our analytical results, and the asserted performance advantages, are further evidenced via computer simulations.