Geometric Sequence Decomposition With k-Simplexes Transform

Abstract

This paper presents a computationally efficient technique for decomposing non-orthogonally superposed k geometric sequences. The method, which is named as geometric sequence decomposition with k-simplexes transform (GSD-ST), is based on the concept of transforming an observed sequence to multiple k-simplexes in a virtual k-dimensional space and correlating the volumes of the transformed simplexes. Hence, GSD-ST turns the problem of decomposing k geometric sequences into one of solving a k-th order polynomial equation. Our technique has significance for wireless communications because sampled points of a radio wave comprise a geometric sequence. This implies that GSD-ST is capable of demodulating randomly combined radio waves, thereby eliminating the effect of interference. To exemplify the potential of GSD-ST, we propose a new radio access scheme, namely non-orthogonal interference-free radio access (No-INFRA). Herein, GSD-ST enables the collision-free reception of uncoordinated access requests. Numerical results show that No-INFRA effectively resolves the colliding access requests when the interference is dominant.