Geometric Sequence Decomposition With <i>k</i>-Simplexes Transform

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