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.

中文翻译：

---

k-单纯形变换的几何序列分解

本文提出了一种分解非正交叠加的计算效率高的技术。 $千$ 几何序列。该方法称为几何序列分解 $千$ -simplexes 变换 (GSD-ST)，基于将观察到的序列转换为多个的概念 $千$ - 虚拟中的单纯形 $千$ 维空间并关联转换后单纯形的体积。因此，GSD-ST 将分解问题 $千$ 几何序列转化为求解一个 $千$ -th 阶多项式方程。我们的技术对无线通信具有重要意义，因为无线电波的采样点包括几何序列。这意味着 GSD-ST 能够解调随机组合的无线电波，从而消除干扰的影响。为了举例说明 GSD-ST 的潜力，我们提出了一种新的无线电接入方案，即非正交无干扰无线电接入 (No-INFRA)。在此，GSD-ST 实现了非协调访问请求的无冲突接收。数值结果表明，当干扰占优势时，No-INFRA 有效地解决了冲突接入请求。