Geometric Sequence Decomposition with k-simplexes Transform
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This paper presents a computationally-efficient technique for decomposing the non-orthogonally superposed k geometric sequences. The method, namely geometric sequence decomposition with k-simplexes transform (GSD-ST), is based on the idea of transforming an observed sequence to multiple k-simplexes in a virtual k-dimensional space and correlating the volumes of the transformed simplexes. Hence, the GSD-ST turns the problem of decomposing k geometric sequences into a solving of a k-th order polynomial equation. Our technique has significance to wireless communications because sampled points of a radio wave comprise a geometric sequence. This means that the GSD-ST is capable of demodulating the randomly combined radio waves, thus eliminating the effect of interference. To exemplify the potential of GSD-ST, we propose a new radio access scheme, non-orthogonal interference-free radio access (No-INFRA), in which the 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.
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