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.

In this paper, we propose an array pattern synthesis scheme using semidefinite programming (SDP) under array excitation power constraints. When an array pattern synthesis problem is formulated as an SDP problem, it is known that an additional rank-one constraint is generated inevitably and relaxed via semidefinite relaxation. If the solution to the relaxed SDP problem is not of rank one, then conventional SDP-based array pattern synthesis approaches fail to obtain optimal solutions because the additional rank-one constraint is not handled appropriately. To overcome this drawback, we adopted a bisection technique combined with a penalty function method. Numerical applications are presented to demonstrate the validity of the proposed scheme.

In this paper, we propose a beamformer design scheme for wireless physical layer security using partial channel state information (CSI) in millimeter wave channels. The partial CSI used in this work is the range of angle-of-departure (AOD). Assuming that the AOD range of each node is available, we design a transmit beamformer using semidefinite programming based on array pattern synthesis. Numerical results are presented to verify the secrecy rates achieved by the proposed scheme.