Reconfigurable intelligent surfaces (RISs) are envisioned to be a disruptive wireless communication technique that is capable of reconfiguring the wireless propagation environment. In this paper, we study a far-field RIS-assisted multiple-input singl
e-output (MISO) communication system operating in free space. To maximize the received power of the receiver from the physics and electromagnetic nature point of view, an optimization, including beamforming of the transmitter, phase shifts of the RIS, orientation and position of the RIS is formulated and solved. After exploiting the property of line-of-sight (LoS), we derive closed-form solutions of beamforming and phase shifts. For the non-trivial RIS position optimization problem in arbitrary three-dimensional space, a dimensional-reducing theory is proved. The simulation results show that the proposed closed-form beamforming and phase shifts are near-optimal solutions. Besides, the RIS significantly enhances the performance of the communication system when it is deployed at the optimal position.
This paper considers a secure multigroup multicast multiple-input single-output (MISO) communication system aided by an intelligent reflecting surface (IRS). Specifically, we aim to minimize the transmit power at the Alice via jointly optimizing the
transmit beamformer, AN vector and phase shifts at the IRS subject to the secrecy rate constraints as well as the unit modulus constraints of IRS phase shifts. However, the optimization problem is non-convex and directly solving it is intractable. To tackle the optimization problem, we first transform it into a semidefinite relaxation (SDR) problem, and then alternately update the transmit beamformer and AN matrix as well as the phase shifts at the IRS. In order to reduce the high computational complexity, we further propose a low-complexity algorithm based on second-order cone programming (SOCP). We decouple the optimization problem into two sub-problems and optimize the transmit beamformer, AN vector and the phase shifts alternately by solving two corresponding SOCP sub-problem. Simulation results show that the proposed SDR and SOCP schemes require half or less transmit power than the scheme without IRS, which demonstrates the advantages of introducing IRS and the effectiveness of the proposed methods.
Small $p$-values are often required to be accurately estimated in large scale genomic studies for the adjustment of multiple hypothesis tests and the ranking of genomic features based on their statistical significance. For those complicated test stat
istics whose cumulative distribution functions are analytically intractable, existing methods usually do not work well with small $p$-values due to lack of accuracy or computational restrictions. We propose a general approach for accurately and efficiently calculating small $p$-values for a broad range of complicated test statistics based on the principle of the cross-entropy method and Markov chain Monte Carlo sampling techniques. We evaluate the performance of the proposed algorithm through simulations and demonstrate its application to three real examples in genomic studies. The results show that our approach can accurately evaluate small to extremely small $p$-values (e.g. $10^{-6}$ to $10^{-100}$). The proposed algorithm is helpful to the improvement of existing test procedures and the development of new test procedures in genomic studies.
