Integrability of Lie systems through Riccati equations

Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides us with a unified geometrical viewpoint that allows us to analyse some previous works on the topic and explain new properties. Moreover, this new approach can be straightforwardly generalised to describe integrability conditions for any Lie system. Finally, we show the usefulness of our treatment in order to study the problem of the linearisability of Riccati equations.Comment: Corrected typo

JOINT TRANSMIT PRECODERS AND PASSIVE REFLECTION BEAMFORMER DESIGN IN IRS-AIDED IOT NETWORKS

peer reviewedThis work considers an IoT network comprising of several IoT sensor nodes (SNs), a passive intelligent reflecting surface (IRS), and a fusion center (FC). Each IoT SN observes multiple physical phenomena, and transmits its observations to the FC for post processing. This necessitates the need for efficient preprocessing of each SN's observations to combat wireless fading effects and optimize transmit power utilization. In this context, this paper presents a novel approach that jointly designs the transmit precoding matrix (TPM) for IoT SNs and optimizes the phase reflection matrix (PRM) for the IRS. The resulting non-convex optimization problem is tackled through an alternating optimization framework, where the individual TPM and PRM design subproblems are further addressed using the majorization minimization (MM) framework. Notably, the proposed solution yields closed-form expressions for TPM and PRM in each MM iteration, making it particularly suitable for low-cost IoT SNs. Numerical results demonstrate the efficacy of the proposed approach by showcasing significant enhancements in estimation performance compared to IoT networks lacking an IRS component.U-AGR-7061 - C20/IS/1499710/SENCOM - OTTERSTEN Björn9. Industry, innovation and infrastructur