Geographical Fairness in Multi-RIS-Assisted Networks in Smart Cities: A Robust Design

Abstract

In this work, we consider a typical scenario in a harsh urban propagation environment which is typical for a smart city scenario where multiple reconfigurable intelligent surfaces (RISs) are deployed in different hotspot areas to overcome signal blockage between the base station and users. Our goal is to ensure uninterrupted service availability to users in different hotspot areas regardless of their location. Consistent service availability can be achieved by guaranteeing that each RIS deployed in a hotspot area can support a certain number of users. This plays a critical role in smart city applications in the context of emergency communications and ubiquitous connectivity since the design ensures service availability to as many users as possible in all relevant locations. Taking into consideration the challenges in obtaining channel state information (CSI) given the passive nature of RIS and dynamic environments, we formulate a robust fairness problem to maximize the minimum expected number of served users in proximity to each RIS while considering the available transmit power and the worst-case quality of service (QoS) constraints within the bounded CSI error model framework. The resulting problem is a mixed integer non-convex program which is highly coupled and challenging to solve in polynomial time. Thus, we resort to binary variable relaxation, convex approximation techniques, and alternating optimization to tackle the problem. Additionally, we handle the semi-infinite uncertainty constraints by employing the S-procedure and general sign-definiteness. Simulation results demonstrate the effectiveness of the proposed design in obtaining consistent and reliable service in different hotspot areas compared to the relevant benchmark schemes. In addition, the proposed design shows flexibility in serving users with their target QoS given different channel uncertainty levels.