Sustainability-aware user association for RIS-assisted mmWave networks in dense blockage environment

Millimeter wave (mmWave) technology offers vast bandwidth and ultra-high data rates but suffers from severe path loss and blockages. Reconfigurable intelligent surfaces (RISs) can mitigate the impact of blockages, but dense deployment of RISs adversely affect the overall energy requirement of the network. However, most of the existing work on RIS-assisted mmWave networks either assume passive RIS operation or rely on external power supply. The need to consider sustainable RIS operation in user association remains unaddressed, where sustainability refers to the RIS's ability to operate continuously by harvesting energy from received RF signals without an external power source. This paper incorporates the concept of RIS energy sustainability into the user association probability of an RIS-assisted link. In this paper, a stochastic geometry based analytical framework for user association in a mmWave network assisted by self-sustainable RISs has been proposed. In addition, a baseline model for a conventional RIS-assisted link has also been developed that serves as a benchmark for comparison with the proposed model. Unlike conventional approach, each RIS in the proposed model operates in a self-sustainable manner. We have introduced a two-stage thinning process to identify RISs that are simultaneously in line-of-sight (LoS) with the user and capable of sustainable operation. Analytical expressions for RIS sustainability probability and user association probability have been derived, considering both direct, sustainable and conventional RIS-assisted communication links. We have performed a comparison of our proposed model with a learning based Deep Deterministic Policy Gradient (DDPG) model to validate the applicability of the proposed model for dense urban mmWave networks. The results obtained in this investigation reveal that increasing RIS deployment density significantly enhances the availability of sustainable LoS RISs, thereby improving the sustainability-aware user association probability and reducing outage in dense blockage environments. However, in highly dense environments, a tradeoff exists between increasing RIS deployment density to improve user association probability and ensuring self-sustainable RIS operation, thereby revealing a feasible RIS deployment region for sustainable operation. We demonstrate that, the proposed system remains fair and computationally inexpensive under varying network load, highlighting its applicability for large-scale and dense networks.