Relay Selection and User Equipment Admission in Resource-Efficient NextG Sidelink Communications

5G/6G sidelink communications addresses the challenge of connecting outer UEs, which are unable to directly access a base station (gNodeB), through inner UEs that act as relays to connect to the gNodeB. The key performance indicators include the achievable rates, the number of outer UEs that can connect to a gNodeB, and the latency experienced by outer UEs in establishing connections. We consider problem of determining the assignment of outer UEs to inner UEs based on the channel, interference, and traffic characteristics. We formulate an optimization problem to maximize a weighted sum rate of UEs, where weights can represent priority, waiting time, and queue length. This optimization accommodates constraints related to channel and interference characteristics that influence the rates at which links can successfully carry assigned traffic. While an exhaustive search can establish an upper bound on achievable rates by this non-convex optimization problem, it becomes impractical for larger number of outer UEs due to scalability issues related to high computational complexity. To address this, we present a greedy algorithm that incrementally selects links to maximize the sum rate, considering already activated links. This algorithm, although effective in achieving high sum rates, may inadvertently overlook some UEs, raising concerns about fairness. To mitigate this, we introduce a fairness-oriented algorithm that adjusts weights based on waiting time or queue length, ensuring that UEs with initially favorable conditions do not unduly disadvantage others over time. We show that this strategy not only improves the average admission ratio of UEs but also ensures a more equitable distribution of service among them, thereby providing a balanced and fair solution to sidelink communications.