Mathematical Modelling of Throughput in Peer-Assisted Symbiotic 6G with SIC and Relays

Sixth-generation (6G) communication systems, with ultra-wide bands, energy-autonomous end nodes, and dense connectivity, challenge existing network designs. Optimizing time resources with energy harvesting, backscatter communication, and relays is essential to maximize the total bit rate in multi-user symbiotic radio networks (SRNs) with blocked direct paths. The literature lacks a unified optimization treatment that explicitly accounts for imperfect successive interference cancellation (SIC). This study addresses this gap by proposing the first optimization framework to maximize total bit rate for energy-harvesting TDMA/PD–NOMA-based multi-cluster and relay-assisted peer-assisted SR networks. The two-phase architecture defines a tractable constrained optimization problem that jointly adjusts cluster-specific time slots (τ and λ). Incorporating QoS, signal power, and reflection coefficient constraints, it provides a compact formulation and numerical solutions for both perfect and imperfect SIC. Detailed simulations performed under typical 6G power levels, bandwidths, and energy-harvesting efficiencies demonstrate graphically that imperfect SIC significantly limits total throughput due to residual interference, while perfect SIC completely eliminates this ceiling under the same conditions, providing a significant capacity advantage. Furthermore, the gap between the two scenarios rapidly closes with increasing relay time margin. The findings demonstrate that network capacity is primarily determined by the triad of base station output power, channel noise, and SIC accuracy, and that the proposed framework achieves strong performance across the explored parameter space.