Analytical Modelling of NB-IoT Uplink Resource Split Between NPRACH and NPUSCH for Device Density Optimization
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Narrowband Internet of Things (NB-IoT) networks must support large numbers of sporadically active devices within a narrow uplink bandwidth. A key configuration choice is the split between random-access resources, Narrowband Physical Random Access Channel (NPRACH), and data-channel resources, Narrowband Physical Uplink Shared Channel (NPUSCH), which we capture with a single parameter, , defined as the fraction of uplink resources reserved for NPRACH. We develop a stylized analytical model that couples a multichannel slotted-ALOHA description of NPRACH with a simple NPUSCH capacity model and use it to characterize how the parameter affects random-access collisions, data-channel utilization, and end-to-end reliability. For representative single-cell parameters, the analysis indicates that very small values of , for example, below about 0.10, drive NPRACH into an overloaded regime with per-attempt collision probabilities exceeding 99 percent, while an intermediate range between 0.25 and 0.40 yields a stable operating region. Packet-level simulations for three traffic profiles, 30-byte, 150-byte, and 450-byte packets, confirm these trends and quantify their impact, relative to baseline configurations resembling typical deployments, tuning within the stable region increases the maximum supportable device density by approximately 61 to 238 percent, about 1.6 to 3.4 times, at a 99 percent packet-delivery target. These gains are achieved purely through software-level reconfiguration of the NPRACH/NPUSCH split, without changes to hardware or spectrum.
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