The Interplay of Spectral Efficiency, User Density, and Energy in Random Access Protocols with Retransmissions

The fifth-generation of wireless communication networks is required to support a range of use cases such as enhanced mobile broadband (eMBB), ultra-reliable, low-latency communications (URLLC), massive machine-type communications (mMTCs), with heterogeneous data rate, delay, and power requirements. The 4G LTE air interface uses extra overhead to enable scheduled access, which is not justified for small payload sizes. We employ a random access communication model with retransmissions for multiple users with small payloads at the low spectral efficiency regime. The radio resources are split non-orthogonally in the time and frequency dimensions. Retransmissions are combined via Hybrid Automatic Repeat reQuest (HARQ) methods, namely Chase Combining and Incremental Redundancy with a finite buffer size constraint $C_{\sf buf}$. We determine the best scaling for the spectral efficiency (SE) versus signal-to-noise ratio (SNR) per bit and for the user density versus SNR per bit, for the sum-optimal regime and when the interference is treated as noise, using a Shannon capacity approximation. Numerical results show that the scaling results are applicable over a range of $\eta$, $T$, $C_{\sf buf}$, $J$, at low received SNR values. The proposed analytical framework provides insights for resource allocation in general random access systems and specific 5G use cases for massive URLLC uplink access.