The Interplay of Spectral Efficiency, User Density, and Energy in Grant-Based Access Protocols

We employ grant-based access with retransmissions for multiple users with small payloads, particularly at low spectral efficiency (SE). The radio resources are allocated via non-orthogonal multiple access (NOMA) in the time into
$T$
slots and frequency dimensions, with a measure of non-orthogonality
$\eta $
. Retransmissions are stored in a receiver buffer with a finite size
$C_{\sf buf}$
and combined via Hybrid Automatic Repeat reQuest (HARQ), using Chase Combining (CC) and Incremental Redundancy (IR). We determine the best scaling for the SE (bits/rdof) and for the user density
$J/n$
, for a given number of users
$J$
and a blocklength
$n$
, versus signal-to-noise ratio (SNR,
$\rho $
) per bit, i.e., the ratio
$E_{b}/N_{0}$
, for the sum-rate optimal regime and when the interference is treated as noise (TIN), using a finite blocklength analysis. Contrasting the classical scheme (no retransmissions) with CC-NOMA, CC-OMA, and IR-OMA strategies in TIN and sum-rate optimal cases, the numerical results on the SE demonstrate that CC-NOMA outperforms, almost in all regimes, the other approaches. For high
$C_{\sf buf}$
and small
$\eta $
, IR-OMA could surpass CC-NOMA. At low
$E_{b}/N_{0}$
, the SE of CC-OMA with TIN, as it exploits CC and offers lower interference, can approach the trend of CC-NOMA and outperform the other TIN-based methods. In the sum-rate optimal regime, the scalings of
$J/n$
versus
$E_{b}/N_{0}$
deteriorate with
$T$
, yet from the most degraded to the least, the ordering of the schemes is as 1) classical, 2) CC-OMA, 3) IR-OMA, and 4) CC-NOMA, demonstrating the robustness of CC-NOMA. Contrasting TIN models at low
$\rho $
, the scalings of
$J/n$
for CC-based models improve the best, whereas, at high
$\rho $
, the scaling of CC-NOMA is poor due to higher interference, and CC-OMA becomes prominent due to combining retransmissions and its reduced interference. The scaling results are applicable over a range of
$\eta $
,
$T$
,
$C_{\sf buf}$
, and
$J$
, at low received SNR. The proposed analytical framework provides insights into resource allocation in grant-based access and specific 5G use cases for massive ultra-reliable low-latency communications (URLLC) uplink access.