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

TL;DR

This work analyzes grant-based uplink access with HARQ and NOMA for massive, low-latency communications. By deriving SE and $E_b/N_0$ for sum-rate optimal and interference-as-noise decoders across CC-NOMA, CC-OMA, and IR-OMA, and by exploring the impact of retransmission count $T$, non-orthogonality $oldsymbol{ u}$, and decoder buffer $C_{ extsf{buf}}$, the authors reveal that CC-NOMA typically delivers the strongest SE scaling across many regimes, especially at low SNR per bit. CC-OMA provides robust performance with retransmissions by reducing interference, while IR-OMA can close the gap to classical schemes when buffer resources are ample. The results quantify the tradeoffs between spectral efficiency, energy per bit, and user density, offering design insights for 5G URLLC uplink use cases and guiding resource allocation under finite blocklength constraints. Overall, the framework highlights the favorable role of coordinated retransmissions and non-orthogonal sharing in pushing the density of supported users while controlling energy consumption.

Abstract

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 NOMA in the time into $T$ slots and frequency dimensions, with a measure of non-orthogonality $η$. Retransmissions are stored in a receiver buffer with a finite size $C_{\sf buf}$ and combined via 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 SNR ($ρ$) 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. 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 (i) classical, (ii) CC-OMA, (iii) IR-OMA, and (iv) CC-NOMA, demonstrating the robustness of CC-NOMA. Contrasting TIN models at low $ρ$, the scalings of $J/n$ for CC-based models improve the best, whereas, at high $ρ$, 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 $η$, $T$, $C_{\sf buf}$, 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 URLLC uplink access.

Figures (7)

• Figure 1: (a) Non-orthogonal user signatures at time slots $1$ and $t$. Each user uses the same signature across all time-frequency resources. The second user in slot $1$ is repeated in slot $t$ (same signature). (b) The frame structure where time is partitioned into $T$ transmit opportunities, and the time-frequency resources are shared in a non-orthogonal manner by the users.
• Figure 2: (Left) CC-HARQ, where the retransmissions contain the same data and parity bits, which are summed at the receiver prior to decoding. (Right) IR-HARQ, where each retransmission provides some additional bits, and is self-decodable.
• Figure 3: Scaling of SE versus $E_b/N_0$ for varying $T$ for $\eta=1$ and $J=10$. (Row I) moderate buffer size, $C_{\sf buf}=T$. (Row II) small buffer size, $C_{\sf buf}=0.1T$.
• Figure 4: Scaling of SE versus $E_b/N_0$. (Row I) $\eta=0.5$, $J=10$, $C_{\sf buf}=0.1T$. (Row II) $\eta=0.5$, $J=100$, $C_{\sf buf}=10T$.
• Figure 5: (Sum-rate optimal) Scaling of $J/n$ versus $E_b/N_0$ for varying $\rho$ and $C_{\sf buf}=10T$. (Rows I-II) $\rho=0.1$, and $\rho=1$.

Theorems & Definitions (23)

• Definition 1
• Definition 2
• Corollary 1
• Proposition 1
• proof
• Corollary 2
• proof
• Proposition 2
• proof
• Corollary 3