Delay Violation Probability and Effective Rate of Downlink NOMA over $α$-$μ$ Fading Channels

TL;DR

This work addresses delay-constrained performance of a two-user downlink NOMA system over Generalized $α$-$μ$ fading by deriving a delay-violation-probability upper bound and exact sum ER, along with high- and low-SNR ER approximations and an ergodic sum-rate bound. The authors formulate the system with strong and weak users, use stochastic-network-calculus and Mellin transforms to obtain closed-form expressions for DVP and ER in terms of the fading PDFs $f_{g_s}$ and $f_{g_{min}}$, and provide tractable high-/low-SNR analyses. They also compare NOMA with OMA, deriving upper bounds on the ergodic rates and showing how channel nonlinearity $α$, clustering $μ$, and delay QoS exponent $θ$ influence the rate gains and the rate loss between ergodic capacity and effective rate. The results demonstrate that NOMA outperforms OMA across practical SNRs, but gains shrink under severe fading or stringent delay constraints, offering valuable guidance for QoS-aware design in B5G/6G systems.

Abstract

Non-orthogonal multiple access (NOMA) is a potential candidate to further enhance the spectrum utilization efficiency in beyond fifth-generation (B5G) standards. However, there has been little attention on the quantification of the delay-limited performance of downlink NOMA systems. In this paper, we analyze the performance of a two-user downlink NOMA system over generalized α-μ fading in terms of delay violation probability (DVP) and effective rate (ER). In particular, we derive an analytical expression for an upper bound on the DVP and we derive the exact sum ER of the downlink NOMA system. We also derive analytical expressions for high and low signal-to-noise ratio (SNR) approximations to the sum ER, as well as a fundamental upper bound on the sum ER which represents the ergodic sum-rate for the downlink NOMA system. We also analyze the sum ER of a corresponding time-division-multiplexed orthogonal multiple access (OMA) system. Our results show that while NOMA consistently outperforms OMA over the practical SNR range, the relative gain becomes smaller in more severe fading conditions, and is also smaller in the presence a more strict delay quality-of-service (QoS) constraint.

Figures (12)

• Figure 1: ER for the downlink NOMA system with $\alpha = \mu = 2$, $a_s = 0.2$ and $\theta = 1$.
• Figure 2: Difference between the sum ER of downlink NOMA and downlink OMA with $\alpha = \mu = 2$, $a_s = 0.2$, $\Omega_s = 1$ and $\theta = 1$.
• Figure 3: ER of the strong and weak users for $\theta = 0.5$ and $\rho = 20$ dB in downlink NOMA. Markers and (continuous) solid lines denote the numerically and analytically evaluated results, respectively.
• Figure 4: Delay violation probability for $\alpha = 2$, $\mu = 1$, $\rho = 10$ dB and $N = 168$ in downlink NOMA. Here the bounds are plotted using the derived analytical expressions.
• Figure 5: Analytically evaluated upper bound on the delay violation probability for $\mu = 1$, $\lambda = 2$, $\rho = 10$ dB and $N = 168$.

Theorems & Definitions (6)

• Theorem 1
• proof
• Theorem 2
• proof
• Theorem 3
• proof