Closed-Form BER Analysis for Uplink NOMA with Dynamic SIC Decoding

TL;DR

This paper provides the first closed-form error performance analysis of uplink PD-NOMA with dynamic SIC decoding, showing improved error rates and practical insights for system deployment.

Contribution

It introduces a novel analytical framework for dynamic SIC in uplink PD-NOMA, deriving closed-form PDFs and PEPs, and extends BER analysis to various modulation schemes.

Findings

Dynamic SIC removes error floors at high SNR.

Larger power differences improve higher-order modulation performance.

Analytical results match numerical simulations.

Abstract

This paper, for the first time, presents a closed-form error performance analysis of uplink power-domain non-orthogonal multiple access (PD-NOMA) with dynamic successive interference cancellation (SIC) decoding, where the decoding order is adapted to the instantaneous channel conditions. We first develop an analytical framework that characterizes how dynamic ordering affects error probabilities in uplink PD-NOMA systems. For a two-user system over independent and non-identically distributed Rayleigh fading channels, we derive closed-form probability density functions (PDFs) of ordered channel gains and the corresponding unconditional pairwise error probabilities (PEPs). To address the mathematical complexity of characterizing ordered channel distributions, we employ a Gaussian fitting to approximate truncated distributions while maintaining analytical tractability. Finally, we extend the bit error rate analysis for various $M$-quadrature amplitude modulation schemes (QAM) in both homogeneous and heterogeneous scenarios. Numerical results validate the theoretical analysis and demonstrate that dynamic SIC eliminates the error floor issue observed in fixed-order SIC, achieving significantly improved performance in high signal-to-noise ratio regions. Our findings also highlight that larger power differences are essential for higher-order modulations, offering concrete guidance for practical uplink PD-NOMA deployment.