On the Detection Limits of Power-Domain NOMA: Information-Theoretic Bounds and Spatial Diversity

Abstract

Power-domain non-orthogonal multiple access (NOMA) relies on successive interference cancellation (SIC) at the receiver, leading to the prevailing but incomplete view that power allocation merely enables SIC. This paper develops an information-theoretic framework for the detection limits of power-domain NOMA under finite-alphabet modulation. We identify two distinct roles of power allocation: setting the sequential SIC decoding order (architecture-specific) and shaping the geometric separability of the composite signal constellation (architecture-independent). Building on this dual role, we derive a hierarchy of constellation-constrained mutual information bounds spanning treat-interference-as-noise, marginal maximum a posteriori (MAP), and oracle detection, and establish a Fano-type lower bound on the symbol error rate and a pairwise error probability upper bound on the oracle error rate. Extending the framework to the multiple-input multiple-output (MIMO) NOMA uplink reveals a transition governed by the receive-antenna count <inline-formula> <tex-math notation="LaTeX">$N_{r}$ </tex-math></inline-formula> relative to the number of users <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>: for <inline-formula> <tex-math notation="LaTeX">$N_{r} \ge K$ </tex-math></inline-formula>, linear minimum mean-square error SIC (MMSE-SIC) approaches the MAP bound and closes the gaps that dominate single-input single-output (SISO) NOMA, whereas for <inline-formula> <tex-math notation="LaTeX">$N_{r} \lt K$ </tex-math></inline-formula> the MAP detector substantially outperforms MMSE-SIC. Numerical results for three-user NOMA validate the bounds and show that the MAP-to-oracle SER gap is an information-theoretic limit in SISO, while spatial diversity progressively closes both the structural and oracle gaps.