Achievable Rates of Coded NOMA With Finite-Alphabet Inputs and Suboptimal Detection
Abstract
Power-domain non-orthogonal multiple access (NOMA) is conventionally analyzed under Gaussian input assumptions, where successive interference cancellation (SIC) achieves the multiple-access channel (MAC) capacity region. Practical systems, however, employ finite-alphabet modulations and suboptimal detectors, which reshapes the achievable rate landscape in ways the Gaussian theory does not predict. This paper establishes a hierarchy of detector-dependent achievable rates for uplink NOMA with constellation-constrained (CC) inputs: <inline-formula> <tex-math notation="LaTeX">$R_{\mathrm {TIN}} \leq R_{\mathrm {MMSE}} \leq R_{\mathrm {MAP}} \leq R_{\mathrm {oracle}} \leq \log _{2} M$ </tex-math></inline-formula>. We prove a calibration catastrophe for hard-decision SIC: the generalized mutual information (GMI) at the unscaled LLR magnitude becomes negative when the LLR-sign bit-error probability exceeds a closed-form threshold <inline-formula> <tex-math notation="LaTeX">$p_{e}^{\ast }(L_{\max })$ </tex-math></inline-formula>, meaning the decoder is actively misled by overconfident wrong LLRs. For the weak user with <inline-formula> <tex-math notation="LaTeX">$p_{e} \approx 0.3$ </tex-math></inline-formula>, the unscaled hard SIC GMI is approximately −7.66 bits per bit, rendering the practical hard-SIC decoder family infeasible for any code rate <inline-formula> <tex-math notation="LaTeX">$R \geq 1/2$ </tex-math></inline-formula>. We establish a NOMA–OMA crossover theorem: unlike the Gaussian case where NOMA always achieves a higher sum rate, with CC inputs there exists a per-user crossover SNR below which pooled-power orthogonal multiple access (OMA) outperforms NOMA for the power-disadvantaged user even with optimal MAP detection. Numerical results with LDPC coding confirm the theoretical predictions: MAP turbo detection achieves a waterfall BER consistent with the achievable rate analysis, hard SIC exhibits an error floor above 30% explained by its negative GMI, and the OMA baseline validates the crossover phenomenon.