RPDMA: A PAPR-Aware Multiple Access Scheme

This article proposes a novel Multiple Access (MA) scheme called Ramanujan Periodic-subspace Division Multiple Access (RPDMA) for subcarrier sizes $N = 2^{m},\ m\in \mathbb {N}$, to address the high Peak-to-Average Power Ratio (PAPR) in Orthogonal Frequency Division Multiple Access (OFDMA). Building on the properties of Ramanujan subspaces, we design transmitter and receiver models that allocate users on a subspace-wise basis, ensuring zero inter-user interference, providing inherent frequency diversity. We analyze the computational complexity of OFDMA, SC-FDMA, and RPDMA, and find that RPDMA has substantially lower per-user transmitter complexity than both OFDMA and SC-FDMA, while its receiver complexity is comparable to SC-FDMA and higher than that of OFDMA. We further introduce a generalized framework, termed Nested Periodic-subspace Division Multiple Access (NPDMA), which unifies both RPDMA and OFDMA under a common family of multi-carrier MA schemes. We derive the theoretical PAPR of RPDMA and demonstrate its superiority over OFDMA. The analysis is validated through numerical simulations under two multi-user scenarios with diverse Quality of Service (QoS) requirements. The results demonstrate that RPDMA achieves lower PAPR than both OFDMA and SC-FDMA, with users assigned larger subspaces benefiting from even greater PAPR reduction. We prove that both the sum and per-user Spectral Efficiency (SE) of RPDMA are identical to those of OFDMA and SC-FDMA. In terms of Bit Error Rate (BER), SC-FDMA achieves the best performance, while RPDMA still outperforms OFDMA as the SNR increases.