PAPR Performance Evaluation of OFDM, RPDM, and ORPDM Multicarrier Modulation Schemes

Multicarrier Modulation (MCM) schemes based on Nested Periodic Matrices (NPMs) offer promising solutions to the high Peak-to-Average Power Ratio (PAPR) problem in Orthogonal Frequency Division Multiplexing (OFDM). Among these, Ramanujan Periodic-subspace Division Multiplexing (RPDM) emerges as a candidate and has been analyzed when the number of subcarriers q is an integer power of 2, which represents a small subset of N. Moreover, RPDM’s transformation matrix loses orthogonality for non-integer-power-of-two subcarriers, leading to increased computational complexity. To address these limitations, this work introduces Orthogonal Ramanujan Periodic-subspace Division Multiplexing (ORPDM), an MCM scheme leveraging Orthogonal Ramanujan Bases (ORBs) that retain transformation matrix orthogonality for all qN with an enhanced computational efficiency over RPDM. The PAPR performance of OFDM, RPDM, and ORPDM is comprehensively evaluated across all natural numbers. Our theoretical and numerical analyses reveal: 1) RPDM and ORPDM consistently provide lower PAPR than OFDM; 2) For prime q, RPDM provides the lowest PAPR; 3) For prime power (q=pm), ORPDM excels for smaller prime powers (p<7), while RPDM is superior when p≥7; 4) For composite q, if all prime factors are ≤5, ORPDM achieves the best PAPR reduction; if all prime factors are ≥7, RPDM remains optimal. In addition to PAPR, we evaluate and compare spectral efficiency, Out-of-Band (OOB) emissions, and Bit Error Rate (BER) performance across the three MCM schemes.