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 $\mathbb {N}$ . 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 $q\in \mathbb {N}$ 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 $(q=p^{m})$ , ORPDM excels for smaller prime powers $(p\lt 7)$ , while RPDM is superior when $p\geq 7$ ; 4) For composite q, if all prime factors are $\leq 5$ , ORPDM achieves the best PAPR reduction; if all prime factors are $\geq 7$ , 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.