  In this paper, a new modulation method defined as Ramanujan Periodic Subspace
Division Multiplexing (RPSDM) is proposed using Ramanujan subspaces. Each
subspace contains an integer valued Ramanujan Sum (RS) and its circular
downshifts as a basis. The proposed RPSDM decomposes the linear time-invariant
wireless channels into a Toeplitz stair block diagonal matrices, whereas
Orthogonal Frequency Division Multiplexing (OFDM) decompose the same into
diagonal. Advantages of such structured subspaces representation are studied
and compared with an OFDM representation in terms of Peak-Average Power Ratio
(PAPR) and Bit-Error-Rate (BER). Zero Forcing (ZF) and Minimum Mean Square
Error (MMSE) detectors are applied to evaluate the performance of OFDM and
RPSDM techniques. Finally, the simulation results show that the proposed design
(with an additional receiver complexity) outperforms OFDM under both detectors.
