Ramanujan Subspaces and its Applications to Frequency Selective Channels

Abstract

In this thesis, a unified framework to design new signals using Ramanujan sums newlineis presented for wireless communication applications. Primarily, a new modulation newlineand demodulation method referred to as Ramanujan Periodic Subspace Division newlineMultiplexing (RPSDM) that involves periodic Ramanujan Subspaces is proposed newlinefor multi-carrier systems. These Ramanujan Subspaces are constructed using Ramanujan sums. In addition, a theoretical framework describing how Ramanujan Periodic Subspaces decompose linear-time invariant channels with cyclic prefix(s)(CP) newline(random circulant matrices) are presented. newline a joint PAPR reduction and precoding newlinescheme using approximate message passing (AMP) is proposed for Massive MIMORPSDM. Finally, it is proved that RPSDM outperforms OFDM in terms of PAPR newlineand BER with extra computational complexity. newline