A Truncated SVD approach for fixed complexity spectrally efficient FDM receivers

Spectrally Efficient Frequency Division Multiplexing (SEFDM) systems aim to reduce the utilized spectrum by multiplexing non-orthogonal overlapped carriers. Since the per carrier transmission rate is maintained, SEFDM yields higher spectral efficiency relative to an equivalent Orthogonal Frequency Division Multiplexing (OFDM) system. Yet, due to the loss of the orthogonality, detection of the SEFDM system requires overly complex detectors. In this work, new SEFDM receivers that offer substantial complexity reduction with a competitive Bit Error Rate (BER) performance are presented. The Truncated Singular Value Decomposition (TSVD) is proposed as an efficient tool to overcome the ill conditioning of the system caused by the orthogonality collapse. The performance of the system with respect to the system size and spectrum saving is examined by extensive numerical simulations. It is shown that the TSVD detector outperforms linear detectors such as Zero Forcing (ZF) and Minimum Mean Squared Error (MMSE) detectors in terms of BER. Furthermore, a combination of TSVD with the Fixed Sphere Decoder (FSD) algorithm is proposed and tested for the first time. This novel FSD-TSVD receiver achieves near -optimum performance in terms of BER with a fixed and reduced complexity for systems with bandwidth savings of up to 40%.