A new quasi-optimal detection algorithm for a non orthogonal Spectrally Efficient FDM

Abstract-Non-orthogonal Spectrally Efficient Frequency Division Multiplexing (SEFDM) signals of a small dimensionality can be optimally detected using the Sphere Decoder (SD) algorithm. However, the employment of such detectors is restricted by two factors; the ill-conditioning of the SEFDM projections matrix in the system linear statistical model and the sensitivity of the SD complexity to noise. A solution to the latter could be given by a fixed complexity detection based on the Semidefinite Programming (SDP). Notwithstanding, SDP error performance appears to be suboptimal. In order to diminish the error performance gap between the SDP and the optimal detector we propose a modified SD that investigates only the points of the SEFDM lattice within a hypersphere whose size is determined by a first SDP estimate. In addition, the new SD tree is pruned to include only the branches that have a heuristically predefined Hamming distance from the SDP estimate. We show that the introduced scheme achieves a quasi optimal Bit Error Rate (BER) for an SEFDM scheme with 20% spectral gain compared to Orthogonal FDM (OFDM). Moreover, we demonstrate by simulation that the new scheme is superior in terms of computational effort compared to an equivalent SDP brute force Maximum Likelihood (ML) scheme. Finally, it is shown that the new pruned SD reduces by more than 30% the number of the visits to the nodes of the SD tree made by the conventional SD using the Schnorr Euchner (SE) reordering strategy.