Message passing receiver for SEFDM signaling over multipath channels

In this paper, we design a low-complexity factor graph based iterative receiver for spectrally efficient frequency division multiplexing (SEFDM) systems over unknown multipath channels. By factorizing the a posteriori probability of the transmitted symbols, we construct a multi-layer factor graph. Belief propagation (BP) is performed on factor graph to derive closed form message expressions with the aid of Gaussian approximations of discrete transmitted symbols. To tackle infeasible channel estimation using BP rules, we resort to the variational message passing (VMP) to obtain the channel coefficients. As a result, the overall complexity grows linearly with the number of transmitted symbols. Simulation results show that normalized mean square error (NMSE) and bit error ratio (BER) of the proposed iterative method are better than those of the typical partial channel estimation combined with successive interference cancellation (PCE-SIC) method. Compared with OFDM systems with perfect channel information, the performance loss of SEFDM systems employing the proposed iterative receiver is less than 0.7 dB for the packing factor α ≥ 0.8.