Low-Complexity Factor Graph-Based Joint Channel Estimation and Equalization for SEFDM Signaling

In this paper, we propose a low-complexity joint channel estimation and equalization algorithm based on factor graph for SEFDM signaling communicating over frequency-selective fading channels. By taking full advantage of the limited length of channel memory and the truncated intercarrier interferences (ICIs), we reformulate the joint channel estimation and equalization problem into a linear state-space model. Accordingly, a multi-layer factor graph is constructed and then parametric message updating expressions on factor graph are derived using Gaussian message passing (GMP). To deal with the intractable message passing problem of the inner product node between the channel estimator and the equalizer, we employ expectation-maximization (EM) rules on an equivalent soft node to obtain Gaussian messages. To validate the reliability of the proposed channel estimator, we also derive the Cramer-Rao lower bound (CRLB) in closed-form. The complexity of the proposed channel estimator only grows linearly with the number of subcarriers and logarithmically with the length of the channel's memory. Simulation results demonstrate that SEFDM systems relying on the proposed GMP-EM method can improve the spectral efficiency up to 25% with an acceptable bit error rate (BER) or mean square error (MSE) performance loss, compared to its Nyquist counterpart or the CRLB.