Circular Faster-Than-Nyquist Signaling for High Spectral Efficiencies: Optimized EP-Based Receivers

This paper proposes unprecedented Expectation Propagation (EP)-based receivers for Circular Faster-Than-Nyquist (CFTN) signaling. This concept yields a Minimum Mean-Square-Error equalizer for InterSymbol Interference (ISI) processing combined with a block which we call Constellation Matcher in charge of the symbol estimates realignment with the constellation. From this framework, we explore different scheduling strategies leading to iterative EP-based receivers with our without decision feedback. Then, by extending the family of the EP process to a subset of non-circular Gaussian distributions results in a Widely Linear (WL) equalization. This new WL-EP receiver best fits the CFTN model, allowing enhanced performance at the cost of a slightly increased complexity. Also, we propose to restrict the Gaussian family to circular Gaussian distributions with identity covariance matrices up to a scaling factor. Combined with CFTN, this particular family allows a low-complexity Frequency-Domain processing of the equalization without requiring any cyclic prefix. The proposed EP-based receivers for CFTN are then evaluated for different spectral efficiencies and computational complexities. Our simulations show that they completely handle the ISI up to 5 bits/s/Hz and double the spectral efficiency compared to Nyquist signaling with almost no performance loss.