Parametric Bilinear Iterative Generalized Approximate Message Passing Reception of FTN Multi-Carrier Signaling

A low-complexity parametric bilinear generalized approximate message passing (PBiGAMP)-based receiver is conceived for multi-carrier faster-than-Nyquist (MFTN) signaling over frequency-selective fading channels. To mitigate the inherent ill-conditioning problem of MFTN signaling, we construct a segment-based frequency-domain received signal model in the form of a block circulant linear transition matrix, which can be efficiently calculated by applying a two dimensional fast Fourier transform. Based on the eigenvalue decomposition of the block circulant matrices, we can diagonalize the covariance matrix of the complex-valued colored noise process imposed by the associated two dimensional non-orthogonal matched filtering. Building on this model, a PBiGAMP-based parametric joint channel estimation and equalization (JCEE) algorithm is proposed for MFTN systems. In this algorithm, we introduce a pair of additive terms for characterizing the interferences arising from adjacent segments and employ the exact discrete a priori probabilities of the transmitted symbols for improving the bit error rate (BER) performance. To further enhance the system's robustness in the presence of ill-conditioned matrices, we develop a refined PBiGAMP-based JCEE algorithm by introducing a series of scaled identity matrices. Moreover, the proposed PBiGAMP-based JCEE algorithms may be readily decomposed into GAMP-based equalization algorithms, when the channel state information is perfectly known. The overall complexity of the proposed algorithms only increases logarithmically with the total number of transmitted symbols. Our simulation results demonstrate the benefits of the proposed PBiGAMP-based iterative message passing receiver conceived for MFTN signaling.