Joint Channel Estimation and Equalization for Index-Modulated Spectrally Efficient Frequency Division Multiplexing Systems

Abstract

Spectrally efficient frequency division multiplexing (SEFDM) relying on index modulation (IM) has emerged as a promising multicarrier technique. In this paper, we develop a joint channel estimation and equalization method based on factor graphs for SEFDM-IM signaling over frequency-selective fading channels. By approximating the interference in the frequency domain, we reformulate the problem to obey a linear state-space model and construct a multi-layer factor graph. To support a reconfigurable architecture, non-orthogonal demodulation is adopted and the colored noise encountered is approximated by a complex auto-regressive (CAR) model. For deriving a low-complexity parametric Gaussian message passing (GMP)based method, we exploit an expectation propagation (EP)-based technique for approximating the discrete a posteriori distributions of the transmitted symbols in a Gaussian form. To further simplify the result, variational message passing (VMP) is applied to an equivalent soft node to obtain a Gaussian form. Moreover, we also derive the Cramér-Rao lower bound (CRLB) in closedform. The overall complexity only grows linearly with the number of subcarriers and logarithmically with the length of the channel's memory. Compared to its Nyquist signaling based counterpart, SEFDM-IM signaling relying on the proposed algorithm exhibits up to 25% higher bandwidth efficiency without any bit error rate (BER) performance degradation. Index Terms-Spectrally efficient frequency division multiplexing, index modulation, channel estimation, complex-valued colored noise, variational message passing.

The Evolution of Faster-Than-Nyquist Signaling

“…Non-orthogonal symbol multiplexing has also been considered in the FD under the terminologies of nonorthogonal frequency-division multiplexing (NOFDM) and spectrally-efficient FDM (SEFDM) [69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86]. More specifically, NOFDM employs tighter subcarrier spacing than that defined by classic orthogonal FDM (OFDM), hence resulting in higher bandwidth efficiency.…”

“…Similar to the ISI introduced by FTN signaling, inter-carrier interference (ICI) is induced between the subcarriers in NOFDM. Hence, efficient detection algorithms capable of eliminating the ICI effects have been extensively studied in the context of NOFDM [70,72,79,81,82,84,85].…”

“…Most recently, in [51], the TD SCIM concept was amalgamated with EVD-precoded FTN signaling combined with optimal power allocation. Furthermore, the IM concept has also been combined with NOFDM [81,84].…”

Secrecy Performance of Eigendecomposition-Based FTN Signaling and NOFDM in Quasi-Static Fading Channels

“…This implies that, if both the schemes employ, for example, a root-raised cosine (RRC) shaping filter, which has excess bandwidth, the FTN signaling may exhibit an information-theoretic gain over the Nyquist-based counterpart. Furthermore, a frequency-domain counterpart of FTN signaling was independently developed as spectrally efficient frequency-division multiplexing (SEFDM) [25][26][27][28][29][30], where subcarrier spacing in a multicarrier systems is set smaller than that of orthogonal frequency-division multiplexing (OFDM). Moreover, FTN signaling was applied to secure information transmissions [31,32].…”

MIMO Channel Estimation in an SDR Platform for Evaluation of D&F Relay Nodes

“…We are working to upgrade it to be compatible with 5G technology, which will allow us to implement the NOMA technique [17] and new algorithms for the channel estimation of the pilot symbols and interpolation of data symbols [18]. Furthermore, we will consider a turbo operation between the equalization and channel estimation steps [19].…”