Joint Channel Estimation and Equalization for Index-Modulated Spectrally Efficient Frequency Division Multiplexing Systems
Yunsi Ma, Nan Wu, Weijie Yuan, Derrick Wing Kwan Ng, Lajos Hanzo
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 closed-form. 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.