{'fraction_non_alphanumeric': 0.02991725015913431, 'fraction_numerical': 0.001273074474856779, 'mean_word_length': 5.68936170212766, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Joint Channel Estimation and Equalization for Index-Modulated Spectrally Efficient Frequency Division Multiplexing Systems

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.