As the scale of Internet of Things (IoT) grows rapidly, accurate active user detection has emerged as an important problem in massive connectivity scenarios. This paper presents a novel low-complexity expectation propagation (LC-EP) algorithm for massive connectivity. Different from traditional methods that reduce the complexity of EP through channel hardening, LC-EP exploits a new statistical convergence property of the Gram matrix for the complexity reduction. Meanwhile, the decision method is modified from the original log-likelihood ratio (LLR)-based approach to an order-based method for the future performance gain. Simulation results demonstrate that the proposed LC-EP algorithm improves both detection accuracy and efficiency.

We consider the turbo frequency domain equalization (FDE) approach based on expectation propagation (EP) to the single-carrier with index modulation (SCIM) transmission over frequency-selective channels. The SCIM-FDE system implements vector-by-vector signal transmission in the time domain, in which elements within each transmitted symbol vector display correlation. In this paper, we propose a novel vector-wise EP (VW-EP) equalization, where the discrete prior distribution of each symbol vector is approximated with a multivariate complex Gaussian distribution. Hence the extrinsic information in the EP feedback is extended to be in terms of the mean vector and covariance matrix. The effectiveness of the proposed scheme can be validated through the error-correction performance and extrinsic information transfer (EXIT) analysis. Numerical results show that the SCIM-FDE transmission with the VW-EP turbo equalization demonstrates remarkable performance.