Robust Blind Equalization for NB-IoT Driven by QAM Signals

The expansion of data coverage and the accuracy of decoding of the narrowband-Internet of Things (NB-IoT) mainly depend on the quality of channel equalizers. Without using training sequences, blind equalization is an effective method to overcome adverse effects in the Internet of Things (IoT). The constant modulus algorithm (CMA) has become a favorite blind equalization algorithm due to its least mean square (LMS)-like complexity and desirable robustness property. However, the transmission of high-order quadrature amplitude modulation (QAM) signals in the IoT can degrade its performance and the convergence speed. This article investigates a family of modified CMAs (MCMAs) for blind equalization of IoT using high-order QAM. Our theoretical analysis for the first time illustrates that the classical CMA has the problem of artificial error using high-order QAM signals. In order to effectively deal with these issues, an MCMA is proposed to decrease the modulus matched error, which can efficiently suppress the artificial error and misadjustment at the expense of reduced sample usage rate. Moreover, a generalized form of the MCMA (GMCMA) is developed to improve the sample usage rate and guarantee the desirable equalization performance. Two modified Newton methods (MNMs) for the proposed MCMA and GMCMA are constructed to obtain the optimal equalizer. Theoretical proofs are presented to show the fast convergence speed of the two MNMs. Numerical results show that our methods outperform other methods in terms of equalization performance and convergence speed.