Narrowband internet-of-things (NB-IoT) is a competitive 5G technology for massive machine-type communication scenarios, but meanwhile introduces narrowband interference (NBI) to existing broadband transmission such as the long term evolution (LTE) systems in enhanced mobile broadband (eMBB) scenarios. In order to facilitate the harmonic and fair coexistence in wireless heterogeneous networks, it is important to eliminate NB-IoT interference to LTE systems. In this paper, a novel sparse machine learning based framework and a sparse combinatorial optimization problem is formulated for accurate NBI recovery, which can be efficiently solved using the proposed iterative sparse learning algorithm called sparse cross-entropy minimization (SCEM). To further improve the recovery accuracy and convergence rate, regularization is introduced to the loss function in the enhanced algorithm called regularized SCEM. Moreover, exploiting the spatial correlation of NBI, the framework is extended to multiple-input multiple-output systems. Simulation results demonstrate that the proposed methods are effective in eliminating NB-IoT interference to LTE systems, and significantly outperform the state-of-the-art methods.
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