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We propose a new sparsity-aware framework to model and mitigate the joint effects of narrow-band interference (NBI) and impulsive noise (IN) in hybrid powerline and unlicensed wireless communication systems. The proposed mitigation techniques, based on the principles of compressive sensing, exploit the inherent (non-contiguous or contiguous) sparse structures of NBI and IN in the frequency and time domains, respectively. For the non-contiguous NBI and IN, we develop a multi-level orthogonal matching pursuit recovery algorithm that exploits prior knowledge about the sparsity level at each receive antenna and powerline to further reduce computational complexity without performance loss. In addition, for the non-contiguous asynchronous NBI scenario, we investigate the application of time-domain windowing to enhance the NBI's sparsity and, hence, improve the NBI mitigation performance. For the contiguous NBI and IN scenario, we estimate the NBI and IN signals by modeling their burstiness as block-sparse vectors with and without prior knowledge of the bursts' boundaries. Moreover, we show how to exploit the spatial correlations of the NBI and IN across the receive antennas and powerlines to convert a non-contiguous NBI and IN problem to a block-sparse estimation problem with much lower complexity. Furthermore, we investigate a Bayesian linear minimum mean square error-based approach for estimating both non-contiguous and contiguous NBI and IN based on their second-order statistics to further improve the estimation performance. Finally, our numerical results illustrate the superiority of the joint processing of our proposed NBI and IN sparsity-based mitigation techniques compared to separate processing of the wireless and powerline received signals.

Sparsity-Based Joint NBI and Impulse Noise Mitigation in Hybrid PLC-Wireless Transmissions