In the context of learning and inference for non-Gaussian additive noise processes, several non-Bussgang learning criteria have emerged, such as, the maximum correntropy, minimum error entropy, and the maximum Versoria criterion. However, these existing learning criteria are known to depend on hyperparameters such as the shape and the spread parameters, which make these approaches susceptible to arbitrary hyperparameter choices. This work proposes an online hyperparameter free criterion learning algorithm that comprehensively alleviates dependence on hyperparameter choices and self-adapts to underlying noise distributions. For the proposed hyperparameter-free criterion learning, analytical results are derived, and case-studies are presented for its validation.

Additive non-Gaussian noise processes and nonlinear channel characteristics are found to present a performance bottleneck for next-generation communication systems, since most classical links are currently designed with Gaussian and linear system assumption. The joint effect of these impairments not only make channel characterization difficult, but also make optimal receiver design non-trivial and complex. In such scenarios, the joint application of reproducing kernel Hilbert space (RKHS) based machine learning methods, and information-theoretic learning (ITL) criteria, allows for near-optimal mitigation of channel nonlinearity and non-Gaussian noise for upcoming beyond 5G systems. Across different deployment scenarios, RKHS based learning allows for hyperparameter independence, improves generalization in the low-data regime and complements other existing signal processing solutions such as deep learning. Also, existing ITL criteria based algorithms are found to deliver improved performance for machine learning over non-Gaussian additive noise scenarios. Furthermore, existing analytical frameworks for these RKHS based approaches readily allow for the extension of classical performance analysis methods; existing works report rigorous analytical results, and the near-optimality of RKHS based approaches. This paper highlights the benefits and the potential of hyperparameter free RKHS and ITL based methods for simple and generic mitigation of unknown underlying hardware impairments and noise processes.

MmWave MIMO (millimeter wave multiple-input multiple-output) systems are critical for enabling the efficient use of spectrum and ultra-fast transmission speeds required by 5G and beyond 5G wireless networks. However, accurate channelestimation over mmWave MIMO systems is challenging due to presence of impulsive noise due to environmental factors, which significantly degrades performance of classical Bussgang/meansquared based channel-estimation methods. To mitigate signal impairments due to unknown non-Gaussian noise processes, this work proposes novel information theoretic learning (ITL) based sparse channel estimation algorithms, namely, zero attracting MCC, and Hyperparameter-Free zero-attracting MCC (ZAMCC). These ITL based algorithms exploit the sparse nature of mmWave MIMO channels and mitigate the adverse effects of impulsive noise. Computer simulations are presented for the performance evaluation for the proposed ITL based algorithms assuming realistic mmWave MIMO scenarios. From the simulations, it is inferred that the proposed ITL based algorithms are promising for accurate hyperparameter-free channel-estimation for practical mmWave MIMO channels impaired by unknown non-Gaussian noises.

In the context of learning and inference over non-Gaussian additive noise processes encountered in modern circuits and systems, several non-Bussgang learning criteria have emerged, such as, the maximum correntropy, minimum error entropy, and the maximum Versoria criterion. However, these existing learning criteria are known to depend on hyperparameters, such as, the shape and the spread parameters. Besides, some of these learning methods are known to depend on suitable informationpotential (IP) choices for general non-Gaussian noisestatistics. This work proposes an online hyperparameterfree criterion learning algorithm that comprehensively alleviates dependence on hyperparameter choices and learns the IP by self-adapting to underlying noise distributions. For the proposed hyperparameter-free criterion learning, analytical results are derived, and case-studies are presented for its validation.