Information theoretic learning (ITL) criteria have emerged useful for mitigating degradations caused by unknown non-Gaussian noise processes in future wireless communication systems. Specifically, the reproducing kernel Hilbert space (RKHS) based approaches relying on ITL based learning criteria are envisioned to provide nearoptimal mitigation of unknown hardware impairments and non-Gaussian noises. Among several ITL criteria, the recent works find the minimum error entropy with fiducial points (MEE-FP) promising due to its guarantee of unbiased estimation and generalization over generic noise distributions. However, MEE-FP based learning approaches are known to depend on an accurate kernel-width initialization. Also, the optimal value of this kernelwidth is well-known to vary temporally and across deployment scenarios. To remove the dependency on kernelwidth, a hyperparameter-free MEE-FP based adaptive algorithm is derived using random-Fourier features with sampled kernel widths (RFF-SKW). In addition, a detailed convergence analysis is presented for the proposed hyperparameter-free MEE-FP, which promises a near-optimal error-floor independent of step-size and guarantees convergence for a wide range of step sizes. The promised hyperparameter-independence and improved convergence for the proposed hyperparameter-free MEE-FP are validated by computer simulations considering different case studies.