  Channel estimation is an essential part of modern communication systems as it
enhances the overall performance of the system. In recent past a variety of
adaptive learning methods have been designed to enhance the robustness and
convergence speed of the learning process. However, the need for an optimal
technique is still there. Herein, for non-Gaussian noisy environment we propose
a new class of stochastic gradient algorithm for channel identification. The
proposed $q$-least mean fourth ($q$-LMF) is an extension of least mean fourth
(LMF) algorithm and it is based on the $q$-calculus which is also known as
Jackson derivative. The proposed algorithm utilizes a novel concept of
error-correlation energy and normalization of signal to ensure high convergence
rate, better stability and low steady-state error. Contrary to the conventional
LMF, the proposed method has more freedom for large step-sizes. Extensive
experiments show significant gain in the performance of the proposed $q$-LMF
algorithm in comparison to the contemporary techniques.
