Deep Neural Network-Driven Adaptive Filtering

Abstract: This paper proposes a deep neural network (DNN)-driven framework to address the longstanding generalization challenge in adaptive filtering (AF). In contrast to traditional AF frameworks that emphasize explicit cost function design, the proposed framework shifts the paradigm toward direct gradient acquisition. The DNN, functioning as a universal nonlinear operator, is structurally embedded into the core architecture of the AF system, establishing a direct mapping between filtering residuals and learning gradients. The maximum likelihood is adopted as the implicit cost function, rendering the derived algorithm inherently data-driven and thus endowed with exemplary generalization capability, which is validated by extensive numerical experiments across a spectrum of non-Gaussian scenarios. Corresponding mean value and mean square stability analyses are also conducted in detail.