Frequency-domain diffusion adaptation over networks with missing input data

Recently, a modified adapt-then-combine diffusion (mATC) strategy has been developed to handle distributed estimation problem with missing regressions (inputs). However, the mATC algorithm only considers the white input scenario and suffers from high complexity for long model filter lengths. To overcome these shortcomings, this paper proposes novel regularization-based frequency-domain diffusion algorithms for networks with missing input data. First, bias-eliminating cost function based on regularization is established by using the frequency-domain diagonal approximation. Then, with stochastic gradient descent, periodic update, and power normalization schemes, we design the regularization-based frequency-domain least mean square (R-FDLMS) algorithm as well as its normalized variant (R-FDNLMS). The latter converges faster than the former under colored inputs. The stability and steady-state behavior of the R-FDNLMS algorithm are also analyzed. Moreover, two effective power estimation methods are presented for both situations without and with the power ratio between the input signal and perturbation noise, along with a reset mechanism in the first case to enhance tracking performance. Finally, simulations are conducted to illustrate the superiority of the proposed algorithms and the validity of theoretical findings.