Time-Averaged Fractionally pth-order Moments Algorithm for Cyclostationary Signals Under non-Gaussian Environments*

Recently, adaptive filter algorithms for jointly wide-sense cyclostationary signals based on a minimal time-averaged mean-square error (TA-MSE) framework have been developed. Algorithms based on this framework have demonstrated their estimating efficiency when the total number of the possible filter coefficients to implement the linear estimator for cyclostationary signals is limited. However, it is known from the literature that algorithms relying on the mean-square error (MSE) cost function suffer significantly when impulsive noises are present. Thus, in this work, we introduce an adaptive filtering algorithm for cyclostationary signals that is robust in the presence of α-stable noise environments. The proposed algorithm is based on the optimization of the time-averaged fractional pth-order moments of the error cost function, which is called the minimum time-averaged least-mean fractional pth-order moments (TA-LMP) algorithm. We analyzed the proposed approach in α-stable distribution model with the characteristic exponents {1 < p < α ≤ 2} with an approximate solution using Taylor's expansion. The bound conditions analysis in terms of the mean convergent behavior is derived. Finally, the algorithm is used in practical simulation studies in system identification to compare the performance of TA-LMP in α-stable noise environments to demonstrate its robustness compared to that of its competitor.