A new normalized LMAT algorithm and its performance analysis

• A new normalized LMAT algorithm is proposed.
• By limiting the amplitude of square of the feedback error in weight update rule, the robust performance of the proposed algorithm can be improved in impulsive noise environment.
• The range of the algorithm step-size is derived in detail.
• The performance of the NLMAT algorithm is analyzed in terms of the steady-state MSD, EMSE and MSE.

As one of adaptive filtering algorithms based on the high order error power (HOEP) criterion, the least mean absolute third (LMAT) algorithm outperforms the least mean square (LMS) algorithm in terms of the convergence performance. However, the choice range of its step-size is dependent on the power of the input signal. To overcome this shortcoming, a new normalized LMAT (NLMAT) algorithm is presented in this paper. The proposed algorithm has a good anti-jamming capability against the impulsive noise via assigning a upper-bound to the square of the feedback error in the weight update rule. Moreover, the range of the step-size is derived in detail to guarantee the stability of the proposed algorithm in the mean and mean-square senses. Furthermore, the performance of the proposed algorithm is analyzed in terms of the steady-state mean square deviation (MSD) and mean square error (MSE) as well as computational complexity. Simulation results in the context of system identifications illustrate that the proposed algorithm performs much better than the existing algorithms in various noise environments, with a fast convergence rate, low steady-state error and good tacking capability.

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