2-Dimensional Variable Step-Size Sequential Adaptive Gradient Algorithms With Applications

W B. Mikhael
S M. Ghosh


This paper develops the optimality criterion governing the choice of the convergence factor for the two-dimensional sequential adaptive gradient algorithms. Two two-dimensional variable step-size sequential algorithms satisfying the proposed optimality constraint are derived and investigated. These are the two-dimensional individual adaptation (TDIA) algorithm and the two-dimensional homogeneous adaptation (TDHA) algorithm. The TDIA algorithm uses optimal convergence factors tailored for each two-dimensional adaptive filter coefficient at each iteration. The TDHA algorithm uses the same convergence factor for all the filter coefficients, but the convergence factor is optimally updated at each iteration. Neither algorithm requires any a priori knowledge about the statistics of the system signals. In addition, the convergence factors are easily obtained from readily available signals without any differentiation or matrix inversions. The convergence characteristics and adaptation accuracy are greatly improved at the expense of a modest increase in computational complexity in comparison with fixed step-size LMS algorithms. This is verified using computer simulations in system identification and noise cancellation applications.