Convergence Analysis of Hirschman Optimal Transform (HOT) LMS Adaptive Filter

We present a general convergence analysis of the recently introduced HOT LMS Adaptive filter and show that the autocorrelation matrix in the HOT domain is asymptotically Block diagonal and the HOT LMS adjusts the learning rate of each block to improve the convergence speed of the adaptive filter as compared to LMS. The theoretical findings were verified through numerical calculations and simulations.