On the convergence of the CORDIC adaptive lattice filtering (CALF) algorithm

In this paper, the convergence of a previously proposed CORDIC adaptive lattice filtering (CALF) algorithm is proved. It is shown that the update of the rotation angle (which is equivalent to the reflection coefficient) can be modeled by the state transition of a regular Markov chain, with each rotation angle being a state. The convergence of the CALF algorithm then is established as this Markov chain converges from an initial state probability distribution to its limiting state probability distribution. Formulae that enable explicit calculation of the limiting state distribution are derived. Moreover, it is shown that the algorithm has an exponential convergence rate.