Convergence properties of the block orthogonal projection algorithm

The normalized LMS (N-LMS) algorithm has a disadvantage that the convergence rate is much worse when the input signal is colored. To overcome this, the affine projection algorithm and the block orthogonal projection (BOP) algorithm which applied the block signal processing technique to the N-LMS algorithm are proposed although the reason why they are tough against the colored signal is not given yet. This paper gives the convergence rate of the BOP algorithm for colored input signals, which shows the superiority of the BOP algorithm. To put it concretely, we derive the expression of the convergence rate, propose an approximation method to calculate it, and confirm the result by computer simulations. We also consider the relation between the block size and the convergence rate formally and geometrically