  In high sample-rate applications of the least-mean-square (LMS) adaptive
filtering algorithm, pipelining or/and block processing is required. As opposed
to earlier work, pipelining and block processing are jointly considered to
obtain what we refer to as the delayed block LMS (DBLMS) algorithm. Different
stochastic analyses for the steady and transient states to estimate the
step-size bound, adaptation accuracy, and adaptation speed based on the
recursive relation of delayed block excess mean square error (MSE) are
presented. The effect of different amounts of pipelining delays and block sizes
on the adaptation accuracy and speed of the adaptive filter with different
filter lengths and speed-ups are studied. It is concluded that for a constant
speed-up, a large delay and small block size lead to a slower convergence rate
compared to a small delay and large block size with almost the same
steady-state MSE. Monte Carlo simulations indicate a good agreement with the
proposed estimates for Gaussian inputs.
