The main theme of this thesis is adaptive echo cancellation. Two novel independent
approaches are proposed for the design of long echo cancellers with improved
In the first approach, we present a novel structure for bulk delay estimation in
long echo cancellers which considerably reduces the amount of excess error. The
miscalculation of the delay between the near-end and the far-end sections is one
of the main causes of this excess error. Two analyses, based on the Least Mean
Squares (LMS) algorithm, are presented where certain shapes for the transitions
between the end of the near-end section and the beginning of the far-end one are
considered. Transient and steady-state behaviours and convergence conditions
for the proposed algorithm are studied. Comparisons between the algorithms
developed for each transition are presented, and the simulation results agree well
with the theoretical derivations.
In the second approach, a generalised performance index is proposed for the
design of the echo canceller. The proposed algorithm consists of simultaneously
applying the LMS algorithm to the near-end section and the Least Mean Fourth
(LMF) algorithm to the far-end section of the echo canceller. This combination results
in a substantial improvement of the performance of the proposed scheme over
both the LMS and other algorithms proposed for comparison. In this approach,
the proposed algorithm will be henceforth called the Least Mean Mixed-Norm
The advantages of the LMMN algorithm over previously reported ones are two
folds: it leads to a faster convergence and results in a smaller misadjustment error.
Finally, the convergence properties of the LMMN algorithm are derived and
the simulation results confirm the superior performance of this proposed algorithm
over other well known algorithms.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.