Nonlinear Adaptive Filters for Acoustic Echo Cancellation in Mobile Terminals - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 225

reduced increase in computational complexity with respect to linear filters.
In particular, the recursive bilinear filter 22 and different realizations of the
nonrecursive quadratic filters are considered. The latter filters, also known
as second-order Volterra filters, admit, within some simplifying conditions,
implementation structures with reduced complexity. In particular, the real-
izations considered here are the cascade structure with a memoryless pre-
processor and a linear filter, 38 the multi-memory-decomposition 14 structure,
the parallel-cascade 30 structure, and the simplified Volterra filters. 12 To make
the whole nonlinear echo canceler efficient, it is necessary to equip it with
an adaptation algorithm granting fast adaptation and tracking rates. In Sec-
tion 7.3, extension of the theory of the affine projection (AP) algorithms from
linear to quadratic filters is presented. We compare the performances of such
adaptation algorithms with those of the classical least-mean square (LMS)
and normalized least-mean square (NLMS) algorithms and show that the AP
technique offers better convergence and tracking capabilities. We complete the
chapter by comparing in Section 7.4 the performances of the above-mentioned
realizations for nonrecursive quadratic filters and those of the bilinear filter.
Our final remarks, reported in Section 7.5, note that the reduced complexity
of specific realizations and the fast adaptation and tracking rates of the AP
algorithms make simple polynomial echo cancelers attractive for real-time
implementations in high-quality handset devices.

7.2 Low-Complexity Nonlinear Adaptive Acoustic

Echo Cancelers

In recent years, cellular vendors have been greatly concerned about the qual-
ity of the audio of handset receivers. One of the main issues concerning audio
quality is the need for suppression of the sound signal that propagates be-
tween the loudspeaker and the microphone of the handset terminal and then
reaches the far end. Therefore, the far-end speaker hears a delayed replica of
his or her voice, which results in a quite annoying disturbance. This effect
may be particularly relevant in hands-free systems for vehicular or telecon-
ference applications. The problem also exists in modern ultracompact GSM
and 3-G handset receivers because of their small size and, consequently, the
close proximity of the loudspeaker and the microphone, and because of the
long propagation delay between the two communication sides. The technical
solution to this problem consists of using an acoustic echo canceler (AEC),
which is a digital adaptive filter whose output y

( n ) estimates the reference

signal d , i.e., the echo signal, in order to cancel it by subtraction, as shown

in Figure 7.1. The adaptivity of the AEC is a key point because compen-
sations obtained with filters having fixed coefficients are not able to model

( n )