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EURASIP Journal on Audio, Speech, and Music Processing, 2007,
-106 pp.
System identification is an important
task in many application areas including, for example,
telecommunications, control engineering, sensing, and
acoustics. It would be widely accepted that the science for
identification of stationary and dynamic systems is mature.
However, several new applications have recently become of
heightened interest for which system identification needs to be
performed on high-order moving average systems that are either
sparse in the time domain or need to be estimated using sparse
computation due to complexity constraints. In this special
issue, we have brought together a collection of articles on
recent work in this field giving specific consideration to (a)
algorithms for identification of sparse systems and (b)
algorithms that exploit sparseness in the coefficient update
domain. The distinction between these two types of sparseness
is important, as we hope will become clear to the reader in the
main body of the special issue.
A driving force behind the development of algorithms for sparse
system identification in telecommunications has been echo
cancellation in packet switched telephone networks. The
increasing popularity of packet-switched telephony has led to a
need for the integration of older analog systems with, for
example, IP or ATM networks. Network gateways enable the
interconnection of such networks and provide echo cancellation.
In such systems, the hybrid echo response is delayed by an
unknown bulk delay due to propagation through the network. The
overall effect is, therefore, that an active region associated
with the true hybrid echo response occurs with an unknown delay
within an overall response window that has to be sufficiently
long to accommodate the worst case bulk delay. In the context
of network echo cancellation the direct application of
well-known algorithms, such as normalized least-mean-square
(NLMS), to sparse system identification gives unsatisfactory
performance when the echo response is sparse. This is because
the adaptive algorithm has to operate on a long filter and the
coefficient noise for nearzero- valued coefficients in the
inactive regions is relatively large. To address this problem,
the concept of proportionate updating was introduced.
An important consideration for adaptive filters is the
computational complexity that increases with the number of
coefficients to be updated per sampling period. A
straightforward approach to complexity reduction is to update
only a small number of filter coefficients at every iteration.
This approach is termed partial-update adaptive filtering. Two
key questions arise in the context of partial updating.
Firstly, consideration must be given as to how to choose which
coefficients to update. Secondly, the performance and
complexity of the partial update approach must be compared with
the standard full update algorithms in order to assess the
cost-tobenefit ratio for the partial update schemes. Usually, a
compromise has to be made between affordable complexity and
desired convergence speed.
We have grouped the papers in this special issue into four
areas. The first area is sparse system identification and
comprises three papers. In Set-membership proportionate affine
projection algorithms, Stefan Werner et al. develop affine
projection algorithms with proportionate update and set
membership filtering. Proportionate updates facilitate fast
convergence for sparse systems, and set membership filtering
reduces the update complexity. The second paper in this area is
Wavelet-based MPNLMS adaptive algorithm for network echo
cancellation by H. Deng and M. Doroslovacki, which develops a
wavelet-domain μ-law proportionate NLMS algorithm for
identification and cancelling of sparse telephone network
echoes. This work exploits the whitening and good
time-frequency localisation properties of the wavelet transform
to speed up the convergence for coloured input signals and to
retain sparseness of echo response in the wavelet transform
domain. In A low delay and fast converging improved
proportionate algorithm for sparse system identification, Andy
W. H. Khong et al. propose a multidelay filter (MDF)
implementation for improved proportionate NLMS for sparse
system identification, inheriting the beneficial properties of
both; namely, fast convergence and computational efficiency
coupled with low bulk delay. As the authors show, the MDF
implementation is nontrivial and requires time-domain
coefficient updating.
The second area of papers is partial-update active noise
control. In the first paper in this area Analysis of transient
and steady-state behavior of a multichannel filtered-x
partial-error affine projection algorithm, A. Carini and S. L.
Sicuranza apply partial-error complexity reduction to
filtered-x affine projection algorithm for multichannel active
noise control, and provide a comprehensive analysis of the
transient and steady-state behaviour of the adaptive algorithm
drawing on energy conservation. In Step size bound of the
sequential partial update LMS algorithm with periodic input
signals Pedro Ramos et al. show that for periodic input signals
the sequential partial update LMS and filtered-x LMS algorithms
can achieve the same convergence performance as their
full-update counterparts by increasing the step-size
appropriately. This essentially avoids any convergence penalty
associated with sequential updating.
The third area focuses on general partial update algorithms. In
the first paper in this area, Detection guided fast affine
projection channel estimator for speech applications, Yan Wu
Jennifer et al. consider detection guided identification of
active taps in a long acoustic echo channel in order to shorten
the actual channel and integrate it into the fast affine
projection algorithm to attain faster convergence. The proposed
algorithm is well suited for highly correlated input signals
such as speech signals. In Efficient multichannel NLMS
implementation for acoustic echo cancellation, Fredric
Lindstrom et al. propose a multichannel acoustic echo
cancellation algorithm based on normalized least-mean-square
with partial updates favouring filters with largest
misadjustment.
The final area is devoted to blind source separation. In Time
domain convolutive blind source separation employing
selective-tap adaptive algorithms, Q. Pan and T. Aboulnasr
propose time-domain convolutive blind source separation
algorithms employing M-max and exclusive maximum selective-tap
techniques. The resulting algorithms have reduced complexity
and improved convergence performance thanks to partial updating
and reduced interchannel coherence. In the final paper
Underdetermined blind audio source separation using modal
decomposition, Abdeljalil Aıssa-El-Bey et al. present a novel
blind source separation algorithm for audio signals using modal
decomposition. In addition to instantaneous mixing, the authors
consider convolutive mixing and exploit the sparseness of audio
signals to identify the channel responses before applying modal
decomposition.
In summary, we can say that sparseness in the context of
adaptive filtering presents both challenges and opportunities.
Standard adaptive algorithms suffer a degradation in
performance when the system to be identified is sparse. This
has created the need for new algorithms for sparse adaptive
filtering—a challenge that has been well met to date for the
particular applications addressed. When sparseness exists, or
can be safely assumed, in input signals, this can be exploited
to achieve both computational savings in partial update schemes
and, in certain specific cases, performance improvements. There
remain several open research questions in this context and we
look forward to an ongoing research effort in the scientific
community and opportunities for algorithm deployment in
real-time applications.
Adaptive Partial-Update and Sparse
System Identification
Set-Membership Proportionate Affine Projection Algorithms
Wavelet-Based MPNLMS Adaptive Algorithm for Network Echo
Cancellation
A Low Delay and Fast Converging Improved Proportionate
Algorithm for Sparse System Identification
Analysis of Transient and Steady-State Behavior of a
Multichannel Filtered-x Partial-Error Affine Projection
Algorithm
Step Size Bound of the Sequential Partial Update LMS Algorithm
with Periodic Input Signals
Detection-Guided Fast Affine Projection Channel Estimator for
Speech Applications
Efficient Multichannel NLMS Implementation for Acoustic Echo
Cancellation
Time-Domain Convolutive Blind Source Separation Employing
Selective-Tap Adaptive Algorithms
Underdetermined Blind Audio Source Separation Using Modal
Decomposition