222 research outputs found
A Theory of Cramer-Rao Bounds for Constrained Parametric Models
A simple expression for the Cram'er-Rao bound (CRB) is presented for the scenario of estimating parameters that are required to satisfy a differentiable constraint function . A proof of this constrained CRB (CCRB) is provided using the implicit function theorem, and the encompassing theory of the CCRB is proven in a similar manner. This theory includes connecting the CCRB to notions of identifiability of constrained parameters; the linear model under a linear constraint; the constrained maximum likelihood problem, it's asymptotic properties and the method of scoring with constraints; and hypothesis testing. The value of the tools developed in this theory are then presented in the communications context for the convolutive mixture model and the calibrated array model
Identifiability Conditions for Compressive Multichannel Blind Deconvolution
In applications such as multi-receiver radars and ultrasound array systems,
the observed signals can often be modeled as a linear convolution of an unknown
signal which represents the transmit pulse and sparse filters which describe
the sparse target scenario. The problem of identifying the unknown signal and
the sparse filters is a sparse multichannel blind deconvolution (MBD) problem
and is in general ill-posed. In this paper, we consider the identifiability
problem of sparse-MBD and show that, similar to compressive sensing, it is
possible to identify the sparse filters from compressive measurements of the
output sequences. Specifically, we consider compressible measurements in the
Fourier domain and derive identifiability conditions in a deterministic setup.
Our main results demonstrate that -sparse filters can be identified from
Fourier measurements from only two coprime channels. We also show that
measurements per channel are necessary. The sufficient condition sharpens
as the number of channels increases asymptotically in the number of channels,
it suffices to acquire on the order of Fourier samples per channel. We also
propose a kernel-based sampling scheme that acquires Fourier measurements from
a commensurate number of time samples. We discuss the gap between the
sufficient and necessary conditions through numerical experiments including
comparing practical reconstruction algorithms. The proposed compressive MBD
results require fewer measurements and fewer channels for identifiability
compared to previous results, which aids in building cost-effective receivers.Comment: 13 pages, 5 figure
System Identification with Applications in Speech Enhancement
As the increasing popularity of integrating hands-free telephony on mobile portable devices
and the rapid development of voice over internet protocol, identification of acoustic
systems has become desirable for compensating distortions introduced to speech signals
during transmission, and hence enhancing the speech quality. The objective of this research
is to develop system identification algorithms for speech enhancement applications
including network echo cancellation and speech dereverberation.
A supervised adaptive algorithm for sparse system identification is developed for
network echo cancellation. Based on the framework of selective-tap updating scheme
on the normalized least mean squares algorithm, the MMax and sparse partial update
tap-selection strategies are exploited in the frequency domain to achieve fast convergence
performance with low computational complexity. Through demonstrating how
the sparseness of the network impulse response varies in the transformed domain, the
multidelay filtering structure is incorporated to reduce the algorithmic delay.
Blind identification of SIMO acoustic systems for speech dereverberation in the
presence of common zeros is then investigated. First, the problem of common zeros is
defined and extended to include the presence of near-common zeros. Two clustering algorithms
are developed to quantify the number of these zeros so as to facilitate the study
of their effect on blind system identification and speech dereverberation. To mitigate such
effect, two algorithms are developed where the two-stage algorithm based on channel
decomposition identifies common and non-common zeros sequentially; and the forced
spectral diversity approach combines spectral shaping filters and channel undermodelling
for deriving a modified system that leads to an improved dereverberation performance.
Additionally, a solution to the scale factor ambiguity problem in subband-based blind system identification is developed, which motivates further research on subbandbased
dereverberation techniques. Comprehensive simulations and discussions demonstrate
the effectiveness of the aforementioned algorithms. A discussion on possible directions
of prospective research on system identification techniques concludes this thesis
Robust equalization of multichannel acoustic systems
In most real-world acoustical scenarios, speech signals captured by distant microphones from a source are reverberated due to multipath propagation, and the reverberation may impair speech intelligibility. Speech dereverberation can be achieved
by equalizing the channels from the source to microphones. Equalization systems can
be computed using estimates of multichannel acoustic impulse responses. However,
the estimates obtained from system identification always include errors; the fact that
an equalization system is able to equalize the estimated multichannel acoustic system does not mean that it is able to equalize the true system. The objective of this
thesis is to propose and investigate robust equalization methods for multichannel
acoustic systems in the presence of system identification errors.
Equalization systems can be computed using the multiple-input/output inverse theorem or multichannel least-squares method. However, equalization systems
obtained from these methods are very sensitive to system identification errors. A
study of the multichannel least-squares method with respect to two classes of characteristic channel zeros is conducted. Accordingly, a relaxed multichannel least-
squares method is proposed. Channel shortening in connection with the multiple-
input/output inverse theorem and the relaxed multichannel least-squares method is
discussed.
Two algorithms taking into account the system identification errors are developed. Firstly, an optimally-stopped weighted conjugate gradient algorithm is
proposed. A conjugate gradient iterative method is employed to compute the equalization system. The iteration process is stopped optimally with respect to system identification errors. Secondly, a system-identification-error-robust equalization
method exploring the use of error models is presented, which incorporates system
identification error models in the weighted multichannel least-squares formulation
Design of optimal equalizers and precoders for MIMO channels
Channel equalization has been extensively studied as a method of combating ISI and ICI for high speed MIMO data communication systems. This dissertation focuses on optimal channel equalization in the presence of non-white observation noises with unknown PSD but bounded power-norm. A worst-case approach to optimal design of channel equalizers leads to an equivalent optimal H-infinity filtering problem for the MIMO communication systems. An explicit design algorithm is derived which not only achieves the zero-forcing (ZF) condition, but also minimizes the RMS error between the transmitted symbols and the received symbols. The second part of this dissertation investigates the design of optimal precoders which minimize the bit error rate (BER) subject to a fixed transmit-power constraint for the multiple antennas downlink communication channels under the perfect reconstruction (PR) condition. The closed form solutions are derived and an efficient design algorithm is proposed. The performance evaluations indicate that the optimal precoder design for multiple antennas communication systems proposed herein is an attractive/reasonable alternative to the existing precoder design techniques
Blind channel identification/equalization with applications in wireless communications
Ph.DDOCTOR OF PHILOSOPH
Blind Signal Separation for Digital Communication Data
to appear in EURASIP E-reference in Signal Processing, invited paper.International audienceBlind source separation, often called independent component analysis , is a main field of research in signal processing since the eightees. It consists in retrieving the components, up to certain indeterminacies, of a mixture involving statistically independent signals. Solid theoretical results are known; besides, they have given rise to performent algorithms. There are numerous applications of blind source separation. In this contribution, we particularize the separation of telecommunication sources. In this context, the sources stem from telecommunication devices transmitting at the same time in a given band of frequencies. The received data is a mixed version of all these sources. The aim of the receiver is to isolate (separate) the different contributions prior to estimating the unknown parameters associated with a transmitter. The context of telecommunication signals has the particularity that the sources are not stationary but cyclo-stationary. Now, in general, the standard methods of blind source separation assume the stationarity of the sources. In this contribution , we hence make a survey of the well-known methods and show how the results extend to cyclo-stationary sources
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