Source enumeration and prewhitening techniques for highresolution and robust multidimensional array processing
基於高分辨及魯棒的多維陣列信號處理的信源數目估計和噪聲預白化技術研究
Student thesis: Doctoral Thesis
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Award date  2 Oct 2013 
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Permanent Link  https://scholars.cityu.edu.hk/en/theses/theses(561c131bb5ab4a159089d4433928887f).html 

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Abstract
Estimating the number of sources impinging on an array of sensors, termed as source
enumeration, is required prior to the use of parametric methods, e.g., estimation of
signal parameters via rotational invariance techniques (ESPRIT) and multiple signal
classification (MUSIC), for extraction of the signal parameters in sensor array
applications.
For source enumeration from a matrix of measurements, whose rows and columns
typically correspond to the spatial and temporal dimensions, respectively, is termed as
onedimensional (1D) source enumeration. Numerous 1D source enumerators have
been developed in the literature, including the classical information theoretic criterion
(ITC) based methods, which are optimal when the number of snapshots is much
larger than the number of sensors, and the random matrix theory (RMT) algorithm
that is designed for relatively small snapshot scenarios. As the first contribution,
we investigate the optimal choice of the number of source signals in the threshold
region of nonlinear parameter estimators. Due to the low signaltonoise ratio (SNR)
and/or presence of closelyspaced sources, some signal parameters can be accurately
estimated while others cannot. By introducing the concept of the effective source
number (ESN), which is the number of available accurate parameter estimates, it is
proposed to combine a radical source enumerator that tends to overestimate the number
of signals with a conservative source enumerator that tends to underestimation
for parameter estimation. Such a scheme retains the benefit of the underenumerators
with only accurate estimates while remarkably improves the estimation accuracy.
For source enumeration from a multidimensional matrix of measurements, whose
dimensions can correspond to the spatial dimensions such as 1D linear or 2D planar
arrays at the transmitter and/or receiver, as well as time, propagation delay and
polarization, much less attention has been paid in the literature compared to 1D source enumeration. In sensor array applications, often the noisefree signals follows
the parallel factor (PARAFAC) model, in which case two approaches to RD source
enumeration can be applied: matrixbased and tensorbased.
In matrixbased solutions to RD source enumeration, the measurement tensor
is unfolded into a matrix along individual (e.g., temporal) dimensions, and then the
1D eigenvalue or eigenvector/subspacebased detection methods are applied. For
eigenvaluebased detection, we generalize the rmode unfolding of a tensor so that
the unfolding along merged dimensions is included. Using the generalized unfolding
of the measurement tensor, more unfolded matrices and hence mode eigenvalues
are available for use. By optimally applying one or combining more sets of mode
eigenvalues in 1D source enumerators, we devise RD extensions of the 1D RMT,
1D eigenvalue fluctuation information criterion (EFIC) and 1D minimum description
length (MDL). Moreover, using the sequential source enumeration scheme, the
identifiable number of signals in RD RMT/EFIC/MDL reaches up to the size of the
most squared" unfolded matrix minus one, which is a significant improvement for
R ≥ 3. For eigenvectorbased detection, we devise RD extensions of the subspacebased
estimation error (ESTER), which is used for uniform RD HR in colored noise
environments.
The matrixbased RD source enumerators have limited identifiability (identifiable
number of signals) due to the unfolding operation. Instead, the CORe CONsistency
DIAgnostic (CORCONDIA), which is a tensorbased RD detection method relying
on the computationally expensive alternating least squares (ALS) PARAFAC decomposition,
is able to identify more signals. The core consistency, defined as the relative
distance of the estimated core and an identity tensor, is compared with a predefined
threshold for determining the number of signals. One drawback of the CORCONDIA
is its low detection probability even at sufficiently high SNRs. To tackle this,
it is proposed to utilize the reconstruction error to assist in detecting the number of
components. The resultant scheme presents accurate detection at both low and high
SNRs.
In subspace based RD parameter estimation, the signal and noise subspaces are
utilized for parameters estimation. In the presence of colored noise or interference, estimation of the signal subspace may be seriously affected due to the overlap between
the signal and noise subspaces. To improve the performance of signal subspace/
parameter estimation, prewhitening is required prior to the use of subspace
based RD parameter estimators. In electroencephalogram/magnetoencephalogram
and multipleinput multipleoutput (MIMO) applications, the multidimensional colored
noise has a Kronecker correlation structure which for the 2D case means that
the noise covariance matrix in joint spatiotemporal dimensions is equal to the Kronecker
product of the spatial and temporal covariance matrices. By exploiting the
Kronecker correlation structure of the multidimensional colored noise, the multidimensional
prewhitening (MDPWT) algorithm is developed by removing the noise
correlation sequentially along individual dimensions, using the corresponding correlation
factors estimated from the noiseonly measurements. The MDPWT employing
only a few noiseonly snapshots significantly improves the performance of the closedform
PARAFAC based parameter estimator (CFPPE). When noiseonly measurements
are unavailable, an algorithm for joint estimation of noise and signal parameters
and prewhitening is proposed by iteratively alternating MDPWT and CFPPE.
Moreover, to reduce the algorithm complexity, adaptive convergence thresholds are
designed as the stopping conditions such that the iterative algorithm automatically
stops at an optimal number of iterations. Simulation results show that the iterative
prewhitening scheme performs nearly the same as the MDPWT utilizing an equal
number of noiseonly and signalbearing snapshots, in all scenarios except for a special
one of intermediate SNRs and high noise correlation levels.
 Signal processing, Digital techniques, Array processors