423 research outputs found
Euler-Bessel and Euler-Fourier Transforms
We consider a topological integral transform of Bessel (concentric
isospectral sets) type and Fourier (hyperplane isospectral sets) type, using
the Euler characteristic as a measure. These transforms convert constructible
\zed-valued functions to continuous -valued functions over a vector
space. Core contributions include: the definition of the topological Bessel
transform; a relationship in terms of the logarithmic blowup of the topological
Fourier transform; and a novel Morse index formula for the transforms. We then
apply the theory to problems of target reconstruction from enumerative sensor
data, including localization and shape discrimination. This last application
utilizes an extension of spatially variant apodization (SVA) to mitigate
sidelobe phenomena
Do the Barker Codes End?
A Barker code is a binary code with k^th autocorrelation <= 1 for all nonzero k.
At the workshop, the Barker code group split into four non-disjoint subgroups:
- An "algebra group", who explored symmetries of the search space that preserve the autocorrelations' magnitude.
- A "computing group", who explored methods for quickly finding binary codes with very good autocorrelation properties.
- A "statistics group", who explored ways to quantify what has been empirically observed about autocorrelation in the search space S_2^N.
- A "continuous group", who explored a non-discrete analogue of the problem of finding sequences with good autocorrelations
Spatial Compressive Sensing for MIMO Radar
We study compressive sensing in the spatial domain to achieve target
localization, specifically direction of arrival (DOA), using multiple-input
multiple-output (MIMO) radar. A sparse localization framework is proposed for a
MIMO array in which transmit and receive elements are placed at random. This
allows for a dramatic reduction in the number of elements needed, while still
attaining performance comparable to that of a filled (Nyquist) array. By
leveraging properties of structured random matrices, we develop a bound on the
coherence of the resulting measurement matrix, and obtain conditions under
which the measurement matrix satisfies the so-called isotropy property. The
coherence and isotropy concepts are used to establish uniform and non-uniform
recovery guarantees within the proposed spatial compressive sensing framework.
In particular, we show that non-uniform recovery is guaranteed if the product
of the number of transmit and receive elements, MN (which is also the number of
degrees of freedom), scales with K(log(G))^2, where K is the number of targets
and G is proportional to the array aperture and determines the angle
resolution. In contrast with a filled virtual MIMO array where the product MN
scales linearly with G, the logarithmic dependence on G in the proposed
framework supports the high-resolution provided by the virtual array aperture
while using a small number of MIMO radar elements. In the numerical results we
show that, in the proposed framework, compressive sensing recovery algorithms
are capable of better performance than classical methods, such as beamforming
and MUSIC.Comment: To appear in IEEE Transactions on Signal Processin
Adaptive Sparse Array Beamformer Design by Regularized Complementary Antenna Switching
In this work, we propose a novel strategy of adaptive sparse array beamformer
design, referred to as regularized complementary antenna switching (RCAS), to
swiftly adapt both array configuration and excitation weights in accordance to
the dynamic environment for enhancing interference suppression. In order to
achieve an implementable design of array reconfiguration, the RCAS is conducted
in the framework of regularized antenna switching, whereby the full array
aperture is collectively divided into separate groups and only one antenna in
each group is switched on to connect with the processing channel. A set of
deterministic complementary sparse arrays with good quiescent beampatterns is
first designed by RCAS and full array data is collected by switching among them
while maintaining resilient interference suppression. Subsequently, adaptive
sparse array tailored for the specific environment is calculated and
reconfigured based on the information extracted from the full array data. The
RCAS is devised as an exclusive cardinality-constrained optimization, which is
reformulated by introducing an auxiliary variable combined with a piece-wise
linear function to approximate the -norm function. A regularization
formulation is proposed to solve the problem iteratively and eliminate the
requirement of feasible initial search point. A rigorous theoretical analysis
is conducted, which proves that the proposed algorithm is essentially an
equivalent transformation of the original cardinality-constrained optimization.
Simulation results validate the effectiveness of the proposed RCAS strategy
Broadband adaptive beamforming with low complexity and frequency invariant response
This thesis proposes different methods to reduce the computational complexity as well as increasing the adaptation rate of adaptive broadband beamformers. This is performed exemplarily for the generalised sidelobe canceller (GSC) structure. The GSC is an alternative implementation of the linearly constrained minimum variance beamformer, which can utilise well-known adaptive filtering algorithms, such as the least mean square (LMS) or the recursive least squares (RLS) to perform unconstrained adaptive optimisation.A direct DFT implementation, by which broadband signals are decomposed into frequency bins and processed by independent narrowband beamforming algorithms, is thought to be computationally optimum. However, this setup fail to converge to the time domain minimum mean square error (MMSE) if signal components are not aligned to frequency bins, resulting in a large worst case error. To mitigate this problem of the so-called independent frequency bin (IFB) processor, overlap-save based GSC beamforming structures have been explored. This system address the minimisation of the time domain MMSE, with a significant reduction in computational complexity when compared to time-domain implementations, and show a better convergence behaviour than the IFB beamformer. By studying the effects that the blocking matrix has on the adaptive process for the overlap-save beamformer, several modifications are carried out to enhance both the simplicity of the algorithm as well as its convergence speed. These modifications result in the GSC beamformer utilising a significantly lower computational complexity compare to the time domain approach while offering similar convergence characteristics.In certain applications, especially in the areas of acoustics, there is a need to maintain constant resolution across a wide operating spectrum that may extend across several octaves. To attain constant beamwidth is difficult, particularly if uniformly spaced linear sensor array are employed for beamforming, since spatial resolution is reciprocally proportional to both the array aperture and the frequency. A scaled aperture arrangement is introduced for the subband based GSC beamformer to achieve near uniform resolution across a wide spectrum, whereby an octave-invariant design is achieved. This structure can also be operated in conjunction with adaptive beamforming algorithms. Frequency dependent tapering of the sensor signals is proposed in combination with the overlap-save GSC structure in order to achieve an overall frequency-invariant characteristic. An adaptive version is proposed for frequency-invariant overlap-save GSC beamformer. Broadband adaptive beamforming algorithms based on the family of least mean squares (LMS) algorithms are known to exhibit slow convergence if the input signal is correlated. To improve the convergence of the GSC when based on LMS-type algorithms, we propose the use of a broadband eigenvalue decomposition (BEVD) to decorrelate the input of the adaptive algorithm in the spatial dimension, for which an increase in convergence speed can be demonstrated over other decorrelating measures, such as the Karhunen-Loeve transform. In order to address the remaining temporal correlation after BEVD processing, this approach is combined with subband decomposition through the use of oversampled filter banks. The resulting spatially and temporally decorrelated GSC beamformer provides further enhanced convergence speed over spatial or temporal decorrelation methods on their own
An evolutionary algorithm approach to simultaneous multi-mission radar waveform design
It would be beneficial with today’s cluttered electromagnetic spectrum to be able to perform multiple radar missions simultaneously from a single platform. The design of a waveform for this application would greatly benefit the radar community. Radar systems are used to perform many missions, some of which include the detection and tracking of airborne and ground moving targets as well as Synthetic Aperture Radar (SAR) imaging. There are many systems that can operate in multiple modes to perform these missions, although there is no one radar that can simultaneously perform multiple missions using the same waveform [1]. Each mission can be mathematically reduced to an objective or set of objectives that can be used to evaluate their success. These objectives are functions of numerous radar and spatial parameters such as pulse repetition frequency (prf), center frequency, bandwidth, antenna beamwidth, and azimuth look angle, among others. In this thesis, an evolutionary multi-objective optimization technique known as the Strength Pareto Evolutionary Algorithm 2 (SPEA2), developed by Zitzler and Thiele [2], was applied to the simultaneous multi-mission radar waveform design problem. Several of the radar parameters mentioned above were varied to produce diverse waveforms that were manipulated using SPEA2. Due to computational constraints, the problem was approached by using two different scaled down real world scenarios to evaluate the performance of the evolutionary waveform design on a multi-objective moving target indication (MTI) mission and a multi-objective SAR mission, respectively. Multiple experiments showed that SPEA2 can select a set of Pareto optimal waveforms that accomplish these multi-objective missions effectively according to the objective functions that were developed for these missions. Finally, a procedure is outlined to combine these multi-objective MTI and SAR missions into one scaled experiment in which a distributed computing environment could be used to provide more computational resources
A Low-Cost Robust Distributed Linearly Constrained Beamformer for Wireless Acoustic Sensor Networks with Arbitrary Topology
We propose a new robust distributed linearly constrained beamformer which
utilizes a set of linear equality constraints to reduce the cross power
spectral density matrix to a block-diagonal form. The proposed beamformer has a
convenient objective function for use in arbitrary distributed network
topologies while having identical performance to a centralized implementation.
Moreover, the new optimization problem is robust to relative acoustic transfer
function (RATF) estimation errors and to target activity detection (TAD)
errors. Two variants of the proposed beamformer are presented and evaluated in
the context of multi-microphone speech enhancement in a wireless acoustic
sensor network, and are compared with other state-of-the-art distributed
beamformers in terms of communication costs and robustness to RATF estimation
errors and TAD errors
Advanced signal processing techniques for WiFi-based Passive Radar for short-range surveillance
In this work, advanced signal processing techniques for a Passive Radar (PR) based on WiFi transmissions are considered. The possibility to exploit such a ubiquitous and accessible source is shown to be an appropriate choice for the detection, localization and imaging of vehicles, people and aircrafts within short ranges in both outdoor and indoor environments
- …