Bill Moran | University of Melbourne (original) (raw)
Papers by Bill Moran
2010 International Conference on Electromagnetics in Advanced Applications, 2010
Limitations to current long range weather radars include reduced coverage of the lower atmosphere... more Limitations to current long range weather radars include reduced coverage of the lower atmosphere, coarse cross range resolution and coarse temporal resolution due to the mechanical scanning. A proposed network of low cost, short range digital radars for monitoring hydrometeor phenomena is described and its potential benefit in providing lower atmospheric coverage is discussed. The benefits of replacing the scanning
arXiv preprint arXiv:1211.4518, Nov 19, 2012
Abstract: Consider a countably infinite set of nodes, which sequentially make decisions between t... more Abstract: Consider a countably infinite set of nodes, which sequentially make decisions between two given hypotheses. Each node takes a measurement of the underlying truth, observes the decisions from some immediate predecessors, and makes a decision between the given hypotheses. We consider two classes of broadcast failures: 1) each node broadcasts a decision to the other nodes, subject to random erasure in the form of a binary erasure channel; 2) each node broadcasts a randomly flipped decision to the other nodes ...
Proceedings of the London Mathematical Society, 1975
... 388 WILLIAM MORAN Ui-Qfi = ZpXn (/* e M(G)) to form another member of A. In this way, A becom... more ... 388 WILLIAM MORAN Ui-Qfi = ZpXn (/* e M(G)) to form another member of A. In this way, A becomes a semigroup with a separately ... value z). A standard compact-ness argument yields that C(/u) consists of those complex numbers z for which there exists a net (ya) of characters ...
Mathematische Annalen, 1995
Journal of the London Mathematical Society, 1975
... (m \ m — 1 z bn2-' = n n=1 / n=1 n n=m+l m — 1 oo n = l n=m +1 It follows that / may be ... more ... (m \ m — 1 z bn2-' = n n=1 / n=1 n n=m+l m — 1 oo n = l n=m +1 It follows that / may be chosen piecewise continuous only if there exists a positive integer m0, such that for all m ^ m0, oo oo ' 4m/ 11 v1 ^n/ V1 sm^ 11 I1 ty . n=m+1 n=m+1 If this occurs, we have, for /„ = p
Journal of the London Mathematical Society, 1968
Bulletin of the London Mathematical Society, 1973
Proceedings of the London Mathematical Society, 1983
Let G be a discrete abelian group on which there is a multiplier a: GxG-* T. It is shown that if ... more Let G be a discrete abelian group on which there is a multiplier a: GxG-* T. It is shown that if all the irreducible representations of (G, a) are induced from 1-dimensional representations of subgroups then all of the representations of (G, a) are Type I. This represents the first step in the proof of the corresponding result for arbitrary discrete nilpotent groups.
Journal of Number Theory, 1995
ABSTRACT This paper considers normality of real numbers to distinct non- integer bases. Specifica... more ABSTRACT This paper considers normality of real numbers to distinct non- integer bases. Specifically, using the method of Riesz products, it is shown for almost all real numbers θ > 3 that, unlike in the integer case, normality to base θk does not imply normality to base θl unless l = k.
Journal of the London Mathematical Society, 1983
IEEE Transactions on Information Theory, 2012
We study the detection error probability associated with a balanced binary relay tree, where the ... more We study the detection error probability associated with a balanced binary relay tree, where the leaves of the tree correspond to N identical and independent detectors. The root of the tree represents a fusion center that makes the overall detection decision. Each of the other nodes in the tree are relay nodes that combine two binary messages to form a single output binary message. In this way, the information from the detectors is aggregated into the fusion center via the intermediate relay nodes. In this context, we describe the evolution of Type I and Type II error probabilities of the binary data as it propagates from the leaves towards the root. Tight upper and lower bounds for the total error probability at the fusion center as functions of N are derived. These characterize how fast the total error probability converges to 0 with respect to N , even if the individual sensors have error probabilities that converge to 1/2.
IEEE Transactions on Aerospace and Electronic Systems, 2009
Returns from radar transmitters are filtered to concentrate target power and improve SNR prior to... more Returns from radar transmitters are filtered to concentrate target power and improve SNR prior to detection. An ideal "thumbtack" filter response in delay and Doppler is impossible to achieve. In practice target power is distributed over the delay-Doppler plane either in a broad main lobe or in sidelobes with inherent limitations given by Moyal's identity. Many authors have considered the use of pairs or sets of complementary codes as the basis of radar waveforms. The set of filter outputs when combined reduces output to a thumbtack shape, at least on part of the delay-Doppler domain. This paper shows firstly that a pair of complementary codes cannot be multiplexed in frequency because of a phase difference which depends on the unknown range to any targets, thereby preventing the individual filter outputs from being combined coherently. It is shown that the phase term can be removed by multiplexing the second code twice, at offsets equally spaced above and below carrier, enabling the recovery of the sum of squared ambiguity functions. A proposed modification to the Golay pair results in codes whose squared ambiguities cancel upon addition. This enables complementary behaviour to be achieved by codes which are separated in frequency at the expense of introducing cross-terms when multiple closely separated returns are present. The modified Golay codes are shown to successfully reveal low power returns which are hidden in sidelobes when other waveforms are used.
Digital Signal Processing, 2011
In this work, multiple radar waveforms are simultaneously transmitted, emitted from different ant... more In this work, multiple radar waveforms are simultaneously transmitted, emitted from different antennas. The goal is to process the returns in such a way that the overall ambiguity function is a sum of individual ambiguity functions, such that the sum better approximates the ideal thumbtack shape. A unitary design for the illustrative 4 × 4 example prescribes the scheduling of the waveforms over four transmit antennas over four PRIs. Further, it dictates how the matched filtering of the returns over four PRIs is combined in such a way so as to achieve both perfect separation (of the superimposed returns) AND perfect reconstruction. Perfect reconstruction implies that the sum of the time-autocorrelations associated with each of the four waveforms is a delta function. The net result of the processing of four PRIs over four virtual antennas yields 16 crosscorrelations all of which ideally exhibit a sharp peak at the target delay. Conditions for both perfect separation and perfect reconstruction are developed, and a variety of waveform sets satisfying both are presented. Doppler compensation is achieved by a data-dependent weighting of the different PRI matched-filtered outputs prior to summing. Simulations are presented verifying the efficacy of the proposed unitary waveform matrix designs in conjunction with the proposed Doppler compensation technique.
Digital Signal Processing, 2011
We consider how information rate in a Multiple-Input Multiple-Output (MIMO) wireless communicatio... more We consider how information rate in a Multiple-Input Multiple-Output (MIMO) wireless communication system is affected by the use of non-Gaussian source distributions. Of particular interest is the comparison of information rate for a legitimate receiver with that available to an eavesdropping receiver, as the source distribution becomes less Gaussian or, equivalently, as the magnitude of the source kurtosis increases. A legitimate receiver will usually be able to perform maximum likelihood channel estimation using knowledge of a symbol training sequence embedded in the transmitted data. An eavesdropper however may not have this prior knowledge and will therefore be unable to directly estimate the channel. We compare, via simulations, the performance of a well-known Blind Source Separation (BSS) algorithm with theoretically derived results and where the source distributions are taken from the discrete digital constellations: Quadrature Amplitude Modulation (QAM), Phase Shift Keying (PSK). By incorporating a sample timing offset in the simulations we show how the kurtosis of these digital sources is altered. We also show how the legitimate user and eavesdropper information rates are affected as the source kurtosis is varied.
2006 40th Annual Conference on Information Sciences and Systems, 2006
In this paper we extend the idea of adaptive waveform selection for radar target tracking to inte... more In this paper we extend the idea of adaptive waveform selection for radar target tracking to interacting multiple model (IMM) trackers to permit the modelling of maneuvering targets by allowing multiple possible dynamical models. We develop a one step ahead solution to the problem of waveform selection, which is designed to decrease dynamic model uncertainty for the target of interest. It is based on maximization of the expected information obtained about the dynamical model of the target from the next measurement. We also discuss the design of waveform libraries for target tracking applications.
IEEE Transactions on Automatic Control, 2004
IEEE Transactions on Image Processing, 2018
Final Program and Abstracts on Information, Decision and Control, 2002
Abstract A cooperative sensor network is an array of sensors interconnected by a local or wide ar... more Abstract A cooperative sensor network is an array of sensors interconnected by a local or wide area communications network. Data is shared between the sensors and used as input to an estimator to measure a process. In the paper a stochastic sensor scheduling framework is applied to the localisation of multiple emitter targets using a cooperative sensor network in which the information rate between sensor nodes has been constrained. The stochastic sensor scheduling problem is presented and a practical sub-optimal sensor ...
While the use of complementary waveforms has been considered as a technique for providing essenti... more While the use of complementary waveforms has been considered as a technique for providing essentially perfect range sidelobe performance in radar systems, its lack of resilience to Doppler is often cited as a reason not to deploy it. This work describes and examines techniques both for providing Doppler resilience as well as tailoring Doppler performance to specific aims. The Doppler performance can be varied by suitably changing the order of transmission of multiple sets of complementary waveforms.
2010 International Conference on Electromagnetics in Advanced Applications, 2010
Limitations to current long range weather radars include reduced coverage of the lower atmosphere... more Limitations to current long range weather radars include reduced coverage of the lower atmosphere, coarse cross range resolution and coarse temporal resolution due to the mechanical scanning. A proposed network of low cost, short range digital radars for monitoring hydrometeor phenomena is described and its potential benefit in providing lower atmospheric coverage is discussed. The benefits of replacing the scanning
arXiv preprint arXiv:1211.4518, Nov 19, 2012
Abstract: Consider a countably infinite set of nodes, which sequentially make decisions between t... more Abstract: Consider a countably infinite set of nodes, which sequentially make decisions between two given hypotheses. Each node takes a measurement of the underlying truth, observes the decisions from some immediate predecessors, and makes a decision between the given hypotheses. We consider two classes of broadcast failures: 1) each node broadcasts a decision to the other nodes, subject to random erasure in the form of a binary erasure channel; 2) each node broadcasts a randomly flipped decision to the other nodes ...
Proceedings of the London Mathematical Society, 1975
... 388 WILLIAM MORAN Ui-Qfi = ZpXn (/* e M(G)) to form another member of A. In this way, A becom... more ... 388 WILLIAM MORAN Ui-Qfi = ZpXn (/* e M(G)) to form another member of A. In this way, A becomes a semigroup with a separately ... value z). A standard compact-ness argument yields that C(/u) consists of those complex numbers z for which there exists a net (ya) of characters ...
Mathematische Annalen, 1995
Journal of the London Mathematical Society, 1975
... (m \ m — 1 z bn2-' = n n=1 / n=1 n n=m+l m — 1 oo n = l n=m +1 It follows that / may be ... more ... (m \ m — 1 z bn2-' = n n=1 / n=1 n n=m+l m — 1 oo n = l n=m +1 It follows that / may be chosen piecewise continuous only if there exists a positive integer m0, such that for all m ^ m0, oo oo ' 4m/ 11 v1 ^n/ V1 sm^ 11 I1 ty . n=m+1 n=m+1 If this occurs, we have, for /„ = p
Journal of the London Mathematical Society, 1968
Bulletin of the London Mathematical Society, 1973
Proceedings of the London Mathematical Society, 1983
Let G be a discrete abelian group on which there is a multiplier a: GxG-* T. It is shown that if ... more Let G be a discrete abelian group on which there is a multiplier a: GxG-* T. It is shown that if all the irreducible representations of (G, a) are induced from 1-dimensional representations of subgroups then all of the representations of (G, a) are Type I. This represents the first step in the proof of the corresponding result for arbitrary discrete nilpotent groups.
Journal of Number Theory, 1995
ABSTRACT This paper considers normality of real numbers to distinct non- integer bases. Specifica... more ABSTRACT This paper considers normality of real numbers to distinct non- integer bases. Specifically, using the method of Riesz products, it is shown for almost all real numbers θ > 3 that, unlike in the integer case, normality to base θk does not imply normality to base θl unless l = k.
Journal of the London Mathematical Society, 1983
IEEE Transactions on Information Theory, 2012
We study the detection error probability associated with a balanced binary relay tree, where the ... more We study the detection error probability associated with a balanced binary relay tree, where the leaves of the tree correspond to N identical and independent detectors. The root of the tree represents a fusion center that makes the overall detection decision. Each of the other nodes in the tree are relay nodes that combine two binary messages to form a single output binary message. In this way, the information from the detectors is aggregated into the fusion center via the intermediate relay nodes. In this context, we describe the evolution of Type I and Type II error probabilities of the binary data as it propagates from the leaves towards the root. Tight upper and lower bounds for the total error probability at the fusion center as functions of N are derived. These characterize how fast the total error probability converges to 0 with respect to N , even if the individual sensors have error probabilities that converge to 1/2.
IEEE Transactions on Aerospace and Electronic Systems, 2009
Returns from radar transmitters are filtered to concentrate target power and improve SNR prior to... more Returns from radar transmitters are filtered to concentrate target power and improve SNR prior to detection. An ideal "thumbtack" filter response in delay and Doppler is impossible to achieve. In practice target power is distributed over the delay-Doppler plane either in a broad main lobe or in sidelobes with inherent limitations given by Moyal's identity. Many authors have considered the use of pairs or sets of complementary codes as the basis of radar waveforms. The set of filter outputs when combined reduces output to a thumbtack shape, at least on part of the delay-Doppler domain. This paper shows firstly that a pair of complementary codes cannot be multiplexed in frequency because of a phase difference which depends on the unknown range to any targets, thereby preventing the individual filter outputs from being combined coherently. It is shown that the phase term can be removed by multiplexing the second code twice, at offsets equally spaced above and below carrier, enabling the recovery of the sum of squared ambiguity functions. A proposed modification to the Golay pair results in codes whose squared ambiguities cancel upon addition. This enables complementary behaviour to be achieved by codes which are separated in frequency at the expense of introducing cross-terms when multiple closely separated returns are present. The modified Golay codes are shown to successfully reveal low power returns which are hidden in sidelobes when other waveforms are used.
Digital Signal Processing, 2011
In this work, multiple radar waveforms are simultaneously transmitted, emitted from different ant... more In this work, multiple radar waveforms are simultaneously transmitted, emitted from different antennas. The goal is to process the returns in such a way that the overall ambiguity function is a sum of individual ambiguity functions, such that the sum better approximates the ideal thumbtack shape. A unitary design for the illustrative 4 × 4 example prescribes the scheduling of the waveforms over four transmit antennas over four PRIs. Further, it dictates how the matched filtering of the returns over four PRIs is combined in such a way so as to achieve both perfect separation (of the superimposed returns) AND perfect reconstruction. Perfect reconstruction implies that the sum of the time-autocorrelations associated with each of the four waveforms is a delta function. The net result of the processing of four PRIs over four virtual antennas yields 16 crosscorrelations all of which ideally exhibit a sharp peak at the target delay. Conditions for both perfect separation and perfect reconstruction are developed, and a variety of waveform sets satisfying both are presented. Doppler compensation is achieved by a data-dependent weighting of the different PRI matched-filtered outputs prior to summing. Simulations are presented verifying the efficacy of the proposed unitary waveform matrix designs in conjunction with the proposed Doppler compensation technique.
Digital Signal Processing, 2011
We consider how information rate in a Multiple-Input Multiple-Output (MIMO) wireless communicatio... more We consider how information rate in a Multiple-Input Multiple-Output (MIMO) wireless communication system is affected by the use of non-Gaussian source distributions. Of particular interest is the comparison of information rate for a legitimate receiver with that available to an eavesdropping receiver, as the source distribution becomes less Gaussian or, equivalently, as the magnitude of the source kurtosis increases. A legitimate receiver will usually be able to perform maximum likelihood channel estimation using knowledge of a symbol training sequence embedded in the transmitted data. An eavesdropper however may not have this prior knowledge and will therefore be unable to directly estimate the channel. We compare, via simulations, the performance of a well-known Blind Source Separation (BSS) algorithm with theoretically derived results and where the source distributions are taken from the discrete digital constellations: Quadrature Amplitude Modulation (QAM), Phase Shift Keying (PSK). By incorporating a sample timing offset in the simulations we show how the kurtosis of these digital sources is altered. We also show how the legitimate user and eavesdropper information rates are affected as the source kurtosis is varied.
2006 40th Annual Conference on Information Sciences and Systems, 2006
In this paper we extend the idea of adaptive waveform selection for radar target tracking to inte... more In this paper we extend the idea of adaptive waveform selection for radar target tracking to interacting multiple model (IMM) trackers to permit the modelling of maneuvering targets by allowing multiple possible dynamical models. We develop a one step ahead solution to the problem of waveform selection, which is designed to decrease dynamic model uncertainty for the target of interest. It is based on maximization of the expected information obtained about the dynamical model of the target from the next measurement. We also discuss the design of waveform libraries for target tracking applications.
IEEE Transactions on Automatic Control, 2004
IEEE Transactions on Image Processing, 2018
Final Program and Abstracts on Information, Decision and Control, 2002
Abstract A cooperative sensor network is an array of sensors interconnected by a local or wide ar... more Abstract A cooperative sensor network is an array of sensors interconnected by a local or wide area communications network. Data is shared between the sensors and used as input to an estimator to measure a process. In the paper a stochastic sensor scheduling framework is applied to the localisation of multiple emitter targets using a cooperative sensor network in which the information rate between sensor nodes has been constrained. The stochastic sensor scheduling problem is presented and a practical sub-optimal sensor ...
While the use of complementary waveforms has been considered as a technique for providing essenti... more While the use of complementary waveforms has been considered as a technique for providing essentially perfect range sidelobe performance in radar systems, its lack of resilience to Doppler is often cited as a reason not to deploy it. This work describes and examines techniques both for providing Doppler resilience as well as tailoring Doppler performance to specific aims. The Doppler performance can be varied by suitably changing the order of transmission of multiple sets of complementary waveforms.