A Truncated Matched Filter Method for Interrupted Sampling Repeater Jamming Suppression Based on Jamming Reconstruction

Interrupted sampling repeater jamming (ISRJ) is becoming more widely used in electronic countermeasures (ECM), thanks to the development of digital radio frequency memory (DRFM). Radar electronic counter-countermeasure (ECCM) is much more difficult when the jamming signal is coherent with the emitted signal. Due to the intermittent transmission feature of ISRJ, the energy accumulation of jamming on the matched filter shows a ‘ladder’ characteristic, whereas the real target signal is continuous. As a consequence, the time delay and distribution of the jamming slice can be obtained based on searching the truncated-matched-filter (TMF) matrix. That is composed of pulse compression (PC) results under matched filters with different lengths. Based on the above theory, this paper proposes a truncated matched filter method by the reconstruction of jamming slices to suppress ISRJ of linear frequency modulation (LFM) radars. The numerical simulations indicate the effectiveness of the proposed method and validate the theoretical analysis.

Detection of Motor-Evoked Potentials Below the Noise Floor: Rethinking the Motor Threshold

Background: Motor-evoked potentials (MEP) are one of the most prominent responses to brain stimulation, such as supra-threshold transcranial magnetic stimulation (TMS) and electrical stimulation. Understanding of the neurophysiology and the determination of the lowest stimulation strength that evokes responses requires the detection of even smaller responses, e.g., from single motor units. However, available detection and quantization methods suffer from a large noise floor. Objective: This paper develops a detection method that extracts MEPs hidden below the noise floor. With this method, we aim to estimate excitatory activations of the corticospinal pathways well below the conventional detection level. Methods: The presented MEP detection method presents a self-learning matched-filter approach for improved robustness against noise. The filter is adaptively generated per subject through iterative learning. For responses that are reliably detected by conventional detection, the new approach is fully compatible with established peak-to-peak readings and provides the same results but extends the dynamic range below the conventional noise floor. Results: In contrast to the conventional peak-to-peak measure, the proposed method increases the signal-to-noise ratio by more than a factor of 5. The first detectable responses appear to be substantially lower than the conventional threshold definition of 50 μV median peak-to-peak amplitude. Conclusion: The proposed method shows that stimuli well below the conventional 50 μV threshold definition can consistently and repeatably evoke muscular responses and thus activate excitable neuron populations in the brain. As a consequence, the IO curve is extended at the lower end, and the noise cut-off is shifted. Importantly, the IO curve extends so far that the 50 μV point turns out to be closer to the center of the logarithmic sigmoid curve rather than close to the first detectable responses. The underlying method is applicable to a wide range of evoked potentials and other biosignals, such as in electroencephalography.

Code Optimisation Framework for Multicode Sonar Systems

<p>The ocean is a temporally and spatially varying environment, the characteristics of which pose significant challenges to the development of effective underwater wireless communications and sensing systems. An underwater sensing system such as a sonar detects the presence of a known signal through correlation. It is advantageous to use multiple transducers to increase surveying area with reduced surveying costs and time. Each transducers is assigned a dedicated code. When using multiple codes, the sidelobes of auto- and crosscorrelations are restricted to theoretical limits known as bounds. Sets of codes must be optimised in order to achieve optimal correlation properties, and, achieve Sidelobe Level (SLL)s as low as possible. In this thesis, we present a novel code-optimisation method to optimise code-sets with any number of codes and up to any length of each code. We optimise code-sets for a matched filter for application in a multi-code sonar system. We first present our gradient-descent based algorithm to optimise sets of codes for flat and low crosscorrelations and autocorrelation sidelobes, including conformance of the magnitude of the samples of the codes to a target power profile. We incorporate the transducer frequency response and the channel effects into the optimisation algorithm. We compare the correlations of our optimised codes with the well-known Welch bound. We then present a method to widen the autocorrelation mainlobe and impose monotonicity. In many cases, we are able to achieve SLLs beyond the Welch bound. We study the Signal to Noise Ratio (SNR) improvement of the optimised codes for an Underwater Acoustic (UWA) channel. During its propagation, the acoustic wave suffers non-constant transmission loss which is compensated by the application of an appropriate Time Variable Gain (TVG). The effect of the TVG modifies the noise received with the signal. We show that in most cases, the matched filter is still the optimum filter. We also show that the accuracy in timing is very important in the application of the TVG to the received signal. We then incorporate Doppler tolerance into the existing optimisation algorithm. Our proposed method is able to optimise sets of codes for multiple Doppler scaling factors and non-integer delays in the arrival of the reflection, while still conforming to other constraints. We suggest designing mismatched filters to further reduce the SLLs, firstly using an existing Quadratically Constrained Qaudratic Program (QCQP) formulation and secondly, as a local optimisation problem, modifying our basic optimisation algorithm.</p>

Code Optimisation Framework for Multicode Sonar Systems

<p>The ocean is a temporally and spatially varying environment, the characteristics of which pose significant challenges to the development of effective underwater wireless communications and sensing systems. An underwater sensing system such as a sonar detects the presence of a known signal through correlation. It is advantageous to use multiple transducers to increase surveying area with reduced surveying costs and time. Each transducers is assigned a dedicated code. When using multiple codes, the sidelobes of auto- and crosscorrelations are restricted to theoretical limits known as bounds. Sets of codes must be optimised in order to achieve optimal correlation properties, and, achieve Sidelobe Level (SLL)s as low as possible. In this thesis, we present a novel code-optimisation method to optimise code-sets with any number of codes and up to any length of each code. We optimise code-sets for a matched filter for application in a multi-code sonar system. We first present our gradient-descent based algorithm to optimise sets of codes for flat and low crosscorrelations and autocorrelation sidelobes, including conformance of the magnitude of the samples of the codes to a target power profile. We incorporate the transducer frequency response and the channel effects into the optimisation algorithm. We compare the correlations of our optimised codes with the well-known Welch bound. We then present a method to widen the autocorrelation mainlobe and impose monotonicity. In many cases, we are able to achieve SLLs beyond the Welch bound. We study the Signal to Noise Ratio (SNR) improvement of the optimised codes for an Underwater Acoustic (UWA) channel. During its propagation, the acoustic wave suffers non-constant transmission loss which is compensated by the application of an appropriate Time Variable Gain (TVG). The effect of the TVG modifies the noise received with the signal. We show that in most cases, the matched filter is still the optimum filter. We also show that the accuracy in timing is very important in the application of the TVG to the received signal. We then incorporate Doppler tolerance into the existing optimisation algorithm. Our proposed method is able to optimise sets of codes for multiple Doppler scaling factors and non-integer delays in the arrival of the reflection, while still conforming to other constraints. We suggest designing mismatched filters to further reduce the SLLs, firstly using an existing Quadratically Constrained Qaudratic Program (QCQP) formulation and secondly, as a local optimisation problem, modifying our basic optimisation algorithm.</p>

Low Correlation Codes for Sonar Systems

<p>Sonar is a vital technology for the detection of objects in the water. Sonarsystems have been redefined over many decades, but research is still beingconducted into optimal detection methods. Codes, and the filters thatprocess the codes, have been at the forefront of this research. An importantobjective has been the minimization of interference caused by reflections.Matched filters are commonly used in sonar systems. They are equivalent tocorrelation filters, which are bound by the Welch bound. The Welch boundgoverns the minimum peak correlation for points outside of detection.This thesis investigated matched filters and their bounds, and it wasfound that by relaxing the condition for detection, properties beyond theWelch bound could be achieved. By relaxing these conditions, the Welchbound no longer applies, and so a modified Welch bound was developedto accurately investigate the nature of these codes. In this thesis, methodsto generate codes for these new codes were investigated. Generating codesfor a matched filter is a non-convex problem, so gradient based methodswere utilised. Methods to improve correlation and power characteristicswere developed, along with methods for mapping a sequence for use witha digital transmitter having particular limitations. Mis-matched filters wereused to improve signal characteristics that may be lost due to this mapping.The performance of the generated codes was evaluated, and the rela-tionships between input parameters and output properties of the resultingsignal were observed. These performance assessments demonstrate thattradeoffs are required between various properties, and a balance is neededto obtain codes useful for sonar. The optimization was parametrized by anexample set of requirements for sonar. The signals were found to meet the given requirements, and when compared to codes typically used in sonar,the optimized signals were shown to have significantly better correlationproperties. Furthermore, compared to the general bounds for the propertiesof codes, it was found that the new codes had nearly optimal properties,and performed better than equivalent codes bounded by the Welch bound.The performance of codes were also investigated in a water tank toverify their feasibility. There were several additional considerations whichlimit codes that can be tested, and once these are taken into account thetest provided a robust method to verify the design process. Initial testsshowed results that differed from simulations, but after the inclusion ofzero padding before upscaling, the results from empirical testing agreewith simulation.Summarizing the research in this thesis, a new set of codes were devel-oped using a gradient based optimization method. The codes were mappedto a digital transmitter, and the filter adjusted using a mis-matched filter. The optimization was shown to generate near optimal codes which met allthe given sonar system requirements</p>

Low Correlation Codes for Sonar Systems

<p>Sonar is a vital technology for the detection of objects in the water. Sonarsystems have been redefined over many decades, but research is still beingconducted into optimal detection methods. Codes, and the filters thatprocess the codes, have been at the forefront of this research. An importantobjective has been the minimization of interference caused by reflections.Matched filters are commonly used in sonar systems. They are equivalent tocorrelation filters, which are bound by the Welch bound. The Welch boundgoverns the minimum peak correlation for points outside of detection.This thesis investigated matched filters and their bounds, and it wasfound that by relaxing the condition for detection, properties beyond theWelch bound could be achieved. By relaxing these conditions, the Welchbound no longer applies, and so a modified Welch bound was developedto accurately investigate the nature of these codes. In this thesis, methodsto generate codes for these new codes were investigated. Generating codesfor a matched filter is a non-convex problem, so gradient based methodswere utilised. Methods to improve correlation and power characteristicswere developed, along with methods for mapping a sequence for use witha digital transmitter having particular limitations. Mis-matched filters wereused to improve signal characteristics that may be lost due to this mapping.The performance of the generated codes was evaluated, and the rela-tionships between input parameters and output properties of the resultingsignal were observed. These performance assessments demonstrate thattradeoffs are required between various properties, and a balance is neededto obtain codes useful for sonar. The optimization was parametrized by anexample set of requirements for sonar. The signals were found to meet the given requirements, and when compared to codes typically used in sonar,the optimized signals were shown to have significantly better correlationproperties. Furthermore, compared to the general bounds for the propertiesof codes, it was found that the new codes had nearly optimal properties,and performed better than equivalent codes bounded by the Welch bound.The performance of codes were also investigated in a water tank toverify their feasibility. There were several additional considerations whichlimit codes that can be tested, and once these are taken into account thetest provided a robust method to verify the design process. Initial testsshowed results that differed from simulations, but after the inclusion ofzero padding before upscaling, the results from empirical testing agreewith simulation.Summarizing the research in this thesis, a new set of codes were devel-oped using a gradient based optimization method. The codes were mappedto a digital transmitter, and the filter adjusted using a mis-matched filter. The optimization was shown to generate near optimal codes which met allthe given sonar system requirements</p>

Using low-frequency earthquakes to monitor slow tectonic deformation in the central Southern Alps, New Zealand

<p>This thesis involves the study of low-frequency earthquakes (LFEs) in the central Southern Alps. The Alpine Fault is the principal locus of deformation within the Australia–Pacific plate boundary in the South Island of New Zealand and it is late in its typical ∼300-year seismic cycle. Surveying the seismicity associated with slow deformation in the vicinity of the Alpine Fault may provide constraints on the stresses acting on a major transpressive margin prior to an anticipated great (≥M8) earthquake. Here, we use 8 years of data from the Southern Alps Microearthquake Borehole Array (SAMBA) (amongst those, 3 years of data were collected as part of this project) in order to: (1) generate an updated LFE catalogue using an improved matched-filter technique that incorporates phase-weighted stacking; (2) compute LFE focal mechanisms and invert them to infer the crustal stress field on the deep extent of the Alpine Fault; (3) expand the LFE catalogue to cover a wider range of spatial/temporal behaviours; (4) study LFE families’ characteristics to identify periods where slow slip might happen. We first use fourteen primary LFE templates in an iterative matched-filter and stacking routine, which allows the detection of similar signals and produces LFE families sharing common locations. We generate an 8-yr catalogue containing 10,000 LFEs that are combined for each of the 14 LFE families using phase-weighted stacking to produce signals with the highest possible signal-to-noise ratios. We find LFEs to occur almost continuously during the 8-yr study period and we highlight two types of LFE distributions: (1) discrete behaviour with an inter-event time exceeding 2 minutes; (2) burst-like behaviour with an inter-event time below 2 minutes. The discrete events are interpreted as small-scale frequent deformation on the deep extent of the Alpine Fault and the LFE bursts (corresponding in most cases to known episodes of tremor or large regional earthquakes) are interpreted as brief periods of increased slip activity indicative of slow slip. We compute improved non-linear earthquake locations using a 3D velocity model and find LFEs to occur below the seismogenic zone at depths of 17–42 km, on or near the hypothesised deep extent of the Alpine Fault. We then compute the first estimates of LFE focal mechanisms associated with continental faulting. Focal mechanisms, in conjunction with recurrence intervals, are consistent with quasi-continuous shear faulting on the deep extent of the Alpine Fault. We then generate a new catalogue that regroups hundreds of LFE families. This time 638 synthetic LFE waveforms are generated using a 3D grid and used as primary templates in a matched-filter routine. Of those, 529 templates yield enough detections during the first iteration of the matched-filter routine (≥ 500 detections over the 8-yr study period) and are kept for further analysis. We then use the best 25% of correlated events for each LFE family to generate linear stacks which create new LFE templates. From there, we run a second and final iteration of the matched-filter routine with the new LFE templates to obtain our final LFE catalogue. The remaining 529 templates detect between 150 and 1,671 events each totalling 300,996 detections over the 8-yr study period. Of those 529 LFEs, we manage to locate 378 families. Their depths range between 11 and 60 km and LFEs locate mainly in the southern part of the SAMBA network. We finally examine individual LFE family rates and occurrence patterns. They indicate that LFE sources seem to evolve from an episodic or ‘stepped’ to a continuous behaviour with depth. This transition may correspond to an evolution from a stick-slip to a stable-sliding slip regime. Hence, we propose that the distinctive features of LFE occurrence patterns reflect variations in the in-situ stress and frictional conditions at the individual LFE source locations on the Alpine Fault. Finally, we use this new extensive catalogue as a tool for in-depth analyses of the deep central Alpine Fault structure and its slip behaviour. We identify eight episodes of increased LFE activity between 2009 and 2017 and provide time windows for further investigations of tremor and slow slip. We also study the spatial and temporal behaviours of LFEs and find that LFEs with synchronous occurrence patterns tend to be clustered in space. We thus suggest that individual LFE sources form spatially coherent clusters that may represent localised asperities or elastic patches on the deep Alpine Fault interface. We infer that those clusters may have a similar rheological response to tectonic forcing or to potential slow slip events. Eventually, we discover slow (10km/day) and rapid (∼20-25km/h) migrations of LFEs along the Alpine Fault. The slow migration might be controlled by slow slip events themselves while the rapid velocities could be explained by the LFE sources’ intrinsic properties.</p>