Maxwell-compensated design of asymmetric gradient waveforms for tensor-valued diffusion encoding

Purpose: Asymmetric gradient waveforms are attractive for diffusion encoding due to their superior efficiency, however, the asymmetry may cause a residual gradient moment at the end of the encoding. Depending on the experiment setup, this residual moment may cause significant signal bias and image artifacts. The purpose of this study was to develop an asymmetric gradient waveform design for tensor-valued diffusion encoding that is not affected by concomitant gradient. Methods: The Maxwell index was proposed as a scalar invariant that captures the effect of concomitant gradients and was constrained in the numerical optimization to 100 (mT/m)$^2$ms to yield Maxwell-compensated waveforms. The efficacy of this design was tested in an oil phantom, and in a healthy human brain. For reference, waveforms from literature were included in the analysis. Simulations were performed to investigate if the design was valid for a wide range of experiments and if it could predict the signal bias. Results: Maxwell-compensated waveforms showed no signal bias in oil or in the brain. By contrast, several waveforms from literature showed gross signal bias. In the brain, the bias was large enough to markedly affect both signal and parameter maps, and the bias could be accurately predicted by theory. Conclusion: Constraining the Maxwell index in the optimization of asymmetric gradient waveforms yields efficient tensor-valued encoding with concomitant gradients that have a negligible effect on the signal. This waveform design is especially relevant in combination with strong gradients, long encoding times, thick slices, simultaneous multi-slice acquisition and large/oblique FOVs

Wideband Waveform Design for Robust Target Detection

Future radar systems are expected to use waveforms of a high bandwidth, where the main advantage is an improved range resolution. In this paper, a technique to design robust wideband waveforms for a Multiple-Input-Single-Output system is developed. The context is optimal detection of a single object with partially unknown parameters. The waveforms are robust in the sense that, for a single transmission, detection capability is maintained over an interval of time-delay and time-scaling (Doppler) parameters. A solution framework is derived, approximated, and formulated as an optimization by means of basis expansion. In terms of probabilities of detection and false alarm, numerical evaluation shows the efficiency of the proposed method when compared with a Linear Frequency Modulated signal and a Gaussian pulse.Comment: This paper is submitted for peer review to IEEE letters on signal processin

A note on least squares fitting of signal waveforms

Signal waveforms are very fast dampening oscillatory time series composed of exponential functions. The regular least squares fitting techniques are often unstable when used to fit exponential functions to such signal waveforms since such functions are highly correlated. Of late, some attempts have been made to estimate the parameters of such functions by Monte Carlo based search/random walk algorithms. In this study we use the Differential Evaluation based method of least squares to fit the exponential functions and obtain much more accurate results.Signal waveform; exponential functions; Differential Evolution; Global optimization; Nonlinear Least Squares; Monte Carlo; Curve fitting; parameter estimation; Random Walk; Search methods; Fortran

Fast Implementation of Transmit Beamforming for Colocated MIMO Radar

Multiple-input Multiple-output (MIMO) radars benefit from spatial and waveform diversities to improve the performance potential. Phased array radars transmit scaled versions of a single waveform thereby limiting the transmit degrees of freedom to one. However MIMO radars transmit diverse waveforms from different transmit array elements thereby increasing the degrees of freedom to form flexible transmit beampatterns. The transmit beampattern of a colocated MIMO radar depends on the zero-lag correlation matrix of different transmit waveforms. Many solutions have been developed for designing the signal correlation matrix to achieve a desired transmit beampattern based on optimization algorithms in the literature. In this paper, a fast algorithm for designing the correlation matrix of the transmit waveforms is developed that allows the next generation radars to form flexible beampatterns in real-time. An efficient method for sidelobe control with negligible increase in mainlobe width is also presented

Electrically tunable collective response in a coupled micromechanical array

We employ optical diffraction to study the mechanical properties of a grating array of suspended doubly clamped beams made of Au. The device allows application of electrostatic coupling between the beams that gives rise to formation of a band of normal modes of vibration (phonons). We parametrically excite these collective modes and study the response by measuring the diffraction signal. The results indicate that nonlinear effects strongly affect the dynamics of the system. Further optimization will allow employing similar systems for real-time mechanical spectrum analysis of electrical waveforms

Particle Swarm Optimization and gravitational wave data analysis: Performance on a binary inspiral testbed

The detection and estimation of gravitational wave (GW) signals belonging to a parameterized family of waveforms requires, in general, the numerical maximization of a data-dependent function of the signal parameters. Due to noise in the data, the function to be maximized is often highly multi-modal with numerous local maxima. Searching for the global maximum then becomes computationally expensive, which in turn can limit the scientific scope of the search. Stochastic optimization is one possible approach to reducing computational costs in such applications. We report results from a first investigation of the Particle Swarm Optimization (PSO) method in this context. The method is applied to a testbed motivated by the problem of detection and estimation of a binary inspiral signal. Our results show that PSO works well in the presence of high multi-modality, making it a viable candidate method for further applications in GW data analysis.Comment: 13 pages, 5 figure