Optimal Pulse Design Research Articles

Optimal pulse design for visible light positioning systems

The problem of optimal pulse design for light-emitting diode (LED) transmitters is investigated in an indoor visible light positioning (VLP) setup. In particular, the problem of localization performance maximization is formulated for both asynchronous and synchronous VLP systems with consideration of practical limitations related to power consumption, illumination levels, and/or effective bandwidths, while quantifying the localization accuracy via the Cramér–Rao lower bound (CRLB). In both asynchronous and synchronous scenarios, the formulated problems are shown to be convex optimization problems, and some properties of the optimal solutions are derived. In addition, the pulse design problem for minimum power consumption is formulated under a CRLB constraint along with other practical limitations; and this problem is also revealed to be a convex optimization problem. Based on the solutions of the proposed optimization problems, pulse design procedures are described to determine the parameters of optimal pulse shapes. Numerical results illustrate the benefits of the proposed optimal pulse design approach in comparison with the state-of-the-art optimal power allocation scheme in the literature. In particular, electrical power consumption can be reduced by around 45% or localization accuracy can be improved by as much as 25% via the proposed optimal pulse design approach in certain scenarios.

Highly Linear and Symmetric Weight Modification in HfO2‐Based Memristive Devices for High‐Precision Weight Entries

AbstractIn this study, highly reliable and accurate weight‐modification behaviors are realized using a W/Al2O3 (3 nm)/HfO2 (7 nm)/TiN memristive device. The accuracy of the simulated inference of the MNIST dataset when considering the weight‐modification behavior is ≈95%. It is determined the optimal programming voltage pulsing conditions considering i) a high linearity in the weight‐modification, ii) symmetry between potentiation and depression, and iii) an alleviation of the voltage‐driving circuit overhead for the related part of weight‐modification process. Particular emphasis is placed on the last concern, and thus, the fixed shape of each programming pulse for both potentiation and depression are utilized. The optimal pulse design is 500 µs for the pulse rising, plateau, and falling times and a 2 V amplitude at the absolute scale. Additionally, the nonparametric method to evaluate the linearity and symmetry as opposed to the application of several parametric methods are proposed. The nonparametric method is based on an evaluation of actual data rather than models, and thus considers the actual variability in the conductance change, which is otherwise often ignored in the parameter optimization process.

Statistics of the MLE and Approximate Upper and Lower Bounds–Part II: Threshold Computation and Optimal Pulse Design for TOA Estimation

Threshold and ambiguity phenomena are studied in Part I of this paper where approximations for the mean-squared error (MSE) of the maximum-likelihood estimator are proposed using the method of interval estimation (MIE), and where approximate upper and lower bounds are derived. In this part, we consider time-of-arrival estimation and we employ the MIE to derive closed-form expressions of the begin-ambiguity, end-ambiguity and asymptotic signal-to-noise ratio (SNR) thresholds with respect to some features of the transmitted signal. Both baseband and passband pulses are considered. We prove that the begin-ambiguity threshold depends only on the shape of the envelope of the ACR, whereas the end-ambiguity and asymptotic thresholds only on the shape of the ACR. We exploit the results on the begin-ambiguity and asymptotic thresholds to optimize, with respect to the available SNR, the pulse that achieves the minimum attainable MSE. The results of this paper are valid for various estimation problems.

Low-Complexity ICI/ISI Equalization in Doubly Dispersive Multicarrier Systems Using a Decision-Feedback LSQR Algorithm

We propose a low-complexity intercarrier interference/intersymbol interference (ICI/ISI) equalizer for multicarrier transmissions over doubly dispersive channels. Decision-feedback (or interference cancellation) is used with respect to both time and frequency. The ICI stage employs an extension of the iterative LSQR algorithm using groupwise interference cancellation with reliability-based sorting of sets of subcarriers and a band approximation of the frequency-domain channel matrix. The LSQR algorithm is attractive because of its excellent numerical properties and low complexity. Optimal pulse design is optionally considered for shaping the ICI/ISI. Simulation results demonstrate the excellent performance of the proposed ICI/ISI equalizer.

Optimal pulse design in quantum control: A unified computational method

Many key aspects of control of quantum systems involve manipulating a large quantum ensemble exhibiting variation in the value of parameters characterizing the system dynamics. Developing electromagnetic pulses to produce a desired evolution in the presence of such variation is a fundamental and challenging problem in this research area. We present such robust pulse designs as an optimal control problem of a continuum of bilinear systems with a common control function. We map this control problem of infinite dimension to a problem of polynomial approximation employing tools from geometric control theory. We then adopt this new notion and develop a unified computational method for optimal pulse design using ideas from pseudospectral approximations, by which a continuous-time optimal control problem of pulse design can be discretized to a constrained optimization problem with spectral accuracy. Furthermore, this is a highly flexible and efficient numerical method that requires low order of discretization and yields inherently smooth solutions. We demonstrate this method by designing effective broadband π/2 and π pulses with reduced rf energy and pulse duration, which show significant sensitivity enhancement at the edge of the spectrum over conventional pulses in 1D and 2D NMR spectroscopy experiments.

A pseudospectral method for optimal control of open quantum systems

In this paper, we present a unified computational method based on pseudospectral approximations for the design of optimal pulse sequences in open quantum systems. The proposed method transforms the problem of optimal pulse design, which is formulated as a continuous-time optimal control problem, to a finite-dimensional constrained nonlinear programming problem. This resulting optimization problem can then be solved using existing numerical optimization suites. We apply the Legendre pseudospectral method to a series of optimal control problems on open quantum systems that arise in nuclear magnetic resonance spectroscopy in liquids. These problems have been well studied in previous literature and analytical optimal controls have been found. We find an excellent agreement between the maximum transfer efficiency produced by our computational method and the analytical expressions. Moreover, our method permits us to extend the analysis and address practical concerns, including smoothing discontinuous controls as well as deriving minimum-energy and time-optimal controls. The method is not restricted to the systems studied in this article and is applicable to optimal manipulation of both closed and open quantum systems.

Compensation of a Non-idealUWB Antenna Performance

Non-ideal hardware degrades the performance in UWB systems. Especially the non-isotropic transmit antenna is critical: To meet the regulation, the maximal antenna gain must be substracted from the regulation which leads to reduced transmit power, and hence decreased signal-to-noise-ratio. This contribution briefly describes the modeling of a complete, non-ideal impulse radio system and, based on this, shows strategies to improve the performance. This includes optimal pulse design with joint compensation of the frequency response of the non-isotropic transmit antenna. For this two different compensation methods are presented. An UWB communication system simulation delivers the achievable bit error rates and clearly shows the improvement by the compensation measures. Index Terms – UWB, antenna compensation, non-ideal hardware, optimal pulse design, bit error rate, system simulation

Optimal pulse design for communication-oriented slow-light pulse detection

We present techniques for designing pulses for linear slow-light delay systems which are optimal in the sense that they maximize the signal-to-noise ratio (SNR) and signal-to-noise-plus-interference ratio (SNIR) of the detected pulse energy. Given a communication model in which input pulses are created in a finite temporal window and output pulse energy in measured in a temporally-offset output window, the SNIR-optimal pulses achieve typical improvements of 10 dB compared to traditional pulse shapes for a given output window offset. Alternatively, for fixed SNR or SNIR, window offset (detection delay) can be increased by 0.3 times the window width. This approach also invites a communication-based model for delay and signal fidelity.

Time optimal control in spin systems

In this paper, we study the design of pulse sequences for NMR spectroscopy as a problem of time optimal control of the unitary propagator. Radio frequency pulses are used in coherent spectroscopy to implement a unitary transfer of state. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we give an analytical characterization of such time optimal pulse sequences applicable to coherence transfer experiments in multiple-spin systems. We have adopted a general mathematical formulation, and present many of our results in this setting, mindful of the fact that new structures in optimal pulse design are constantly arising. Moreover, the general proofs are no more difficult than the specific problems of current interest. From a general control theory perspective, the problems we want to study have the following character. Suppose we are given a controllable right invariant system on a compact Lie group, what is the minimum time required to steer the system from some initial point to a specified final point? In NMR spectroscopy and quantum computing, this translates to, what is the minimum time required to produce a unitary propagator? We also give an analytical characterization of maximum achievable transfer in a given time for the two spin system.