32,848 research outputs found

    True Cramer-Rao bounds for carrier and symbol synchronization

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    This contribution considers the Cramer-Rao bound (CRB) related to estimating the synchronization parameters (carrier phase, carrier frequency and time delay) of a noisy linearly modulated signal with random data symbols. We explore various scenarios, involving the estimation of a subset of the parameters while the other parameters are either considered as nuisance parameters or a priori known to the receiver. In addition, some results related to the CRB for coded transmission will be presented

    Linear Kalman Filter-Based Grid Synchronization Technique: An Alternative Implementation

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    Grid synchronization techniques play a significant role in integrating renewable energy sources to the electric power grid. In this context, estimating the phase and frequency of the grid voltage signal is an interesting problem. Out of various techniques available in the literature, Linear Kalman Filter (LKF) is one of the most popular one. In this paper, we propose an alternative implementation of the LKF for grid synchronization application. The proposed implementation uses a linear parametric model of the grid voltage signal including DC offset. It does not involve any quadrature signal generation, rather it works by estimating the phase angle. This helps to estimate the unknown grid frequency directly from the phase angle. This clearly differentiates the proposed alternative implementation with respect to the existing implementations. Performance improvement by the proposed technique is verified extensively through comparative numerical simulation and experimental studies. Comparative results demonstrate the suitability of the proposed technique with respect to other state-of-the-art techniques namely SecondOrder Generalized Integrator Phase-Locked Loop (SOGI-PLL) and Enhanced Phase-Locked Loop (EPLL)

    Two-Time Procedure for Calculation of Carrier Frequency of Phasomodulated in Communication Systems

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    The use in radio communication systems of phase modulation of a signal intended for the transmission of useful information in a continuous mode creates the problem of frequency uncertainty of the received signal by frequency.In practice, it is not possible to implement frequency estimation in the conditions of chat uncertainty of the signal in the channel with low energy of the signal received in the continuous mode. Therefore, the estimation of the carrier frequency offset of the signal received relative to the nominal value is carried out before other synchronization procedures are included, namely: phase synchronization and clock synchronization. The paper generalizes the procedure and forms a two-step procedure for calculating the carrier frequency of the phase-modulated signal of a radio communication system for data transmission in a continuous mode, taking into account the condition of uncertainty of all signal parameters. Achieving the minimum observation interval in the given order of calculation of the carrier frequency is ensured by the use of the fast Fourier transform function. In order to analyze the effectiveness of this procedure, the process of estimating the carrier frequency of the phase-modulated signal of the radio communication system during data transmission in continuous mode and functional dependences of the maximum frequency in the signal spectrum and the minimum variance of carrier frequency estimation. This procedure allows a two-stage assessment of the carrier frequency according to the rule of maximum likelihood, taking into account the condition of uncertainty of all parameters of the signal received by the satellite communication system in a continuous mode with a minimum observation interval. Achieving the minimum observation interval in the given order of carrier frequency estimation is ensured by using the fast Fourier transform function and two estimation steps. The analysis of the efficiency of the estimation of the specified order was carried out on the basis of comparison of a ratio of the received minimum variance of an estimation of a carrier frequency and theoretically possible border of the minimum variance

    Bispectrum Inversion with Application to Multireference Alignment

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    We consider the problem of estimating a signal from noisy circularly-translated versions of itself, called multireference alignment (MRA). One natural approach to MRA could be to estimate the shifts of the observations first, and infer the signal by aligning and averaging the data. In contrast, we consider a method based on estimating the signal directly, using features of the signal that are invariant under translations. Specifically, we estimate the power spectrum and the bispectrum of the signal from the observations. Under mild assumptions, these invariant features contain enough information to infer the signal. In particular, the bispectrum can be used to estimate the Fourier phases. To this end, we propose and analyze a few algorithms. Our main methods consist of non-convex optimization over the smooth manifold of phases. Empirically, in the absence of noise, these non-convex algorithms appear to converge to the target signal with random initialization. The algorithms are also robust to noise. We then suggest three additional methods. These methods are based on frequency marching, semidefinite relaxation and integer programming. The first two methods provably recover the phases exactly in the absence of noise. In the high noise level regime, the invariant features approach for MRA results in stable estimation if the number of measurements scales like the cube of the noise variance, which is the information-theoretic rate. Additionally, it requires only one pass over the data which is important at low signal-to-noise ratio when the number of observations must be large
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