A Conjugate-Cyclic-Autocorrelation Projection-Based Algorithm for Signal Parameter Estimation
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A Conjugate-Cyclic-Autocorrelation Projection-Based Algorithm for Signal Parameter Estimation Valentina De Angelis,1 Luciano Izzo,1 Antonio Napolitano,2 and Mario Tanda1 1 Dipartimento
di Ingegneria Elettronica e delle Telecomunicazioni, Universit`a di Napoli “Federico II,” Via Claudio 21, 80125 Napoli, Italy 2 Dipartimento per le Tecnologie, Universit` a di Napoli “Parthenope,” Via Acton 38, 80133 Napoli, Italy Received 1 March 2005; Revised 8 March 2006; Accepted 13 March 2006 Recommended for Publication by Alex Gershman A new algorithm to estimate amplitude, delay, phase, and frequency offset of a received signal is presented. The frequency-offset estimation is performed by maximizing, with respect to the conjugate cycle frequency, the projection of the measured conjugatecyclic-autocorrelation function of the received signal over the true conjugate second-order cyclic autocorrelation. It is shown that this estimator is mean-square consistent, for moderate values of the data-record length, outperforms a previously proposed frequency-offset estimator, and leads to mean-square consistent estimators of the remaining parameters. Copyright © 2006 Valentina De Angelis et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Demodulation in digital communication systems requires knowledge of symbol timing, frequency offset, and phase shift of the received signal. Moreover, in several applications (e.g., power control) the knowledge of the amplitude of the received signal is also required. Several blind (i.e., non data-aided) algorithms for estimating some of the parameters of interest have been proposed in the literature. In particular, some of them exploit the cyclostationarity properties exhibited by almost all modulated signals [1]. Cyclostationary signals have statistical functions such as the autocorrelation function, moments, and cumulants that are almost-periodic functions of time. The frequencies of the Fourier series expansion of such almostperiodic functions are called cycle frequencies and are related to parameters such as the carrier frequency and the baud rate. Unlike second-order stationary statistics, secondorder cyclic statistics (e.g., the cyclic autocorrelation function and the conjugate-cyclic-autocorrelation function [1]) preserve phase information and, hence, are suitable for developing blind estimation algorithms. Cyclostationarity-exploiting blind estimation algorithms for synchronization parameters have been proposed and analyzed in [2–10]. In particular, the carrier-frequency-offset (CFO) estimator proposed in [3, 5, 9], termed conjugate-
cyclic-autocorrelation norm (CCAN), performs the maximization, with respect to the conjugate cycle frequency, of the L2 -norm of the conjugate-cyclic-autocorrelation function. In [3], it is shown that such an estimator is asymptotically Gaussian and mean-square consistent (i.e., the me
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