Quasi maximum likelihood estimator of polynomial phase signals for compressed sensed data

Abstract Several papers in the literature cover parameter estimation of frequency modulated (FM) signals under reduced number of signal samples with respect to the Nyquist/Shannon criterion, i.e., within the compressive sensing (CS) framework. However, scope of these papers is mainly limited to sinusoids or sum of sinusoids. In this paper, the CS framework is extended to parameter estimation of higher order polynomial phase signals (PPSs) using the quasi-maximum likelihood (QML) estimator and robust short-time Fourier transform (STFT). The considered signal is assumed to be non-uniformly sampled PPS with smaller number of samples with respect to the Nyquist/Shannon criterion. However, the proposed technique can also be generalized to uniformly sampled signals with missing or unreliable samples.

[1]  Braham Barkat,et al.  Robust time-frequency distributions based on the robust short time fourier transform , 2005, Ann. des Télécommunications.

[2]  Saeed V. Vaseghi,et al.  Advanced Digital Signal Processing and Noise Reduction , 2006 .

[3]  Douglas A. Gray,et al.  Performance bounds for polynomial phase parameter estimation with nonuniform and random sampling schemes , 2000, IEEE Trans. Signal Process..

[4]  E. Candès.  The restricted isometry property and its implications for compressed sensing , 2008 .

[5]  Benjamin Friedlander,et al.  The discrete polynomial-phase transform , 1995, IEEE Trans. Signal Process..

[6]  Saeed V. Vaseghi,et al.  Advanced Digital Signal Processing and Noise Reduction: Vaseghi: Advanced , 2001 .

[7]  Vladimir V. Lukin,et al.  An Overview of the Adaptive Robust DFT , 2010, EURASIP J. Adv. Signal Process..

[8]  Peter O'Shea,et al.  On Refining Polynomial Phase Signal Parameter Estimates , 2010, IEEE Transactions on Aerospace and Electronic Systems.

[9]  D. L. Donoho,et al.  Compressed sensing , 2006, IEEE Trans. Inf. Theory.

[10]  Igor Djurovic,et al.  Robust L-estimation based forms of signal transforms and time-frequency representations , 2003, IEEE Trans. Signal Process..

[11]  Irena Orovic,et al.  Robust Time-Frequency Analysis Based on the L-Estimation and Compressive Sensing , 2013, IEEE Signal Processing Letters.

[12]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[13]  Igor Djurovic,et al.  STFT-based estimator of polynomial phase signals , 2012, Signal Process..

[14]  Athanasios Mouchtaris,et al.  Encoding the sinusoidal model of an audio signal using compressed sensing , 2009, 2009 IEEE International Conference on Multimedia and Expo.

[15]  Boaz Porat,et al.  The Cramer-Rao lower bound for signals with constant amplitude and polynomial phase , 1991, IEEE Trans. Signal Process..

[16]  Vladimir V. Lukin,et al.  Combination of non-linear filters in time and frequency domain , 2005, Proceedings of the Eighth International Symposium on Signal Processing and Its Applications, 2005..

[17]  Peter O'Shea.  Improving Polynomial Phase Parameter Estimation by Using Nonuniformly Spaced Signal Sample Methods , 2012, IEEE Transactions on Signal Processing.

[18]  Vladimir V. Lukin,et al.  Estimation of single-tone signal frequency by using the L-DFT , 2007, Signal Process..

[19]  Vladimir Katkovnik.  Robust M-periodogram , 1998, IEEE Trans. Signal Process..

[20]  Sergio Barbarossa,et al.  Analysis of polynomial-phase signals by the integrated generalized ambiguity function , 1997, IEEE Trans. Signal Process..

[21]  I. Djurovic,et al.  Recent advances in the estimation of the polynomial-phase signals , 2012, 2012 Mediterranean Conference on Embedded Computing (MECO).

[22]  Anna Scaglione,et al.  Product high-order ambiguity function for multicomponent polynomial-phase signal modeling , 1998, IEEE Trans. Signal Process..

[23]  Igor Djurovic,et al.  Are genetic algorithms useful for the parameter estimation of FM signals? , 2012, Digit. Signal Process..

[24]  Vladimir V. Lukin,et al.  Robust DFT with high breakdown point for complex-valued impulse noise environment , 2006, IEEE Signal Processing Letters.

[25]  Boualem Boashash,et al.  Comments on "The Cramer-Rao lower bounds for signals with constant amplitude and polynomial phase" , 1998, IEEE Trans. Signal Process..

[26]  Patrick Flandrin,et al.  Time-Frequency Energy Distributions Meet Compressed Sensing , 2010, IEEE Transactions on Signal Processing.

[27]  Marc Moonen,et al.  Time-Varying FIR Equalization for MIMO Transmission over Doubly Selective Channels , 2010, EURASIP J. Adv. Signal Process..

[28]  Marco F. Duarte,et al.  Spectral compressive sensing , 2013 .

[29]  Igor Djurovic,et al.  A Hybrid CPF-HAF Estimation of Polynomial-Phase Signals: Detailed Statistical Analysis , 2012, IEEE Transactions on Signal Processing.

[30]  Vladimir Katkovnik,et al.  Robust M-estimates of the frequency and amplitude of a complex-valued harmonic , 1999, Signal Process..