Blind NLLS carrier frequency-offset estimation for QAM, PSK, and PAM modulations: performance at low SNR

• Published in: IEEE transactions on communications Vol. 54; no. 10; pp. 1725 - 1730
• Main Authors: Ciblat, P., Ghogho, M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-10-2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Amplitude estimation; Amplitude modulation; Applied sciences; Blind estimation; Blinds; Carriers; Communication systems; Constellation diagram; Detection, estimation, filtering, equalization, prediction; Estimates; Exact sciences and technology; Exact solutions; Frequency estimation; frequency-offset synchronization; Information, signal and communications theory; Least squares approximation; Modulation, demodulation; outlier effect; performance at low signal-to-noise ratio (SNR); Phase estimation; Phase shift keying; Pulse amplitude modulation; Pulse modulation; Quadrature amplitude modulation; quadrature amplitude modulation (QAM) constellation; Signal and communications theory; Signal to noise ratio; Signal, noise; Studies; Symbols; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Performance evaluation; Quadrature amplitude modulation; outlier effect; performance at low signal-to-noise ratio (SNR); quadrature amplitude modulation (QAM) constellation; Error rate; Performance standard; Blind identification; Synchronization; Mean square error; Outlier; Phase shift keying; Blind estimation; Carrier frequency; Least squares method; Telecommunication system; Pulse amplitude modulation; frequency-offset synchronization; Frequency offset; Signal to noise ratio
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2006.881341

We address the problem of blind carrier frequency-offset (CFO) estimation in quadrature amplitude modulation, phase-shift keying, and pulse amplitude modulation communications systems. We study the performance of a standard CFO estimate, which consists of first raising the received signal to the Mth power, where M is an integer depending on the type and size of the symbol constellation, and then applying the nonlinear least squares (NLLS) estimation approach. At low signal-to noise ratio (SNR), the NLLS method fails to provide an accurate CFO estimate because of the presence of outliers. In this letter, we derive an approximate closed-form expression for the outlier probability. This enables us to predict the mean-square error (MSE) on CFO estimation for all SNR values. For a given SNR, the new results also give insight into the minimum number of samples required in the CFO estimation procedure, in order to ensure that the MSE on estimation is not significantly affected by the outliers