IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 7, JULY 2010 1783 Non-Data-Aided Parametric- and Nonparametric-Based Carrier Frequency Estimators for Burst GMSK Communication Systems Mario E. Magaña, Senior Member, IEEE, and Ajay Kandukuri Abstract—In this paper, we propose non-data-aided (NDA) parametric- and nonparametric-based methods for carrier fre- quency estimation of burst Gaussian minimum-shift keying (GMSK), which have improved performance over ad hoc methods such as delay and multiply and have higher resolution capabil- ity. Specifically, three methods are developed for burst GMSK data to improve carrier estimation performance, and their re- sults are compared with the standard delay-and-multiply method. Two of them are parametric-based estimators, and one is a fast nonparametric-based estimator. Parametric-based estimators were studied in detail in this paper due to their high-resolution capabilities and proven performance. However, their computa- tional complexities were found to be relatively high in comparison to nonparametric-based estimators such as the autocorrelation method. The tradeoffs involved with respect to computational load and performance are presented. Index Terms—Autocovariance method, carrier offset esti- mation, Gaussian minimum-shift keying (GMSK) modulation, multiple-signal classification (MUSIC) method, non-data-aided (NDA) estimation, nonparametric estimation, parametric estima- tion, Tufts–Kumaresan (TK) method. I. I NTRODUCTION E STIMATING the carrier frequency plays an important role in communication receivers. This paper investigates the carrier frequency measurement for burst-mode applications, which have short data bursts. The data available to estimate the frequency are limited under the burst-mode assumption, and improved frequency estimators are necessary for a faster lock. The digital frequency estimators are broadly classified as data-aided and non-data-aided (NDA) estimators. Data-aided estimators make use of the signal timing or data information to achieve low variance estimates. NDA techniques, on the other hand, do not use any information about timing. These esti- mators, however, exhibit poorer performance than data-aided methods. This paper focuses on the estimation of large carrier frequency offsets using short data bursts. At large frequency offsets on the order larger than 0.1% of the symbol period, extracting the timing information or data information is ex- Manuscript received February 12, 2008; revised February 17, 2009; accepted February 18, 2009. Date of publication October 9, 2009; date of current version June 9, 2010. M. E. Magaña is with the School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR 97331-5501 USA. A. Kandukuri was with the School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR 97331-5501 USA. He is now with Booz Allen Hamilton, Washington, DC 20004-1145 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2009.2030867 tremely difficult. Under these circumstances, NDA techniques are preferable. A refinement approach is proposed as a means of improving the performance of an NDA delay-and-multiply method most often used in ad hoc estimation [12]. Parametric frequency estimation problems have extensively been studied before [2], [14], and their superior frequency resolution for short data records is well established. These es- timators also have the added advantage of estimating the dom- inant frequency while rejecting any interference. In this paper, we improve performance by using eigenvalue-based frequency estimation over a delay-and-multiply method and compare the performance of signal subspace methods and noise subspace methods, along with their advantages over delay-and-multiply methods. Moreover, we implement an improved estimator for continuous-phase-modulation (CPM) formats with improved performance compared to ad hoc estimators. Specifically, the estimation strategies presented herein are applied to burst transmission of Global System for Mobile Communications (GSM) data. Gaussian minimum-shift keying (GMSK) is a popular modulation type that is used in the GSM standard. The algorithm developed can also be implemented on other CPM formats, as very few restrictions are placed on the format while deriving our structure. The restrictions placed have been verified to also hold for minimum-shift keying (MSK), but other CPMs have not been checked. The research focuses on a digital algorithm since they can be implemented on a DSP chip. MATLAB and Simulink are used in the simulations to verify the analytic results. The ability to measure the carrier when the local carrier offset varies over a wide range compared to the symbol period is important for the case of not-so-good oscillator stabilities. Added to this problem is the nonavailability of data symbols or timing information in the case of large carrier frequency offsets. In such instances, the frequency recovery has to be done without the aid of timing and data symbols. Normally, a phase-locked loop is used to recover a modulated signal carrier frequency. Phase-locked loops have very slow acquisition capabilities and need some kind of an aid to acquire a signal faster. A frequency ramp provided to the voltage- controlled-oscillator (VCO) reference frequency could speed up the process but would require longer data intervals before it can lock. A high rate of frequency ramp would help in reducing estimation times and thereby lock on with limited data. However, a very large rate, as required for large frequency offsets and short data records, would make it lose lock and is 0018-9456/$26.00 © 2009 IEEE