IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 49, NO. 5, SEPTEMBER 2000 1885 Frequency Offset Estimation Algorithm for 4-DQPSK TDMA Mobile Radio Jinsoup Joung, Student Member, IEEE, and Gordon L. Stüber, Fellow, IEEE Abstract—This paper presents a new frequency offset estimation algorithm that uses an indicator of the channel status called the un- certainty factor (UF). The UF is calculated for the burst of interest and used to determine if the frequency offset estimate should be updated. If so, then a number of temporary frequency offset esti- mates are averaged together to obtain an updated frequency offset estimate. Computer simulations show that the UF is inversely re- lated to carrier-to-interference ratio, and directly related to the fre- quency selectivity and Doppler frequency of the channel. The new frequency offset estimation algorithm is shown to significantly out- perform conventional methods. Index Terms—Frequency offset, 4, time-division multiple-ac- cess (TDMA) cellular radio. I. INTRODUCTION T HE JAPANESE personal digital cellular (PDC) and North American IS-54/136 TDMA cellular systems employ receivers that use either differential detection or coherent detection along with a sequence estimator or decision feed- back equalizer (DFE) [15], [10], [6], [3], [13]. Time-division multiple-access (TDMA) receivers must have the ability to syn- chronize accurately on each received burst [9]. Synchronization is difficult to achieve in the presence of signal impairments such as carrier frequency offset, Doppler spread, cochannel interference, multipath fading, thermal noise, and nonlinear distortion [6], [18], [8], [7]. Of these impairments, carrier frequency offset is one of the main causes for the failure of a maximum likelihood sequence estimation (MLSE) receiver. Frequency offset rotates the overall discrete-time channel impulse response so that the adaptive channel estimator in the MLSE receiver cannot track the channel variations [9], [11], [19], [4]. Frequency offset also degrades the performance of differential detectors operating under conditions of high Doppler shift and/or low signal-to-noise ratio (SNR). In this case, the received signal points are likely to cross decision boundaries because the phase of the received signal point is shifted in an amount proportional to the Doppler shift. For these reasons, it is important to correct frequency offset before any further processing on the received signal. There are several frequency estimation methods, including frequency discrimination, frequency-domain transformation, Manuscript received August 19, 1997; revised September 1, 1999. This work was supported by Matsushita Communications Industries, Ltd. The authors are with the Georgia Institute of Technology, Atlanta, GA 30332 USA. Publisher Item Identifier S 0018-9545(00)07895-6. modulation specific techniques, decision directed data-depen- dent methods, and power-of- carrier recovery [9], [14], [17], [2], [1], [5]. The frequency discriminator estimates frequency offset by averaging the instantaneous frequency of the received signal. However, a long time average is required to reduce the estimation error. Furthermore, the estimate can be inaccurate when the spectrum of the received signal is nonsymmetric about the carrier frequency due to frequency-selective fading [9]. The frequency-domain transform method performs a discrete or fast Fourier transform (FFT) on the received signal and uses the result to estimate the frequency offset. The power-of- method works well for flat fading channels but may fail with frequency selective fading channels. The data-dependent technique is not appropriate with frequency-selective fading channels because the correct data are not available before equalization of the received signal. Unfortunately, there is no documented frequency-estimation method that works well over the entire range of channel characteristics that are experienced in digital cellular communications. In general, the radio link between a mobile station (MS) and a base station (BS) changes from being frequency selective to frequency nonselective, and vice versa, during a communication session. The carrier-to-interference ratio (CIR) also varies with MS movement. These properties are exploited in this paper to develop a robust frequency offset estimator that provides satisfactory performance over a wide range of channel char- acteristics. In particular, a novel frequency offset estimation algorithm is proposed for 4-DQPSK on flat fading channels along with an uncertainty factor (UF). The UF indicates the reliability of the frequency offset estimate. The UF is shown to be inversely related to the CIR and directly related to the severity of frequency selectivity and the maximum Doppler shift. The inverse relationship with is evident from the definition of the UF. The UF is incorporated into an overall algorithm, such that the frequency offset is only corrected under good channel conditions, i.e., when the channel experiences flat fading, high CIR, and . The proposed algorithm operates under the premise that the frequency offset, once corrected, will not change unless a handoff or channel change occurs. The performance of the new frequency offset estimation algorithm is evaluated by using a time-varying channel model that includes frequency offset, Doppler shift, frequency selectivity, and cochannel interference. Although the new frequency offset estimation algorithm is derived from ad hoc principles, it is shown to significantly outperform currently known methods, especially at low-to-moderate CIR. 0018–9545/00$10.00 © 2000 IEEE