This thesis deals with joint channel and frequency offset estimation in many scenarios of wireless communications. In additive white Gaussian noise (AWGN) channels, a general literature survey of channel and frequency offset estimators based on the data-aided maximum likelihood (ML) principle is presented. The Cramer-Rao lower bounds (CRLB)s of the joint estimators are presented. Performance analysis of advanced frequency estimators recently proposed in the literature is provided. The performance of the estimators is compared for different application scenarios so that to get a better understanding of the differences, in terms of accuracy, complexity, frequency estimation range, signal to noise ratio (SNR) threshold. The dichotomous search (DS) frequency estimator is found to be the best practical choice. The DS frequency estimator emploies a fast Fourier transform (FFT)-based coarse search and dichotomous fine search of the periodogram peak to approximate the ML optimal estimator. This algorithm achieves the ML-like accuracy over a wide range of SNRs and throughout the wide frequency estimation range. As it relies entirely on linear operations, it is perfectly suitable for real-time implementation. In time-invariant frequency-selective channels, the joint data-aided estimation of channel and frequency offset for signals exploiting multipath diversity is considered. This diversity improves the estimation performance by searching for the peak of the combined periodograms of multipath components. The first estimator is based on the Bayesian approach and can be used when certain prior statistical knowledge about the channel is available. The second estimator is based on the ML approach and can operate when these channel statistics are not available. Both estimators employ the DS frequency estimation technique. These estimators have a high-accuracy performance with an estimation error very close to the CRLBs over a wide range of SNRs and throughout the wide frequency acquisition range. In frequency-flat time-variant fading channels, new joint data-aided channel and frequency offset estimators are derived. The proposed estimators are based on the basis expansion model (BEM) of the fading process and the DS frequency estimation technique. The first estimator is based on the Bayesian approach and exploits prior channel statistics to provide a high performance. The second estimator relies on the ML approach, and with a slightly lower accuracy, can operate when the prior statistics are unknown. The performance of the proposed joint estimators is examined for different scenarios in Rayleigh fading channels. The sensitivity of the Bayesian estimator to the knowledge of the Doppler frequency is investigated using such BEMs as Karhunen-Loeve (KL), discrete prolate spheroidal (DPS), generalised complex exponential (GCE), and B-spline (BS) functions. The BS-BEM is found to be the most robust and the best practical choice. In doubly-selective fading channels, a joint data-aided channel and frequency offset Bayesian estimator is proposed. The joint estimator is based on the BS-BEM representation of the fading process and the DS frequency estimation technique. Simulation results for different scenarios in Rayleigh fading channels show that the proposed estimator achieves a high accuracy performance, which is close to that with perfect knowledge of the frequency offset, over a wide range of SNRs, for different Doppler frequencies and throughout all the frequency acquisition range. Iterative turbo receivers are developed for frequency-flat time-variant fading channels which jointly perform channel and frequency offset estimation together with data detection and decoding. The estimation and detection are based on the BS-BEM of the fading time variations and use the DS frequency estimation. Soft information generated in the turbo decoder is used to improve the quality of detection in the subsequent iterations. Depending on how much knowledge of channel statistics is available, three versions of the joint estimator, the Bayesian, ML and regularised-ML (E-ML) are provided. Simulation results show that the proposed receivers provide as good performance as the corresponding ones operating with perfect knowledge of the frequency offset, and close to that operating with perfect channel knowledge.
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