As the Internet becomes a part of daily life, new applications such as multimedia services are emerging, not just in the wired environment but also in the wireless one. In addition, there have been remarkable developments in communication technology such as turbo receivers and multi-carrier communication systems, which have influenced recent standards, e.g., IEEE 802.11 and IEEE 802.16. Regardless of the communication systems, channel state information is required for reliable demodulation, and different structures pose distinctive channel estimation problems. This thesis studies channel estimation in single-carrier and multi-carrier systems, focusing on recent communication systems, e.g., turbo receivers and OFDM. First, based on the wide sense stationary uncorrelated scatterers (WSSUS) channel model, a soft input Kalman channel estimator is developed for single-carrier systems as the linear optimal minimum-mean-squared-error (LMMSE) estimator. Analysis of this estimator and a related hard decision-based channel estimator is carried out in the context of turbo equalization under Gaussian assumptions of the output of the soft-input/soft-output decoder. We next consider the channel estimation problem in the context of multi-carrier systems equipped with pilot subcarriers. Third, blind channel estimators exploiting finite alphabet constraints are discussed for multi-carrier systems. The joint maximum likelihood (JML) blind estimator is derived and shown to guarantee channel identifiability up to a complex exponential, as long as the number of subcarriers is larger than or equal to twice the time domain channel length. Also, identifiability of the JML algorithm is directly extended to prove identifiability of the minimum distance (MD) finite alphabet blind algorithm. The JML and MD algorithms have a drawback in their high numerical complexity incurred by the exhaustive search over combinations of finite alphabets or ambiguities. An efficient blind algorithm, the reduced complexity minimum distance (RMD) algorithm, is derived using properties of the assumed finite impulse response (FIR) of the channel. The RMD exploits constraints on the unwrapped phase of FIR systems and results in significant reductions in numerical complexity over existing methods.
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