Single-carrier linear modulation techniques combined with frequency-domain equalization provide a viable alternative to multicarrier techniques for combating multipath fading in channels with large delay spread. Such modulations tolerate frequency offset and have well controlled peak to average power ratio. They have comparable complexity to orthogonal frequency division multiplexing (OFDM) systems, and are more robust to synchronization errors. If error correction coding is used, then information can be iteratively passed between the equalizer and the decoder to improve performance. This is referred to as turbo equalization. To date, several turbo equalization schemes have been proposed, but little work has been done to address the problem of channel estimation for the turbo equalization process. The work in this thesis considers frequency-domain turbo equalization with imperfect channel state information (CSI) at the receiver for different wireless channels. A receiver structure incorporating joint frequency-domain turbo equalization and time- domain channel estimation is developed. The novelty of this scheme lies in the combination of time-domain channel estimation and frequency-domain turbo equalization, and in its extension to high level modulation formats. The performance of the system is investigated by a combination of analysis and computer simulation. It is found that the system performs well over a range of dispersive channels.

Sum-product algorithm can be employed for obtaining the marginal probability density functions from a given joint probability density function (p.d.f.). The sum-product algorithm operates on a factor graph which represents the dependencies of the random variables whose joint p.d.f. is given. The sum-product algorithm can not be operated on factor-graphs that contain loops. For these factor graphs iterative sum-product algorithm is used. A factor graph which contains loops can be divided in to loop-free sub-graphs. Sum-product algorithm can be operated in these loop-free sub-graphs and results of these sub-graphs can be combined for obtaining the result of the whole factor graph in an iterative manner. This method may increase the convergence rate of the algorithm significantly while keeping the complexity of an iteration and accuracy of the output constant. A useful by-product of this research that is introduced in this thesis is a good approximation to message calculation in factor nodes of the inter-symbol interference (ISI) factor graphs. This approximation has a complexity that is linearly proportional with the number of neighbors instead of being exponentially proportional. Using this approximation and the sub-graph idea we have designed and simulated joint decoding-equalization (turbo equalization) algorithm and obtained good results besides the low complexity.