We consider channel identification techniques for a transmission scheme which consists of a sequence of frames with each frame consisting of pilots and data. We consider two systems, the first one having pilots in the time multiplexed fashion, and the second one being a multi-carrier system with frequency multiplexed pilots. We consider scenarios in which the channel is both frequency and time selective.For the time multiplexed pilots system, channel estimation performance of the pilot-only technique is limited by pilot spacing. The standard optimal decisiondirected techniques are computationally expensive. In response, we propose a novel two-stage estimation technique whose performance is close to that of the optimal estimators but whose complexity is significantly less. The first stage finds smoothed estimates of the channel during previous frames, while the second stage uses these smoothed estimates for channel prediction within the current frame.The frequency multiplexed pilots system suffers from the inter-carrier interference (ICI) in doubly-selective channels. We present channel estimation techniques which take the ICI effects into account. We also present a novel pilot tone selection criterion and the theoretical MSE calculations show its efficacy for a wide range of Doppler frequencies. The performance limitation due to ICI can be reduced by employing decision-directed estimators. We develop a low-complexity estimation technique and simulation results show good performance of the proposed techniques.ii The frequency multiplexed pilots system suffers from the inter-carrier interference (ICI) in doubly-selective channels. We present channel estimation techniques which take the ICI effects into account. We also present a novel pilot tone selection criterion and the theoretical MSE calculations show its efficacy for a wide range of Doppler frequencies. The performance limitation due to ICI can be reduced by employing decision-directed estimators. We develop a low-complexity estimation technique and simulation results show good performance of the proposed techniques. I thank my parents and sister, for their love and support. I also thank my uncles, aunts and cousins; they gave me the motivation and inspiration to do well in studies.Time spent together with them has always been so much fun.I thank Praveen, Sib, Aditi, Arul for the fun times during lunch breaks and the tough times while solving homeworks! I thank Ravi for his help with linux and latex.I thank members of the IPS lab for their help and friendly conversations.