Recently, with the realization of the World Wide Web, the tremendous need for high-speed data communications has grown. Several access techniques have been proposed which utilize the existing copper twisted pair cabling. Of these, the xDSL family, particularly ADSL and VDSL, have shown great promise in providing broadband or near-broadband access through the common telephone lines. A critical component of the ADSL and VDSL systems is the guard band needed to eliminate the interference caused by the previously transmitted blocks. This guard band must come in the form of redundant samples at the start of every transmit block, and be at least as long as the channel impulse response. Since the required guard band length is much greater than the length of the actual transmitted samples, techniques to shorten the channel impulse response must be considered. In this thesis, a new algorithm based on the RLS error minimization and POCS optimization techniques will be applied to the channel impulse-shortening problem in an ADSL environment. As will be shown, the proposed algorithm will provide a much better solution with a minimal increase in complexity as compared to the existing LMS techniques
