In this thesis a thorough examination of proportionate-type normalized least square (PtNLMS) algorithm is presented. The main application of these algorithms is network echo cancellation. The examination presented includes the analysis of both steady-state and transient regimes of the PtNLMS algorithm. Additionally, the applicability and limitations of common assumptions, such as Gaussianity, used for the joint probability density function of the weight deviation are studied. In fact, a closed form solution for the conditional joint probability density function of the current weight deviation given the preceding weight deviation is presented and shown to differ from Gaussianity assumption in many situations. The examination of PtNLMS algorithms performed in this work also includes the development of new PtNLMS algorithms by choosing gains which optimize user-defined criteria, such as mean square error, at all times. While most of the PtNLMS algorithms examined are designed to operate under the assumption that the impulse response is sparse, a set of algorithms is developed which do not rely on this assumption. The PtNLMS algorithm is then extended from real-valued signals to complex-valued signals. This thesis then closes with an examination of the computational complexity of the algorithms discussed.
|Advisor:||Doroslovacki, Milos I.|
|Commitee:||Eom, Kie-Bum, Loew, Murray, Picciolo, Michael, Wasylkiwskyj, Wasyl|
|School:||The George Washington University|
|School Location:||United States -- District of Columbia|
|Source:||DAI-B 73/08(E), Dissertation Abstracts International|
|Keywords:||Adaptive filtering, Least mean square algorithms, Optimization, Signal processing, Sparse, System identification|
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