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1. Conclusions and Recommendations for Future Work
| Content Provider | Semantic Scholar |
|---|---|
| Abstract | We have explored different ways to improve the performance of adaptive filters. A novel adaptation algorithm, which we called the Normalized LMS algorithm with Orthogonal Correction Factors, was proposed. The proposed algorithm provides faster convergence than the widely used NLMS, especially for colored inputs. The well-known affine projection algorithm (and also a class of algorithms equivalent to it) is a special case of NLMS-OCF. We derived the convergence and tracking properties of NLMS-OCF under certain simplifying assumptions, such as the independence assumption and the discrete orientation assumption. The derived results are applicable to APA and the class of algorithms equivalent to APA as well. The condition for convergence is derived. We showed that increasing the number of orthogonal correction factors M improves the convergence rate, while the improvement itself diminishes as M is increased. It was also shown that, for white input, NLMS-OCF with M OCFs converges at a rate of 20 dB for every () 1 5 + M N iterations, where N is the length of the adaptive filter. Thus, NLMS-OCF provides faster convergence than NLMS even for white inputs. We provided simulation results to corroborate the analytical results. The effect of the user-selectable parameters such as step size µ , number of OCFs M , and input vector delay D on the tracking behavior of NLMS-OCF was analyzed. Expressions were derived for optimal (in the sense that the steady-state error is minimized) values of µ and M. We also showed that the steady-state error increases linearly with D. The theoretical results were found to closely match the simulation results. The NLMS-OCF algorithm based on direct Gram-Schmidt orthogonalization has a complexity of () 2 NM Ο. A fast NLMS-OCF algorithm with a reduced complexity of () NM Ο has been derived. The fast algorithm performs Gram-Schmidt orthogonalization recursively using a lattice structure with vector inputs. Using simulations, it was shown that increasing the input vector delay accelerates the convergence of NLMS-OCF under most conditions. Hence, NLMS-OCF can converge faster than APA, which restricts the input vector delay to unity. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://scholar.lib.vt.edu/theses/available/etd-122099-153321/unrestricted/Chapter11.pdf |
| Alternate Webpage(s) | https://theses.lib.vt.edu/theses/available/etd-122099-153321/unrestricted/Chapter11.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
