Title Page -- Contents -- Preface -- Notation -- Acronyms -- Chapter 1. Introduction to PtNLMS Algorithms -- 1.1. Applications motivating PtNLMS algorithms -- 1.2. Historical review of existing PtNLMS algorithms -- 1.3. Unified framework for representing PtNLMS algorithms -- 1.4. Proportionate-type NLMS adaptive filtering algorithms -- 1.4.1. Proportionate-type least mean square algorithm -- 1.4.2. PNLMS algorithm -- 1.4.3. PNLMS++ algorithm -- 1.4.4. IPNLMS algorithm -- 1.4.5. IIPNLMS algorithm -- 1.4.6. IAF-PNLMS algorithm -- 1.4.7. MPNLMS algorithm -- 1.4.8. EPNLMS algorithm -- 1.5. Summary -- Chapter 2. LMS Analysis Techniques -- 2.1. LMS analysis based on small adaptation step-size -- 2.1.1. Statistical LMS theory: small step-size assumptions -- 2.1.2. LMS analysis using stochastic difference equations with constant coefficients -- 2.2. LMS analysis based on independent input signal assumptions -- 2.2.1. Statistical LMS theory: independent input signal assumptions -- 2.2.2. LMS analysis using stochastic difference equations with stochastic coefficients -- 2.3. Performance of statistical LMS theory -- 2.4. Summary -- 3. PtNLMS Analysis Techniques -- 3.1. Transient analysis of PtNLMS algorithm for white input -- 3.1.1. Link between MSWD and MSE -- 3.1.2. Recursive calculation of the MWD and MSWD for PtNLMS algorithms -- 3.2. Steady-state analysis of PtNLMS algorithm: bias and MSWD calculation -- 3.3. Convergence analysis of the simplified PNLMS algorithm -- 3.3.1. Transient theory and results -- 3.3.2. Steady-state theory and results -- 3.4. Convergence analysis of the PNLMS algorithm -- 3.4.1. Transient theory and results -- 3.4.2. Steady-state theory and results -- 3.5. Summary -- 4. Algorithms Designed Based on Minimization of User-Defined Criteria -- 4.1. PtNLMS algorithms with gain allocation motivated by MSE minimization for white input.

4.1.1. Optimal gain calculation resulting from MMSE -- 4.1.2. Water-filling algorithm simplifications -- 4.1.3. Implementation of algorithms -- 4.1.4. Simulation results -- 4.2. PtNLMS algorithm obtained by minimization of MSE modeled by exponential functions -- 4.2.1. WD for proportionate-type steepest descent algorithm -- 4.2.2. Water-filling gain allocation for minimization of the MSE modeled by exponential functions -- 4.2.3. Simulation results -- 4.3. PtNLMS algorithm obtained by minimization of the MSWD for colored input -- 4.3.1. Optimal gain algorithm -- 4.3.2. Relationship between minimization of MSE and MSWD -- 4.3.3. Simulation results -- 4.4. Reduced computational complexity suboptimal gain allocation for PtNLMS algorithm with colored input -- 4.4.1. Suboptimal gain allocation algorithms -- 4.4.2. Simulation results -- 4.5. Summary -- Chapter 5. Probability Density of WD for PtLMS Algorithms -- 5.1. Proportionate-type least mean square algorithms -- 5.1.1. Weight deviation recursion -- 5.2. Derivation of the Conditional PDF of WD for the PtLMS algorithm -- 5.2.1. Conditional PDF derivation -- 5.3. Applications using the conditional PDF -- 5.3.1. Methodology for finding the steady-state joint PDF using the conditional PDF -- 5.3.2. Algorithm based on constrained maximization of the conditional PDF -- 5.4. Summary -- 6. Adaptive Step-Size PtNLMS Algorithms -- 6.1. Adaptation of μ-law for compression of weight estimates using the output square error -- 6.2. AMPNLMS and AEPNLMS simplification -- 6.3. Algorithm performance results -- 6.3.1. Learning curve performance of the ASPNLMS, AMPNLMS and AEPNLMS algorithms for a white input signal -- 6.3.2. Learning curve performance of the ASPNLMS, AMPNLMS and AEPNLMS algorithms for a color input signal.

6.3.3. Learning curve performance of the ASPNLMS, AMPNLMS and AEPNLMS algorithms for a voice input signal -- 6.3.4. Parameter effects on algorithms -- 6.4. Summary -- 7. Complex PtNLMS Algorithms -- 7.1. Complex adaptive filter framework -- 7.2. cPtNLMS and cPtAP algorithm derivation -- 7.2.1. Algorithm simplifications -- 7.2.2. Alternative representations -- 7.2.3. Stability considerations of the cPtNLMS algorithm -- 7.2.4. Calculation of stepsize control matrix -- 7.3. Complex water-filling gain allocation algorithm for white input signals: one gain per coefficient case -- 7.3.1. Derivation -- 7.3.2. Implementation -- 7.4. Complex colored water-filling gain allocation algorithm: one gain per coefficient case -- 7.4.1. Problem statement and assumptions -- 7.4.2. Optimal gain allocation resulting from minimization of MSWD -- 7.4.3. Implementation -- 7.5. Simulation results -- 7.5.1. cPtNLMS algorithm simulation results -- 7.5.2. cPtAP algorithm simulation results -- 7.6. Transform domain PtNLMS algorithms -- 7.6.1. Derivation -- 7.6.2. Implementation -- 7.6.3. Simulation results -- 7.7. Summary -- Chapter 8. Computational Complexity for PtNLMS Algorithms -- 8.1. LMS computational complexity -- 8.2. NLMS computational complexity -- 8.3. PtNLMS computational complexity -- 8.4. Computational complexity for specific PtNLMS algorithms -- 8.5. Summary -- Conclusion -- Appendix 1. Calculation of β(0)i, β(1) i,j and β(2)i -- Appendix 2. Impluse Response Legend -- Bibliography -- Index.