Adaptive Processing: The Least Mean Squares Approach with Applications in Transmission
Opening with an explanation of transmission systems, this text moves on to discuss the theory of adaptive transversal (FIR) filters, covering the optimal filter, transient error and steady-state fluctuations. Practical implementation of this theory is explored. The LMS filter and simplified sign-algorithms are explained in detail. Several chapters are devoted to methods for tracking time-variations and the book draws to a close with a discussion of adaptive recursive (IIR) filters.
Why Read This Book
You should read this book if you need a clear, focused treatment of LMS-based adaptive filtering and practical techniques for transmission/equalization problems. It blends theoretical convergence and steady-state analysis with implementation-minded chapters (sign algorithms, tracking, and adaptive IIRs) so you can move from analysis to real systems.
Who Will Benefit
Intermediate DSP engineers or graduate students working on channel equalization, echo/noise cancellation, or adaptive filter implementation in communications and signal-processing systems.
Level: Intermediate — Prerequisites: Basic signals & systems, linear systems and convolution, introductory probability/stochastic processes, and familiarity with digital FIR/IIR filter concepts. Some MATLAB or numerical experience is helpful.
Key Takeaways
- Derive and implement the LMS algorithm for transversal (FIR) adaptive filters
- Analyze convergence behavior, transient error, and steady-state (misadjustment) performance
- Apply simplified sign-based and low-complexity algorithms for resource-constrained implementation
- Design and tune tracking methods for time-varying channels and nonstationary inputs
- Extend adaptive filtering concepts to recursive (IIR) adaptive filters and understand stability/implementation issues
- Apply LMS-based techniques to practical transmission problems such as channel equalization and echo cancellation
Topics Covered
- 1. Introduction: Transmission Systems and Adaptive Needs
- 2. Random Signals and System Models for Transmission
- 3. The Optimal Transversal (Wiener) Filter
- 4. Derivation of the LMS Algorithm
- 5. Convergence Analysis: Transient Behavior and Step-Size Selection
- 6. Steady-State Fluctuations and Misadjustment
- 7. Low-Complexity Variants: Sign Algorithms and Simplified LMS
- 8. Tracking Time-Varying Systems and Adaptive Step-Size Rules
- 9. Adaptive Recursive (IIR) Filters: Theory and Practical Limitations
- 10. Implementation Issues: Finite Word-Length and Real-Time Considerations
- 11. Applications in Transmission: Equalization, Echo and Noise Cancellation
- 12. Examples, Simulations and Case Studies
- 13. Conclusions and Further Directions
Languages, Platforms & Tools
How It Compares
More application-focused on LMS and transmission than Haykin's Adaptive Filter Theory (which is broader and deeper on a range of adaptive algorithms) and more modern/practical than the older Widrow & Stearns treatments.
