2. Reduced Complexity Adaptive Filtering Algorithms with Applications to Communications Systems Marcello Luiz Rodrigues de Campos Laboratório de Processamento de Sinais COPPE/UFRJ Maio de 2008

3. ❍ Adaptive – to learn from the environment. ❍ An adaptive filter learns from the environment. ❍ Adaptive filters are widely used in communications systems. Introduction

4. ❍ Specifications may be unknown or time-varying Why adaptive methods?

5. Example Noise Cancellation FBI Learning rate Complexity Final error

6. ❍ Equalization Applications TX AF ❍ System Identification ❍ Interference Suppression ❍ Antenna Array Processing

7. Choosing an Adaptation Algorithm ❍ How fast do we need to have an acceptable solution? ❍ What is an acceptable solution? – bit-error rate, mean-squared error... ❍ What are our computational or power constraints ? ❍ If we want to keep the computational cost low – test the simplest algorithm first – thereafter go for more advanced solutions

8. Goal ❍ To derive and analyze new adaptive filtering algorithm with performance ramping from that of the simplest algorithm to that of the most complex algorithm. ❍ Reduce the average computational load as compared to conventional approaches.

9. ❍ Tranformation of input signal to the adaptive filter. ❍ Application of set-membership framework. ❍ Application of partial-updating of adaptive-filter vector. ❍ Application of a priori information as constraints when developing new algorithms. ❍ Application of known linear-algebra techniques to stabilize fast-converging algorithms. Tools

10. Contributions ❍ Adaptive filters – algorithms with ramping computational complexity – complexity reduction via orthogonal transformation – complexity reduction via set-membership filtering ❍ Training-based adaptive filters

11. Conclusions ❍ Adaptive filtering algorithms with low computational complexity can be useful in high-speed applications such as communications systems. ❍ Algorithms where computational complexity can be chosen in between those of the most costly and the simplest can offer adequate performance. ❍ Set-membership filtering adaptive filtering algorithms appear to be a promising framework because it enables resource sharing or power savings.