Algorithmic engineering in adaptive signal processing: worked examples

Algorithmic engineering provides a rigorous framework for describing and manipulating the type of building blocks commonly used to define parallel algorithms and architectures for digital signal processing. So far, the concept has only been illustrated by means of relatively simple examples relating to the use of QR decomposition (QRD) by Givens rotations for the purposes of adaptive filtering and beamforming. Two more challenging examples are presented that illustrate the use of simple diagrammatic transformations to develop novel algorithms and architectures, and demonstrate the potential power of algorithmic engineering as a formal design technique. The first example constitutes the only known derivation of a modular processing architecture for generalised sidelobe cancellation based on QR decomposition. The second provides a simple derivation of the QRD-based lattice algorithm for multichannel least-squares linear prediction