Chapters 4 through 9 have considered the transient response characteristics and implementation considerations associated with different classes of adaptive algorithms that are widely used for adaptive array applications. Before considering some practical problems associated with adaptive array system design, it is appropriate to summarize the principal characteristics of each algorithm class.

In each chapter of Part Two an algorithm representing a distinct adaptation philosophy has been directly compared with the LMS algorithm to determine the convergence speed relative to LMS adaptation. It is now convenient to compare directly the transient responses of the various algorithms for a selected example to determine the relative convergence speeds. Since the misadjustment versus rate of adaptation trade-offs for the random search algorithms (LRS, ARS, and GARS) and for the DSD algorithm of Chapter 4 are unfavorable compared with the LMS algorithm, recourse to these methods would be taken only if the meager instrumentation required was regarded as a cardinal advantage or non-unimodal performance surfaces were of concern. Furthermore, the Howells-Applebaum maximum SNR algorithm has a misadjustment versus convergence speed trade-off that is nearly identical with the LMS algorithm. Attention for the direct comparison consequently is focused on the following adaptive algorithms:

1. Least mean square (LMS) error algorithm (Section 4.2 of Chapter 4).

2. Powell's accelerated gradient (PAG) algorithm (Section 4.4.1 of Chapter 4).

3. Direct matrix inversion (DMI) [Version (6.24) from Section 6.1.2 of Chapter 6].

4. Recursive (R) algorithm (Section 7.5 of Chapter 7).

5. Gram-Schmidt cascade preprocessor (GSCP) (Section 8.4 of Chapter 8).

Each algorithm is...