Dynamic Range, Stability, and Fault-tolerant Capability of Finite-precision RLS Systolic Array Based on Givens Rotations

Abstract

The QRD RLS algorithm is generally recognized as having good numerical properties under finite-precision implementation. Also, it is very suitable for VLSI implementation since it can be easily mapped onto a systolic array. However, it is still unclear how to obtain the dynamic range of the algorithm such that a wordlength can be chosen to ensure correct operations of the algorithm. In this paper, we first propose a quasi-steady state model by observing the rotation parameters generated by boundary cells will eventually reach quasi steady-state regardless of the input data statistics if l is close to one. With this model, we can obtain upper bounds of the dynamic range of processing cells. Thus, the wordlength can be obtained from upper bounds of the dynamic range to prevent overflow and to ensure correct operations of the QRD RLS algorithm. Then we reconsider the stability problem under quantization effects with more general analysis and obtain tighter bounds than given in a previous work [13]. Finally, two fault-tolerant problems, the missing error detection and the false alarm effect, the arise under finite- precision implementation are considered. Detail analysis on preventing missing error detection with a false alarm free condition is presented.