Dynamic range, stability, and fault-tolerant capability of finite-precision RLS systolic array based on Givens rotations

The QR decomposition recursive least-squares (QRD RLS) algorithm for mapping onto a systolic array for signal processing and communication applications is considered. Detailed analysis is presented to show that the rotation parameters of the RLS algorithm based on the Givens rotation method will eventually reach the quasi-steady-state if the forgetting factor λ is very close to 1. With this model, the dynamic range of each processing cell can be derived, and from this a proper wordlength can be chosen to ensure correct operation of the algorithm. The proposed solutions are simple and effective. Simulations have demonstrated that the wordlengths chosen by the proposed dynamic range work well. The stability of the QRD RLS algorithm is demonstrated under a finite-precision implementation with this observation. Finally, the missing error detection and false alarm problems are considered based on the results obtained from the model. The wordlength is overflow-free without missing error detection and false alarm problems. The results in this study are of practical importance. Not only can a finite-precision QRD RLS systolic array be designed with a minimum wordlength that ensures correct operations, but also a fault-tolerant system that can detect a given error size and is false-alarm-free under the quantization effect can be provided