Finite and Infinite-Precision Properties of QRD-RLS Algorithms
This chapter analyzes the finite and infinite-precision properties of QR-decomposition recursive least-squares (QRD-RLS) algorithms with emphasis on the conventional QRD-RLS and fast QRD-lattice (FQRD-lattice) formulations. The analysis encompasses deriving mean squared values of internal variables in steady-state and also the mean squared error of the deviations of the same variables assuming fixed-point arithmetic. In particular, analytical expressions for the excess of mean squared error and for the variance of the deviation in the tap coefficients of the QRD-RLS algorithm are derived, and the analysis is extended to the error signal of the FQRD-lattice algorithm. All the analytical results are confirmed to be accurate through computer simulations. Conclusions follow.
KeywordsInternal Variable Quantization Error Precision Analysis Systolic Array Array Implementation
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