Fixed-point error analysis of the QR-recursive least square algorithm

This paper presents a detailed analysis of the QR-RLS algorithm in finite and infinite precision environments. The mean squared values of all internal variables in steady state are derived. They are useful to dimension the wordlength of each variable of the algorithm. The recursive equations describing the quantization error propagation are derived and the stability conditions are presented. Then, we derive analytical expressions for the mean squared values of the deviations in the internal variables of the algorithm, for fixed-point arithmetic. In particular, new analytical expressions for the excess of mean squared error and for the variance of the deviation in the tap coefficients are derived. All the analytical results are confirmed to be accurate through computer simulations