SQNR estimation of non-linear fixed-point algorithms

In this paper, a fast and accurate quantization noise estimator aiming at fixed-point implementations of Digital Signal Processing (DSP) algorithms is presented. The estimator enables significant reduction in the computation time required to perform complex wordlength optimizations. The proposed estimator is based on the use of Affine Arithmetic (AA) and it is aimed at differentiable non-linear algorithms with and without feedbacks. The estimation relies on the parameterization of the statistical properties of the noise at the output of fixed-point algorithms. Once the output noise is parameterized (i.e. related to the fixed-point formats of the algorithm signals), a fast estimation can be applied throughout the wordlength optimization process using as a precision metric the SQNR. The estimator is tested using a subset of non-linear algorithms such as vector operations, adaptive filters and a channel equalizers. wordlength optimization times are boosted by three orders of magnitude while keeping the average estimation error down to 13%.