SQNR Estimation of Fixed-Point DSP Algorithms

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 presented in two versions: (i) a general version suitable for differentiable nonlinear algorithms, and Linear Time-Invariant (LTI) algorithms with and without feedbacks; and (ii) an LTI optimized version. The process 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 word-length optimization process using as a precision metric the Signal-to-Quantization Noise Ratio (SQNR). The estimator is tested using different LTI filters and transforms, as well as a subset of non-linear operations, such as vector operations, adaptive filters, and a channel equalizer. Fixed-point optimization times are boosted by three orders of magnitude while keeping the average estimation error down to 4%.